Advertisement
If you have a new account but are having problems posting or verifying your account, please email us on hello@boards.ie for help. Thanks :)
Hello all! Please ensure that you are posting a new thread or question in the appropriate forum. The Feedback forum is overwhelmed with questions that are having to be moved elsewhere. If you need help to verify your account contact hello@boards.ie
Question on time dilation
Options
Comments
-
I note that you have dropped the inverted commas around "her"; why so; and why were they there in the first place? Is it to try and imply, more strongly, that there is something which designates the arbitrary mathematical reference frame that Albert draws on his graph paper, as being more hers, than the arbitrary mathematical reference frame she draws on her graph paper?
But, you are right, when she is describing what she measures she uses "her" reference frame i.e. the co-ordinate system that codifies what she measures, and enables her to calculate what Henry measures; the same reference frame which leads her to calculate, that the physical clock Henry uses in his measurements will be ticking faster than the physical clock she uses in her measurements, and which she codifies on her graph paper.
If this is a way of saying that reciprocal contractions are a mathematical artefact, and not a physical reality, then I would be in complete agreement; but I don't think that is what you intend.
Of course, we can just re-state the issue and say that Evelyn concludes that the hypothetical observer will measure Henry's clock as ticking faster, while Albert concludes that the hypothetical observer will measure Henry's clock as ticking slower; the paradox remains.
Evelyn concludes that the clock that Henry is co-located with, will be ticking faster than the clock she is co-located with; while Albert concludes the contrary.
Albert does not conclude that. Albert agrees with Evelyn. I.e. They both agree that the hypothetical observer implied by Evelyn's choice of reference frame will measure Henry's clock as ticking faster.0 -
Ah, OK, I see what you are getting at; you seem to be suggesting that the two dots, or lines, on Evelyn's graph paper, which represent herself and Albert, are somehow more hypothetical than the two dots, or lines, on Albert's graph paper, which represent himself and Evelyn; that, somehow, Evelyn's representation of herself and Albert isn't as valid as Albert's representation of them. I'm sure you can provide some justification for this, other than the contention that Evelyn performs her measurements in one imaginary, mathematical reference frame, and her calculations in another imaginary, mathematical reference frame.Albert does not conclude that. Albert agrees with Evelyn. I.e. They both agree that the hypothetical observer implied by Evelyn's choice of reference frame will measure Henry's clock as ticking faster.
One of the points you are repeatedly making is that Evelyn performs measurements using the instruments at rest relative to her, so she "her" reference frame is how Albert defines it; but you ignore the fact that Evelyn's mathematical reference frame reflects that she uses instruments at rest relative to her; you also seem to be ignoring the fact that Evelyn calculates that the instruments, relative to which she and Albert are at rest, are contracted, relative to Henry i.e. she concludes that the clock she and Albert use to perform their measurements is ticking slower than Henry's.
Also, hopefully, at the third time of asking, you might clarify why you initially put the word "her" in inverted commas, when referring to what you deem to be Evelyn's correct reference frame i.e. the reference frame as defined by Albert; and then dropped the inverted commas?
I think a large part of the issue may be the conditioning; it seems that people are conditioned into thinking that the way Evelyn defines her arbitrary, imaginary, mathematical reference frame, to assist her in her calculations, is "Henry's reference frame". This of course isn't the case, it is as much Evelyn's imaginary reference frame, as it is Henry's.0 -
Ah, OK, I see what you are getting at; you seem to be suggesting that the two dots, or lines, on Evelyn's graph paper, which represent herself and Albert, are somehow more hypothetical than the two dots, or lines, on Albert's graph paper, which represent himself and Evelyn; that, somehow, Evelyn's representation of herself and Albert isn't as valid as Albert's representation of them. I'm sure you can provide some justification for this, other than the contention that Evelyn performs her measurements in one imaginary, mathematical reference frame, and her calculations in another imaginary, mathematical reference frame.
One of the points you are repeatedly making is that Evelyn performs measurements using the instruments at rest relative to her, so she "her" reference frame is how Albert defines it; but you ignore the fact that Evelyn's mathematical reference frame reflects that she uses instruments at rest relative to her; you also seem to be ignoring the fact that Evelyn calculates that the instruments, relative to which she and Albert are at rest, are contracted, relative to Henry i.e. she concludes that the clock she and Albert use to perform their measurements is ticking slower than Henry's.
Also, hopefully, at the third time of asking, you might clarify why you initially put the word "her" in inverted commas, when referring to what you deem to be Evelyn's correct reference frame i.e. the reference frame as defined by Albert; and then dropped the inverted commas?
I think a large part of the issue may be the conditioning; it seems that people are conditioned into thinking that the way Evelyn defines her arbitrary, imaginary, mathematical reference frame, to assist her in her calculations, is "Henry's reference frame". This of course isn't the case, it is as much Evelyn's imaginary reference frame, as it is Henry's.
By her reference frame, I mean the reference frame with a hypothetical, implied observer co-local with her. The reference frame Evelyn has chosen implies a hypothetical observer that is not co-local with her. Hence, even though her choice of reference frame preserves the fact that she is at rest relative to her clock, it does not preserve the measurements she will make, and she must perform a coordinate transformation to recover her measurements.
Ironically, what is happening is you are misunderstanding how coordinate systems are applied, drawing incorrect statements from such misapplications, and highlighting a paradox arising from the misapplication.0 -
It's not that I am misunderstanding how they are applied, I am challenging the rationale for how they are applied, and the deductions that can be made from them.By her reference frame, I mean the reference frame with a hypothetical, implied observer co-local with her. The reference frame Evelyn has chosen implies a hypothetical observer that is not co-local with her. Hence, even though her choice of reference frame preserves the fact that she is at rest relative to her clock, it does not preserve the measurements she will make, and she must perform a coordinate transformation to recover her measurements.
Ironically, what is happening is you are misunderstanding how coordinate systems are applied, drawing incorrect statements from such misapplications, and highlighting a paradox arising from the misapplication.
The arbitrary mathematical reference frames are a calculational tool, which allow observers to make predictions about the physical world, are they not?
Evelyn uses the calculational tool and predicts that Henry's clock will be ticking faster, while Albert predicts that Henry's clock will be ticking slower. This is a paradox, unless either of their calculations don't correspond to the physical world.
If, of course, the notion of reciprocal contractions are an entirely hypothetical, mathematical artefact, and not a physical reality, then there is no issue.0 -
Evelyn uses the calculational tool and predicts that Henry's clock will be ticking faster, while Albert predicts that Henry's clock will be ticking slower. This is a paradox, unless either of their calculations don't correspond to the physical world.
If I didn't know any better, I would say you are willfully ignoring my posts. Unless Evelyn is a hack philosopher or crank scientist, she does not predict that Henry's clock will be ticking faster.
She does not predict that Henry's clock will be ticking faster.
Again:
She does not predict that Henry's clock will be ticking faster.
And again:
She does not predict that Henry's clock will be ticking faster.
If you are asserting that she predicts that Henry's clock will be ticking faster, you are wrong, because she does not predict that Henry's clock will be ticking faster.
As I said before, you are misunderstanding how coordinate systems are applied, drawing incorrect statements from such misapplications, and highlighting a paradox arising from the misapplication.
There would be a paradox if she predicted that Henry's clock will be ticking faster. But there is no paradox because she does not predict that Henry's clock will be ticking faster. She does not predict what you say she will predict because it is assumed that she understands how coordinate systems are applied.0 -
Advertisement
-
I'm not, but I think you might be misunderstanding mine; in this thread at least.If I didn't know any better, I would say you are willfully ignoring my posts.
I fully understand that "relativity says she has to do a Lorentz transform"; I'm questioning the reasoning being given as to why.
Interesting use of an ad hom.Unless Evelyn is a hack philosopher or crank scientist, she does not predict that Henry's clock will be ticking faster.
You are asserting that she won't predict that Henry's clock will tick slower; you're rationale thus far has been "because relativity says so" or by ascribing physical characteristics to her mathematical reference frame; we have moved onto the notion of the hypothetical observer, which we can further discuss.She does not predict that Henry's clock will be ticking faster.
Again:
She does not predict that Henry's clock will be ticking faster.
And again:
She does not predict that Henry's clock will be ticking faster.
If you are asserting that she predicts that Henry's clock will be ticking faster, you are wrong, because she does not predict that Henry's clock will be ticking faster.
No, I understand how they are applied, it's the justification for this application that is being questioned. When the mathematical reference frame is taken as the calculational tool that it is, that can be used to make predictions, then the paradox is evident; to suggest that there is no paradox implies a number of things; either a reference frame isn't an arbitrary mathematical construct, or it can't be used as a calculational tool for the purpose of predictions.As I said before, you are misunderstanding how coordinate systems are applied, drawing incorrect statements from such misapplications, and highlighting a paradox arising from the misapplication.
Indeed, she might indeed understand how they are "supposed" to be applied, but she might recognise the fact that the justification for such an application is, at best, questionable.There would be a paradox if she predicted that Henry's clock will be ticking faster. But there is no paradox because she does not predict that Henry's clock will be ticking faster. She does not predict what you say she will predict because it is assumed that she understands how coordinate systems are applied.
Included below is your previous post in this tread, with the notion of the hypothetical observer, and the points raised in the other thread referencing the hypothetical observer.By her reference frame, I mean the reference frame with a hypothetical, implied observer co-local with her. The reference frame Evelyn has chosen implies a hypothetical observer that is not co-local with her. Hence, even though her choice of reference frame preserves the fact that she is at rest relative to her clock, it does not preserve the measurements she will make, and she must perform a coordinate transformation to recover her measurements.
Ironically, what is happening is you are misunderstanding how coordinate systems are applied, drawing incorrect statements from such misapplications, and highlighting a paradox arising from the misapplication.
When you say "hypothetical observer", who are you referring to? The hypothetical observers, in her mathematical reference frame, represent herself, Albert, and Henry. Albert is co-local with her, Henry is not; this is precisely as Albert's reference frame depicts it as well.
I also don't see how it doesn't "preserve her measurements". Just as Albert's reference frame leads him to calculate that the clock Henry is using for his measurements is ticking slower, Evelyn calculates that Henry's clock is ticking faster; it preserves the measurements of her clock, she just deduces that they are contracted relative to Henry.
Is the hypothetical observer, she is in motion relative to, called Henry, by any chance? If so, then Albert too is in motion relative to this hypothetical observer.I have addressed this before. She is in motion relative to the hypothetical observer implied by the reference frame. I.e. No tacit assumptions or ascriptions of physical characteristics. Only interpretations of her hypothetical conjecture.
But, to say that she is in motion relative to a hypothetical observer ascribes physical characteristics to this hypothetical observer; because she can only be in motion relative to physical bodies.
No. The reference frames describe how a scenario might be observed.
This point pertains to the other thread also, about 3 ways of labeling the same scenario, but given the reference to the hypothetical observer I thought I'd address it in here.Non-sequitur. No such statements are needed. We can say the three coordinate systems correspond to three ways of labelling the same event because a coordinate system is merely the description of an event, using a hypothetical observer as a reference. Hence, the three scenarios are the same scenario, viewed three different ways.
<snipped repetition>
I should point out first, that the statements you say are not needed, are statements you made yourself, to which I responded. The point followed perfectly from what you had said, but you seem to be suggesting that what you said was wrong.
But, to say that "the three coordinate systems correspond to three ways of labelling the same event because a coordinate system is merely the description of an event, using a hypothetical observer as a reference. Hence, the three scenarios are the same scenario, viewed three different ways" ignores the fact that we can examine those co-ordinate systems, from the perspective of the hypothetical observer to see if the treatment of those reference frames carry any implicit assumptions about absolute motion.
We can deduce the implication of absolute motion based on the treatment of the path length of the photon in the light clock. This is where all the previously raised points are relevant again.
Now this might appear to be going around in circles, but it isn't, what we have been doing is approaching the situation from different angles to try and narrow down the possible explanations, while identifying the conflation of statements about the absolute nature of motion with absolute statements about relative motion; hence the need for all the different threads.
The conclusion we are closing in on is that without implicit assumptions about the absolute nature of motion, relativity only has one way of labeling three physically distinguished scenarios.0 -
Another way of stating the issue would be as follows:
Albert measures Henry's clock to be ticking slower than Albert's clock.
Henry measures Albert's clock to be ticking slower Henry's clock.
If Henry measures Albert's clock to be ticking slower than his own clock; while Albert measures Henry's clock to be ticking slower; Henry should measure his own clock to be ticking slower than itself.
Which, of course, is absurd.0 -
You are asserting that she won't predict that Henry's clock will tick slower; you're rationale thus far has been "because relativity says so" or by ascribing physical characteristics to her mathematical reference frame; we have moved onto the notion of the hypothetical observer, which we can further discuss.
No, I understand how they are applied, it's the justification for this application that is being questioned. When the mathematical reference frame is taken as the calculational tool that it is, that can be used to make predictions, then the paradox is evident; to suggest that there is no paradox implies a number of things; either a reference frame isn't an arbitrary mathematical construct, or it can't be used as a calculational tool for the purpose of predictions.
Indeed, she might indeed understand how they are "supposed" to be applied, but she might recognise the fact that the justification for such an application is, at best, questionable.
When you say "hypothetical observer", who are you referring to? The hypothetical observers, in her mathematical reference frame, represent herself, Albert, and Henry. Albert is co-local with her, Henry is not; this is precisely as Albert's reference frame depicts it as well.
I also don't see how it doesn't "preserve her measurements". Just as Albert's reference frame leads him to calculate that the clock Henry is using for his measurements is ticking slower, Evelyn calculates that Henry's clock is ticking faster; it preserves the measurements of her clock, she just deduces that they are contracted relative to Henry.
Is the hypothetical observer, she is in motion relative to, called Henry, by any chance? If so, then Albert too is in motion relative to this hypothetical observer.
But, to say that she is in motion relative to a hypothetical observer ascribes physical characteristics to this hypothetical observer; because she can only be in motion relative to physical bodies.
This point pertains to the other thread also, about 3 ways of labeling the same scenario, but given the reference to the hypothetical observer I thought I'd address it in here.
But, to say that "the three coordinate systems correspond to three ways of labelling the same event because a coordinate system is merely the description of an event, using a hypothetical observer as a reference. Hence, the three scenarios are the same scenario, viewed three different ways" ignores the fact that we can examine those co-ordinate systems, from the perspective of the hypothetical observer to see if the treatment of those reference frames carry any implicit assumptions about absolute motion.
Now this might appear to be going around in circles, but it isn't, what we have been doing is approaching the situation from different angles to try and narrow down the possible explanations, while identifying the conflation of statements about the absolute nature of motion with absolute statements about relative motion; hence the need for all the different threads.
The conclusion we are closing in on is that without implicit assumptions about the absolute nature of motion, relativity only has one way of labeling three physically distinguished scenarios.
The statements in red are the problem. They are incorrect assertions. To put it succinctly:Another way of stating the issue would be as follows:
Albert measures Henry's clock to be ticking slower than Albert's clock.
Henry measures Albert's clock to be ticking slower Henry's clock.
If Henry measures Albert's clock to be ticking slower than his own clock; while Albert measures Henry's clock to be ticking slower; Henry should measure his own clock to be ticking slower than itself.
Which, of course, is absurd.
It is absurd under Riemannian, Euclidean geometry of Newton and Galileo. It is not absurd under the pseudo-Riemannina, Minkowski geometry of Einstein's relativity.0 -
The statement in red is the problem; it is, thus far, an unjustified assertion.The statements in red are the problem. They are incorrect assertions. To put it succinctly:
Is a reference frame an arbitrary mathematical construct - bearing in mind you've already stated that it is?
Can said mathematical reference frames be used to make predictions about the physical world?
As a mathematical artefact of geometry it might not be absurd, but as a physical occurence it is completely absurd.It is absurd under Riemannian, Euclidean geometry of Newton and Galileo. It is not absurd under the pseudo-Riemannina, Minkowski geometry of Einstein's relativity.
A single physical clock cannot tick both faster and slower than another clock, nor can it tick faster or slower than itself, which the idea of reciprocal contractions require. It might perhaps be possible that such can be measured, but those measurements would have to correspond to an optical illusion as opposed to the underlying physicality of the clock.
Indeed, how the conclusion of pseudo-Riemanian, Minkowski geomerty is reached in Einstein's relativity is the subject of debate between us, with regard to the implicit assumptions made by the treatment of co-ordinate systems.0 -
The statement in red is the problem; it is, thus far, an unjustified assertion.
Your response is a strange one. You repeatedly make unjustified assertions. Then when I point out that they are assertions, you claim I am asserting that they are assertions. It is tedious and counter-productive.
I put it to you to support a single statement I highlighted in red.Is a reference frame an arbitrary mathematical construct - bearing in mind you've already stated that it is?
Can said mathematical reference frames be used to make predictions about the physical world?
Yes to both questions.As a mathematical artefact of geometry it might not be absurd, but as a physical occurence it is completely absurd.
A single physical clock cannot tick both faster and slower than another clock, nor can it tick faster or slower than itself, which the idea of reciprocal contractions require. It might perhaps be possible that such can be measured, but those measurements would have to correspond to an optical illusion as opposed to the underlying physicality of the clock.
Indeed, how the conclusion of pseudo-Riemanian, Minkowski geomerty is reached in Einstein's relativity is the subject of debate between us, with regard to the implicit assumptions made by the treatment of co-ordinate systems.
No. You are tacitly assuming physical occurrences must not be related by hyperbolic, Minkowski geometry. As I have said before many many many many many many many many many many many many many many many many times, you are committing the very offence you are accusing Relativity of committing.
Again (and again and again and again and again and again), your (severe) misunderstanding of relativity is stifling any kind of legitimate investigation into the consequences of relativity.0 -
Advertisement
-
There is a limit to understanding physics, or any mathematical subject, without the language of mathematics. Verbosity is not intelligence.
Lets put this to rest. GPS satellites have to correct their timings relative to the Earth because of both special and general relativity. The mathematical theory holds, whatever "philosophers" who don't really understand the mathematical principles think. A theory which is postulated, mathematically rigorous, and works in practice in the real world is a fact.
As for philosophy and science; of that which we know nothing, we should therefore remain silent, as whatisface said.0 -
Duggys Housemate wrote: »There is a limit to understanding physics, or any mathematical subject, without the language of mathematics. Verbosity is not intelligence.
Lets put this to rest. GPS satellites have to correct their timings relative to the Earth because of both special and general relativity. The mathematical theory holds, whatever "philosophers" who don't really understand the mathematical principles think. A theory which is postulated, mathematically rigorous, and works in practice in the real world is a fact.
As for philosophy and science; of that which we know nothing, we should therefore remain silent, as whatisface said.
Bear in mind that the functioning of GPS is as much a verification of Lorentzian relativity, as it is Einsteinian; some would say moreso, given the use of a preferred Earth Centred Inertial Frame.0 -
Indeed you are asserting that they are assertions.Your response is a strange one. You repeatedly make unjustified assertions. Then when I point out that they are assertions, you claim I am asserting that they are assertions. It is tedious and counter-productive.
I put it to you to support a single statement I highlighted in red.
Physical characteristics
ascribing physical characteristics to her mathematical reference frame
The first point, about the ascription of physical characteristics to mathematical reference frames; you have repeatedly stated that Evelyn is in motion relative to her reference frame. This ascribes physical characteristics to her mathematical reference frame, because she cannot be in motion relative to her mathematical reference frame.
Also, stating that she performs her measurements in in one reference frame and her calculations in another, ascribes physical characteristics to a mathematical reference frame, because she can't do anything in a mathematical reference frame.
You have subsequently changed what you have said to, she is in motion relative to a hypothetical implied observer; does this mean that your earlier statements were incorrect?
Also, to say that she is in motion relative to an implied, hypothetical observer, ascribes physical characteristics to the implied observer, because she cannot be in motion relative to a hypothetical observer.
She is in motion relative to Henry - is this who you mean by the hypothetical observer?
Calculation tool
When the mathematical reference frame is taken as the calculational tool that it is, that can be used to make predictions, then the paradox is evident.
As a mathematical tool, Evelyn is free to construct the reference frame as she chooses, to perform calculations and make predictions about the physical world. She does this and calculates that Henry's clock is ticking faster than her and Albert's shared clock; Albert calculates that Henry's clock is ticking slower.
If we want to say that these pertain to measurements then we have the statements:
Albert measures Henry's physical clock to be physically ticking slower than Albert's clock.
Henry measures Albert's physical clock to be physically ticking slower than Henry's clock.
Therefore Henry's physical clock is measured to be physically ticking slower than Henry's physical clock.
How can Henry's clock physically tick slower than itself?
If the answer reverts back to some form of the reply that each are in different reference frames, then there again is the ascription of physical characteristics to non-phyiscal entities.
either a reference frame isn't an arbitrary mathematical construct, or it can't be used as a calculational tool for the purpose of predictions
Unelss, of course, reciprocal contractions are an entirely hypothetical artefact of mathematical reference frames, and don't correspond to physical clocks.
Just as Albert's reference frame leads him to calculate that the clock Henry is using for his measurements is ticking slower, Evelyn calculates that Henry's clock is ticking faster; it preserves the measurements of her clock, she just deduces that they are contracted relative to Henry.
Albert calculates that Henry's clock is ticking slower; Evelyn uses "Henry's" mathematical reference frame to calculate that their clock is ticking slower.
Of course, it isn't actually "Henry's" reference frame, it's a mathemaical tool that can be used for predictions, by anyone; like Evelyn.
And Evelyn's use of a mathematical reference frame leads her to predict that Henry's clock is ticking faster, while Albert predicts that it is ticking slower.Yes to both questions.No. You are tacitly assuming physical occurrences must not be related by hyperbolic, Minkowski geometry. As I have said before many many many many many many many many many many many many many many many many times, you are committing the very offence you are accusing Relativity of committing.
Again (and again and again and again and again and again), your (severe) misunderstanding of relativity is stifling any kind of legitimate investigation into the consequences of relativity.
We can assume that occurences are related by hyperbolic, Minkowski geometry, in the manner of Einsteinain relativity, but it leads to the conclusion that not only can a physical clock can physically tick both faster and slower than another clock, it can actually tick faster and slower than itself.
Justification
The resolution to the paradox being provided isn't an actualy resolution, it is a mathematical "trick" which only serves to obscure the paradox, as opposed to resolve it.
The justification relies on ascribing physical characteristics to non-physical, mathematical reference frames. We can see this through the challenge to Evelyn't use of the reference framel; she predicts Henry's clock to be ticking faster, but the argument being profferred is that she performs calcuations in one mathematical reference frame, but performs measurements in a different mathematical reference frame.
This has been modified, slightly, to the notion that she is in motion relative to a hypothetical observer, but this doesn't resolve the issue because it remains the exact same; it simply replaces the word "Henry" with "hypothetical observer".0 -
Physical characteristics
ascribing physical characteristics to her mathematical reference frame
The first point, about the ascription of physical characteristics to mathematical reference frames; you have repeatedly stated that Evelyn is in motion relative to her reference frame. This ascribes physical characteristics to her mathematical reference frame, because she cannot be in motion relative to her mathematical reference frame.
Also, stating that she performs her measurements in in one reference frame and her calculations in another, ascribes physical characteristics to a mathematical reference frame, because she can't do anything in a mathematical reference frame.
You have subsequently changed what you have said to, she is in motion relative to a hypothetical implied observer; does this mean that your earlier statements were incorrect?
Also, to say that she is in motion relative to an implied, hypothetical observer, ascribes physical characteristics to the implied observer, because she cannot be in motion relative to a hypothetical observer.
She is in motion relative to Henry - is this who you mean by the hypothetical observer?
Calculation tool
When the mathematical reference frame is taken as the calculational tool that it is, that can be used to make predictions, then the paradox is evident.
As a mathematical tool, Evelyn is free to construct the reference frame as she chooses, to perform calculations and make predictions about the physical world. She does this and calculates that Henry's clock is ticking faster than her and Albert's shared clock; Albert calculates that Henry's clock is ticking slower.
If we want to say that these pertain to measurements then we have the statements:
Albert measures Henry's physical clock to be physically ticking slower than Albert's clock.
Henry measures Albert's physical clock to be physically ticking slower than Henry's clock.
Therefore Henry's physical clock is measured to be physically ticking slower than Henry's physical clock.
How can Henry's clock physically tick slower than itself?
If the answer reverts back to some form of the reply that each are in different reference frames, then there again is the ascription of physical characteristics to non-phyiscal entities.
either a reference frame isn't an arbitrary mathematical construct, or it can't be used as a calculational tool for the purpose of predictions
Unelss, of course, reciprocal contractions are an entirely hypothetical artefact of mathematical reference frames, and don't correspond to physical clocks.
Just as Albert's reference frame leads him to calculate that the clock Henry is using for his measurements is ticking slower, Evelyn calculates that Henry's clock is ticking faster; it preserves the measurements of her clock, she just deduces that they are contracted relative to Henry.
Albert calculates that Henry's clock is ticking slower; Evelyn uses "Henry's" mathematical reference frame to calculate that their clock is ticking slower.
Of course, it isn't actually "Henry's" reference frame, it's a mathemaical tool that can be used for predictions, by anyone; like Evelyn.
And Evelyn's use of a mathematical reference frame leads her to predict that Henry's clock is ticking faster, while Albert predicts that it is ticking slower.
We can assume that occurences are related by hyperbolic, Minkowski geometry, in the manner of Einsteinain relativity, but it leads to the conclusion that not only can a physical clock can physically tick both faster and slower than another clock, it can actually tick faster and slower than itself.
Justification
The resolution to the paradox being provided isn't an actualy resolution, it is a mathematical "trick" which only serves to obscure the paradox, as opposed to resolve it.
The justification relies on ascribing physical characteristics to non-physical, mathematical reference frames. We can see this through the challenge to Evelyn't use of the reference framel; she predicts Henry's clock to be ticking faster, but the argument being profferred is that she performs calcuations in one mathematical reference frame, but performs measurements in a different mathematical reference frame.
This has been modified, slightly, to the notion that she is in motion relative to a hypothetical observer, but this doesn't resolve the issue because it remains the exact same; it simply replaces the word "Henry" with "hypothetical observer".
While this is at least an attempt to justify your assertion. The above all rests on the assertion that all observers in question (Albert Henry and Evelyn) assume coordinate systems are physical. This is the exact opposite of how reference frames are employed.
http://en.wikipedia.org/wiki/General_covariance
"In theoretical physics, general covariance (also known as diffeomorphism covariance or general invariance) is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations. The essential idea is that coordinates do not exist a priori in nature, but are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws."
Evelyn's reference frame, like Henry's and Albert's, is a mathematical construct, describing what a hypothetical observer would observe. Hence, nobody concludes two clocks are intrinsically ticking faster than each other, or themselves. They instead construct what observers would measure, and relate these measurements via Lorentz transformations.0 -
It's one thing to say that co-ordinates don't exist a priori in nature, it's another thing to say that an observer moves relative to a mathematical reference frame.While this is at least an attempt to justify your assertion. The above all rests on the assertion that all observers in question (Albert Henry and Evelyn) assume coordinate systems are physical. This is the exact opposite of how reference frames are employed.
http://en.wikipedia.org/wiki/General_covariance
"In theoretical physics, general covariance (also known as diffeomorphism covariance or general invariance) is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations. The essential idea is that coordinates do not exist a priori in nature, but are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws."
Evelyn's reference frame, like Henry's and Albert's, is a mathematical construct, describing what a hypothetical observer would observe. Hence, nobody concludes two clocks are intrinsically ticking faster than each other, or themselves. They instead construct what observers would measure, and relate these measurements via Lorentz transformations.
Again, the conlcusion is that a clock is measured to tick both faster and slower than itself.0 -
It's one thing to say that co-ordinates don't exist a priori in nature, it's another thing to say that an observer moves relative to a mathematical reference frame.
Again, the conlcusion is that a clock is measured to tick both faster and slower than itself.
> The other, identical discussion we are having on coordinate systems and reciprocity.0
Advertisement