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the Atemporal Universe - Resolving the Problem of Time
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08-06-2019 4:49pm#1So, I've written a philosophy of science syle paper on the "Problem of Time" in Quantum Gravity, with citations. I posted a link to a paper in a different thread a while ago, but this is a much different paper - no reativity paradoxes for one.
The structure and formatting still need a lllooooottttt of work, but the ideas are fairly well fleshed out and it is those I would like to discuss here, just to how they stand up to scrutiny and where they fall down.
Here is a link to the paper on google drive:
https://drive.google.com/file/d/1-2bNJdbfxzNT6Jjqe5iW5FcJG2ou-lZl/view?usp=drivesdk
A brief summary of the ideas follows. Everything is fleshed out in much more detail in the paper, the "conclusion" section here doesn't represent the actual conclusion section of the paper, it was just included here for the sake of fomatting. Also, the section entitled "consequenes" doesn't appear in the paper like that and they are fleshed out in much more detail.
It's primarily the ideas I would like to discuss here, but if anyone can offer guidance on structure and formatting please PM me, as I know it needs tons of work in that regard. It's my first real attempt at writing something like this, so I know it's crap, but hopefully the ideas have some merit.
tl;dr:
Time is a system of measurement - in the sense that the metric system is a system of measurement - it is neither fundamental nor emergent; it is not a dimension of the universe. This resolves "the Probem of Time" in Quantum Gravity.Summary:
If we extend the Galilean principle of relativity to clock synchronisation and simultaneity - there is no experiment that can determine simultaneity or synchronisation - in Einsteinian Relativity, the notion of Relativity of Simultaneity becomes unjustifiable.
In his 1905 paper Einstein effectively states that the simultaneity of events in the "stationary" frame must be assumed - this follows from the fact that his synchronisation convention is established "by definition".Synchronisation ConventionIf we consider the clock synchronisation thought experiment:
the observer in the "stationary" frame is located at the mid-point between 2 clocks. A co-located emitter sends a light pulse to each clock (to start them ticking). The light pulses are reflected to the observer at the mid-point and arrive simultaneously. The observer concludes that their clocks are synchronised because they know the speed of light and the distance to the clocks, and because the light pulses returned simultaneously.
While the observer in the "stationary" frame is performing this clock synchronisation, they observe a relatively moving observer perform the exact same synchronisation process. They are also located midway between 2 clocks. The light pulses are sent to each clock and reflected; crucially, the "stationary" observer sees the light pulses hit each clock not-simultaneously, get reflected, and arrive at the "moving" observer simultaneously. The "moving" observer concludes that their clocks are synchronised. The "stationary" has observed that the clocks are not synchronised.
Here, in the original thought experiment, we are provided with a clear case of why the assumption of synchronisation/simultaneity is unjustified. The oberver in the "stationary" frame observes the "moving" observer perform the exact same synchronisation procedure, with the light pulses simultaneously returning to the mid=point, yet, the clocks are not synchronised. This should, at the very least, cause the 'stationary" observer to question whether their clocks are in fact synchronised.
Imagine, on top of this, both observers are wearing body cameras and record footage of their counterparts synchronisation attempts. They then send the footage to each other - by light signal. Each observer will be presented with observational evidence that their clocks are not synchronised.
The reasonable conclusion in this scenario would be to accept that each was mistaken in their assumption about the simultaneity of the clock synchronisation events, give the observational evidence to the contrary.
Constant Speed of Light
The tendency might be to refer back to Einstein's 2nd postulate about the constancy of the speed of light, as justification for maintaing the assumption of simultaneity/synchronisation - in spite of the observational evidence; but here too we can offer a more parsimonious interpretation.
Light Clock Thought Experiment
For this, we need only consider the thought experiment involving each observer carrying a single light clock - a photon bouncing between mirrors. The "stationary" assumes thata their clock is ticking normally, while they observe the "moving" clock as ticking slowly, as the photon travels a longer, diagonal path between the 2 mirrors.
Again, imagine each exchanging bodycam footage and being presented with evidence that their own clock is also ticking slowly. It makes sense to both observers. They only ever observe the vertical velocity component of the photon. This would be true whether they are "stationary" or ""moving" and whether the photon traced the longer diagonal path, or not.
What about the speed of light? If they measure the speed of light in the light clock, will they not measure it as having a slower speed, if they can only detect the vertical velocity component?
To answer this imagine that each tries to measure the speed of light. How will they perform the measurement only by using their trusty light clock to count the time. The issue should be apparent. Any attempt to measure the speed of light will always yield the same value because their clock will be biased by the same factor.
Conclusion
The above highlights the circular reasoning in the Einsteinian interpretation. It is the assumption of the simultaneity of events in the "stationary" frame which leads to the conclusion of the Reativity of Simultaneity. As has been illustrated, the simultaneity of events in the "stationary" frame is an assumption; an unjustified (dare I say unjustifiable) assumption, which leads to the conclusion of RoS, thereby assuming the conclusion.
Introducing bodycam footage leaves with the assumption of simultaneity in "stationary" frames vs observational evidence to the contrary. This represents a class of evidence that cannot be explained under the Einsteinian interpretation.
Consequences
This restores absolute time and simultaneity to relativity, aligning the conceptualisations of time in QM and GR.
Absolute time is indistinguishable from a timeless universe. Clocks provide units of comparison - they don't measure a background phenomenon called "time". "Time" then is a system of measurement, much like the metric system, neither of which are fundamental or emergent. In this way, time cannot be said to form part of a background structure. This removes the issue of background dependence in Quantum Mechanics which is one of the issues in unifying QM and GR.0
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Why is the observer you're denoting as stationary here correct? You're basically already assuming the existence of a preferred frame whose conclusions are the "correct" ones, then obviously an absolute time emerges and is identified with how they measure time.Synchronisation ConventionIf we consider the clock synchronisation thought experiment:
the observer in the "stationary" frame is located at the mid-point between 2 clocks. A co-located emitter sends a light pulse to each clock (to start them ticking). The light pulses are reflected to the observer at the mid-point and arrive simultaneously. The observer concludes that their clocks are synchronised because they know the speed of light and the distance to the clocks, and because the light pulses returned simultaneously.
While the observer in the "stationary" frame is performing this clock synchronisation, they observe a relatively moving observer perform the exact same synchronisation process. They are also located midway between 2 clocks. The light pulses are sent to each clock and reflected; crucially, the "stationary" observer sees the light pulses hit each clock not-simultaneously, get reflected, and arrive at the "moving" observer simultaneously. The "moving" observer concludes that their clocks are synchronised. The "stationary" has observed that the clocks are not synchronised.
Einstein's point was that there is no reason to prefer the point of view of a given observer (what physically measurable property singles out their frame?), thus the different notions of simultaneity are equally valid.0 -
There might be some confusion here. The thought experiment, as laid out, is simply Einstein's thought experiment on clock synchronisation. In his 1905 paper he designates one frame as the "stationary system", so as to distinguish it from the relatively moving system. That convention is simply followed here. Basically, both observers label their own reference frames as "stationary".Why is the observer you're denoting as stationary here correct? You're basically already assuming the existence of a preferred frame whose conclusions are the "correct" ones, then obviously an absolute time emerges and is identified with how they measure time.
Einstein's point was that there is no reason to prefer the point of view of a given observer (what physically measurable property singles out their frame?), thus the different notions of simultaneity are equally valid.
Relativity of Simultaneity is the idea that events which are simultaneous in one frame are not simultaneous in a relatively moving reference frame. The point being made is that the simutaneity of events in the first frame is presupposed. In actual fact, there is no way of determining if events are actually simultaneous, in any frame. This can be seen as an extension of the Galilean Principle of Relativity i.e. there are no experiments which can determine simultaneity/synchronisation.
To see this, we just need to consider the thought experiment. Let's say we have (good ol') Alice and Bob - Alice on the Platform, Bob on the train. Both are wearing bodycams.
Alice sets up her synchronisation procedure, clocks are equidistant from the emitter, mirrors to reflect the light pulses back to her at the midpoint.
She sees that Bob has the exact same set-up: clocks are equidistant and mirrors to reflect the light pulses back to Bob at the midpoint.
Alice sends the light pulses and sees Bob do the same.
Alice sees the clock at the rear of the train move towards the light pulse while the clock at the front moves away. She oberves that Bob's clocks fail to synchronise.
The light pulses reflect from each clock and return to Alice simultaneously. She assumes her clocks are synchronised.
However, she also sees the light pulses return to Bob simultaneously, despite his clocks failinng to synchronise. Bob also assumes that his clocks are synchronised.
Alice, being capable of self-reflection, wonders if it is possible that the same thing has happened in her synchronisation procedure. What if one of her clocks was moving toward the light pulse while the other was moving away, with the opposite happening on the return leg to the midpoint, exactly canceling out and ensuring the light pulses return simultaneously?
She recalls the Galilean Principle of Relativity and realises she has no way of determining this.
Then, she receives a video file from Bob, it's his bodycam footage. The bodycam footage shows that her clocks failed to synchronise.
So, she is left with her assumpion that the clocks synchronised versus the obervational evidence to the contrary.
Indeed, the Einseinian interpretation requires that a single observer must stick dogmatically to their assumption about the simultaneity/synchronisation in their own "stationary system" while an infinite number of relatively moving observers provide observational evidence to the contrary.
Sounds more like religion than science.
One might try to point to the 2nd postulate, the constancy of the speed of light, but this too can be interpreted more parsimoniously - as outlined above.
Without this assumption of simultaneity in a particular frame, the conclusion of reativity of simultaneity cannot be reached - bcos the circle is broken. This leaves us with absolute simultaneity and absolute time.
Absolute time is effectively indistinguishable from a timeless universe. As per Lee Smolin, "were it not for the external clock, one could already say that time has disappeared" (https://www.edge.org/conversation/lee_smolin-stuart_a_kauffman-a-possible-solution-for-the-problem-of-time-in-quantum).
If there is no time, then there is no background dependence in QM, which is [apparently] one of the major issues with marrying QM and GR in a theory of Quantum Gravity0 -
I know Relativity and Einstein's original argument and who the stationary observer refers to. However for all experimental purposes Alice has no reason to distrust her notion of simultaneity. It fulfills all necessary conditions of a definition of time for her, so she is free to use it. What seeing Bob's video shows her is that simultaneous for her is not simultaneous for Bob.
Your argument just shows that there is no "true" simultaneity, as everybody's attempt at defining it will not be so in another frame. Thus Alice's time is simply a coordinate definition, not an objective demarcation of time. So it is for all observers. This is all compatible with Relativity.0 -
Alice assumes that her clocks are synchronised. She cannot determine the validity of this. Bob sends her observational evidence to the contrary. This challenges the validity of Alice's assumption.I know Relativity and Einstein's original argument and who the stationary observer refers to. However for all experimental purposes Alice has no reason to distrust her notion of simultaneity. It fulfills all necessary conditions of a definition of time for her, so she is free to use it. What seeing Bob's video shows her is that simultaneous for her is not simultaneous for Bob.
Your argument just shows that there is no "true" simultaneity, as everybody's attempt at defining it will not be so in another frame. Thus Alice's time is simply a coordinate definition, not an objective demarcation of time. So it is for all observers. This is all compatible with Relativity.
Only if Alice sticks to her assumption - of the simultaneity of clock synchronising events - inspite of the contradictory obserational evidence, will she conclude that what is "simultaneous for her is not simultaneous for Bob". But that is simply assuming the conclusion.
Alternatively, Alice could look at the observational evidence - Bob's bodycam footage - and conclude that she was mistaken in her assumption. Of course, Bob would do the same.
That is an alternative interpretation that frees each observer from clinging dogmatically to an assumption, in the face of observational evidence to the contrary [from an infinite number of relatively moving observers]. It doesn't change the mathematics - so makes the same predictions - it's more intuitive, it doesn't rely on circular reasoning, and it isn't based on a principle that assumptions rank above observation, or at least, that both are on an equal footing.
It is also an interpretation whiich aligns the concepts of time in both GR and QM, one of the issues in developing a theory of Quantum Gravity.0 -
Alice assumes that her clocks are synchronised
Alice conventionally adopts a frame of reference suitable for her observations. When Bob shows her a record of his observations, she understands that it is a record of his observations and not hers. She isn't compelled to consider Bob's observations as any more or less correct than hers, and she can relate his observations to hers with a coordinate transformation.
She would only be challenged by Bob's record of events if she assumed absolute simultaneity between her clocks. But she doesn't.0 -
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The issue with the concept of time in QM has nothing to do with this issue. The issue of time in QM is that QM is a "single user" theory, i.e. about managing expectations for observational outcomes for a single observer and thus its time is the time of the observer in that application of the theory. This is present even if QM is formulated in a Galilean background.It is also an interpretation whiich aligns the concepts of time in both GR and QM, one of the issues in developing a theory of Quantum Gravity.
You're missing two points.Alice assumes that her clocks are synchronised. She cannot determine the validity of this. Bob sends her observational evidence to the contrary. This challenges the validity of Alice's assumption.
First Alice's method of establishing her time parameter via this method fulfills the definitions of a coordinate, along with her definitions for her spatial coordinates she has a full 4D coordinate system. Comparing her results with Bob however she likes, she will see he uses a different set of coordinates but will find the coordinates are related by a transformation that shows they are different coordinates on a single 4D manifold. This is all Special Relativity claims ultimately. The fact that your own method of establishing a coordinate and having it obey the correct axioms, but that others will disagree with said definition, is exactly what you would expect if you lived on a 4D manifold.
Secondly your objection applies to all observer's, you can see that nobody's time is agreed upon by anybody else. Who has the objective time?0 -
Indeed, she adopts a reference frame for her observations that relies on the Einsteinin clock synchronisation. This involves defining "a common “time” for [two clocks] A and B, [which] cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A." So, she establishes her co-ordinate frame on the assumption of simultaneity of clock synchronisation events.Alice conventionally adopts a frame of reference suitable for her observations. When Bob shows her a record of his observations, she understands that it is a record of his observations and not hers. She isn't compelled to consider Bob's observations as any more or less correct than hers, and she can relate his observations to hers with a coordinate transformation.
She would only be challenged by Bob's record of events if she assumed absolute simultaneity between her clocks. But she doesn't.
Essentially, this boils down to an assumption that the distance traveled by light pulses in her "stationary system" equals the distance that she measures from the emitter to each clock. Her own records of Bob's synchronisation attempt demonstrate to her that this is not a reasonable assumption
Bob's observational records are then juxtaposed with her bare assumption. If she tries to maintain this assumption in the face of observational evidence - from a potentially infinite number of relatively moving observers - she will of course conclude that simultaneity is relative i.e. frame dependent. But that is because, in the statement: Events which are simultaneous in one frame are not simultaneous in a relatively moving frame, she is simply assuming the former, while everyone else provides observational evidene of the latter.
Indeed, it seems to be a quirk of nature that she can adopt this convention and make sense of her observations. But what the above shows is that she cannot ascribe any physical meaning to her choice of mathematical co-oridinates and she cannot make metaphysical claims about simultaneity. In a basic sense, she cannot say that "events in her frame are simultaneous". It' simply not a justifiable position.0 -
You may, of course, be correct however, the opposing viewpoint can also be found in the literature on the subjecct:The issue with the concept of time in QM has nothing to do with this issue. The issue of time in QM is that QM is a "single user" theory, i.e. about managing expectations for observational outcomes for a single observer and thus its time is the time of the observer in that application of the theory. This is present even if QM is formulated in a Galilean background.
The Problem of Time is, in greater generality, a consequence of the mismatch between Background Dependent and Background Independent Paradigms of Physics. Newtonian Physics, SR, QM, and QFT are all Background Dependent,
whereas GR is Background Independent and many approaches to Quantum Gravity expect this to be Background Independent as well. (Anerson, 2017 - The Problem of Time: Quantum Mechanics versus General Relativity
I hope you don't mind, I'm going to repost what I reeplied to Morbert because they are effectively the same point. If they aren't, I apologise, let me know and I will reply in kind.First Alice's method of establishing her time parameter via this method fulfills the definitions of a coordinate, along with her definitions for her spatial coordinates she has a full 4D coordinate system. Comparing her results with Bob however she likes, she will see he uses a different set of coordinates but will find the coordinates are related by a transformation that shows they are different coordinates on a single 4D manifold. This is all Special Relativity claims ultimately. The fact that your own method of establishing a coordinate and having it obey the correct axioms, but that others will disagree with said definition, is exactly what you would expect if you lived on a 4D manifold.
Indeed, she adopts a reference frame for her observations that relies on the Einsteinin clock synchronisation. Herr method of establlishing her time parameter involves defining "a common “time” for [two clocks] A and B, [which] cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A." So, she establishes her co-ordinate frame on the assumption of simultaneity of clock synchronisation events.
Essentially, this boils down to an assumption that the distance traveled by light pulses - from emitter to clock - in her "stationary system", equals the distance that she measures from the emitter to each clock. Her own observations of Bob's synchronisation attempt demonstrate to her that this is not a reasonable assumption.
Bob's observational records are then juxtaposed with her bare assumption. If she tries to maintain this assumption in the face of observational evidence - from a potentially infinite number of relatively moving observers - she will of course conclude that simultaneity is relative i.e. frame dependent. But that is because, in the statement: Events which are simultaneous in one frame are not simultaneous in a relatively moving frame, she is simply assuming the former, while everyone else provides observational evidene of the latter.
Indeed, it seems to be a quirk of nature that she can adopt this convention and make sense of her observations. But what the above shows is that she cannot ascribe any physical meaning to her choice of mathematical co-oridinates and she cannot make metaphysical claims about simultaneity or "the speed at which time ticks". In a basic sense, she cannot say that "events in her frame are simultaneous". It' simply not a justifiable assumption.
As per the title of the thread, there is no objective time. Time is a system of measurement, like the metric system is a system of measurement. Neither of which are fundamental or emergent.Secondly your objection applies to all observer's, you can see that nobody's time is agreed upon by anybody else. Who has the objective time?
EDIT: "Time" is still relational in the Machian sense i.e. it is an abstraction from change. We take examples of regularly repeating systems and use them as a unit of comparison, in a similar manner to how a metre stick is used as a unit of comparison.0 -
QM and QFT can be formulated in a background independent manner for example in QFT in curved spacetimes. SR is about the general physics of a large class of backgrounds or of one fixed background (Minkowski space) but it's not background dependent in the same way Newtonian physics is.You may, of course, be correct however, the opposing viewpoint can also be found in the literature on the subjecct:
The Problem of Time is, in greater generality, a consequence of the mismatch between Background Dependent and Background Independent Paradigms of Physics. Newtonian Physics, SR, QM, and QFT are all Background Dependent,
whereas GR is Background Independent and many approaches to Quantum Gravity expect this to be Background Independent as well. (Anerson, 2017 - The Problem of Time: Quantum Mechanics versus General Relativity
This seems like an invalid classification to me.
It's not just a "quirk" of nature. That "quirk" is the entire point. Yes in Special Relativity there is as such no physical meaning to her choice of coordinates, they seem to be entirely that: simply a choice of coordinate. In fact anyway of attempting to define one's time will have the same problem due to the constancy of the speed of light. Any notion of time will be relative and revealed to be just a coordinate and no more.Indeed, it seems to be a quirk of nature that she can adopt this convention and make sense of her observations. But what the above shows is that she cannot ascribe any physical meaning to her choice of mathematical co-oridinates and she cannot make metaphysical claims about simultaneity or "the speed at which time ticks". In a basic sense, she cannot say that "events in her frame are simultaneous". It' simply not a justifiable assumption.
However the relations between the coordinates of different observers are agreed upon and an objective observational fact for all. The relations form a Lie Group called the Poincaré group. This group is the symmetry group of a four dimensional manifold of a certain type. Thus when comparing everybody's definitions of time you are forced to conclude:
(a) That they are coordinates and no more
(b) They are coordinates on a 4D manifold0 -
As regards trading absolute structures, one has gone from separate absolute t and δij to a unified absolute ημν. We also recognize that this comes with a metric connection, and then notice that Newton and Galileo’s Paradigms also happen to possess a different type of connection. So we pass from four absolute structures in Newton’s own view (the fourth is Vi relative to absolute space) to three in Galileo’s (Vi removed) and to a single but larger one in SR. We subsequently detail how GR removes this last one.QM and QFT can be formulated in a background independent manner for example in QFT in curved spacetimes. SR is about the general physics of a large class of backgrounds or of one fixed background (Minkowski space) but it's not background dependent in the same way Newtonian physics is.
This seems like an invalid classification to me.
The new privileged structures are underlied by SR’s Minkowski spacetime M4 possessing suitable Killing vectors (Anderson, 2017)
"Passing from Newtonian physics to SR is just trading one set of absolute or background structures for another" (Anderson, 2019)
If QM and QFT can be formulated in a background independent manner then that obviously removes that issue. Removing time altogether removes any problem of time.It's not just a "quirk" of nature. That "quirk" is the entire point. Yes in Special Relativity there is as such no physical meaning to her choice of coordinates, they seem to be entirely that: simply a choice of coordinate. In fact anyway of attempting to define one's time will have the same problem due to the constancy of the speed of light. Any notion of time will be relative and revealed to be just a coordinate and no more.
However the relations between the coordinates of different observers are agreed upon and an objective observational fact for all. The relations form a Lie Group called the Poincaré group. This group is the symmetry group of a four dimensional manifold of a certain type. Thus when comparing everybody's definitions of time you are forced to conclude:
(a) That they are coordinates and no more
(b) They are coordinates on a 4D manifold
I presume you are familiar with the empirically equivalent Lorentz-Poincare interpretation of Relativity? Maybe not with the notion that it can be formulated without reference to an ether, such that it just makes reference to an absolute reference frame. This reference to an absolute reference frame can be removed simply by removing the need for an absolute time - an atemporal universe does this.
That represents an alternative to the Einsteinian interpretation, that is not based on the Relativity of Simultaneity, not dependent on an Ether and with no absolute reference frame. It's basically Einsteinian Relativity without the assumption of Simultaneity in any given frame.
Given that Simultaneity/Synchronization - in the frame of the stationary system- is assumed in the Einsteinian interpretation i.e. his synchronization convention, the conclusion of Relativity of Simultaneity is thereby assumed. This is because there are an infinite number of relatively moving observers providing observational evidence that [clock synchronization] events ae not simultaneous in the given frame, and that solitary observer clinging to their assumption that their clocks are synchronised.
So, of course: [infinite] observational evidence of non-simultaneity, plus one assumption of Simultaneity = the Relativity of Simultaneity0 -
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You just need to know how the coordinates are related, the relations are exactly the homogeneous group of Minkowski space. The simplest conclusion is that one exists in a spacetime that is locally Minkowskian.
Since Minkowski space admits several 3+1 slicings, one has conflicting relative notions of simultaneity.0 -
Given that Simultaneity/Synchronization - in the frame of the stationary system- is assumed
Simultaneity isn't assumed. Simultaneity is a description that follows from a choice of reference frame.
Similarly:Essentially, this boils down to an assumption that the distance traveled by light pulses - from emitter to clock - in her "stationary system", equals the distance that she measures from the emitter to each clock.
This isn't assumed. This is a description that follows from a choice of reference frame.
Reference frames aren't established or refuted by some prior metaphysical assumptions about simultaneity or the speed of light. They're a mathematical tool for characterising physical observations.0 -
You just need to know how the coordinates are related, the relations are exactly the homogeneous group of Minkowski space. The simplest conclusion is that one exists in a spacetime that is locally Minkowskian.
Since Minkowski space admits several 3+1 slicings, one has conflicting relative notions of simultaneity.
The Lorentz-Poincare interpretation has no such conflicting notions of Simultaneity.
Einstein's clock synchronization procedure unequivocally states that clocks are assumed to be synchronized in "the stationary system" that is, the clock synchronization events are assumed to be simultaneous.
So, the observer in "the stationary system" assumes that their clocks are synchronized while an infinite number of relatively moving observers have empirical evidence to the contrary. Relativity of Simultaneity rests entirely on this one observers assumption of the Simultaneity of events in their frame - despite the infinite amount of empirical evidence to the contrary.0 -
Simultaneity isn't assumed. Simultaneity is a description that follows from a choice of reference frame.
Similarly:
This isn't assumed. This is a description that follows from a choice of reference frame.
Reference frames aren't established or refuted by some prior metaphysical assumptions about simultaneity or the speed of light. They're a mathematical tool for characterising physical observations.
In the Einsteinian clock synchronization convention, as laid out in his 1905 paper, the Simultaneity of clock synchronization events is assumed.
[A "common time"] cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A.
Here we have the assumption of the Simultaneity of clock synchronization events.
The thought experiment outlined to demonstrate this - and the alleged consequences- only serves to demonstrate that such an assumption is not valid, because an infinite number of relatively moving observers provide empirical evidence that the clocks are not synchronised, while one observer tries to maintain the assumption [that their clocks are synchronised] in the face of the contradictory, observational evidence.
If that observer drops their assumption about the Simultaneity of the clock Synchronisation events then the Relativity of Simultaneity disappears.
If the assumption is dropped, then an alternative interpretation remains that is empirically, and mathematically equivalent to the Einsteinian interpretation, but with fewer assumptions.0 -
Einstein's clock synchronization procedure unequivocally states that clocks are assumed to be synchronized in "the stationary system"
You're still putting the cart before the horse here. The clocks are only considered to be synchronised under the standards of observations defined by the appropriate frame of reference.
It's not a case of "the clocks are synchronised therefore a reference frame is established". It's a case of, "the reference frame in which the system is described as stationary will describe the clocks as synchronised by the appropriate procedure"
It is one thing to suggest some Lorentz-Poincaire-type dynamics as an explanation for relativistic phenomena. It is another to suggest that the orthodox geometric account of relativistic phenomena is inconsistent.
[edit][A "common time"] cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A.
Here we have the assumption of the Simultaneity of clock synchronization events.
This is stipulated by the reference frame. It is a definition established by our choice of reference frame. It is not an assumed metaphysical fact upon which we establish the reference frame.0 -
This occurs in spatial geometry. I could say that one object is directly to the left of another and be correct given my facing. Somebody else facing a different direction would not agree. Notions of left of, behind, in front of are relative to the coordinate system of the observer.So, the observer in "the stationary system" assumes that their clocks are synchronized while an infinite number of relatively moving observers have empirical evidence to the contrary. Relativity of Simultaneity rests entirely on this one observers assumption of the Simultaneity of events in their frame - despite the infinite amount of empirical evidence to the contrary.
I could say that I should regard nothing as "to the left" of anything else since an infinite number of observes would disagree. However that's exactly what I should expect since "left" is a coordinate dependent notion.
Similar in Special Relativity you should expect that different observers would disagree with your notion of "at the same time" because it's a coordinate relative statement.
Others producing evidence to the contrary is exactly what should happen if simultaneity is relative.
However the main point is that the relations between observers form a group with Minkowski space as its homogeneous space. Thus everything is in accord with thinking observers live on a Minkowski spacetime: different coordinates disagree and the relations between coordinates form the Poincaré group.0 -
@Morbert & @Fourier (and anyone else that may chooose to reply), I do want to make it known again, how apprecitive I am of you taking the time to reply. I am acutely aware that I fall distinctly into the "crackpot" category and how infuriatingly annoying it can be to discuss such issues with such "crackpots". I am having similar discussions elsewhere and the posters here on boards, have been the most patient and most helpful in pointing out the errors in my reasoning.
I sometimes find myself replying out of frustration that the point I am trying to make hasn't been "understood" - in previous discussions it has usually been the case that it was I that didn't understand some facet of the Einsteinian interpretation which rendered my "paradoxes" null and void. Sometimes the frustration with which I reply is as a result of the cumulative frustration from the other discussions combined. I just wanted to stress that it is never personal and again that I am deeply appreciative of the time you guys have given me over the years. I don't mean this to sound too sentimental, but you guys do a great service in offering to raise the scientific literacy of anyone ye engange with. Indeed, my [finally] being able to accept the internal consistency of the Einsteinian interpretation - it only took what, 10yrs? - is evidence to that effect.
The end result of this current discussion might be that you guys successfully show me the error in my reasoning again and I continue my [glacial] advancement towards a better understanding of the physical theories of science - I believe Paddy Power are already paying out. There is the smaller, highly improbable chance that I will demonstrate my argument in such a way that I change your perspectives. Such an eventuality would surely have to be taken as evidential support for the many worlds interpretation of QM in the sense that there really is a universe out there for every possible eventuality.
While it might seem like I seem to lack the self-awareness that might lead me to conclude that it is the first of the 2 scenarios above that is the most likely, my reasoning as to why "this time is different" is because I am not arguing against the self-consistency of relativity, I am advocating for a different interpretation. One which can be differentiated from the Einsteinian interpretation on the basis of empirical observation.0 -
I'm not sure if you remember in our previous discussions, but that is precisely how outlined the establishing of a reference frame; it involved populating the universe with synchronised clocks at rest relative to the observer - I think the point I was arguing was how an observer could be at rest relative to a set of imaginary, mathematical co-ordinates. It's not necessarily a point we need to get back intoYou're still putting the cart before the horse here. The clocks are only considered to be synchronised under the standards of observations defined by the appropriate frame of reference.
It's not a case of "the clocks are synchronised therefore a reference frame is established". It's a case of, "the reference frame in which the system is described as stationary will describe the clocks as synchronised by the appropriate procedure"
This would seem to suggest that the set of [imaginary] mathematical co-ordinates [chosen to describe physical events] bestows metaphysical properties upon the universe in the form of the Relativity of Simultaneity; together with the physical structure necessitated to accommodate it.This is stipulated by the reference frame. It is a definition established by our choice of reference frame. It is not an assumed metaphysical fact upon which we establish the reference frame.
Some key points here:It is one thing to suggest some Lorentz-Poincaire-type dynamics as an explanation for relativistic phenomena. It is another to suggest that the orthodox geometric account of relativistic phenomena is inconsistent.
1) I'm not arguing [anymore] that the Einsteinian interpretation is inconsistent, I'm arguing that its self-consistency stems from its assuming its conclusion, an assumption which I am arguing is contradicted by [implied] obervational evidence - implied by the thought experiment used to explain it.
2) We don't need to rely on dynamics in a Lorentz-Poincare style interpretation; bcos an LP style formulation can be derived in an entirely kinematical manner, following the Einsteinian approach - as I will try to outline below.
Somewhat separately, but entirely related, the LP interpretation can be divested of an undetectable Ether - given it plays no [detectable] role in anything. This leaves us with an absolute reference frame. Essentially, we don't need an absolute reference frame, we need a privileged referece frame that defines "true time". There are 2 posssible approaches to removing the need for this privileged reference frame; my preferred route is simply removing the idea that there is a "true time" - an atemporal interpretation does this. Altternatiely, we can simply use a privileged reference frame for the definition of our units of measurement. As a matter of operational necessity, the rest frame of the Earth plays this role because that is how we have defined our units of measurement.
This is not the kinematical derivation, but it addresses some possible "background" issues.
3) The clock synchronisation thought experiment can be taken to represent a possible real-world, experimental set-up that can be used to test the assumption of Einstein's clock synchronisation convention - if the assumption is determined to be invalidated, then we are left with an alternative interpretation that has been derived kinematically.
As per the the Synchronisation Convention, the journey time for a light signal from clock A to clock B is assumed to be the same as the journey time from B to A. This equates to assuming the simultneity of clock synchronisation events. In the thought experiment with Alice and Bob, their emitters and their 2 clocks, we effectively have 3 examples of this in the one set-up.
The thought experiment can be seen as a testing of this assumption, so what is the outcome? Basically, every relatively moving observer provides observational evidence that the clocks are not synchronised i.e. that the clock synchronisation events were not simultaneous. This is juxtaposed with Alice's assumption - in the face of contradictory empirical evidence - that her clocks are synchronised.
Maintaining this assumption leads, by way of necessity, to the conclusion of relativity of simultaneity but only because the "events which are simultaneous in one frame...." part of the definition is assumed i.e. the conclusion is assumed.
Maintaining this assumption requires us to accept a position where observers can be both right and wrong about oberved physical; a seeming paradox in anyone's language but not in the Einsteinian interpretion of relativity; however, it's self-consistency is entirely based on its circularity.
The alternative is one where we equally have to accept that observers are both right and wrong, but it is the infintiely more palatable case where obervers are mistaken in their assumptions and it is the observational evidence which is correct.
Upon dropping the assumption of simultaneity of clock synchronisation events we are left with a purely kinematical derivation of the theory which extends the Galilean Principle of Relativity to simultaneity/synchronisation because, when you think about it, there is no way to determine that two events are simultaneous. We can determine that light signals from two events arrive at a detector simultaneously, but this cannot be used to determine the simultaneity of those events.0 -
The problem with this analogy is that, despite the co-geometrisation of space and time, both still maintain distinct properties, so statements about the properties of one doe not necessarily extend to the other. A key difference is that we can move to and fro in space but we can't move around in time. We can simultaneously hold obejects on the left and right in our conscious observtion, while we cannot do the same with "past" and "future" or "before" and "after", which are key aspects related to the notion of simultaneity.This occurs in spatial geometry. I could say that one object is directly to the left of another and be correct given my facing. Somebody else facing a different direction would not agree. Notions of left of, behind, in front of are relative to the coordinate system of the observer.
I could say that I should regard nothing as "to the left" of anything else since an infinite number of observes would disagree. However that's exactly what I should expect since "left" is a coordinate dependent notion.
Similar in Special Relativity you should expect that different observers would disagree with your notion of "at the same time" because it's a coordinate relative statement.
Can I refer you to my most recent reply to Morbert immediately above this (just in case you haven't read it). I wil give an abridged version of the point here.Others producing evidence to the contrary is exactly what should happen if simultaneity is relative.
However the main point is that the relations between observers form a group with Minkowski space as its homogeneous space. Thus everything is in accord with thinking observers live on a Minkowski spacetime: different coordinates disagree and the relations between coordinates form the Poincaré group.
It is indeed in accord with the Minkowski spacetime interpretation, that is just one such interpretation. One I believe is not justified, on the basis of [implied] obervational evidence. Incidentally, the 4D Minkowski metric applies equally to the Lorentz-Poincare interpretation, however it is treated as a purely mathematical construct i.e. as a mathematical tool. I've read that the same is true in QFT.
The alternative Lorentz-Poincare style interpretation, is one without the relativity of simultaneity, and the clock synchronisation thought experiment represents a potential real-world experiment to test Einstein's synchronisation convention. It ends up with a potential mountain of emprical evidence that clocks in a given "stationary system" are not synchronised versus the assumption of the observer in "the stationary system" that the clocks are synchronised.
The solution to this, in Einsteinian interpretation, is to allow for disgreement between observers and it results in the conclusion that simultaneity is relative. When one observer assumes that events in their frame are simultaneous while all other observers provide evidene that they are not simultaneous - and the assumption is allowed to stand in the face of the contrdictory evidence - the necessary conclusion is RoS. Make no mistake though, it self-consistent only on account of it's circularity.
An alternative interpretation sees the lone observer drop their assumption in the face of conflicting evidence.0 -
That's due to the geometry being different. Since the geometry is of a different type (Lorentzian vs Euclidean) of course there will be features present in one and not present in the other.The problem with this analogy is that, despite the co-geometrisation of space and time, both still maintain distinct properties, so statements about the properties of one doe not necessarily extend to the other. A key difference is that we can move to and fro in space but we can't move around in time. We can simultaneously hold obejects on the left and right in our conscious observtion, while we cannot do the same with "past" and "future" or "before" and "after", which are key aspects related to the notion of simultaneity.
However this doesn't affect features common to both and indeed all geometries, i.e. the relative nature of coordinate statements.
That observational evidence is exactly in accord with the Minkowski spacetime view though, this is what you are missing. If "time" is just part of a coordinate definition on Minkowski spacetime you should expect other observers to disagree with you. There is no observational evidence that contradicts this view.It is indeed in accord with the Minkowski spacetime interpretation, that is just one such interpretation. One I believe is not justified, on the basis of [implied] obervational evidence.
If you mean the metric is treated as a tool in QFT this is false, it's treated the same way as in conventional treatments of Special Relativity.I've read that the same is true in QFT.
Minkowski spacetime is as self-consistent in a non-circular manner as Euclidean geometry, since both can be constructed from the ZFC axioms of mathematics. I don't want to drag this off topic, but you won't get anywhere with this statement as it can be verified by a computer.Make no mistake though, it self-consistent only on account of it's circularity.0 -
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The fact that we can't move to and fro in time or that we can't simultaneosuly view before and after are not matters of geometry, they are simple facts of existence which apply to our empirical obsservations.That's due to the geometry being different. Since the geometry is of a different type (Lorentzian vs Euclidean) of course there will be features present in one and not present in the other.
However this doesn't affect features common to both and indeed all geometries, i.e. the relative nature of coordinate statements.
The idea that the relative notions of "on the left" or "on the right" changes upon rotation doesn't require an assumption. The idea that events are simultaneous in your frame does. The simultaneity of events in your reference frame cannot determined by your choosing of a co-ordinate reference frame. Your co-ordinate reference frame might describe them as being simultaneous, but this implies that there is an underlying assumption of simultaneity.
The contention isn't that it is not in accord with the Minkowski spacetime view. As has been mentioned, the mathematics of Minkowski spacetime apply equally to a Lorentz-Poincare interpretation. The difference being the ontological status attributed to both - in the LP interpretation the mathematics of Minkowski are simply that, mathematical. They are a useful mathematical tool.That observational evidence is exactly in accord with the Minkowski spacetime view though, this is what you are missing. If "time" is just part of a coordinate definition on Minkowski spacetime you should expect other observers to disagree with you. There is no observational evidence that contradicts this view.
The LP interpretation does not incorporate RoS. This demonstrates an alternative interpretation. So, yes, the Einsteinian/Minkowskian (EM) interpretation is one possible interpretation which is internally consistent. The kinematical LP interpretation is another such interpretation.
The clock synchronisation thought experiement can be viewed as a potential real-world experiment, that could possibly tell us something about both interpretations. As has been outlined, the EM interpretation is predicated on a foundational assumption which requires that assumption to be maintained in the face of overwhelming empirical evidence to the contrary.
The Minkowski metric of quantum field theory is generally regarded as a mathematical construct and not a real physical object. (Bryan and Medved, 2018 - the Problem with the Problem of Time)If you mean the metric is treated as a tool in QFT this is false, it's treated the same way as in conventional treatments of Special Relativity.
The synchronisation thought experiment can be taken to represent a real-world experimental set-up which allows us to deduce certain facts about competing interpretations.Minkowski spacetime is as self-consistent in a non-circular manner as Euclidean geometry, since both can be constructed from the ZFC axioms of mathematics. I don't want to drag this off topic, but you won't get anywhere with this statement as it can be verified by a computer.
The thought experiment demonstrates that the assumption of simultaneity of events in "the stationary frame" is juxtaposed with observational evidence to the contrary.
There are [at least] 2 possible interpretations that can applied.
One of them allows the assumption to stand, despite the evidence, and concludes that "events which are simultaneous in one frame are not simultaneous in relatively moving frames" i.e. concludes that simultaneity is relative - as can clearly be seen, this is simply assuming the conclusion. Minkowski spacetime is the physical structure which is required for RoS to have any real physical meaning - something that is not without its own issues. The physicality of Minkowski spactime is an ongoing matter of debate, however, for RoS to be different from/incopatible with the notion of absolute simultaneity, Minkowski spacetime, in the form of "the Block Universe' (or any variation thereof that relies on RoS) must represent the underllying physical structure of the universe. The argument in the paper is that such a universal structure cannot allow for relative motion or the observation thereof.
The other interpretation simply inolves giving higher status to observational evidence than assumptions. It simply requires the assumption of simultaneity [in the "stationary system"] to be dropped in the face of empiricl evidence to the contrary. Dropping this assumption leaves us with a kinematical description that doesn't incorporate RoS and is therefore free of any of the issues associated with "the Block Universe". It also serves to align the conceptualisation of time in relativity with that of QM. Adjusting our idea of "time" and viewing it as a non-fundamental, non-emergent system of measuremen, further allows us to drop any background dependence, that may or may not be an issue.0 -
It's not see:The Minkowski metric of quantum field theory is generally regarded as a mathematical construct and not a real physical object. (Bryan and Medved, 2018 - the Problem with the Problem of Time)
Peskin and Schroeder, Introduction to Quantum Field Theory
Weinberg, The Quantum Theory of fields
Zee, Quantum Field Theory in a Nutshell
Itzykson and Zuber, Quantum Field Theory
These are actual textbooks on Quantum Field Theory used by generations of particle physicists and thus reflect standard usage.
On a personal level, having actually worked in Quantum Field Theory general usage is not as you claim.
In the Minkowskian view they are a consequence of geometry and hence in that view are analogous to "left" and "right". Even how left and right function is a "simple fact of existence", but it is explained in terms of Euclidean geometry.The fact that we can't move to and fro in time or that we can't simultaneosuly view before and after are not matters of geometry, they are simple facts of existence which apply to our empirical obsservations.
The whole point of Minkowski space is how it explains these facts and their relations.
Once again though this isn't evidence to the contrary this is what I have been saying over and over again. It's exactly what you would expect from living in Minkowski space. Empirical evidence to the contrary would be actual observations differing from that predicted by the Minkowski picture, this is not the case here.maintained in the face of overwhelming empirical evidence to the contrary0 -
Minkowski spacetime doesn't require a Block Universe. Some people at times use it to argue for a Blockworld, but these are separate things.The physicality of Minkowski spactime is an ongoing matter of debate, however, for RoS to be different from/incopatible with the notion of absolute simultaneity, Minkowski spacetime, in the form of "the Block Universe' (or any variation thereof that relies on RoS) must represent the underllying physical structure of the universe0 -
Ok, I'll take your point. I'll check out those references, thank you!It's not see:
Peskin and Schroeder, Introduction to Quantum Field Theory
Weinberg, The Quantum Theory of fields
Zee, Quantum Field Theory in a Nutshell
Itzykson and Zuber, Quantum Field Theory
These are actual textbooks on Quantum Field Theory used by generations of particle physicists and thus reflect standard usage.
On a personal level, having actually worked in Quantum Field Theory general usage is not as you claim.
I think you're slightly missing the point. I'm not sayinng that it is evidence contrary to the EM interpretation.In the Minkowskian view they are a consequence of geometry and hence in that view are analogous to "left" and "right". Even how left and right function is a "simple fact of existence", but it is explained in terms of Euclidean geometry.
The whole point of Minkowski space is how it explains these facts and their relations.
Once again though this isn't evidence to the contrary this is what I have been saying over and over again. It's exactly what you would expect from living in Minkowski space. Empirical evidence to the contrary would be actual observations differing from that predicted by the Minkowski picture, this is not the case here.
As mentioned, the thought epxeriment can be taken to represent a [potential] real-world experimental set-up and as such, it allows us to make a number of deductions about our competing interpretations; that is, we can learn something about the interpretations by considering it.
The EM interpretation is fully consistent with the observational evidence. The contention is that it applies an assumption, along with that observational evidence, which the observational evidence itself renders unjustified.
For a moment, try to shelve any thoughts about Minkowski spacetime - bear in mind, I am saying that Minkowski spacetime is consistent with the obervational evidence - and lets consider the thought experiment solely on its own merits. We can view it as an empirical test of Einstein's clock synchronisation convention.
Without going through the whole thing again, Alice performs the synchronisation procedure. The light signals return simultaneously to her and she assumes her clocks are synchronised that is, she assumes the simultaneity of [clock synchronisation events] in her "stationary system".
All other, relatively moving, observers provide empirical evidence that the [clock synchroonisation] events were not simultaneous and that her clocks are not synchronised. This empirical evidence doe not support her attempt to establish a "common time" for her clocks ; her attempt to "establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A" is not supported by the empirical observations.
So, Alice is at a crossroads, two possible interpretations, leading in opposite directions.
She can maintain her insistence that the clock synchronisation events, in her "stationary system", were simultaneously. She can maintain that all other observers are wrong/mistaken and that it is her assumption that is correct. If she chooses this route, she will arrive at the conclusion that simultaneity is relative. This is a conclusion necessitated by maintaining that both her assumption and the observational evidence are correct - despite the observational evidence contradicting her assumption. Incidentally, she must also accept that she is mistaken and that the others are correct.
To reiterate, the Relativity of Simultaneity says that events which are simultaneous in one reference frame [the frame of the "stationary system"] are not simultaneous in a relatively moving frame. The observational evidence says that the [clock synchronisation] events in Alice's frame were not simultaneous, while Alice assumes that they were. Hence, the conclusion is assumed.
Down this route lies Minkowski spacetime.
Back at the crossroads, the other road - the other interpretation - simply involves Alice dropping her assumption.0 -
"The Block Universe" is simply the philosophical interpretation of Minkowski spacetime. While Minkowski spacetime may siimply be a mathematical representation of spacetime, there are deductions that can be made about it that are then illustrated through the block world conceptualisation.Minkowski spacetime doesn't require a Block Universe. Some people at times use it to argue for a Blockworld, but these are separate things.
The same deductions could be made without the imgagination of the 4D block0 -
Alice doesn't assume she is correct though in the standard Minkowskian view though. She assumes she has a working definition of a time coordinate, but not that it is absolutely correct and everybody else is wrong. Doing that would be to assume absolute time. She simply assumes it is a functioning way of defining time for her own purposes and she will be able to demonstrate that it and every other method of defining time will be disagreed with by others. In the Minkowskian view this is fine since all such definitions are ultimately just coordinates so you wouldn't expect anything else.She can maintain her insistence that the clock synchronisation events, in her "stationary system", were simultaneously. She can maintain that all other observers are wrong/mistaken and that it is her assumption that is correct. If she chooses this route, she will arrive at the conclusion that simultaneity is relative
There is no assumption that she is right and others are wrong.0 -
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Again, the contention isn't that the above isn't fine with the Minkowski view. As you highlight above, the Minkowski view is predicated on certain assumptions about the working definition of the time co-ordinate. The thought experiment allows us to investigate alternative interpretations and some of the consequences of those interpretaions.Alice doesn't assume she is correct though in the standard Minkowskian view though. She assumes she has a working definition of a time coordinate, but not that it is absolutely correct and everybody else is wrong. Doing that would be to assume absolute time. She simply assumes it is a functioning way of defining time for her own purposes and she will be able to demonstrate that it and every other method of defining time will be disagreed with by others. In the Minkowskian view this is fine since all such definitions are ultimately just coordinates so you wouldn't expect anything else.
There is no assumption that she is right and others are wrong.
Also, I didn't necessarily state that she assumes that it is absolutely correct and everybody else is wrong, I mentioned at the end that she must also accept that she is wrong and everyone else is right. In anyones language, this would represent a contradiction, but this is taken to be a feature, not a bug, of the Einsteinian interpretation.
Just for the sake of clarifying a point, let's label the implements that Alice uses in her synchronisation set-up. Let's label the emitter as A, the clock on one side as B1 and the clock on the other as B2.
In the real-world experimental set-up, as represented in the thought experiment, she assumes that the time the light signal takes from A to B1 equals the time from B1 to A, as well as assuming that the time the light signal takes from A to B2 equals the time from B2 to A, together with the assumption that the time for A to B1 equals A to B2, and the assumption that B1 to A equals B2 to A.
These assumptions are encoded in her choice of co-ordinate system and working definition of a time coordinate.
The observational results from the experiment do not support the above assumptions.
This is essentially agreeing with the point being made. Yes, she assumes - assumes being the operative word - that it is a functioning way of defining time for her own purposes and she also knows that others will disagree with it. The whole point being made is that Alice assumes it is functioning way of defining time, while others base their disagreements on emprical observations.She simply assumes it is a functioning way of defining time for her own purposes and she will be able to demonstrate that it and every other method of defining time will be disagreed with by others.
Essentially, this disagreement IS the Relativity of Simultaneity. Alice assumes her definition of time is valid, while all other observers disagree on the basis of empirical observation. It is Alice's continuing insistence that her assumption is valid that gives rise to the conclusion of RoS - without her assumption all that is left is the observational evidence that the events were not simultaneous.
Can you, at the very least, see the alternative interpretation that doesn't rely on the Relativity of Simultaneity, and that equally explains all the evidence? One in which the matematics of Poincare/Minkowski are taken to be just a mathematical construct?0 -
I won't necessarily argue that point. I know that Carlo Rovelli - in the Order of Time - argues for a different interpretation. He talks about some kind of a filial structure, like a family tree. He doesn't really put it together very well. Even this sort of structure, however, requires mini-blocks for each structure. There are others too, llike Julian Barbours etc. Am I correct in saying that records theories and theories of shape dynamics (I remember @Morbert mentioning that before), represent other such examples?My point was that there are alternate readings where Minkowski geometry is real, but there isn't a Blockworld. They're not synonymous.
I would say, however, that the very idea of a temporal dimension, or being "extended in time" necessitates a block structure. To be extended in time requires either/both of a systems past and/or future configurations to co-exist along with it's present configurtion. If only the present configurtion makes up part of the universal structure, then the system cannot be said to be "extended in time" in any physically, meaningful way. Also, it would mean that the temporal dimension is pointlike.0 -
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Well although I used the word "assume" I should say she "finds" it to be a functioning definition of time as she will empirically observe it and her definitions of spatial directions to satisfy the axioms of a coordinate system. So the assumption isn't that it behaves like a functioning coordinate definition of time, empirically it does.This is essentially agreeing with the point being made. Yes, she assumes - assumes being the operative word - that it is a functioning way of defining time for her own purposes and she also knows that others will disagree with it. The whole point being made is that Alice assumes it is functioning way of defining time, while others base their disagreements on emprical observations.
The "assumption" is simply that if it empirically seems like a coordinate system on a 4D space, then it is a coordinate system on a 4D space.0
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