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the [possible] fallacy of Lorentz contractions

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  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    There is no such experimental difference. Any experiment carried out by the person on the train will register the ground clock as ticking slowly, and any experiment carried out by the person on the ground will register the train clock ticking slowly.
    It's probably worth highlighting again, that we are discussing a scenario where the relative motion is ascribed to one reference frame or the other, in both reference frames; that is, either the train is moving in both reference frames, or the platform is.

    Whichever frame is not moving, the photon of that clock will not trace the hypotenuse and so will tick faster.


    Morbert wrote: »
    I think you are getting hung up on the shorthand language used to frame the thought experiment. Henry and Albert do not make any metaphysical assumptions about their measurement of 2d being an absolute distance. They acknowledge their experimental reports are using arbitrary reference frames. I.e. Both the observer on the train and on the ground, assuming they are aware of relativity, know that the measurement of a distance 2d for their respective clocks, and a larger distance for the other's clocks, is no more or less valid a measurement than the other's.
    Einsteinian relativity might not expressly state anything about an absolute rest frame, but there are certain issues which suggest that it is a tacit assumption.

    Firstly, the treatment of reference frames, in Einsteinian relativity, is indistinguishable from such a treatment where reference frames are considered to be at absolute rest, from their own perspectives.

    Secondly, the ascription of all motion to the other reference frame, suggests that reference frames are considered to be at absolute rest from their own perspectives; if they weren't, then the vertical velocity component of the photon in their light clock would be less than c and they would thus measure a speed of light lower than c.

    Another issue pertains to the consideration of relative velocities only; as outlined below.

    Morbert wrote: »
    I did this to show the superfluous nature of including absolute velocities in the reference frame. Instead of considering absolute velocities, it is possible to carry out the thought experiment by only only considering relative velocities U and V. I.e. Instead of presupposing an absolute reference frame and deriving relative velocities, we simply consider the relative velocities without any reference to an absolute reference frame.

    Why would he assume the absolute path length is 2d? Why would he consider an absolute path length at all? Special relativity does not postulate that the speed of light is c in some absolute reference frame. It postulates that all observers will measure the speed of light to be c. Time dilation and length contraction are similarly just measurements, and not statements about an absolute "passage of time" and "extension in space".

    Why presuppose an absolute reference frame at all? Why not just start with relative velocities, and make no statement about absolute reference frames at all?
    The issue is that, in the construction, you started off by assuming an absolute reference frame to define the values of U and V; and, theoretically, there should be an infinite number of possibilities that can give rise to the measured relative velocity between two reference frames; where U and V would be perfectly adequate examples; however, this is only possible when there is a common rest frame which can be used to define the velocities.

    The infinite number of possibilities [for making up the relative velocity] should vary from one of the reference frames accounting for 100% of the relative velocity, to both reference frames accounting for 50%, to the other accounting for 100% of the relative velocity, however, if we only consider relative velocities then we have to treat one of the reference frames as being at absolute rest; or, as Einsteinian relativity appears to do, treat each reference frame as being at rest from its own perspecitve.

    If we take the example where the relative velocity is 100km/h; if we want to consider the case where the velocities are U and V for the two reference frames, where U = 30km/h and V=100km/h, then we need a common rest frame against which to define those respective velocities, because relative to each other the velocity will always be 100km/h.

    For this reason, one reference frame has to be treated as being at absolute rest, and has to ascribe all of the velocity component to the other reference frame; it appears as though, under Einsteinian relativity, each reference frame is treated thusly.


    Morbert wrote: »
    They happen any time GPS satellites relay information to each other, or to people on the ground. The equations are entirely general, and do not presuppose and earth-centred physical properties.
    Aren't GPS systems synchronised to an earth centred inertial frame? Does the designation of this preferred frame not marginally favour Lorentzian relativity; despite the fact that Einsteinian relativity could be used.

    Morbert wrote: »
    In the thought experiment, we only consider a train moving at constant velocity, across an infinite plane. This is because the thought experiment is an exploration of the logical consequences of relativity's postulates. But with that said "pendulum" is a redundant detail. "Infinitely precise, independent clock" will do.
    Is there a contemporary real world experiment that correlates to this thought experiment?

    Also, would this scenario be one such scenario where Larmor dilation would apply?


    Morbert wrote: »
    It is not assumed. In fact, length-contraction was initially assumed in order to explain the isotropy of the speed of light, and was later dropped. The dimensions of the apparatus, as described by the person in the train, are perfectly valid, and no less physical than the measurements taken by the person on the ground.
    Length contraction isn't observed in any experiment though is it; at least it doesn't appear to be in the interferometer experiments or in the muon decay experiments.
    Morbert wrote: »
    This is a good time to talk about Lorentzian relativity. You have suggested that the photon is actually travelling a distance greater than 2d, but that the apparatus used by the person in the train is moving more slowly, and hence registering a speed c. This supposes that every possible physical mechanism is slowed by the same amount, everything to his infinitely precise wristwatch, to the neurons in his brain, to the photon apparatus itself. Then, when we consider interfering lightbeams, you suggest that things actually physically contract by some amount, and no matter what material used, or what orientations used, the length contraction effect will always sync up with the "slower moving" effect at precisely the right amount to render the speed of light to be c. Why would a physical process like length-contraction be correlated with a completely separate physical process of "slowed movement"? This is what Lorentzian relativity supposes. In fact, even with these supposed physical processes, it has no physical understanding of therelativity of simultaneity.

    Special relativity, on the other hand, has a very simple framework: The geometry relating all events is a pseudo-Riemannian, Minkowski geometry.
    I'm not familiar with that analysis of Lorentzian relativity tbh, but it looks like a bit of a skewed comparison of the two theories.
    . . . [in the context of contractions] the crucial difference between the two theories, of course, is that the Lorentz contraction, in the former theory, is viewed as a result of the (electromagnetic) forces responsible for the microstructure of matter in the context of Lorentz’s theory of the electron, whereas this same contraction, in Einstein’s theory, is viewed as a direct reflection —independent of all hypotheses concerning microstructure and its dynamics—of a new kinematical structure for space and time involving essential relativized notions of duration, length, and simultaneity. In terms of Poincar´e’s hierarchical conception of the sciences, then, Poincar locates the Lorentz contraction (and the Lorentz group more generally) at the level of experimental physics, while keeping Newtonian structure at the next higher level (what Poincar´e calls mechanics) completely intact. Einstein, by contrast, locates the Lorentz contraction (and the Lorentz group more generally) at precisely this next higher level, while postponing to the future all further discussion of the physical forces and material structures actually responsible for the physical phenomenon of rigidity.
    The Lorentz contraction, in Einstein’s hands, now receives a direct
    kinematical interpretation.
    Minkowski space-time: a glorious non-entity

    Other sources suggest the difference lies in the postulation of an absolute rest frame in Lorentzian relativity
    the last vestiges of a substantial ether had been eliminated from Lorentz's "ether" theory, and it became both empirically and deductively equivalent to special relativity. The only difference was the metaphysical postulate of a unique absolute rest frame, which was empirically undetectable and played no role in the physical predictions of the theory
    wiki-LET current status

    I suspect that even that absolute rest frame could be removed - without treating reference frames as being at absolute rest - by simply having a preferred reference frame, or rest frame, for units of measurement.

    EDIT: just on the point of relativity of siumultaneity; Lorentzian relativity doesn't have a physical understanding of it, because it's not actually part of it; absolute simultaneity is prevalent un LR.


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    It's probably worth highlighting again, that we are discussing a scenario where the relative motion is ascribed to one reference frame or the other, in both reference frames; that is, either the train is moving in both reference frames, or the platform is.

    Whichever frame is not moving, the photon of that clock will not trace the hypotenuse and so will tick faster.

    It doesn't matter how you ascribe anything. There will be no experimental difference.
    Einsteinian relativity might not expressly state anything about an absolute rest frame, but there are certain issues which suggest that it is a tacit assumption.

    Firstly, the treatment of reference frames, in Einsteinian relativity, is indistinguishable from such a treatment where reference frames are considered to be at absolute rest, from their own perspectives.

    Secondly, the ascription of all motion to the other reference frame, suggests that reference frames are considered to be at absolute rest from their own perspectives; if they weren't, then the vertical velocity component of the photon in their light clock would be less than c and they would thus measure a speed of light lower than c.

    The expressions in bold are oxymorons. If you are considering something, relative to a reference frame ('from their own perspective'), they are not making any statements, implicit, suggestive, or otherwise, about absolute reference frames. "The train is at rest, from my perspective" simply means "The coordinate system which labels me as at rest, also labels the train as at rest. This is an entirely arbitrary coordinate, not derived from any implicit or explicit assumption about the concept of absolute rest."
    The issue is that, in the construction, you started off by assuming an absolute reference frame to define the values of U and V; and, theoretically, there should be an infinite number of possibilities that can give rise to the measured relative velocity between two reference frames; where U and V would be perfectly adequate examples; however, this is only possible when there is a common rest frame which can be used to define the velocities.

    The infinite number of possibilities [for making up the relative velocity] should vary from one of the reference frames accounting for 100% of the relative velocity, to both reference frames accounting for 50%, to the other accounting for 100% of the relative velocity, however, if we only consider relative velocities then we have to treat one of the reference frames as being at absolute rest; or, as Einsteinian relativity appears to do, treat each reference frame as being at rest from its own perspecitve.

    If we take the example where the relative velocity is 100km/h; if we want to consider the case where the velocities are U and V for the two reference frames, where U = 30km/h and V=100km/h, then we need a common rest frame against which to define those respective velocities, because relative to each other the velocity will always be 100km/h.

    For this reason, one reference frame has to be treated as being at absolute rest, and has to ascribe all of the velocity component to the other reference frame; it appears as though, under Einsteinian relativity, each reference frame is treated thusly.

    Such a scenario is impossible. V is always -U. I think this explains the confusion. U is the velocity of the train using the coordinate system of the ground observer. V is the velocity of the earth using the coordinate system of the train observer. These terms are not in any way related to some other, third coordinate system, absolute or otherwise.
    Aren't GPS systems synchronised to an earth centred inertial frame? Does the designation of this preferred frame not marginally favour Lorentzian relativity; despite the fact that Einsteinian relativity could be used.

    Is there a contemporary real world experiment that correlates to this thought experiment?

    Also, would this scenario be one such scenario where Larmor dilation would apply?

    Length contraction isn't observed in any experiment though is it; at least it doesn't appear to be in the interferometer experiments or in the muon decay experiments.

    The conversations seems to be fragmenting again. While I don't have an issue going into real-world experiments, we first need to settle any thought experiment issues you might have. Once the consistency and implications of relativity is understood, we can move on to experimental support.
    I'm not familiar with that analysis of Lorentzian relativity tbh, but it looks like a bit of a skewed comparison of the two theories.

    Minkowski space-time: a glorious non-entity

    Other sources suggest the difference lies in the postulation of an absolute rest frame in Lorentzian relativity
    wiki-LET current status

    I suspect that even that absolute rest frame could be removed - without treating reference frames as being at absolute rest - by simply having a preferred reference frame, or rest frame, for units of measurement.

    EDIT: just on the point of relativity of siumultaneity; Lorentzian relativity doesn't have a physical understanding of it, because it's not actually part of it; absolute simultaneity is prevalent un LR.

    To try and keep the topic focused (We could spend a long time talking about obscure facets): Can I ask you why you would be more comfortable with assuming an undetectable absolute reference frame exists, than with the assumption that time, as part of the relation between events, exists?


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    It doesn't matter how you ascribe anything. There will be no experimental difference.
    Would that be the case under the Loerntzian interpretation also?

    Morbert wrote: »
    The expressions in bold are oxymorons. If you are considering something, relative to a reference frame ('from their own perspective'), they are not making any statements, implicit, suggestive, or otherwise, about absolute reference frames. "The train is at rest, from my perspective" simply means "The coordinate system which labels me as at rest, also labels the train as at rest. This is an entirely arbitrary coordinate, not derived from any implicit or explicit assumption about the concept of absolute rest."
    I don't think they are oxymoronic, are they? They are not contradictory in and of themselves; they only become contradictory if we consider that two reference frames treat themselves as being at absolute rest - which will hopefully be clarified further below.

    It is probably worth stating that the tacit assumptions aren't present in the formulation used above, but they are necessary consequences of the treatment discussed below.

    Morbert wrote: »
    Such a scenario is impossible. V is always -U. I think this explains the confusion. U is the velocity of the train using the coordinate system of the ground observer. V is the velocity of the earth using the coordinate system of the train observer. These terms are not in any way related to some other, third coordinate system, absolute or otherwise.
    I think I may have confused the issue by not sticking more rigidly to the terms you defined from the outset, u and v, and U and V.


    The issue is that, in the construction, you started off by assuming an absolute reference frame to define the values of u and v; such that either u or v could have had a higher value, relative to the assumed absolute rest frame; they also could have had equal values, or either could have had a value of zero, relative to the absolute rest frame i.e. it would have been at absolute rest.

    Theoretically, that should be correct; there should be an infinite number of values for u and v that will give rise to the relative velocites of V and U (which are essentially the same value [with opposite signs perhaps]). However, in order to facilitate this possibility, a common rest frame is required to define u and v.


    For example, if the relative velocity (V or U), between two reference frames, is 100km/h; there should be an infinite range of values for u and v which give rise to this relative velocity: u = 30km/h and v = 70km/h; u = 50km/h and v = 50km/h; u = 1km/h and v = 99km/h; etc. etc.. However, this is only possible if we consider a common rest frame, against which to define the values for u and v; because if we only consider the relative velocity between reference frames, the value will always be 100km/h.

    It is for this reason that one reference frame has to be treated as being at absolute rest, and has to ascribe all of the velocity component to the other reference frame; it appears as though, under Einsteinian relativity, from the perspective of each reference frame i.e. from their own perspective, they are treated as being at absolute rest.

    EDIT: If they weren't treated as being at absolute rest, then, in the thought experiment, the vertical velocity component of the photon in their light clock would be less than c and they would thus measure a speed of light to be lower than c.
    Morbert wrote: »
    The conversations seems to be fragmenting again. While I don't have an issue going into real-world experiments, we first need to settle any thought experiment issues you might have. Once the consistency and implications of relativity is understood, we can move on to experimental support.
    Fair enough, but we probably won't be able to differentiate between Lorentzian relativity and Einsteinian will we, because both are equally supported by the evidence? I've read arguments that Lorentzian relativity is the more straight forward approach, when it comes to the GPS system, because of the preferred reference frame, but that Einsteinian relativity can equally be applied.

    Morbert wrote: »
    To try and keep the topic focused (We could spend a long time talking about obscure facets): Can I ask you why you would be more comfortable with assuming an undetectable absolute reference frame exists, than with the assumption that time, as part of the relation between events, exists?
    There are probably a number of reasons; some of them include the fact that what a clock counter actually measures, or rather counts, is the number of events in the clock, not necessarily the relation between them; that only a spatial relationship between the events in a clock can be deduced, and not a temporal one; the fact that there is no experiment that can ever be conducted that will not be in the present moment, meaning that the temporal dimension (past and future) have to be assumed to exist.

    Another reason is that I don't think it is necessary for Lorentzian relativity to assume that an undetectable, absolute reference frame actually exists, we can just treat the possibility that it could exist; as per the principle of invariance; we just wouldn't be able to detect such a frame, even if it did exist.

    I also think the need for an absolute reference frame, in LR, is negated simply by defining a rest frame for units of measurement; which is something which, arguably, occurs necessarily in the real world.


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    Would that be the case under the Loerntzian interpretation also?

    Yes, provided you included the usual neo-lorentzian plethora of assumptions about the co-incidental behaviour of the laws of physics.
    I don't think they are oxymoronic, are they? They are not contradictory in and of themselves; they only become contradictory if we consider that two reference frames treat themselves as being at absolute rest - which will hopefully be clarified further below.

    It is probably worth stating that the tacit assumptions aren't present in the formulation used above, but they are necessary consequences of the treatment discussed below.

    I think I may have confused the issue by not sticking more rigidly to the terms you defined from the outset, u and v, and U and V.

    The issue is that, in the construction, you started off by assuming an absolute reference frame to define the values of u and v; such that either u or v could have had a higher value, relative to the assumed absolute rest frame; they also could have had equal values, or either could have had a value of zero, relative to the absolute rest frame i.e. it would have been at absolute rest.

    Theoretically, that should be correct; there should be an infinite number of values for u and v that will give rise to the relative velocites of V and U (which are essentially the same value [with opposite signs perhaps]). However, in order to facilitate this possibility, a common rest frame is required to define u and v.

    And I don't need to define u and v at all. I am certainly free to. There is nothing special about the reference frames where u = U or v = V, but I don't have to. U and V are arbitrary labels adopted by the observers, with no compulsion to adopt them, or any other reference frame.
    For example, if the relative velocity (V or U), between two reference frames, is 100km/h; there should be an infinite range of values for u and v which give rise to this relative velocity: u = 30km/h and v = 70km/h; u = 50km/h and v = 50km/h; u = 1km/h and v = 99km/h; etc. etc.. However, this is only possible if we consider a common rest frame, against which to define the values for u and v; because if we only consider the relative velocity between reference frames, the value will always be 100km/h.

    And why consider u and v at all? Why introduce a third rest frame at all? And furthermore, even if we did arbitrarily choose a third rest frame, why call it absolute?
    It is for this reason that one reference frame has to be treated as being at absolute rest, and has to ascribe all of the velocity component to the other reference frame; it appears as though, under Einsteinian relativity, from the perspective of each reference frame i.e. from their own perspective, they are treated as being at absolute rest.

    Again, this is a contradiction in terms. If they acknowledge "from their own perspective", they acknowledge that they are not being treated "absolutely" in any way. What you should have said is "from their own perspective, they are labelled as at rest". This in no way implies "from their own perspective, they are labelled as at absolute rest".
    EDIT: If they weren't treated as being at absolute rest, then, in the thought experiment, the vertical velocity component of the photon in their light clock would be less than c and they would thus measure a speed of light to be lower than c.

    That does not follow in any way from the coordinate labels or transformations.

    If I may be blunt, I think you might have an agenda. Your belief that relativity must be somehow inherently wrong or inconsistent gets in the way of understanding the simple and uncontroversial formalism of relativity:

    Coordinate labels are arbitray.
    Coordinate labels all label the speed of light as c.
    Coordinate labels can be related by lorentz transformations.

    These in no way imply an "absolute" non-arbitrary coordinate label. Even advocates of neo-Lorentzian relativity fully accept this.
    Fair enough, but we probably won't be able to differentiate between Lorentzian relativity and Einsteinian will we, because both are equally supported by the evidence? I've read arguments that Lorentzian relativity is the more straight forward approach, when it comes to the GPS system, because of the preferred reference frame, but that Einsteinian relativity can equally be applied.

    The different formalisms of Einstein's relativity are more easily applicable in different situations. Sometimes it is useful and illuminating to talk about reference frames and coordinate time (GPS systems). Sometimes it is more useful to talk about symmetry groups and spacetime structure (Particle accelerator), but both are very much a part of Einsteinian relativity. Lorentzian relativity, as it stands, is a less elegant interpretation of data, with a greater number of assumptions. It is most common among theologians like William Lain Craig, who want there to be a privileged reference frame for God.
    There are probably a number of reasons; some of them include the fact that what a clock counter actually measures, or rather counts, is the number of events in the clock, not necessarily the relation between them; that only a spatial relationship between the events in a clock can be deduced, and not a temporal one; the fact that there is no experiment that can ever be conducted that will not be in the present moment, meaning that the temporal dimension (past and future) have to be assumed to exist.

    That is like saying a ruler counts the number of atoms between two events, not necessarily the spatial relation between the events. You cannot say time is any less real than space. And again, I stress that relativity itself says time, on its own, is illusory, and space on its own is illusory, and only consider relation between events as a whole, are they in some way preserved.
    Another reason is that I don't think it is necessary for Lorentzian relativity to assume that an undetectable, absolute reference frame actually exists, we can just treat the possibility that it could exist; as per the principle of invariance; we just wouldn't be able to detect such a frame, even if it did exist.

    You can do that either way. That is just a rephrasing of the statement "Lorentzian and Einsteinian relativity both predict the same things".
    I also think the need for an absolute reference frame, in LR, is negated simply by defining a rest frame for units of measurement; which is something which, arguably, occurs necessarily in the real world.

    And that rest frame can be arbitrarily chosen. You are presumably not, however, arguing that the present can be arbitrarily chosen. You are claiming there is an actual, non-arbitrary rest frame that labels the true present as the present.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    It might be worth addressing this point first.
    Morbert wrote: »
    If I may be blunt, I think you might have an agenda. Your belief that relativity must be somehow inherently wrong or inconsistent gets in the way of understanding the simple and uncontroversial formalism of relativity:
    I think your being blunt can be entirely beneficial to the discussion; whether we like to admit it or not, both of us are biased, for different reasons perhaps; we are both entering this with pre-existing beliefs; our attachment to which can affect our understanding of the points being made. I'm sure you are familiar with the "God is in the neurons" youtube video, which outlines how our attachment to our pre-existing beliefs can materially affect how we receive information.

    I'm not entirely sure what you mean, or mean to imply, by "agenda". I don't take it negatively, although I suspect that it may, in some way, be linked to the mention, below, of a certain theologian. This may, perhaps, be one of your own preconceptions - indeed, it could simply be my pre-conceived idea of what your preconceptions are :D.

    Either way, my "agenda" is little more than the [saccharine] desire to develop a better understanding of the nature of reality. Inevitably I have empirically based, pre-existing beliefs with which I am approaching this. That I have pre-existing beliefs does not imply that they are incorrect; that I, inevitably, apply confirmation bias does not mean that the proposition being confirmed is incorrect; no more than it means that the, inevitable, presence of the same cognitive biases in yourself, invalidates your pre-existing beliefs. It is precisely through such reasoned discussions that we both have the opportunity to cut through those cognitive biases, and hopefully shed those erroneous beliefs that affect our perception of reality.


    We could of course discuss the nature of belief and knowledge, and the nature of attachment to belief, which would make for a more holistic discussion, but for the time being, and in this thread, I think we can concentrate on the existing theme of the thread.

    Morbert wrote: »
    Yes, provided you included the usual neo-lorentzian plethora of assumptions about the co-incidental behaviour of the laws of physics.
    It might be better to discuss this in the thread on neo-Lorentzian relativity.

    Morbert wrote: »
    And I don't need to define u and v at all. I am certainly free to. There is nothing special about the reference frames where u = U or v = V, but I don't have to. U and V are arbitrary labels adopted by the observers, with no compulsion to adopt them, or any other reference frame.

    And why consider u and v at all? Why introduce a third rest frame at all? And furthermore, even if we did arbitrarily choose a third rest frame, why call it absolute?
    The reason for considering u and v is because, in your example, you started off by assuming an absolute rest frame to define the velocities, u and v, of two systems moving relative to that absolute rest frame; you then derived a formula for relative velocity between those two systems, based on the initial velocities, relative to that absolute rest frame.

    The labels, 'u' & 'v' and 'U' & 'V', themselves, are essentially immaterial, but we need some placeholders for the relative velocity, so they are as good as any other arbitrary labels. What is under discussion is what those labels represent, and the logical consequences of what they represent.


    Relative velocity
    As mentioned before, theoretically, there should be an infinite number of values that can contribute to the relative velocity between two systems. The example above was of two systems with a relative velocity of 100km/h, where one system could be traveling at a velocity of 30km/h, and the other at 70km/h, or the infinite range of values that could contribute to a relative velocity of 100km/h. This, however, requires an arbitrary, not necessarily absolute, common rest frame, in order to define that infinite range of values. Einsteinian relativity doesn't allow for such a common rest frame, because only the relative velocities between systems is considered; with contractions being reciprocal between relatively moving systems.

    By only considering the relative velocities, one of the systems has to be treated as being at absolute rest; because, in the absence of a common rest frame, or "background", 100% of the velocity has to be ascribed to the other reference frame, meaning that one of the reference frames is ascribed a zero velocity; a system with zero velocity is, I presume, a system at absolute rest.

    Morbert wrote: »
    Again, this is a contradiction in terms. If they acknowledge "from their own perspective", they acknowledge that they are not being treated "absolutely" in any way. What you should have said is "from their own perspective, they are labelled as at rest". This in no way implies "from their own perspective, they are labelled as at absolute rest".
    Apologies, my terminology may have been a little loose, but the point is essentially a semantical.

    I should probably have said that their co-ordinate system ascribes a zero velocity to their reference frame and therefore treats that reference frame as being at absolute rest. There is the alternative where their co-ordinate system ascribes a zero velocity to the other reference frame, but that just means that the other reference frame is treated as being at absolute rest.


    Morbert wrote: »
    That does not follow in any way from the coordinate labels or transformations.

    Coordinate labels are arbitray.
    Coordinate labels all label the speed of light as c.
    Coordinate labels can be related by lorentz transformations.

    These in no way imply an "absolute" non-arbitrary coordinate label. Even advocates of neo-Lorentzian relativity fully accept this.
    The point being made is that the co-ordinate labeling system, tacitly, treats specific reference frames as being at absolute rest.

    Whether it is mere coincidence or not, the thought experiment involving Albert and Henry lends itself to comparison with a similar thought experiment, where either Albert or Henry is at absolute rest. This is because the two scenarios are indistinguishable from one another. That is, if we consider the Einsteinian thought experiment from Albert's perspective, there would be no difference if we were to consider a similar thought experiment where Albert is at absolute rest. So, we are free to start with this possibility and see what conclusions we can derive.

    This is another reason for considering an absolute rest frame.

    Henry & Albert
    Just for the purpose of explanation, we can formulate the thought experiment where both Albert and Henry are in separate train carriages; replacing Albert's platform for a train carriage doesn't have any material effects; I just think it's more intuitive to talk about a train moving than it is the platform, but either is fine.

    If we simply start with the idea of the relative velocity, between Henry and Albert, both, as mentioned above, ascribe a zero velocity (and therefore absolute rest) to their own reference frames; but we can hopefully be demonstrate the point more clearly by considering the mechanics (is that the right use of the term?) of the situation.

    The issue is difficult to see initially, if we only consider the Einsteinian thought experiment at it is, with no apparent tacit assumptions or consequences pertaining to absolute rest. However, if we juxtapose the Einsteinian thought experiment with the same thought experiment, except with the notion of absolute rest included, we can, hopefully, see those tacit consequences and/or assumptions emerge.

    Absolute Frames
    If we start with Albert being at absolute rest, then the photon in his clock would trace a path perpendicular to the centre point of both mirrors, and a path length of 2d.

    If Henry were moving relative to Albert's absolute reference frame, then Albert would observe the photon in Hnery's clock to travel a path represented by the hypotenuse of a right angled triangle; hence he would observer his clock to be ticking slower (and lengths in Henry's reference frame as contracted). On the other hand, if Henry was at absolute rest and it was Albert moving relative to this frame, then Henry would see the same effects in Albert's reference frame.

    As mentioned, this is indistinguishable from the Einsteinian thought experiment, except with an absolute reference frame expressly stated. What can hopefully demonstrated is that the Einsteinian thought experiment necessarily includes this absolute reference frame.

    Absolute Albert
    For the purpose of explanation, we can consider the scenario where Albert's co-ordinate labeling system labels him as "at rest".

    If Albert's train were traveling at an inertial velocity, relative to the absolute rest frame - as would be necessitated by the scenario where "at rest" doesn't imply "absolute rest" - then the photon in his clock would be imparted with a horizontal velocity component, equal to the horizontal velocity of the train and the clock - much like he would observe in Henry's reference frame. This horizontal velocity component, along with the existing vertical velocity component, would cause the photon to trace a diagonal line between the centre points of the mirrors - because a line perpendicular from the centre point of one mirror would not meet the centre point of the other mirror, if both mirrors are moving; the path of the photon could be represented by the hypotenuse of a right angled triangle. The photon would still travel a distance of 2d relative to the carriage, because the horizontal velocity component of both would be equal. However, as you highlighted in the example above, this would cause the photon to have a vertical velocity component of less than c.

    Because Albert measures the vertical velocity component of the photon to be c, it implies that that the clock, the carriage, and Albert himself, are at absolute rest.


    Morbert wrote: »
    The different formalisms of Einstein's relativity are more easily applicable in different situations. Sometimes it is useful and illuminating to talk about reference frames and coordinate time (GPS systems). Sometimes it is more useful to talk about symmetry groups and spacetime structure (Particle accelerator), but both are very much a part of Einsteinian relativity. Lorentzian relativity, as it stands, is a less elegant interpretation of data, with a greater number of assumptions. It is most common among theologians like William Lain Craig, who want there to be a privileged reference frame for God.
    Lorentzian relativity applies just as well in the case of particle accelerators, I presume, or else there might be a way to distinguish between the two. As for elegance, I'm not sure reality relies on elegance to decide what is real and what is not. Indeed, Einsteinian relativity might have a number of tacit assumptions itself, that migh make it appear less "elegant".

    With regard to Craig: it was only through discussing Einsteinian relativity that I became aware of Lorentzian relativity; and only through searching for information about the latter that I found out that Craig had latched onto Lorentzian relativity for the reason you state above. It is perhaps, paradoxically, both fortunate and unfortunate at the same time. However, I don't think his motivation for doing so should be allowed to cast aspersions on the theory of the late Dutchman; nor should they prejudice people's interpretation of his analysis - even if they do prejudice his own analysis (which is not to suggest that they actually do).

    Although, I'm not au fait with Craigs arguments in favour of Lorentzian relativity, I have come across a few tidbits of information pertaining to the same. From what I can gather, he advocates an A-theory of time, as opposed to a B-theory. I'm not familiar enough, however, to know if timelessness fits in with his argument.

    Morbert wrote: »
    That is like saying a ruler counts the number of atoms between two events, not necessarily the spatial relation between the events. You cannot say time is any less real than space. And again, I stress that relativity itself says time, on its own, is illusory, and space on its own is illusory, and only consider relation between events as a whole, are they in some way preserved.
    Not necessarily; the counter on an atomic clock actually counts the number of "events" inside the clock without any measurement of the relation between theose events, while there is no counter on a ruler which counts the number of atoms.

    Morbert wrote: »
    You can do that either way. That is just a rephrasing of the statement "Lorentzian and Einsteinian relativity both predict the same things".
    I don't think it is; it more a question of removing what are perceived to be superfluous assumptions form the theory; without, unintentionally hiding them.

    Morbert wrote: »
    And that rest frame can be arbitrarily chosen. You are presumably not, however, arguing that the present can be arbitrarily chosen. You are claiming there is an actual, non-arbitrary rest frame that labels the true present as the present.
    The suggestion is not that there is a rest frame which labels the present as the "true present"; the suggestion is that absolute simultaneity prevails in the universe; that a timeless A-theory, if you will, prevails.


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  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    The reason for considering u and v is because, in your example, you started off by assuming an absolute rest frame to define the velocities, u and v, of two systems moving relative to that absolute rest frame; you then derived a formula for relative velocity between those two systems, based on the initial velocities, relative to that absolute rest frame.

    The labels, 'u' & 'v' and 'U' & 'V', themselves, are essentially immaterial, but we need some placeholders for the relative velocity, so they are as good as any other arbitrary labels. What is under discussion is what those labels represent, and the logical consequences of what they represent.

    Relative velocity
    As mentioned before, theoretically, there should be an infinite number of values that can contribute to the relative velocity between two systems. The example above was of two systems with a relative velocity of 100km/h, where one system could be traveling at a velocity of 30km/h, and the other at 70km/h, or the infinite range of values that could contribute to a relative velocity of 100km/h. This, however, requires an arbitrary, not necessarily absolute, common rest frame, in order to define that infinite range of values. Einsteinian relativity doesn't allow for such a common rest frame, because only the relative velocities between systems is considered; with contractions being reciprocal between relatively moving systems.

    By only considering the relative velocities, one of the systems has to be treated as being at absolute rest; because, in the absence of a common rest frame, or "background", 100% of the velocity has to be ascribed to the other reference frame, meaning that one of the reference frames is ascribed a zero velocity; a system with zero velocity is, I presume, a system at absolute rest.

    Apologies, my terminology may have been a little loose, but the point is essentially a semantical.

    I should probably have said that their co-ordinate system ascribes a zero velocity to their reference frame and therefore treats that reference frame as being at absolute rest. There is the alternative where their co-ordinate system ascribes a zero velocity to the other reference frame, but that just means that the other reference frame is treated as being at absolute rest.

    The point being made is that the co-ordinate labeling system, tacitly, treats specific reference frames as being at absolute rest.

    Whether it is mere coincidence or not, the thought experiment involving Albert and Henry lends itself to comparison with a similar thought experiment, where either Albert or Henry is at absolute rest. This is because the two scenarios are indistinguishable from one another. That is, if we consider the Einsteinian thought experiment from Albert's perspective, there would be no difference if we were to consider a similar thought experiment where Albert is at absolute rest. So, we are free to start with this possibility and see what conclusions we can derive.

    This is another reason for considering an absolute rest frame.

    Henry & Albert
    Just for the purpose of explanation, we can formulate the thought experiment where both Albert and Henry are in separate train carriages; replacing Albert's platform for a train carriage doesn't have any material effects; I just think it's more intuitive to talk about a train moving than it is the platform, but either is fine.

    If we simply start with the idea of the relative velocity, between Henry and Albert, both, as mentioned above, ascribe a zero velocity (and therefore absolute rest) to their own reference frames; but we can hopefully be demonstrate the point more clearly by considering the mechanics (is that the right use of the term?) of the situation.

    The issue is difficult to see initially, if we only consider the Einsteinian thought experiment at it is, with no apparent tacit assumptions or consequences pertaining to absolute rest. However, if we juxtapose the Einsteinian thought experiment with the same thought experiment, except with the notion of absolute rest included, we can, hopefully, see those tacit consequences and/or assumptions emerge.

    Absolute Frames
    If we start with Albert being at absolute rest, then the photon in his clock would trace a path perpendicular to the centre point of both mirrors, and a path length of 2d.

    If Henry were moving relative to Albert's absolute reference frame, then Albert would observe the photon in Hnery's clock to travel a path represented by the hypotenuse of a right angled triangle; hence he would observer his clock to be ticking slower (and lengths in Henry's reference frame as contracted). On the other hand, if Henry was at absolute rest and it was Albert moving relative to this frame, then Henry would see the same effects in Albert's reference frame.

    As mentioned, this is indistinguishable from the Einsteinian thought experiment, except with an absolute reference frame expressly stated. What can hopefully demonstrated is that the Einsteinian thought experiment necessarily includes this absolute reference frame.

    Absolute Albert
    For the purpose of explanation, we can consider the scenario where Albert's co-ordinate labeling system labels him as "at rest".

    If Albert's train were traveling at an inertial velocity, relative to the absolute rest frame - as would be necessitated by the scenario where "at rest" doesn't imply "absolute rest" - then the photon in his clock would be imparted with a horizontal velocity component, equal to the horizontal velocity of the train and the clock - much like he would observe in Henry's reference frame. This horizontal velocity component, along with the existing vertical velocity component, would cause the photon to trace a diagonal line between the centre points of the mirrors - because a line perpendicular from the centre point of one mirror would not meet the centre point of the other mirror, if both mirrors are moving; the path of the photon could be represented by the hypotenuse of a right angled triangle. The photon would still travel a distance of 2d relative to the carriage, because the horizontal velocity component of both would be equal. However, as you highlighted in the example above, this would cause the photon to have a vertical velocity component of less than c.

    Because Albert measures the vertical velocity component of the photon to be c, it implies that that the clock, the carriage, and Albert himself, are at absolute rest.

    What you have shown (and what my earlier consideration showed), is that "absolute" is entirely superfluous. You can start out defining an absolute rest, or you can start out explicitly stating there is no absolute rest, and you will still get the same result. To phrase it more formally, if an absolute rest was implicitly assumed, then the additional assumption ("There is no such thing as absolute rest") should lead to a contradiction, yet clearly it doesn't, as the entire thought experiment can be carried out using "at rest according to coordinate system A/B" without any supposition of "absolute" rest.
    Lorentzian relativity applies just as well in the case of particle accelerators, I presume, or else there might be a way to distinguish between the two. As for elegance, I'm not sure reality relies on elegance to decide what is real and what is not. Indeed, Einsteinian relativity might have a number of tacit assumptions itself, that migh make it appear less "elegant".

    It applies if you introduce more mysterious ad-hoc dynamical processes that all happen to provide an illusion of spacetime.
    With regard to Craig: it was only through discussing Einsteinian relativity that I became aware of Lorentzian relativity; and only through searching for information about the latter that I found out that Craig had latched onto Lorentzian relativity for the reason you state above. It is perhaps, paradoxically, both fortunate and unfortunate at the same time. However, I don't think his motivation for doing so should be allowed to cast aspersions on the theory of the late Dutchman; nor should they prejudice people's interpretation of his analysis - even if they do prejudice his own analysis (which is not to suggest that they actually do).

    True, but it should be pointed out that objections to Einstein's relativity do not stem from perceived insufficiencies in the theory, and Craig is an example of this.
    Not necessarily; the counter on an atomic clock actually counts the number of "events" inside the clock without any measurement of the relation between theose events, while there is no counter on a ruler which counts the number of atoms.

    And the the relation between points on a ruler is defined by counting the number of units or "simultaneous events" between the points on the ruler. Hence the 1,2,3,4... marks on the ruler.
    The suggestion is not that there is a rest frame which labels the present as the "true present"; the suggestion is that absolute simultaneity prevails in the universe; that a timeless A-theory, if you will, prevails.

    If my frame of reference says the lightning bolts strike at the same time, and yours say they strike at different times, is there a way to determine which is the absolute present?


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    What you have shown (and what my earlier consideration showed), is that "absolute" is entirely superfluous. You can start out defining an absolute rest, or you can start out explicitly stating there is no absolute rest, and you will still get the same result. To phrase it more formally, if an absolute rest was implicitly assumed, then the additional assumption ("There is no such thing as absolute rest") should lead to a contradiction, yet clearly it doesn't, as the entire thought experiment can be carried out using "at rest according to coordinate system A/B" without any supposition of "absolute" rest.
    I don't think that arriving at the same results, when including the absolute reference frame, demonstrates that it is superfluous; I would be more inclined to say that it demonstrates that the absolute reference frame is a tacit assumption. Also, simply stating that there is no absolute rest, does not mean that absolute rest is not a tacit assumption; in itself, it is indeed a contradiction, but, in order to see more clearly, where the contradictions arise, we need to examine the thought experiment critically.

    We can look at it in two ways: ignoring the absolute rest frame and considering only the relative velocity; or including the absolute rest frame and considering the mechanics.

    Relative velocity
    If we consider only the relative velocity, then we can see that the co-ordinate labeling system of Einsteinian relativity necessitates that one reference frame be ascribed a zero velocity. Again, I presume that a reference frame with a velocity of zero is a reference frame at absolute rest.

    Mechanics
    Demonstrating the tacit assumption, of absolute rest, is best done by considering the mechanics of both scenarios: where Albert is at absolute rest; and where Albert is not at absolute rest. The position of absolute rest is exactly the same as the thought experiment. But if we consider the scenario where he is not at absolute rest, then the conclusions do not concur with Einsteinian relativity.

    Again, if Albert is at absolute rest, then the photon in his clock will have no horizontal velocity component, only a vertical one; which will equal c. If Albert is not at absolute rest - the scenario where "at rest" under his labeling system doesn't mean "absolute rest" - then the photon in his clock will have a horizontal velocity component equal to that of the train (or platform) and clock. As you highlighted above, if this is the case, then the vertical velocity component will be less than c.

    If Albert measures the speed of light in his clock to be c, then it implies that he is at absolute rest - or that the vertical velocity component is greater than c, such that it yields a measurement of c, relative to the moving carriage.

    Alternatively, the contention of Lorentzian relativity could apply; that the instruments in Albert's reference frame are contracted by an amount unknown to him, due to the motion of the reference frame (where "at rest" doesn't mean "absolute rest"); relative to what, though, is the question which is begged. It can't be relative to Henry's reference frame, because he labels his reference frame as "at rest" relative to that (itself a contradiction perhaps), and he has to ascribe all the velocity to Henry's reference frame; meaning he has to label himself as having a zero velocity.

    Morbert wrote: »
    It applies if you introduce more mysterious ad-hoc dynamical processes that all happen to provide an illusion of spacetime.
    . . . the crucial difference between the two theories, of course, is that
    the Lorentz contraction, in the former theory, is viewed as a result
    of the (electromagnetic) forces responsible for the microstructure of matter in the context of Lorentz’s theory of the electron, whereas
    this same contraction, in Einstein’s theory, is viewed as a direct
    reflection—independent of all hypotheses concerning microstructure
    and its dynamics—of a new kinematical structure for space and time
    involving essential relativized notions of duration, length, and simultaneity.
    On the one hand we have a theory which seeks to explain things in the context of the micro-structure of matter (which we know to exist); on the other we have a theory which explains things by introducing a "new kinematical structure for space and time involving essential relativized notions of duration, length, and simultaneity"; which can, incidentally, only be detected by measuring the effects of the micro-structure of matter, or the macro-structure of matter, which we know to be comprised of the micro-structure of matter. In the latter "complex material bodies are constrained (somehow!) to 'directly reflect' its [spacetime's] structure, in a way that is 'independent of all hypotheses concerning microstructure and its dynamics' [again, things we know to exist]."
    One can postpone (as Einstein did) the detailed investigation into the forces and structures actually responsible for the phenomena that are paradigmatic of space-time’s Minkowskian geometry, without thereby relinquishing the idea that these forces and structures are, indeed, 'actually responsible' for the phenomena in question
    Brown & Pooley (2004)

    The emphasis and brackets are mine, and the quotes are taken out of context and don't represent the authors opinions; but the points made are applicable here.

    Morbert wrote: »
    True, but it should be pointed out that objections to Einstein's relativity do not stem from perceived insufficiencies in the theory, and Craig is an example of this.
    I haven't read any of his writings on the subject, so I can't offer too much insight; but I would imagine that his entire analysis is not based solely on the contention that a preferred reference frame fits with his theory of God. That is more based on comments in a paper by Brown & Pooley (Minkowski spacetime: a glorious non-entity).

    Morbert wrote: »
    And the the relation between points on a ruler is defined by counting the number of units or "simultaneous events" between the points on the ruler. Hence the 1,2,3,4... marks on the ruler.
    This just demonstrates that matter has a spatial dimension; the same cannot be said for a temporal dimension.


    Morbert wrote: »
    If my frame of reference says the lightning bolts strike at the same time, and yours say they strike at different times, is there a way to determine which is the absolute present?
    Experimentally, is there a way to determine relativity of simultaneity?


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    I don't think that arriving at the same results, when including the absolute reference frame, demonstrates that it is superfluous; I would be more inclined to say that it demonstrates that the absolute reference frame is a tacit assumption. Also, simply stating that there is no absolute rest, does not mean that absolute rest is not a tacit assumption; in itself, it is indeed a contradiction, but, in order to see more clearly, where the contradictions arise, we need to examine the thought experiment critically.

    We can look at it in two ways: ignoring the absolute rest frame and considering only the relative velocity; or including the absolute rest frame and considering the mechanics.

    Relative velocity
    If we consider only the relative velocity, then we can see that the co-ordinate labeling system of Einsteinian relativity necessitates that one reference frame be ascribed a zero velocity. Again, I presume that a reference frame with a velocity of zero is a reference frame at absolute rest.

    You do not need to claim the reference frame has a velocity of 0. When mathematicians say a reference frame S' has a velocity V in reference frame S, what they mean is an object that is labelled as stationary in S' will have a velocity V in S. You can explicitly state the nearly tautological fact that a reference frame will have a velocity of 0, according to itself, or an object that is labelled as stationary in S' will have a velocity of 0 in S', but that is no more a statement about absolute rest than "I am at rest with respect to myself".
    Mechanics
    Demonstrating the tacit assumption, of absolute rest, is best done by considering the mechanics of both scenarios: where Albert is at absolute rest; and where Albert is not at absolute rest. The position of absolute rest is exactly the same as the thought experiment. But if we consider the scenario where he is not at absolute rest, then the conclusions do not concur with Einsteinian relativity.

    Again, if Albert is at absolute rest, then the photon in his clock will have no horizontal velocity component, only a vertical one; which will equal c. If Albert is not at absolute rest - the scenario where "at rest" under his labeling system doesn't mean "absolute rest" - then the photon in his clock will have a horizontal velocity component equal to that of the train (or platform) and clock. As you highlighted above, if this is the case, then the vertical velocity component will be less than c.

    If Albert measures the speed of light in his clock to be c, then it implies that he is at absolute rest - or that the vertical velocity component is greater than c, such that it yields a measurement of c, relative to the moving carriage.

    The bit in red is incorrect. Einstein's relativity says all observers will measure the speed of light to be c. Therefore Albert would measure the speed of light in his clock to be c regardless of whether or not he is at absolute rest, so the implication that he is at absolute rest cannot be made.
    Alternatively, the contention of Lorentzian relativity could apply; that the instruments in Albert's reference frame are contracted by an amount unknown to him, due to the motion of the reference frame (where "at rest" doesn't mean "absolute rest"); relative to what, though, is the question which is begged. It can't be relative to Henry's reference frame, because he labels his reference frame as "at rest" relative to that (itself a contradiction perhaps), and he has to ascribe all the velocity to Henry's reference frame; meaning he has to label himself as having a zero velocity.

    On the one hand we have a theory which seeks to explain things in the context of the micro-structure of matter (which we know to exist); on the other we have a theory which explains things by introducing a "new kinematical structure for space and time involving essential relativized notions of duration, length, and simultaneity"; which can, incidentally, only be detected by measuring the effects of the micro-structure of matter, or the macro-structure of matter, which we know to be comprised of the micro-structure of matter. In the latter "complex material bodies are constrained (somehow!) to 'directly reflect' its [spacetime's] structure, in a way that is 'independent of all hypotheses concerning microstructure and its dynamics' [again, things we know to exist]."

    Brown & Pooley (2004)

    The emphasis and brackets are mine, and the quotes are taken out of context and don't represent the authors opinions; but the points made are applicable here.

    I haven't read any of his writings on the subject, so I can't offer too much insight; but I would imagine that his entire analysis is not based solely on the contention that a preferred reference frame fits with his theory of God. That is more based on comments in a paper by Brown & Pooley (Minkowski spacetime: a glorious non-entity).

    Brown and Pooley argue that Einstein's relativity has the same issues as Lorentzian relativity. It doesn't, for the following reasons.

    (a) The 'constraint' of Minkowski geometry occurs precisely because of the absence of mysterious dynamical forces. Brown and Pooley argue that a Minkowski geometry doesn't necessarily mean the laws of physics are Lorentz invariant. This is true insofar as you can postulate mysterious accidental dynamics to break Lorentz invariance, just as neo-Lorentzian relativity postulates mysterious dynamics to break Galilean invariance. But in the absence of such mysterious dynamics, Minkowski kinematics implies Lorentz invariant laws. And since the absence of mysterious dynamics is the virtue of Einstein's relativity, there is no problem.

    (b) Neo-Lorentzian relativity does not explain this "accidental" microstructure of matter. Brown and Pooley adimit as much ("all explanation must stop somewhere").

    (c) There is an interesting rebuttal found here

    http://philsci-archive.pitt.edu/3895/

    as well as other criticisms

    http://philsci-archive.pitt.edu/3655/1/Constructive_Relativity.pdf

    http://philsci-archive.pitt.edu/3108/1/Physical_Relativityfin.pdf

    I don't draw anything particular from them (yet) as directly relevant to our conversation, but you might find them interesting.

    When it comes to the "philosophy" of relativity, I take the (seemingly dismissive) position that Minkowski spacetime is the simplest mathematical model connecting the postulates of relativity to experimental observations.
    This just demonstrates that matter has a spatial dimension; the same cannot be said for a temporal dimension.

    And a clock just demonstrates that a set of events (not a single event) has a temporal dimension, just as the set of simultaneous events across a ruler (not a single event) has a spatial dimension. We can generalise this by saying there is a spatio-temporal relation between events.
    Experimentally, is there a way to determine relativity of simultaneity?

    In other words: "I accept that the postulated true present is unknown, and cannot even be known to exist at all, but you cannot tender an experiment to show it definitely does not exist". This is true(ish) insofar as any test of simultaneity could be explained by invoking contrived neo-lorentzian dynamics, but relativity of simultaneity is simply the relaxation of the assumption that there is a true, simultaneous present. Why assume what you cannot demonstrate?


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    You do not need to claim the reference frame has a velocity of 0. When mathematicians say a reference frame S' has a velocity V in reference frame S, what they mean is an object that is labelled as stationary in S' will have a velocity V in S. You can explicitly state the nearly tautological fact that a reference frame will have a velocity of 0, according to itself, or an object that is labelled as stationary in S' will have a velocity of 0 in S', but that is no more a statement about absolute rest than "I am at rest with respect to myself".
    The issue isn't quite as simplistic as saying "I am at rest with respect to myself".


    EDIT: of course, the "I am at rest with respect to myself" applies just as much to an observer at absolute rest.

    If we were considering a lone observer in an empty universe, or considering the observer without reference to anything else in the universe, then a co-ordinate system which implies "I am at rest with respect to myself" would be fine; but we are considering the co-ordinate labeling system which labels the reference frame as "at rest" and a relatively moving reference frame as "in motion".

    When we do this, there is no need to claim that a reference frame has a velocity of zero, it is a logical consequence of the co-ordinate labeling system. If you only consider the relative velocity between systems, then it is impossible not to label one as having a zero velocity, and, therefore, as being at absolute rest; regardless of what mathematicians wish to imply, that is a consequence of such a labeling system. This is what is meant by saying that the co-ordinate labeling system of Einsteinian relativity treats reference frames as being at absolute rest, from it's own perspective, or "according to itself".

    The "from it's own perspective" or "according to itself" is a semantical point, with which we shouldn't get bogged down. The essential point is that the co-ordinate labeling system applied to reference frames in Einsteinian relativity, treat that reference frame as being at absolute rest, precisely because it ascribes a zero velocity to it.

    Infinite reference frames
    If we consider the infinite, possible, reference frames in the universe, and - sticking with the basic thought experiment for now - if we start with the perspective of one observer; then 100% of the velocity, of any relatively moving system, is ascribed to the other system, under that observers co-ordinate labeling system. That means that the co-ordinate labeling system ascribes a zero velocity to the "at rest" reference frame.

    If it doesn't imply "at absolute rest" then the reference frame must be in motion relative to something other than the other detectable, relatively moving reference frames; an undetectable reference frame perhaps. But even if we postulate an infinite number of undetectable reference frames which would help satisfy the condition that "at rest" doesn't mean "absolute rest", if we extend the logic of the co-ordinate labeling system, then the co-ordinate labeling system would still apply 100% of the relative velocity to those undetectable reference frames, and consequently imply a state of absolute rest.

    The co-ordinate labeling system could, of course, ascribe 100% of the relative velocity to an observers own reference frame, but this just shifts the problem of absolute rest to another reference frame.


    Morbert wrote: »
    The bit in red is incorrect. Einstein's relativity says all observers will measure the speed of light to be c. Therefore Albert would measure the speed of light in his clock to be c regardless of whether or not he is at absolute rest, so the implication that he is at absolute rest cannot be made.
    To say that Einsteinian relativity says all observers will measure the speed of light to be c, therefore Albert will measure the speed of light to be c, is circular reasoning. The point, which is presumably clear enough at this stage, is that the implication of absolute rest can indeed be made, even if Einsteinian relativity doesn't expressly state it.

    I presume you don't have an issue with the notion that the photon in the clock will inherit the horizontal velocity component of the train (or platform) and the clock, if the train is in motion; or if the train is not at absolute rest (which are just two ways of saying the same thing). If not, then there shouldn't really be any issue in following the logic.

    "at rest"
    If "at rest" doesn't mean "at absolute rest", then it means that "at rest" also means "in motion", which itself is a contradiction in terms; but that is a semantical argument, which doesn't need to be pursued. We only need to reason from some simple principles we already appear to have established - namely, the imparting of a horizontal velocity component to the photon.

    If "at rest" doesn't mean "at absolute rest", then, by necessity, the photon in the light clock will be imparted with a horizontal velocity component. You stated above that this would result in the vertical velocity component being less than c, and so the observer on the train would measure the speed of light to be less than c; this would be at odds with Einsteinian relativity.

    Alternatively, we can draw the conclusion that the vertical velocity component of the photon is greater than c, such that the observer on the train measures the speed of light to be c, relative to the train carriage; this too is at odds with Einsteinian relativity.

    We could conclude that the photon doesn't get imparted with a horizontal velocity component, and only has a vertical velocity component; this however would result in the photon "falling out of the clock"; this is also at odds with Einsteinian relativity, and is contrary to something we have established in discussion.

    Another alternative is that Albert is at absolute rest; this fits perfectly with the Einsteinian thought experiment, and indeed with practicalities of Einsteinian relativity, even if it is at odds with certain beliefs about Einsteinian relativity.

    Another alternative, if "at rest" doesn't mean "at absolute rest", is that the equipment in Albert's reference frame is contracted by an amount unknown to himself, due to his motion relative to an undetectable reference frame; which result in his measuring a speed of c for the light. This, however, is closer to Lorentzian relativity than it is Einsteinian.
    Morbert wrote: »
    Brown and Pooley argue that Einstein's relativity has the same issues as Lorentzian relativity. It doesn't, for the following reasons.

    <snip>
    My apologies, I know I added to this line of the discussion, but I'll respond in the neo-Lorentzian thread.

    The choice seems to be between mysterious dynamics affecting something we know to exist - the microstructure of matter - and a mysterious universe wide entity, which can only be detected through the observations of the micro-structure of matter, or the macro-structure of matter (which is comprised of the micro-structure).

    Morbert wrote: »
    And a clock just demonstrates that a set of events (not a single event) has a temporal dimension, just as the set of simultaneous events across a ruler (not a single event) has a spatial dimension. We can generalise this by saying there is a spatio-temporal relation between events.
    We've been discussing this already in the thread on clocks, and I don't think it was established that a clock demonstrates a temporal dimension at all; only a spatial relationship between the events in a clock can be demonstrated. This applies equally to any other process.

    Morbert wrote: »
    In other words: "I accept that the postulated true present is unknown, and cannot even be known to exist at all, but you cannot tender an experiment to show it definitely does not exist". This is true(ish) insofar as any test of simultaneity could be explained by invoking contrived neo-lorentzian dynamics, but relativity of simultaneity is simply the relaxation of the assumption that there is a true, simultaneous present. Why assume what you cannot demonstrate?
    In other words, "just as 'the true present' cannot be established experimentally, neither can relativity of simultaneity. Also, there is only evidence for the present moment; there is no experiment which has ever been conducted, or can ever be conducted, that was not, or will not be, in the present; therefore, there is no evidence that either 'past' or 'future' exist - they have to be assumed to exist. There is also no evidence for the existence of time, because it cannot be demonstrated that a clock measures time, without the assumption that it does.

    Why indeed assume something that cannot be demonstrated?

    Also, Einsteinian relativity appears to treat reference frames as being at absolute rest"

    Morbert wrote: »
    If my frame of reference says the lightning bolts strike at the same time, and yours say they strike at different times, is there a way to determine which is the absolute present?
    If the above scenario occurs, is there a way to determine relativity of simultaneity?


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    The issue isn't quite as simplistic as saying "I am at rest with respect to myself".

    EDIT: of course, the "I am at rest with respect to myself" applies just as much to an observer at absolute rest.

    If we were considering a lone observer in an empty universe, or considering the observer without reference to anything else in the universe, then a co-ordinate system which implies "I am at rest with respect to myself" would be fine; but we are considering the co-ordinate labeling system which labels the reference frame as "at rest" and a relatively moving reference frame as "in motion".

    When we do this, there is no need to claim that a reference frame has a velocity of zero, it is a logical consequence of the co-ordinate labeling system. If you only consider the relative velocity between systems, then it is impossible not to label one as having a zero velocity, and, therefore, as being at absolute rest; regardless of what mathematicians wish to imply, that is a consequence of such a labeling system. This is what is meant by saying that the co-ordinate labeling system of Einsteinian relativity treats reference frames as being at absolute rest, from it's own perspective, or "according to itself".

    The "from it's own perspective" or "according to itself" is a semantical point, with which we shouldn't get bogged down. The essential point is that the co-ordinate labeling system applied to reference frames in Einsteinian relativity, treat that reference frame as being at absolute rest, precisely because it ascribes a zero velocity to it.


    Infinite reference frames
    If we consider the infinite, possible, reference frames in the universe, and - sticking with the basic thought experiment for now - if we start with the perspective of one observer; then 100% of the velocity, of any relatively moving system, is ascribed to the other system, under that observers co-ordinate labeling system. That means that the co-ordinate labeling system ascribes a zero velocity to the "at rest" reference frame.

    If it doesn't imply "at absolute rest" then the reference frame must be in motion relative to something other than the other detectable, relatively moving reference frames; an undetectable reference frame perhaps. But even if we postulate an infinite number of undetectable reference frames which would help satisfy the condition that "at rest" doesn't mean "absolute rest", if we extend the logic of the co-ordinate labeling system, then the co-ordinate labeling system would still apply 100% of the relative velocity to those undetectable reference frames, and consequently imply a state of absolute rest.

    The co-ordinate labeling system could, of course, ascribe 100% of the relative velocity to an observers own reference frame, but this just shifts the problem of absolute rest to another reference frame.

    To say that Einsteinian relativity says all observers will measure the speed of light to be c, therefore Albert will measure the speed of light to be c, is circular reasoning. The point, which is presumably clear enough at this stage, is that the implication of absolute rest can indeed be made, even if Einsteinian relativity doesn't expressly state it.

    I presume you don't have an issue with the notion that the photon in the clock will inherit the horizontal velocity component of the train (or platform) and the clock, if the train is in motion; or if the train is not at absolute rest (which are just two ways of saying the same thing). If not, then there shouldn't really be any issue in following the logic.

    "at rest"
    If "at rest" doesn't mean "at absolute rest", then it means that "at rest" also means "in motion", which itself is a contradiction in terms; but that is a semantical argument, which doesn't need to be pursued. We only need to reason from some simple principles we already appear to have established - namely, the imparting of a horizontal velocity component to the photon.

    If "at rest" doesn't mean "at absolute rest", then, by necessity, the photon in the light clock will be imparted with a horizontal velocity component. You stated above that this would result in the vertical velocity component being less than c, and so the observer on the train would measure the speed of light to be less than c; this would be at odds with Einsteinian relativity.

    Alternatively, we can draw the conclusion that the vertical velocity component of the photon is greater than c, such that the observer on the train measures the speed of light to be c, relative to the train carriage; this too is at odds with Einsteinian relativity.

    We could conclude that the photon doesn't get imparted with a horizontal velocity component, and only has a vertical velocity component; this however would result in the photon "falling out of the clock"; this is also at odds with Einsteinian relativity, and is contrary to something we have established in discussion.

    Another alternative is that Albert is at absolute rest; this fits perfectly with the Einsteinian thought experiment, and indeed with practicalities of Einsteinian relativity, even if it is at odds with certain beliefs about Einsteinian relativity.

    Another alternative, if "at rest" doesn't mean "at absolute rest", is that the equipment in Albert's reference frame is contracted by an amount unknown to himself, due to his motion relative to an undetectable reference frame; which result in his measuring a speed of c for the light. This, however, is closer to Lorentzian relativity than it is Einsteinian.

    You are not treating your co-ordinate systems consistently. Points highlighted in orange are examples of where you are mushing together reference frames, and hence producing inconsistencies. Reference frames are the arbitrary coordinate systems. They do not sit in some higher absolute coordinate system. Points highlighted in blue are mistakes in logic. The claim "At rest does not imply absolute rest", for example, does not imply anything about the necessity of absolute rest. Points highlighted in red are factual errors. Hence, your conclusions do not hold.

    This mishandling of reference frames is probably due to a lack of practise with them. You need to start from the beginning, and strip everything down to its essentials.

    We start with a set of three events:

    A photon leaves an emitter/detector.
    A photon bounces off a mirror.
    A photon returns to the emitter/detector.

    Now let us apply an arbitrary coordinate system, in order to label these events.

    A photon leaves an emitter/detector. (r_1,t_1)
    A photon bounces off a mirror. (r_2,t_2)
    A photon returns to the emitter/detector. (r_3,t_3)

    We can transform this arbitrary coordinate system into any other arbitrary coordinate system via the Lorentz transformations. This is how you treat coordinates, and this is how you make coordinate dependent statements. Note that, since we employ arbitrary coordinate systems, we can only relate coordinate systems to each other, and cannot infer that any coordinate system is "absolute". Again (for emphasis), we discuss arbitrary coordinate systems, and the relation between those coordinate systems, but we do not talk about an absolute coordinate system.

    Any absolutes come in as coordinate independent relations between events (spacetime structure) and the laws governing events (general covariance).
    My apologies, I know I added to this line of the discussion, but I'll respond in the neo-Lorentzian thread.

    The choice seems to be between mysterious dynamics affecting something we know to exist - the microstructure of matter - and a mysterious universe wide entity, which can only be detected through the observations of the micro-structure of matter, or the macro-structure of matter (which is comprised of the micro-structure).

    It is not mysterious at all, and instead has a very well defined mathematical structure, described with pseudo-riemannian differential geometry, that has been directly incorporated into not only "clocks and planes/trains" experiments, but also particle experiments, where the spacetime metric explicitly appears in equations.
    We've been discussing this already in the thread on clocks, and I don't think it was established that a clock demonstrates a temporal dimension at all; only a spatial relationship between the events in a clock can be demonstrated. This applies equally to any other process.

    My point is you are treating the measures inconsistently. You say the measure of time is merely a construct built from the set of events between ticks in a clock, but you say the measure of space is not just a construct built from the set of events across a ruler.
    In other words, "just as 'the true present' cannot be established experimentally, neither can relativity of simultaneity. Also, there is only evidence for the present moment; there is no experiment which has ever been conducted, or can ever be conducted, that was not, or will not be, in the present; therefore, there is no evidence that either 'past' or 'future' exist - they have to be assumed to exist. There is also no evidence for the existence of time, because it cannot be demonstrated that a clock measures time, without the assumption that it does.

    What is the evidence for the present moment (and according to whom)?
    If the above scenario occurs, is there a way to determine relativity of simultaneity?

    I am going to interpret this as an admission that you believe that the "true" present exists, but accept that it cannot be experimentally verified. It then comes back to the discussion on neo-Lorentzian relativity, where, instead of relaxing the assumption of Newtonian presentism, you postulate a variety of mysterious ad-hoc dynamics to explain away the details.


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  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    You are not treating your co-ordinate systems consistently. Points highlighted in orange are examples of where you are mushing together reference frames, and hence producing inconsistencies. Reference frames are the arbitrary coordinate systems. They do not sit in some higher absolute coordinate system. Points highlighted in blue are mistakes in logic. The claim "At rest does not imply absolute rest", for example, does not imply anything about the necessity of absolute rest. Points highlighted in red are factual errors. Hence, your conclusions do not hold.

    This mishandling of reference frames is probably due to a lack of practise with them. You need to start from the beginning, and strip everything down to its essentials.

    We start with a set of three events:

    A photon leaves an emitter/detector.
    A photon bounces off a mirror.
    A photon returns to the emitter/detector.

    Now let us apply an arbitrary coordinate system, in order to label these events.

    A photon leaves an emitter/detector. (r_1,t_1)
    A photon bounces off a mirror. (r_2,t_2)
    A photon returns to the emitter/detector. (r_3,t_3)

    We can transform this arbitrary coordinate system into any other arbitrary coordinate system via the Lorentz transformations. This is how you treat coordinates, and this is how you make coordinate dependent statements. Note that, since we employ arbitrary coordinate systems, we can only relate coordinate systems to each other, and cannot infer that any coordinate system is "absolute". Again (for emphasis), we discuss arbitrary coordinate systems, and the relation between those coordinate systems, but we do not talk about an absolute coordinate system.

    Any absolutes come in as coordinate independent relations between events (spacetime structure) and the laws governing events (general covariance).
    Mushing reference frames

    There is no "mushing together" of reference frames, whatsoever. We only
    need to consider one single reference frame, Albert's for example; Albert's co-ordinate system ascribes a zero velocity to his reference frame, and ascribes 100% of the [relative] velocity to any other reference frame that is moving relative to his, Henry's for example. Again, a system with a zero velocity is a system at absolute rest. This doesn't involve mixing reference frames any more than the Einsteinian thought experiment does.

    Mistakes in logic
    If you believe there are mistakes in the logic, it might be worth pointing out where the logic breaks down.


    Circular reasoning
    If the starting assumption is that all observers will measure the speed of light to be c, regardless of whether they are in motion or at absolute rest, and the conclusion which follows directly afterwards is, therefore an observer will measure the speed of light to be c, regardless of whether they are in motion or at absolute rest; then it is circular reasoning.


    Zero velocity

    A system at absolute rest has a velocity of zero; and any system moving relative to that system is "responsible" for 100% of the relative velocity; therefore, any system with a velocity of zero is at absolute rest.

    Example: an observer on a train has a velocity of zero relative to the train; there is a relative velocity of X between the train (and observer) and another relatively moving system. If the other system is "responsible" for all of X (positive or minus signs are immaterial), then the train and the observer are at absolute rest.


    If a co-ordinate system ascribes a zero velocity to a reference frame, then that co-ordinate system treats the zero velocity reference frame as being at absolute rest - because any system with a velocity of zero is at absolute rest.


    "at rest" & "at absolute rest"
    If a system is not at absolute rest, then, by necessity, it must be "in motion". If "at rest" doesn't mean "at absolute rest", then [by necessity] it means that "at rest" also means "in motion".

    If "at rest" means "in motion" then it must mean in motion relative to something. If a co-ordinate labeling system ascribes a zero velocity to a reference frame - and therefore implies that it is not in motion - and ascribes 100% of the relative velocity of all detectable, relatively moving reference frames, to those other reference frames, then, if "at rest" does not mean "at absolute rest" (and therefore means "in motion"), the motion must be relative to some other undetectable relatively moving reference frame. Again, however, the co-ordinate labeling system would still ascribe 100% of the relative velocity to all other detectable, and undetectable reference frames; thereby treating the particular reference frame as being at absolute rest.

    Horizontal velocity component
    The photon in a clock that is in motion will be imparted with a horizontal velocity component equal to the horizontal velocity component of the clock.

    If "at rest" doesn't mean "at absolute rest", then, by necessity, it also means "in motion"; if a clock is "at rest", but not "at absolute rest", then, by necessity, it is "in motion"; if a clock is "in motion" then the photon in the clock will be imparted with a horizontal velocity component equal to that of the clock. Therefore, If "at rest" doesn't mean "at absolute rest", then, by necessity, the photon in the light clock will be imparted with a horizontal velocity component.

    Factual errors
    As above, if a system is not at absolute rest, then, by necessity, it must be "in motion"; therefore, saying a train is in motion and saying a train is not at absolute rest are just two ways of saying the same thing.

    Morbert wrote: »
    It is not mysterious at all, and instead has a very well defined mathematical structure, described with pseudo-riemannian differential geometry, that has been directly incorporated into not only "clocks and planes/trains" experiments, but also particle experiments, where the spacetime metric explicitly appears in equations.
    A physical entity, which has no substance, permeating the entire universe, which bends, warps, tears, slows down and forms tunnels, due to the presence of matter, or the motion of a system, or some other reason, but which cannot be detected, and whose effects can only be detected through observation of the micro- and macro-structures of matter, sounds a little mysterious to me.

    In an ontological sense, it also sounds a little superfluous, even if it is mathematically useful. If there is no region of space that is not filled with matter, then surely all that exists is matter. Any of the observed effects that "give the illiusion of spacetime" are equally attributable effects observed in matter; more so, because they are actually observed in matter. The question of how, might just be another one of those things we don't yet have an answer to; attributing it to a mysterious spacetime structure that exactly resembles all matter and natural forces, which permeates the entire universe, but doesn't affect the micro-structure of matter when it contracts and warps, seems like answering the question of "why something instead of nothing" with the answer that an invisible bearded man in the sky did it.


    Morbert wrote: »
    My point is you are treating the measures inconsistently. You say the measure of time is merely a construct built from the set of events between ticks in a clock, but you say the measure of space is not just a construct built from the set of events across a ruler.
    I don't think I've made that point; but it is perhaps best saved for the other thread.

    Morbert wrote: »
    What is the evidence for the present moment (and according to whom)?
    Have you ever existed in a time that wasn't the present; not the present moment "in time", but that wasn't the present tense?

    Morbert wrote: »
    I am going to interpret this as an admission that you believe that the "true" present exists, but accept that it cannot be experimentally verified. It then comes back to the discussion on neo-Lorentzian relativity, where, instead of relaxing the assumption of Newtonian presentism, you postulate a variety of mysterious ad-hoc dynamics to explain away the details.
    I wouldn't quite say that; it might be worth pointing out that looking for evidence of an absolute present is a category mistake; it is like being presented with the buildings of a university and saying there is no evidence of the university. Given that the only evidence that any observer has, had, or will ever have, is of the present moment, I would say that evidence to the contrary is required.

    Also, the the alternative, as opposed to, euphemistically, requiring a "relaxing" of the assumption of presentism, requires a "new kinematical structure for space and time involving essential relativized notions of duration, length, and simultaneity"; assumptions which directly contradict the experience of every observer, living or dead, as well as assumptions about the measurement of time.

    It also seems to require the treatment of reference frames as being at absolute rest, under their respective co-ordinate labeling systems.


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    Mushing reference frames

    There is no "mushing together" of reference frames, whatsoever. We only
    need to consider one single reference frame, Albert's for example; Albert's co-ordinate system ascribes a zero velocity to his reference frame, and ascribes 100% of the [relative] velocity to any other reference frame that is moving relative to his, Henry's for example. Again, a system with a zero velocity is a system at absolute rest. This doesn't involve mixing reference frames any more than the Einsteinian thought experiment does.

    You are doing it again here. If Albert ascribes a velocity of absolute zero to his reference frame, he is referencing an external frame to describe his own reference frame. You have implicitly introduced an absolute reference frame to describe Albert's reference frame, and treating it as his own. Instead, you should have said, "When we describe Albert's measurements, we use the arbitrary coordinate system that labels Albert as stationary."

    Again, I explicitly stated as much in my last post, and you seem to have ignored it. Here is is again.

    We start with a set of three events:

    A photon leaves an emitter/detector.
    A photon bounces off a mirror.
    A photon returns to the emitter/detector.

    Now let us apply an arbitrary coordinate system, in order to label these events.

    A photon leaves an emitter/detector. (r_1,t_1)
    A photon bounces off a mirror. (r_2,t_2)
    A photon returns to the emitter/detector. (r_3,t_3)

    We can transform this arbitrary coordinate system into any other arbitrary coordinate system via the Lorentz transformations. This is how you treat coordinates, and this is how you make coordinate dependent statements. Note that, since we employ arbitrary coordinate systems, we can only relate coordinate systems to each other, and cannot infer that any coordinate system is "absolute". Again (for emphasis), we discuss arbitrary coordinate systems, and the relation between those coordinate systems, but we do not talk about an absolute coordinate system.

    Any absolutes come in as coordinate independent relations between events (spacetime structure) and the laws governing events (general covariance).
    Mistakes in logic
    If you believe there are mistakes in the logic, it might be worth pointing out where the logic breaks down.

    "P does not imply Q", does not imply anything about Q, other than it is not implied by P. "At rest does not imply absolute rest" does not imply anything about absolute rest, other than it is not implied by "at rest".
    Circular reasoning
    If the starting assumption is that all observers will measure the speed of light to be c, regardless of whether they are in motion or at absolute rest, and the conclusion which follows directly afterwards is, therefore an observer will measure the speed of light to be c, regardless of whether they are in motion or at absolute rest; then it is circular reasoning.

    I don't think you are following this line of the discussion. The assumption that all observers will measure the speed of light to be c is not what you are disputing. You presumably accept that assumption. If you don't then you not only reject relativity, but also neo-Lorentzian relativity, and all experimental evidence. Hence, any line of reasoning I tender is an exploration of the consequences of that assumption, not an attempt to prove the assumption. The reasoning I tendered was "All observers will measure the speed of light to be c." implies "You cannot infer any statement about absolute rest from a measurement of the speed of light."

    Zero velocity

    A system at absolute rest has a velocity of zero; and any system moving relative to that system is "responsible" for 100% of the relative velocity; therefore, any system with an [absolute] velocity of zero is at absolute rest.

    Without my added "[absolute]", the above is a non-sequitur. "A system at absolute rest has an absolute velocity of zero" does not imply "Employing an arbitrary coordinate system that labels an object as stationary implies the object is at absolute rest". Again, a coordinate system is just a set of labels we place on events.
    Example: an observer on a train has a velocity of zero relative to the train;

    Correct. In more rigorous circumlocution, we say the coordinate system that labels the train as "at rest" also labels the observer on the train as "at rest".
    there is a relative velocity of X between the train (and observer) and another relatively moving system.

    If by this you mean: "The coordinate system which labels the train (and observer) as stationary will label another object (E.g. the ground) as moving with a velocity X" then you are correct.
    If the other system is "responsible" for all of X (positive or minus signs are immaterial), then the train and the observer are at absolute rest.

    This is where the problems arise. I do not know what it means to claim the other system is responsible for X. It does not follow from any of the previous statements, hence the conditional cannot be used to imply the train and observer are actually at absolute rest.
    If a co-ordinate system ascribes a zero velocity to a reference frame, then that co-ordinate system treats the zero velocity reference frame as being at absolute rest - because any system with an [absolute] velocity of zero is at absolute rest.

    As before, the statement in blue is a non-sequitur unless you include the [absolute].

    The statement in orange is again a mishandling of coordinate systems. A coordinate system is a reference frame. A reference frame is an arbitrary labelling system. So arbitrarily adding an "extra" arbitrary labelling system to label your arbitrary labelling system as at rest does not imply the extra arbitrary labelling system is anything other than arbitrary.
    "at rest" & "at absolute rest"
    If a system is not at absolute rest, then, by necessity, it must be "in motion". If "at rest" doesn't mean "at absolute rest", then [by necessity] it means that "at rest" also means "in motion".

    If "at rest" means "in motion" then it must mean in motion relative to something. If a co-ordinate labeling system ascribes a zero velocity to a reference frame - and therefore implies that it is not in motion - and ascribes 100% of the relative velocity of all detectable, relatively moving reference frames, to those other reference frames, then, if "at rest" does not mean "at absolute rest" (and therefore means "in motion"), the motion must be relative to some other undetectable relatively moving reference frame. Again, however, the co-ordinate labeling system would still ascribe 100% of the relative velocity to all other detectable, and undetectable reference frames; thereby treating the particular reference frame as being at absolute rest.

    The bit in blue is a non-sequitur. Arbitrarily labelling something as at rest does not imply it is absolutely at rest or in motion.
    Horizontal velocity component
    The photon in a clock that is in motion will be imparted with a horizontal velocity component equal to the horizontal velocity component of the clock.

    Correct. This is an example of an absolute or "invariant" statement. It is true, independent of whatever coordinate system you use. It is the conservation of momentum.
    If "at rest" doesn't mean "at absolute rest", then, by necessity, it also means "in motion"; if a clock is "at rest", but not "at absolute rest", then, by necessity, it is "in motion"; if a clock is "in motion" then the photon in the clock will be imparted with a horizontal velocity component equal to that of the clock. Therefore, If "at rest" doesn't mean "at absolute rest", then, by necessity, the photon in the light clock will be imparted with a horizontal velocity component.

    This is the same non-sequitur as before. Arbitrarily labelling a system as at rest says nothing about whether or not the system is at absolute rest. if what you said was true, then even neo-lorentzian relativity would fall apart.
    A physical entity, which has no substance, permeating the entire universe, which bends, warps, tears, slows down and forms tunnels, due to the presence of matter, or the motion of a system, or some other reason, but which cannot be detected, and whose effects can only be detected through observation of the micro- and macro-structures of matter, sounds a little mysterious to me.

    You are describing an aether. This is not what spacetime is. Spacetime, as previously mentioned before, is a structure, a "field" in the physical sense (specifically, the gravitational field). "It bends and warps" is mysterious and imprecise language, but in the strict language of physics, we say it exhibits non-euclidean geometry between events.
    In an ontological sense, it also sounds a little superfluous, even if it is mathematically useful. If there is no region of space that is not filled with matter, then surely all that exists is matter. Any of the observed effects that "give the illiusion of spacetime" are equally attributable effects observed in matter; more so, because they are actually observed in matter. The question of how, might just be another one of those things we don't yet have an answer to; attributing it to a mysterious spacetime structure that exactly resembles all matter and natural forces, which permeates the entire universe, but doesn't affect the micro-structure of matter when it contracts and warps, seems like answering the question of "why something instead of nothing" with the answer that an invisible bearded man in the sky did it.

    Again, spacetime is not mysterious at all. "Mysterious" implies a "filler" or a "gap" for something not understood. Spacetime has a very precise and well understood structure. What is genuinely mysterious is the dynamics of neo-Lorentzian relativity.
    I don't think I've made that point; but it is perhaps best saved for the other thread.

    You have been saying a clock does not demonstrate time, but a ruler demonstrates space.
    Have you ever existed in a time that wasn't the present; not the present moment "in time", but that wasn't the present tense?

    Who's present? Yours? Yes. But since we are moving at such slow speeds relative to each other, "the present" is a good approximation for both of us.
    I wouldn't quite say that; it might be worth pointing out that looking for evidence of an absolute present is a category mistake; it is like being presented with the buildings of a university and saying there is no evidence of the university. Given that the only evidence that any observer has, had, or will ever have, is of the present moment, I would say that evidence to the contrary is required.

    It is not a category mistake. We know that different observers must disagree about what is the present, according to their reference frames. This much is agreed upon by everyone. The neo-Lorentzian position says "we will recover the idea of an absolute present by postulating mysterious and unexplained dynamics to explain this apparent discrepancy in simultaneity".
    Also, the the alternative, as opposed to, euphemistically, requiring a "relaxing" of the assumption of presentism, requires a "new kinematical structure for space and time involving essential relativized notions of duration, length, and simultaneity"; assumptions which directly contradict the experience of every observer, living or dead, as well as assumptions about the measurement of time.

    How do they directly contradict experience at all? You are parting ways even with the neo-Lorentzian crowd.
    It also seems to require the treatment of reference frames as being at absolute rest, under their respective co-ordinate labeling systems.

    An assertion you have not shown. Let's try something. In all future posts, let's use the more rigorous phrasing, because it is clear that your misunderstanding stems from the shorthand language used in thought experiments. For example:

    "A train has a velocity of zero" -> "Consider an arbitrary coordinate system labelling the train as stationary."

    "The speed of the ground, relative to the train, is X" -> "A coordinate system that labels the train as stationary, labels the ground has having a speed |X|"


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    You are doing it again here. If Albert ascribes a velocity of absolute zero to his reference frame, he is referencing an external frame to describe his own reference frame. You have implicitly introduced an absolute reference frame to describe Albert's reference frame, and treating it as his own. Instead, you should have said, "When we describe Albert's measurements, we use the arbitrary coordinate system that labels Albert as stationary."
    There is no implicit introduction of an external, or separate reference frame, because the absolute reference frame is one and the same with Albert's, by virtue of his arbitrary co-ordinate labeling system. We don't say, there is an absolute rest frame and then there is Albert's reference frame; what is being said is that Albert's arbitrary co-ordinate labeling system treats his reference frame as one and the same thing as an absolute reference frame; not external, not separate, but the same - arbitrarily or otherwise.


    His arbitrary, co-ordinate labeling system makes no distinction between "absolute" zero and plain old zero, because no distinction can be made without implying that Albert's reference frame is in motion relative to an undetectable reference frame; because his co-ordinate labeling system labels him as having a zero velocity relative to all other, detectable, reference frames. So, if Albert's zero velocity [relative to all detectable reference frames] doesn't correspond to an absolute velocity of zero, then Albert's reference frame must have a velocity relative to some other, undetectable reference frame.

    However, even if there was relative velocity between Albert's reference frame and any number of other infinite, undetectable reference frames, Albert's arbitrary co-ordinate labeling system would still label him as being at absolute rest, because it would ascribe a zero velocity him and ascribe 100% of the relative velocity to the other, relatively moving, reference frames.

    Morbert wrote: »
    Again, I explicitly stated as much in my last post, and you seem to have ignored it. Here is is again.

    We start with a set of three events:

    A photon leaves an emitter/detector.
    A photon bounces off a mirror.
    A photon returns to the emitter/detector.

    Now let us apply an arbitrary coordinate system, in order to label these events.

    A photon leaves an emitter/detector. (r_1,t_1)
    A photon bounces off a mirror. (r_2,t_2)
    A photon returns to the emitter/detector. (r_3,t_3)

    We can transform this arbitrary coordinate system into any other arbitrary coordinate system via the Lorentz transformations. This is how you treat coordinates, and this is how you make coordinate dependent statements. Note that, since we employ arbitrary coordinate systems, we can only relate coordinate systems to each other, and cannot infer that any coordinate system is "absolute". Again (for emphasis), we discuss arbitrary coordinate systems, and the relation between those coordinate systems, but we do not talk about an absolute coordinate system.

    Any absolutes come in as coordinate independent relations between events (spacetime structure) and the laws governing events (general covariance).
    We are discussing the implications of the co-ordinate labeling system, and the expected behaviour of the photon under different circumstances, and seeing what logical conclusions we can draw from that; we don't need to consider transforming the arbitrary co-ordinate labels into another reference frame just yet.

    Morbert wrote: »
    "P does not imply Q", does not imply anything about Q, other than it is not implied by P. "At rest does not imply absolute rest" does not imply anything about absolute rest, other than it is not implied by "at rest".
    "P does not imply Q"; however "P and Q are not mutually exclusive"; indeed "Q satisfies the conditions for P, while A-Z (excluding P & Q) arguably don't"; therefore "P must be Q".

    Morbert wrote: »
    I don't think you are following this line of the discussion. The assumption that all observers will measure the speed of light to be c is not what you are disputing. You presumably accept that assumption. If you don't then you not only reject relativity, but also neo-Lorentzian relativity, and all experimental evidence. Hence, any line of reasoning I tender is an exploration of the consequences of that assumption, not an attempt to prove the assumption. The reasoning I tendered was "All observers will measure the speed of light to be c." implies "You cannot infer any statement about absolute rest from a measurement of the speed of light."
    The assumption that is, effectivily, being challenged is, that the photon in Albert's clock won't be imparted with a horizontal velocity component, which would mean that the vertical velocity component would be less than c, such that he would measure the speed of light to be less than c, unless - and this is an important point - unless his instruments are contracted by an amount unknown to himself, due to his motion relative to an undetectable, absolute reference frame. We can examine this simply by considering Albert's reference frame, according to his own arbitrary labeling system, in the two possible scenarios under discussion: at absolute rest; and not at absolute rest. As has been outlined, only a position of absolute rest satisfies the conditions for Einsteinian relativity.

    Keypoints
    OK, so there are two key points that we need to consider, just to see where the issue lies in this; do you agree with the following?

    - a system that is not at absolute rest, is, by necessity, in motion? If not, why not?
    - the photon in any clock that is in motion will be imparted with a horizontal velocity component equal to the motion of the system? If not, why not?


    Morbert wrote: »
    Without my added "[absolute]", the above is a non-sequitur. "A system at absolute rest has an absolute velocity of zero" does not imply "Employing an arbitrary coordinate system that labels an object as stationary implies the object is at absolute rest". Again, a coordinate system is just a set of labels we place on events.
    That a co-ordinate system is just a set of arbitrary labels is not in question; what is in question is the logical implications of such a co-ordinate system. If a co-ordinate system arbitrarily treats a reference frame as being at absolute rest, then regardless of the arbitrariness, it still treats that reference frame as being at absolute rest.

    If we look at the two contentions:
    A system at absolute rest has a velocity of zero

    "Employing an arbitrary coordinate system that labels an object as [having a velocity of zero] implies the object is at absolute rest"


    Morbert wrote: »
    Correct. In more rigorous circumlocution, we say the coordinate system that labels the train as "at rest" also labels the observer on the train as "at rest".

    If by this you mean: "The coordinate system which labels the train (and observer) as stationary will label another object (E.g. the ground) as moving with a velocity X" then you are correct.

    This is where the problems arise. I do not know what it means to claim the other system is responsible for X. It does not follow from any of the previous statements, hence the conditional cannot be used to imply the train and observer are actually at absolute rest.
    I'm not sure how you can deduce that the conditional can't be used, if you don't know what it means.

    What was meant is probably easier explained with an example; if we imagine the relative velocity between two cars is 100 km/h; theoretically there is an infinite range of values that could contribute to the relative velocity of 100km/h; one car could be traveling at 70km/h, the other at 30; both could be traveling at 50km/h; one could be traveling at 99km/h while the other is traveling at 1km/h; of course, another possibility is that one car is stationary, while the other car is traveling at 100km/h. In the intended context, we would say that the proportion of the relative velocity that each car is responsible for corresponds to their speeds.

    It is probably further clarified using the now familiar absolute rest frame. If there is relative velocity between the absolute rest frame and another system, then the other system is "responsible" for all of the relative velocity.

    If a co-ordinate system ascribes 100% of the relative velocity to every other, relatively moving, reference frame, then that arbitrary, co-ordinate labeling system treats the zero velocity reference frame as being at absolute rest - because it makes every other reference frame "responsible" for the entirety of the relative velocity;à la the absolute reference frame.


    Morbert wrote: »
    As before, the statement in blue is a non-sequitur unless you include the [absolute].

    The statement in orange is again a mishandling of coordinate systems. A coordinate system is a reference frame. A reference frame is an arbitrary labelling system. So arbitrarily adding an "extra" arbitrary labelling system to label your arbitrary labelling system as at rest does not imply the extra arbitrary labelling system is anything other than arbitrary.
    I think you might be getting caught up in semantics here; but I'm sure you get the point that is being made, because you've been discussing it thus far without recourse to semantics (at every turn).

    Albert's co-ordinate labeling system ascribes a zero velocity to him, and ascribes 100% of the relative velocity to other relatively moving reference frames, à la the absolute reference frame.


    Morbert wrote: »
    The bit in blue is a non-sequitur. Arbitrarily labelling something as at rest does not imply it is absolutely at rest or in motion.
    The questions are posed abvoe, but for the purpose of re-iteration they can be restated:

    Do you agree with the following?

    -If something is not at absolute rest, then, by necessity it is in motion
    if not, why not?


    If you agree that something which is not at absolute rest is, by necessity, in motion, then we can reason thusly:

    If something not at absolute rest is necessarily in motion; then, if something doesn't imply absolute rest, it must imply motion; therefore, if "at rest" doesn't imply "absolute rest" then it necessarily implies motion - arbitrarily or otherwise.
    Morbert wrote: »
    Correct. This is an example of an absolute or "invariant" statement. It is true, independent of whatever coordinate system you use. It is the conservation of momentum.
    Excellent, so we have a point of agreement. The outstanding issue then is whether "not at absolute rest" implies "in motion" or not.


    Morbert wrote: »
    This is the same non-sequitur as before. Arbitrarily labelling a system as at rest says nothing about whether or not the system is at absolute rest. if what you said was true, then even neo-lorentzian relativity would fall apart.
    I don't think there's any need to restate the contention above.


    Morbert wrote: »
    You are describing an aether. This is not what spacetime is. Spacetime, as previously mentioned before, is a structure, a "field" in the physical sense (specifically, the gravitational field). "It bends and warps" is mysterious and imprecise language, but in the strict language of physics, we say it exhibits non-euclidean geometry between events.



    Again, spacetime is not mysterious at all. "Mysterious" implies a "filler" or a "gap" for something not understood. Spacetime has a very precise and well understood structure. What is genuinely mysterious is the dynamics of neo-Lorentzian relativity.



    You have been saying a clock does not demonstrate time, but a ruler demonstrates space.



    Who's present? Yours? Yes. But since we are moving at such slow speeds relative to each other, "the present" is a good approximation for both of us.



    It is not a category mistake. We know that different observers must disagree about what is the present, according to their reference frames. This much is agreed upon by everyone. The neo-Lorentzian position says "we will recover the idea of an absolute present by postulating mysterious and unexplained dynamics to explain this apparent discrepancy in simultaneity".



    How do they directly contradict experience at all? You are parting ways even with the neo-Lorentzian crowd.
    I'll have to take my share of the responsibility but the discussion appears to be fragmenting again; it would probably be better to establish, or refute, the "absolute rest" contention.

    Morbert wrote: »
    An assertion you have not shown. Let's try something. In all future posts, let's use the more rigorous phrasing, because it is clear that your misunderstanding stems from the shorthand language used in thought experiments. For example:

    "A train has a velocity of zero" -> "Consider an arbitrary coordinate system labelling the train as stationary."

    "The speed of the ground, relative to the train, is X" -> "A coordinate system that labels the train as stationary, labels the ground has having a speed |X|"
    I'm not sure introducing euphemisms will be entirely productive, even if euphemisms is the language usually employed.

    How about:
    "A train has a velocity of zero" -> "Consider an arbitrary coordinate system labelling the train as having a zero velocity"

    "The relative velocity between the the ground and the train, is X" -> "A coordinate system that labels the train as having a zero velocity, labels the ground has having a velocity |X| i.e. it ascribes the entirety of the relative velocity to the ground"


    If we're going to be more rigorous then I don;t think semantics is the way to go; we need to consider the logical implications of the language.


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    There is no implicit introduction of an external, or separate reference frame, because the absolute reference frame is one and the same with Albert's, by virtue of his arbitrary co-ordinate labeling system. We don't say, there is an absolute rest frame and then there is Albert's reference frame; what is being said is that Albert's arbitrary co-ordinate labeling system treats his reference frame as one and the same thing as an absolute reference frame; not external, not separate, but the same - arbitrarily or otherwise.

    It is not one and the same at all. Albert may not be at absolute rest, or he might be at absolute rest. If his reference frame is arbitrary, it is independent of whether or not he is at absolute rest. It is independent of whether or not an absolute rest exists at all. It says nothing about absolute rest. It is a physical labelling system, not a metaphysical claim.

    I have identified a single line of reasoning in the following paragraphs:
    His arbitrary, co-ordinate labeling system makes no distinction between "absolute" zero and plain old zero, because no distinction can be made without implying that Albert's reference frame is in motion relative to an undetectable reference frame; because his co-ordinate labeling system labels him as having a zero velocity relative to all other, detectable, reference frames. So, if Albert's zero velocity [relative to all detectable reference frames] doesn't correspond to an absolute velocity of zero, then Albert's reference frame must have a velocity relative to some other, undetectable reference frame.

    However, even if there was relative velocity between Albert's reference frame and any number of other infinite, undetectable reference frames, Albert's arbitrary co-ordinate labeling system would still label him as being at absolute rest, because it would ascribe a zero velocity him and ascribe 100% of the relative velocity to the other, relatively moving, reference frames.

    We are discussing the implications of the co-ordinate labeling system, and the expected behaviour of the photon under different circumstances, and seeing what logical conclusions we can draw from that; we don't need to consider transforming the arbitrary co-ordinate labels into another reference frame just yet.

    "P does not imply Q"; however "P and Q are not mutually exclusive"; indeed "Q satisfies the conditions for P, while A-Z (excluding P & Q) arguably don't"; therefore "P must be Q".

    The assumption that is, effectivily, being challenged is, that the photon in Albert's clock won't be imparted with a horizontal velocity component, which would mean that the vertical velocity component would be less than c, such that he would measure the speed of light to be less than c, unless - and this is an important point - unless his instruments are contracted by an amount unknown to himself, due to his motion relative to an undetectable, absolute reference frame. We can examine this simply by considering Albert's reference frame, according to his own arbitrary labeling system, in the two possible scenarios under discussion: at absolute rest; and not at absolute rest. As has been outlined, only a position of absolute rest satisfies the conditions for Einsteinian relativity.

    Keypoints
    OK, so there are two key points that we need to consider, just to see where the issue lies in this; do you agree with the following?

    - a system that is not at absolute rest, is, by necessity, in motion? If not, why not?
    - the photon in any clock that is in motion will be imparted with a horizontal velocity component equal to the motion of the system? If not, why not?

    That a co-ordinate system is just a set of arbitrary labels is not in question; what is in question is the logical implications of such a co-ordinate system. If a co-ordinate system arbitrarily treats a reference frame as being at absolute rest, then regardless of the arbitrariness, it still treats that reference frame as being at absolute rest.

    If we look at the two contentions:
    A system at absolute rest has a velocity of zero

    "Employing an arbitrary coordinate system that labels an object as [having a velocity of zero] implies the object is at absolute rest"

    I'm not sure how you can deduce that the conditional can't be used, if you don't know what it means.

    What was meant is probably easier explained with an example; if we imagine the relative velocity between two cars is 100 km/h; theoretically there is an infinite range of values that could contribute to the relative velocity of 100km/h; one car could be traveling at 70km/h, the other at 30; both could be traveling at 50km/h; one could be traveling at 99km/h while the other is traveling at 1km/h; of course, another possibility is that one car is stationary, while the other car is traveling at 100km/h. In the intended context, we would say that the proportion of the relative velocity that each car is responsible for corresponds to their speeds.

    It is probably further clarified using the now familiar absolute rest frame. If there is relative velocity between the absolute rest frame and another system, then the other system is "responsible" for all of the relative velocity.

    If a co-ordinate system ascribes 100% of the relative velocity to every other, relatively moving, reference frame, then that arbitrary, co-ordinate labeling system treats the zero velocity reference frame as being at absolute rest - because it makes every other reference frame "responsible" for the entirety of the relative velocity;à la the absolute reference frame.

    I think you might be getting caught up in semantics here; but I'm sure you get the point that is being made, because you've been discussing it thus far without recourse to semantics (at every turn).

    Albert's co-ordinate labeling system ascribes a zero velocity to him, and ascribes 100% of the relative velocity to other relatively moving reference frames, à la the absolute reference frame.

    The questions are posed abvoe, but for the purpose of re-iteration they can be restated:

    Do you agree with the following?

    -If something is not at absolute rest, then, by necessity it is in motion
    if not, why not?

    If you agree that something which is not at absolute rest is, by necessity, in motion, then we can reason thusly:

    If something not at absolute rest is necessarily in motion; then, if something doesn't imply absolute rest, it must imply motion; therefore, if "at rest" doesn't imply "absolute rest" then it necessarily implies motion - arbitrarily or otherwise.

    I'm not sure introducing euphemisms will be entirely productive, even if euphemisms is the language usually employed.

    "A train has a velocity of zero" -> "Consider an arbitrary coordinate system labelling the train as having a zero velocity"

    "The relative velocity between the the ground and the train, is X" -> "A coordinate system that labels the train as having a zero velocity, labels the ground has having a velocity |X| i.e. it ascribes the entirety of the relative velocity to the ground"

    If we're going to be more rigorous then I don;t think semantics is the way to go; we need to consider the logical implications of the language.

    I have a few issues with the above paragraphs (E.g. the euphemism claim), but to avoid further fragmentation, I will focus on the only important one. You are claiming that, since Albert's reference frame, which labels him as "at rest" is consistent with the metaphysical statement "Albert is at absolute rest", it must mean Albert's reference frame is making a metaphysical statement about absolute rest. This is the non-sequitur that is causing all the problems. Albert's reference frame is also consistent, for example, with the metaphysical claim "Albert is not at absolute rest" or even "There is no such thing as absolute rest." They are consistent because Albert's coordinate labels are not metaphysical claims at all. They are book-keeping tools. Analogously, the laws of physics are consistent with the metaphysical claim "The absolute truth is we are all brains in a jar, hooked up to the matrix". But this does not show that we are all hooked up to the matrix.

    In other words, show that the following two suppositions are inconsistent.

    Suppose Albert is not at absolute rest.
    Suppose Albert uses his arbitrary reference frame to label all events (the reference frame which labels himself as at rest).

    I argue that there is no inconsistency at all.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    It is not one and the same at all. Albert may not be at absolute rest, or he might be at absolute rest. If his reference frame is arbitrary, it is independent of whether or not he is at absolute rest. It is independent of whether or not an absolute rest exists at all. It says nothing about absolute rest. It is a physical labelling system, not a metaphysical claim.

    I have identified a single line of reasoning in the following paragraphs:



    I have a few issues with the above paragraphs (E.g. the euphemism claim), but to avoid further fragmentation, I will focus on the only important one. You are claiming that, since Albert's reference frame, which labels him as "at rest" is consistent with the metaphysical statement "Albert is at absolute rest", it must mean Albert's reference frame is making a metaphysical statement about absolute rest. This is the non-sequitur that is causing all the problems. Albert's reference frame is also consistent, for example, with the metaphysical claim "Albert is not at absolute rest" or even "There is no such thing as absolute rest." They are consistent because Albert's coordinate labels are not metaphysical claims at all. They are book-keeping tools. Analogously, the laws of physics are consistent with the metaphysical claim "The absolute truth is we are all brains in a jar, hooked up to the matrix". But this does not show that we are all hooked up to the matrix.

    In other words, show that the following two suppositions are inconsistent.

    Suppose Albert is not at absolute rest.
    Suppose Albert uses his arbitrary reference frame to label all events (the reference frame which labels himself as at rest).

    I argue that there is no inconsistency at all.

    The point being made isn't simply: since Albert's reference frame, which labels him as "at rest" is consistent with the metaphysical statement "Albert is at absolute rest", it must mean Albert's reference frame is making a metaphysical statement about absolute rest.

    The point being made is that, given the fact that a photon will inherit the horizontal velocity component of a clock that is in motion, then only a position of absolute rest satisfies the conditions for Einsteinian relativity.


    The issue can be distilled down to one foundational question (and possibly a follow up question):
    Is a system which is not at absolute rest, necessarily in motion?

    If not, why not?


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    The point being made isn't simply: since Albert's reference frame, which labels him as "at rest" is consistent with the metaphysical statement "Albert is at absolute rest", it must mean Albert's reference frame is making a metaphysical statement about absolute rest.

    The point being made is that, given the fact that a photon will inherit the horizontal velocity component of a clock that is in motion, then only a position of absolute rest satisfies the conditions for Einsteinian relativity.

    The issue can be distilled down to one foundational question (and possibly a follow up question):
    Is a system which is not at absolute rest, necessarily in motion?

    If not, why not?

    You are confusing Einsteinian relativity with Galilean relativity. Einsteinian relativity says all coordinate systems measure the speed of light to be c, the laws of physics are the same under all coordinate systems, and all coordinate systems are related by lorentz transformations. Inheriting horizontal velocity is not a problem.

    Consider the three relevant events:

    A photon leaves the emitter.
    A photon bounces off a mirror.
    A photon hits the detector.

    Now consider two coordinate systems S and S'. The apparatus is stationary in S, and is moving at a speed of 0.5 c in S'. The distance between the detector and the mirror in S is 1 lightsecond. Now let us look at the positions of the three events (and hence the speed of the photon) in each case. First, we consider the Galilean transformation.

    2pzlfl3.jpg

    The time (T) dimension is on the Y axis, and position (X) is on the X axis (both in natural units). The red line is the photon path between the three events in S. The green line is the photon path in S'. Note that, in diagrams like these, velocity is represented by the inverse of slope of the line (speed/time). You can see that the slope is different for S and S'. This is because of the inherited velocity of the photon. It is travelling faster in S' than it is in S. But now consider lorentz transformations.

    f38gfn.jpg

    Note that the slopes are the same in each case. This is because, even though the photon inherits the velocity of the apparatus, lorentz transformations tell us S and S' will not label events with the same time stamps (unlike galilean transformations).

    Hence, the issue of absolute rest doesn't even come up. It is entirely superflous.


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    Oh yes, I should mention that the diagrams shown are for an apparatus oriented along the direction of motion. I can do the same for apparatus oriented perpendicular to the direction of motion, though the diagrams will require an extra dimension.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    You are confusing Einsteinian relativity with Galilean relativity. Einsteinian relativity says all coordinate systems measure the speed of light to be c, the laws of physics are the same under all coordinate systems, and all coordinate systems are related by lorentz transformations. Inheriting horizontal velocity is not a problem.

    Consider the three relevant events:

    A photon leaves the emitter.
    A photon bounces off a mirror.
    A photon hits the detector.

    Now consider two coordinate systems S and S'. The apparatus is stationary in S, and is moving at a speed of 0.5 c in S'. The distance between the detector and the mirror in S is 1 lightsecond. Now let us look at the positions of the three events (and hence the speed of the photon) in each case. First, we consider the Galilean transformation.

    <removed to shorten reply length>

    The time (T) dimension is on the Y axis, and position (X) is on the X axis (both in natural units). The red line is the photon path between the three events in S. The green line is the photon path in S'. Note that, in diagrams like these, velocity is represented by the inverse of slope of the line (speed/time). You can see that the slope is different for S and S'. This is because of the inherited velocity of the photon. It is travelling faster in S' than it is in S. But now consider lorentz transformations.

    <removed to shorten reply length>

    Note that the slopes are the same in each case. This is because, even though the photon inherits the velocity of the apparatus, lorentz transformations tell us S and S' will not label events with the same time stamps (unlike galilean transformations).

    Hence, the issue of absolute rest doesn't even come up. It is entirely superflous.
    I may have it wrong; I may not be explaining it correctly; conditioning in Einsteinian relativity might be making it difficult to see; or it could be a combination of the latter two; but hopefully I can state this lucidly enough to try and negate the latter two, or highlight where my misunderstanding lies, and we can hopefully resolve it.

    It might initially seem like I am mistaking Einsteinian relativity of Galilean, but I'll try to illucidate why this isn't the case; this will, largely, be done by considering only the Einsteinian thought experiment, and highlighting where the relevant Galilean, Einsteinian, or Lorentzian conclusions would apply.


    "not at absolute rest"
    Firstly, we need to establish whether a reference frame that is not at "absolute rest" is, by necessity, "in motion"; I would like to say that I could take the fact that you didn't answer the question, directly, as an acceptance of that point, but I don't think I can; however, I think it's a matter of definition, so I think it is a fair point; unless you reason otherwise.

    Horizontal velocity
    If the above point is accepted, and if "at rest" doesn't imply "at absolute rest", then we can reason that Albert's labeling system (or reference frame), which labels him as "at rest" is actually in motion. This means that the photon in Albert's clock will be imparted with a horizontal velocity component.

    Now, under Galilean relativity, this would indeed lead to the vertical velocity component being less than c, such that Albert would measure the speed of light to be lower than c.

    However, if this isn't the case, and Albert measures the speed of light to be c, as Einsteinian relativity states, then Albert's measuring instruments must have contracted by an amount unknown to himself, due to the motion of his "not at absolute rest" reference frame. This, however, is a Lorentzian interpretation.

    relative to what?
    The question is, relative to what is Alberts' "not at absolute rest" reference frame in motion? Presumably it must be an undetectable reference frame, because Albert's, arbitrary, co-ordinate labeling system labels him as at rest relative to all other relatively moving, detectable reference frames (itself somewhat contradictory, but that isn't necessary here).

    This too would be a Lorentzian interpretation.


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    I may have it wrong; I may not be explaining it correctly; conditioning in Einsteinian relativity might be making it difficult to see; or it could be a combination of the latter two; but hopefully I can state this lucidly enough to try and negate the latter two, or highlight where my misunderstanding lies, and we can hopefully resolve it.

    It might initially seem like I am mistaking Einsteinian relativity of Galilean, but I'll try to illucidate why this isn't the case; this will, largely, be done by considering only the Einsteinian thought experiment, and highlighting where the relevant Galilean, Einsteinian, or Lorentzian conclusions would apply.


    "not at absolute rest"
    Firstly, we need to establish whether a reference frame that is not at "absolute rest" is, by necessity, "in motion"; I would like to say that I could take the fact that you didn't answer the question, directly, as an acceptance of that point, but I don't think I can; however, I think it's a matter of definition, so I think it is a fair point; unless you reason otherwise.

    This brings me back to "P does not imply Q" does not mean "P implies notQ". That we cannot say a reference frame implies absolute rest, does not mean we can say a reference frame implies absolute motion. You can metaphysically suppose absolute rest, or you can metaphysically reject absolute rest. It will not have any effect on the coordinate descriptions of Einstein's relativity.
    Horizontal velocity
    If the above point is accepted, and if "at rest" doesn't imply "at absolute rest", then we can reason that Albert's labeling system (or reference frame), which labels him as "at rest" is actually in motion. This means that the photon in Albert's clock will be imparted with a horizontal velocity component.

    Now, under Galilean relativity, this would indeed lead to the vertical velocity component being less than c, such that Albert would measure the speed of light to be lower than c.

    However, if this isn't the case, and Albert measures the speed of light to be c, as Einsteinian relativity states, then Albert's measuring instruments must have contracted by an amount unknown to himself, due to the motion of his "not at absolute rest" reference frame. This, however, is a Lorentzian interpretation.

    Under Galilean relativity, the vertical velocity component would be unchanged, but one frame describes the photon as also having a non-zero horizontal velocity, and hence a speed greater than c. This does not happen under lorentz transformations because, under lorentz transformations, time is transformed as well as space.
    relative to what?
    The question is, relative to what is Alberts' "not at absolute rest" reference frame in motion? Presumably it must be an undetectable reference frame, because Albert's, arbitrary, co-ordinate labeling system labels him as at rest relative to all other relatively moving, detectable reference frames (itself somewhat contradictory, but that isn't necessary here).

    This too would be a Lorentzian interpretation.

    This relates back to the above: "We do not say Albert is at absolute rest" is not the same as "We say Albert is not at absolute rest." You can suppose absolute rest, or you can suppose no absolute rest. The physics won't change.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    This brings me back to "P does not imply Q" does not mean "P implies notQ". That we cannot say a reference frame implies absolute rest, does not mean we can say a reference frame implies absolute motion. You can metaphysically suppose absolute rest, or you can metaphysically reject absolute rest. It will not have any effect on the coordinate descriptions of Einstein's relativity.
    That depends on what P and Q are though; when dealing with the law of the excluded middle, as I believe we are, not P does imply Q, just as not Q does imply P.

    As far as I can see it is a matter of definition; if something is "not at absolute rest" it must, by necessity, be "in motion".

    Morbert wrote: »
    Under Galilean relativity, the vertical velocity component would be unchanged, but one frame describes the photon as also having a non-zero horizontal velocity, and hence a speed greater than c. This does not happen under lorentz transformations because, under lorentz transformations, time is transformed as well as space.
    OK, I presume that this is taking the assumption that Albert will measure the speed of light to be c, relative to the carriage. In the case above you mentioned that the vertical velocity component would be less than c, this would be the case without the assumption I take it.

    Morbert wrote: »
    This relates back to the above: "We do not say Albert is at absolute rest" is not the same as "We say Albert is not at absolute rest." You can suppose absolute rest, or you can suppose no absolute rest. The physics won't change.
    The implications of the co-ordinate labeling system are a little more explicit, however, because they make positive statements about Albert, as opposed to negative statements i.e. they say what Albert is, not what he isn't.

    The co-ordinate labeling system labels Albert with a zero velocity and labels him as "at rest", despite the fact that there is motion relative to another reference frame. The question is, does this "at rest" mean at absolute rest, or not? Not expressly stating which it is, is fine; but we are free to deduce what it must mean i.e. what the tacit assumption (or consequence) must be.

    If Albert's reference frame, which is labelled as "at rest" is not at absolute rest, then as above, according to the law of the excluded middle, it must mean that Albert's reference frame is necessarily in motion. Which begs the question, relative to what is it in motion? It must be an undetectable reference frame because his co-ordinate labeling system labels all relatively moving, detectable reference frames as "in motion"; it ascribes 100% of the velocity to them, and labels Albert as "at rest" with a zero velocity.

    If his reference frame is "in motion", then, if he measures the speed of light to be c, his instruments must be contracted by an amount unknown to himself, due to this motion relative to the undetectable reference frame.

    As mentioned, this is the conclusion of Lorentzian relativity.


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  • Registered Users Posts: 1,005 ✭✭✭Enkidu


    I think you may be over complicating the notion of absolute rest roosh. Relativity says there is no absolute rest in the sense that there exists no experiment which all observers can agree on which would assign a velocity of v = 0 to some object. This is unlike acceleration, where everybody can agree if an object has a=0, since it will have no force exerted on it.


  • Registered Users Posts: 1,005 ✭✭✭Enkidu


    roosh wrote: »
    The co-ordinate labeling system labels Albert with a zero velocity and labels him as "at rest", despite the fact that there is motion relative to another reference frame. The question is, does this "at rest" mean at absolute rest, or not? Not expressly stating which it is, is fine; but we are free to deduce what it must mean i.e. what the tacit assumption (or consequence) must be.
    It is not at absolute rest. Relativity has no absolute rest. Rather one says Albert is inertial. That is, since he has "a = 0", something all observers agree on, there exists a frame with respect to which he is at rest.
    roosh wrote: »
    If Albert's reference frame, which is labelled as "at rest" is not at absolute rest, then as above, according to the law of the excluded middle, it must mean that Albert's reference frame is necessarily in motion.
    This is not valid reasoning. There is no absolute rest in relativity and neither is there absolute motion. All one says is that Albert is at rest in some frames and in motion in others. You are missing the point that if you can not absolutely say Albert is at rest, you cannot absolutely say he is in motion.


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    To echo what Enkidu has said, you are making a logic error.

    Analogously, you are trying to infer statements about the matrix from Newton's laws.
    That depends on what P and Q are though; when dealing with the law of the excluded middle, as I believe we are, not P does imply Q, just as not Q does imply P.

    You are not invoking the law of the excluded middle correclty, for two reasons. Firstly, in our case

    P: There exists a coordinate system where Albert is "at rest".
    Q: Albert is at absolute rest.

    What I am saying is
    P → (Q ∨ ¬Q)

    Hence, no implicit assumption is made about Q.

    Secondly, the law of the excluded middle is
    (Q ∨ ¬Q)
    Either Albert is at absolute rest (Q), or Albert is not at absolute rest (¬Q). If we introduce another proposition M "Albert is in absolute motion", then we have the relations

    Q → ¬M
    M → ¬Q
    ¬Q → (M ∨ ¬M)
    ¬M → (Q ∨ ¬Q)

    You are introducing a false dichotomy (Q ∨ M), and trying to justify it with the law of the excluded middle. Your dichotomy assumes absolute space exists, when the very message of relativity is that it is physically meaningless.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Enkidu wrote: »
    I think you may be over complicating the notion of absolute rest roosh. Relativity says there is no absolute rest in the sense that there exists no experiment which all observers can agree on which would assign a velocity of v = 0 to some object. This is unlike acceleration, where everybody can agree if an object has a=0, since it will have no force exerted on it.
    The point being made isn't so much that there is, or must be, an absolute rest frame, it is that the co-ordinate labeling system used in Einsteinian relativity treats specific reference frames, or observers, as being at absolute rest. For example, Albert's co-ordinate labeling system labels him as having a zero velocity, just as Henry's labels Henry as having a zero velocity.

    While Einsteinian relativity might not expressly say anything about absolute rest, or might even claim that there is no such thing, we can examine it critically and see that it is a tacit assumption, or consequence, of the co-ordinate labeling system.


    Enkidu wrote: »
    It is not at absolute rest. Relativity has no absolute rest. Rather one says Albert is inertial. That is, since he has "a = 0", something all observers agree on, there exists a frame with respect to which he is at rest.
    Again, we can critically examine the consequences of different scenarios and deduce that it is a tacit assumption, or consequence, of the co-ordinate labeling system. That it isn't expressly stated in the formalism of Einsteinian relativity is immaterial.

    Albert's co-ordinate labeling system labels him and "his" train (or platform) as having a zero velocity; that is, his reference frame is ascribed a zero velocity, despite there being motion relative another reference frame. 100% of the relative velocity is ascribed to the relatively moving reference frame à la an absolute rest frame.

    Enkidu wrote: »
    This is not valid reasoning. There is no absolute rest in relativity and neither is there absolute motion. All one says is that Albert is at rest in some frames and in motion in others. You are missing the point that if you can not absolutely say Albert is at rest, you cannot absolutely say he is in motion.
    We need to move beyond the fact that Einsteinian relativity doesn't expressly include an absolute reference frame, or even says that such doesn't exist; we need to apply reason to the possible scenarios and see that it can be deduced that it is a tacit assumption, or consequence, of the co-ordinate labeling system.

    Taking the simplistic example, Albert's co-ordinate labeling system will always label him as having a zero velocity, regardless of the motion relative to another reference frame. If a co-ordinate labeling system labels Albert as having a zero velocity, then that co-ordinate labeling system treats him as though he were at absolute rest.

    If Albert's "at rest" label doesn't mean "at absolute rest" then it must mean he is in motion relative to an undetectable reference frame, because his co-ordinate labeling system applies 100% of the relative velocity to all relatively moving, detectable reference frames.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    To echo what Enkidu has said, you are making a logic error.

    Analogously, you are trying to infer statements about the matrix from Newton's laws.



    You are not invoking the law of the excluded middle correclty, for two reasons. Firstly, in our case

    P: There exists a coordinate system where Albert is "at rest".
    Q: Albert is at absolute rest.

    What I am saying is
    P → (Q ∨ ¬Q)

    Hence, no implicit assumption is made about Q.

    Secondly, the law of the excluded middle is
    (Q ∨ ¬Q)
    Either Albert is at absolute rest (Q), or Albert is not at absolute rest (¬Q). If we introduce another proposition M "Albert is in absolute motion", then we have the relations

    Q → ¬M
    M → ¬Q
    ¬Q → (M ∨ ¬M)
    ¬M → (Q ∨ ¬Q)

    You are introducing a false dichotomy (Q ∨ M), and trying to justify it with the law of the excluded middle. Your dichotomy assumes absolute space exists, when the very message of relativity is that it is physically meaningless.

    Apologies, my formulation may have been a bit sloppy. Firstly though, the concept of "absolute rest" is indirectly referenced through the Galilean Principle of Invariance (PoI) and the special Principle of Relativity (PoR), in the stated consequence that relatively moving observers cannot determine, by experiment, which one is moving*.


    [EDIT]
    The stated consequence of the Galilean PoI, is that an inertial observer cannot determine if they are "in motion" or "at rest"; in the Galilean case it is indisputable that the concept of "absolute rest" is what is being referenced.

    PoR
    The special Principle of Relativity (PoR), together with the equivalence principle, is just an extension of this principle to include accelerating reference frames, such that two relatively moving observers cannot determine which one is moving. Again, this implies that one of the observers might not be moving.

    The question is, how can an observer not be moving, when there is relative velocity between them and another observer? The answer is: only if they are at "absolute rest" - a very old, and pretty well understood, concept in scientific philosophy.


    Put another way
    If we take the example of two lone observers, in the universe, at rest relative to each other; there is no experiment which they can conduct to determine if they are moving; this leaves two options: either they are moving, or they aren't.

    If they are moving, and it isn't relative to each other, then it must be relative to an undetectable reference frame.

    Clearly they can conduct numerous experiments to determine if the are moving relative to each other, so the only alternative is that they are at "absolute rest" - as per the well understood concept.

    [/EDIT]

    Assumption of absolute space
    Secondly, we don't need to assume that absolute space exists; the concept of absolute rest is a fairly well understood concept which has existed in scientific philosophy for hundreds of years, even if it has been rejected. All we need to do is to compare the Einsteinian thought experiment to this already existing concept and see what comparisons can be drawn. "Absolute rest" can remain a purely abstract, mathematical construct for the purpose of examination.



    Excluded middle
    What was intended with the point of the excluded middle is that something is either "at absolute rest" or it is "in motion"; if it isn't one, then, by definition, it is the other.

    You are saying that Albert's "at rest" doesn't imply he is at absolute rest, and you're right, it doesn't imply either absolute rest or absolute motion, but, logically, it must be one or the other.; it is either "at absolute rest" or it is "in motion". If it is "in motion" then it must be relative to an undetectable reference frame, and Albert's instruments must be contracted by an amount unknown to himself due to this motion - which would be the contention of Lorentzian relativity, not Einsteinian.



    *Note: this is not supposed to be an expression, or interpretation, of either principle, it is the often stated consequence of the same.


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    Apologies, my formulation may have been a bit sloppy. Firstly though, the concept of "absolute rest" is indirectly referenced through the Galilean Principle of Invariance (PoI) and the special Principle of Relativity (PoR), in the stated consequence that relatively moving observers cannot determine, by experiment, which one is moving*.

    [EDIT]
    The stated consequence of the Galilean PoI, is that an inertial observer cannot determine if they are "in motion" or "at rest"; in the Galilean case it is indisputable that the concept of "absolute rest" is what is being referenced.

    It is referenced to highlight that relativity says nothing about it. The same way the laws of physics say nothing about metaphysical claims about the matrix.
    PoR
    The special Principle of Relativity (PoR), together with the equivalence principle, is just an extension of this principle to include accelerating reference frames, such that two relatively moving observers cannot determine which one is moving. Again, this implies that one of the observers might not be moving.

    The question is, how can an observer not be moving, when there is relative velocity between them and another observer? The answer is: only if they are at "absolute rest" - a very old, and pretty well understood, concept in scientific philosophy.

    Hence, relativity says nothing about the claim in blue.

    It might be relevant (not sure yet) to point out that relativity does permit a form of absolute motion in the context of spacetime, if motion is defined as a non-geodesic spacetime path. But such a definition of motion and rest is only possible in the context of spacetime, and very different to the concept you are advocating. Hence Minkowski's famous quote:

    "Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."
    Put another way
    If we take the example of two lone observers, in the universe, at rest relative to each other; there is no experiment which they can conduct to determine if they are moving; this leaves two options: either they are moving, or they aren't.

    The above includes the tacit assumption that absolute space is meaningful. You are tacitly assuming absolute space to argue that relativity assumes absolute space. The only thing the law of the excluded middle allows you to say is "They are at absolute rest or they are not". I does not allow you to say "If they are not at absolute rest they must be in absolute motion".
    [/EDIT]
    Assumption of absolute space
    Secondly, we don't need to assume that absolute space exists; the concept of absolute rest is a fairly well understood concept which has existed in scientific philosophy for hundreds of years, even if it has been rejected. All we need to do is to compare the Einsteinian thought experiment to this already existing concept and see what comparisons can be drawn. "Absolute rest" can remain a purely abstract, mathematical construct for the purpose of examination.

    Comparisons can indeed be drawn. And such comparisons show that relativity is independent of such a concept. You can suppose it, or you can reject it.
    Excluded middle
    What was intended with the point of the excluded middle is that something is either "at absolute rest" or it is "in motion"; if it isn't one, then, by definition, it is the other.

    You are saying that Albert's "at rest" doesn't imply he is at absolute rest, and you're right, it doesn't imply either absolute rest or absolute motion, but, logically, it must be one or the other.; it is either "at absolute rest" or it is "in motion". If it is "in motion" then it must be relative to an undetectable reference frame, and Albert's instruments must be contracted by an amount unknown to himself due to this motion - which would be the contention of Lorentzian relativity, not Einsteinian.

    *Note: this is not supposed to be an expression, or interpretation, of either principle, it is the often stated consequence of the same.


    What you are tendering as the law of the excluded middle is

    ¬Q → M

    which is not the law of the excluded middle. If something is not at absolute rest, it means either A) Something is in absolute motion, or B) Absolute space does not exist.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    It is referenced to highlight that relativity says nothing about it. The same way the laws of physics say nothing about metaphysical claims about the matrix.
    The concept of absolute rest is referenced in Galilean principle of invariance, not to demonstrate that Einsteinian relativity says nothing about it - for obvious historical reasons - but because the concept of absolute rest was a central concept in Galilean relativity.

    The special principle of relativity is just an extension of the Galilean principle - I'm not sure you could argue that it is referenced to demonstrate that Einsteinian relativity says nothing about it. Also, I'm not familiar with any principle of relativity that indirectly references "the matrix" for the purpose of highlighting that nothing is said about it.



    I don't think re-ordering the paragraphs, below, should affect the point, but let me know if it does.
    Morbert wrote: »
    Hence, relativity says nothing about the claim in blue.


    The above includes the tacit assumption that absolute space is meaningful. You are tacitly assuming absolute space to argue that relativity assumes absolute space. The only thing the law of the excluded middle allows you to say is "They are at absolute rest or they are not". I does not allow you to say "If they are not at absolute rest they must be in absolute motion".
    Just to address the point of the tacit assumption first.

    If we start with the stated consequences first, and then consider a number of applicable scenarios, we can see what can be deduced, as opposed to assumed:
    First

    Consequence: Inertial observers cannot determine, by experiment, if they are "in motion" or "at rest" (or if they are moving or not); this applies equally to Galilean relativity as it does Einsteinian, if I'm not mistaken.

    Scenario: Two non-accelerating observers at rest relative to each other .

    Conclusions: The observers can determine, by experiment, if they are at rest relative to each other - so this cannot be what is meant by the stated consequence above.

    If they cannot determine if they are "in motion" or at "rest" it means that they are either "in motion" or "at rest"; if they are "in motion" but not relative to each other then they must be in motion relative to an undetectable reference frame.

    If they are "at rest" then, relative to what, are they "at rest"? It can't mean relative to each other, for the reason stated above.

    If they are "in motion", relative to what are they "in motion"; obviously it isn't relative to each other?


    The point being made is that it references the well-known concept of "absolute rest"; not least because it appears to resemble it in every way.

    Second

    Consequence: Two inertial observers, moving relative to each other, cannot determine, by experiment, which one is moving.

    Scenario: As above.

    Conclusions: The consequence here can be fleshed out to include the one above; each observer cannot determine if they are "in motion" or "at rest", but because there is relative motion between them, at least one of them has to be "in motion", but they cannot determine which one it is.

    This allows for one of the observers being "at rest", while one is "in motion"; again, the question is, relative to what, is the observer "at rest"? This is where the claim in blue comes in, because the only other alternative is that both are "in motion" and neither is "at rest" i.e. one of the possibilities is that one of the observers is not moving. That Einsteinian relativity doesn't expressly state anything about the claim doesn't prevent deductions being made.

    Again, the point being made is that here "absolute rest" is tacitly referenced.

    Morbert wrote: »
    It might be relevant (not sure yet) to point out that relativity does permit a form of absolute motion in the context of spacetime, if motion is defined as a non-geodesic spacetime path. But such a definition of motion and rest is only possible in the context of spacetime, and very different to the concept you are advocating. Hence Minkowski's famous quote:

    "Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."
    I was expecting this point to be made more forcefully; tbh, I'm not sure of the relevance either. I would say, though, that as long as the thought experiment referenced here is representative of Einsteinian relativity, the points should hold. I think if we treat reference frames as being at absolute rest, according to their own co-ordinate labeling system, then the conclusion we would draw would be similar, if not identical to, minkowski spacetime.


    Morbert wrote: »
    Comparisons can indeed be drawn. And such comparisons show that relativity is independent of such a concept. You can suppose it, or you can reject it.
    I think the comparisons show that the Einsteinian co-ordinate labeling systems resemble it in almost every way.

    Morbert wrote: »
    What you are tendering as the law of the excluded middle is

    ¬Q → M

    which is not the law of the excluded middle. If something is not at absolute rest, it means either A) Something is in absolute motion, or B) Absolute space does not exist.
    Apologies, my use of terminology is not precise at the best of time, but I think you know the point that is being made.

    I'm not sure that the concept of absolute space is required for the concept of absolute rest; it may indeed have arisen in that context, but I'm not sure it is required, in the Galilean or Newtonian sense. I think the fact that we cannot determine if we are "at rest" or "in motion" demonstrates that, because it is as true under Minkowskian spacetime as it is under absolute space and time.

    The notion of absolute space comes, I think, from the notion that absolute rest and velocity could, theoretically be measured; however, that would be a contradiction in terms, as measurement is, by it's very nature, relative. Absolute motion is a simple 'yes' or 'no' answer to the question, is there motion? Or, with regard to specific objects or observers, is the object/observer in motion, "yes" or "no"?

    If we consider the ancient belief that the earth was the centre of the universe and that everything was in motion around it, the idea of absolute space isn't really necessary. Every observable entity in the universe can be "in motion" while the earth doesn't move; of course, there is relative motion between the earth and everything else, but the earth is ascribed a velocity of zero and the relative velocity is ascribed to everything else - this is partly what makes geocentrism "technically plausible" even today.



    But, all that being said, we are still left with the question of what Albert's "at rest" means. If we consider just Albert and Henry alone in the universe, Albert's co-ordinate labeling system will still label him as "at rest" despite the relative motion between him and Henry. The question is, relative to what is Albert "at rest"?

    Is this "at rest" different to the "at rest" that Albert cannot determine through experiment?


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    The concept of absolute rest is referenced in Galilean principle of invariance, not to demonstrate that Einsteinian relativity says nothing about it - for obvious historical reasons - but because the concept of absolute rest was a central concept in Galilean relativity.

    The special principle of relativity is just an extension of the Galilean principle - I'm not sure you could argue that it is referenced to demonstrate that Einsteinian relativity says nothing about it. Also, I'm not familiar with any principle of relativity that indirectly references "the matrix" for the purpose of highlighting that nothing is said about it.

    Einstein's relativity is an extension of Galileo's relativity insofar as Galilean relativity was incompatible with electromagnetism (The laws of electromagnetism are not Galilean invariant). Einstein's principle of general covariance explicitly states that coordinate systems are constructs, and not fundamental properties. I.e. Physics is independent of any supposition regarding absolute rest.

    I don't think re-ordering the paragraphs, below, should affect the point, but let me know if it does.

    Just to address the point of the tacit assumption first.

    If we start with the stated consequences first, and then consider a number of applicable scenarios, we can see what can be deduced, as opposed to assumed:
    First

    Consequence: Inertial observers cannot determine, by experiment, if they are "in motion" or "at rest" (or if they are moving or not); this applies equally to Galilean relativity as it does Einsteinian, if I'm not mistaken.

    Scenario: Two non-accelerating observers at rest relative to each other .

    Conclusions: The observers can determine, by experiment, if they are at rest relative to each other - so this cannot be what is meant by the stated consequence above.

    If they cannot determine if they are "in motion" or at "rest" it means that they are either "in motion" or "at rest"; if they are "in motion" but not relative to each other then they must be in motion relative to an undetectable reference frame.

    If they are "at rest" then, relative to what, are they "at rest"? It can't mean relative to each other, for the reason stated above.

    If they are "in motion", relative to what are they "in motion"; obviously it isn't relative to each other?


    The point being made is that it references the well-known concept of "absolute rest"; not least because it appears to resemble it in every way.

    Second

    Consequence: Two inertial observers, moving relative to each other, cannot determine, by experiment, which one is moving.

    Scenario: As above.

    Conclusions: The consequence here can be fleshed out to include the one above; each observer cannot determine if they are "in motion" or "at rest", but because there is relative motion between them, at least one of them has to be "in motion", but they cannot determine which one it is.

    This allows for one of the observers being "at rest", while one is "in motion"; again, the question is, relative to what, is the observer "at rest"? This is where the claim in blue comes in, because the only other alternative is that both are "in motion" and neither is "at rest" i.e. one of the possibilities is that one of the observers is not moving. That Einsteinian relativity doesn't expressly state anything about the claim doesn't prevent deductions being made.

    Again, the point being made is that here "absolute rest" is tacitly referenced.

    Apologies, my use of terminology is not precise at the best of time, but I think you know the point that is being made.

    I'm not sure that the concept of absolute space is required for the concept of absolute rest; it may indeed have arisen in that context, but I'm not sure it is required, in the Galilean or Newtonian sense. I think the fact that we cannot determine if we are "at rest" or "in motion" demonstrates that, because it is as true under Minkowskian spacetime as it is under absolute space and time.

    The notion of absolute space comes, I think, from the notion that absolute rest and velocity could, theoretically be measured; however, that would be a contradiction in terms, as measurement is, by it's very nature, relative. Absolute motion is a simple 'yes' or 'no' answer to the question, is there motion? Or, with regard to specific objects or observers, is the object/observer in motion, "yes" or "no"?

    If we consider the ancient belief that the earth was the centre of the universe and that everything was in motion around it, the idea of absolute space isn't really necessary. Every observable entity in the universe can be "in motion" while the earth doesn't move; of course, there is relative motion between the earth and everything else, but the earth is ascribed a velocity of zero and the relative velocity is ascribed to everything else - this is partly what makes geocentrism "technically plausible" even today.

    But, all that being said, we are still left with the question of what Albert's "at rest" means. If we consider just Albert and Henry alone in the universe, Albert's co-ordinate labeling system will still label him as "at rest" despite the relative motion between him and Henry. The question is, relative to what is Albert "at rest"?

    Is this "at rest" different to the "at rest" that Albert cannot determine through experiment?

    The bit in blue is where the problem is. Absolute rest does indeed require an absolute space to define itself. So it is not a case of "at absolute rest" or "in absolute motion". Taking your second scenario as an example, you can say there is no coordinate label which says both observers are at rest. This does not mean, however, that one of the reference frames has to be incorrect, or "less representative of reality". What physically matters is that both observers' frames are inertial, and the fact that no coordinate system has both as "at rest" does not mean we can infer that at least one has to be in motion with respect to some absolute space. Hence, absolute space is not assumed.
    I think the comparisons show that the Einsteinian co-ordinate labeling systems resemble it in almost every way.

    And it also resembles a spacetime structure where no such absolute exists.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    Einstein's relativity is an extension of Galileo's relativity insofar as Galilean relativity was incompatible with electromagnetism (The laws of electromagnetism are not Galilean invariant). Einstein's principle of general covariance explicitly states that coordinate systems are constructs, and not fundamental properties. I.e. Physics is independent of any supposition regarding absolute rest.
    It was more the relativity principles of each that was meant.

    Morbert wrote: »
    The bit in blue is where the problem is.
    It is probably worth noting that in our deductive process we are speaking solely about relative motion, so the asserted problem with the bit in blue doesn't apply.

    A stated consequence of the PoR is that inertial observers cannot determine, by experiment, if they are "in motion" or "at rest".

    This leaves us with the possibilities that they are "in motion" relative to something or they are "at rest" relative to something. The question we are asking is, what is that something?

    Given that they can determine, by experiment, that they are at rest relative to each other, what is the something, relative to which they cannot determine their motion, or lack thereof?


    Similarly, inertial observers moving relative to each other cannot determine if they are moving or if their counterpart is moving; given that they can determine, by experiment, that they are moving relative to each other, relative to what can they not determine their motion?
    Morbert wrote: »
    Absolute rest does indeed require an absolute space to define itself. So it is not a case of "at absolute rest" or "in absolute motion". Taking your second scenario as an example, you can say there is no coordinate label which says both observers are at rest. This does not mean, however, that one of the reference frames has to be incorrect, or "less representative of reality". What physically matters is that both observers' frames are inertial, and the fact that no coordinate system has both as "at rest" does not mean we can infer that at least one has to be in motion with respect to some absolute space. Hence, absolute space is not assumed.
    Absolute motion is a simple "yes" or "no" answer to the question, is there motion? There is no need for absolute space to define it; equally, there is no need for absolute space to define absolute rest, it is, similarly, a "yes" or "no" answer to the question, is something moving. That we cannot determine if one thing or another is moving, does not mean we cannot determine that there is absolute motion; relative motion is proof of absolute motion.

    For two relatively moving observers is there motion? Yes, of course there is, so there must be absolute motion; we may not be able to determine which one is absolutely moving, but we can reason that one must absolutely be moving. If neither observer was in motion, then there would be no relative motion, they would be at rest relative to each other.

    If we take the example of two observers at rest relative to each other; then relative motion occurs. In order for this relative motion to occur, at least one of the observers has to move; if both observers remained at rest then there would be no relative motion, in anyone's reference frame. So, if both observers say that they themselves didn't move, that it was their counterpart that moved, then one of them must be wrong; that we cannot determine which one is right and which one is wrong is immaterial, we can reason that one of them must, absolutely, be wrong.


    With two inertial observers at rest relative to each other, the principle of relativity says they cannot determine

    Morbert wrote: »
    And it also resembles a spacetime structure where no such absolute exists.
    Indeed, which is indistinguishable from what we would conclude if all observers were treated as being at absolute rest by their co-ordinate labeling systems.


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  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    It was more the relativity principles of each that was meant.

    It is probably worth noting that in our deductive process we are speaking solely about relative motion, so the asserted problem with the bit in blue doesn't apply.

    A stated consequence of the PoR is that inertial observers cannot determine, by experiment, if they are "in motion" or "at rest".

    This leaves us with the possibilities that they are "in motion" relative to something or they are "at rest" relative to something. The question we are asking is, what is that something?

    Given that they can determine, by experiment, that they are at rest relative to each other, what is the something, relative to which they cannot determine their motion, or lack thereof?

    Similarly, inertial observers moving relative to each other cannot determine if they are moving or if their counterpart is moving; given that they can determine, by experiment, that they are moving relative to each other, relative to what can they not determine their motion?

    Absolute space. Hence, we are not compelled to assume absolute space even exists. Similarly, we cannot determine by experiment whether or not we are in the Matrix, hence we are not compelled to assume the Matrix exists.
    Absolute motion is a simple "yes" or "no" answer to the question, is there motion? There is no need for absolute space to define it; equally, there is no need for absolute space to define absolute rest, it is, similarly, a "yes" or "no" answer to the question, is something moving. That we cannot determine if one thing or another is moving, does not mean we cannot determine that there is absolute motion; relative motion is proof of absolute motion.

    Again, if by "absolute motion" you mean that there is no reference frame which labels both observers as "at rest", then you are right. But this definition means we still don't have to tacitly assume absolute rest, or absolute space exists, and hence we don't have to assume one reference frame is more correct than another.
    For two relatively moving observers is there motion? Yes, of course there is, so there must be absolute motion; we may not be able to determine which one is absolutely moving, but we can reason that one must absolutely be moving. If neither observer was in motion, then there would be no relative motion, they would be at rest relative to each other.

    If we take the example of two observers at rest relative to each other; then relative motion occurs. In order for this relative motion to occur, at least one of the observers has to move; if both observers remained at rest then there would be no relative motion, in anyone's reference frame. So, if both observers say that they themselves didn't move, that it was their counterpart that moved, then one of them must be wrong; that we cannot determine which one is right and which one is wrong is immaterial, we can reason that one of them must, absolutely, be wrong.

    You are tacitly assuming absolute space here by switching definitions of "absolute motion". We have established that there is no reference frame which labels both observers as at rest. This in no way implies one observer must be wrong, unless you tacitly assume absolute space exists.
    Indeed, which is indistinguishable from what we would conclude if all observers were treated as being at absolute rest by their co-ordinate labeling systems.

    Which is indistinguishable from what we would conclude if all observers assumed absolute rest did not exist. Hence, absolute space and absolute rest are entirely superfluous concepts.


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