Question on time dilation

roosh

Just wondering about the following scenario.


It's probably easiest to explain in the context of this explanation of Lorentz contractions

https://www.youtube.com/watch?v=DRDN7ceu6UU

The video outlines a common thought experiment in Einsteinian relativity, of two inertial, relatively moving observers, each with a light clock. It primarily shows things from the perspective of Albert, the observer on the platform. Moving relative to Albert is Henry; from Albert's perspective Henry's clock runs slower due to time dilation. Generally, the thought experiment is explained from the perspective of each observer, who label themselves as being "at rest" and ascribe the relative velocity to their counterpart; it is, of course, possible for each observer to labels themselves as "in motion" and their counterpart as "at rest" and measure their velocity relative to their counterpart, as opposed to themselves. In this case the contractions are reversed, presumably.


Albert & Evelyn
Let's say that Albert is joined by his cousin, Evelyn, on the platform; she is there when Henry passes, traveling at an inertial speed; Albert and Evelyn are at rest relative to each other. Now, let's say that Albert and Evelyn both decide to construct a mathematical reference frame to describe the scenario, and to find out the relative motion and relevant contractions.


Albert constructs his reference frame and labels himself as "at rest"; he measures Henry's relative velocity to be something like 0.8c. He concludes time, for Henry, is dilated, or that his clock is running slower than the clock shared by Albert and Evelyn.


Now, while Albert was busy at work, so too was Evelyn; but unlike Albert, Evenlyn constructed a reference frame which labelled Henry as "at rest"; Evelyn measured her and Albert's velocity, relative to Henry, as 0.8c. Evelyn concludes that the clock herself and Albert share is running slower than Henry's i.e. that time, for Albert and herself is dilated.


Both reference frames are equally valid, and supposedly represent the exact same scenario, but they seem to be contradictory. Who is right; for whom does time run slowly; or where have I gone wrong?




It is probably worth stating that, I don't think stating that reference frames have been mixed adequately addresses the question, because both reference frames are equally valid and both Albert and Evelyn are entitled to construct them how they wish; both should accurately represent the given scenario.

Morbert

roosh wrote: »

Just wondering about the following scenario.


It's probably easiest to explain in the context of this explanation of Lorentz contractions

https://www.youtube.com/watch?v=DRDN7ceu6UU

The video outlines a common thought experiment in Einsteinian relativity, of two inertial, relatively moving observers, each with a light clock. It primarily shows things from the perspective of Albert, the observer on the platform. Moving relative to Albert is Henry; from Albert's perspective Henry's clock runs slower due to time dilation. Generally, the thought experiment is explained from the perspective of each observer, who label themselves as being "at rest" and ascribe the relative velocity to their counterpart; it is, of course, possible for each observer to labels themselves as "in motion" and their counterpart as "at rest" and measure their velocity relative to their counterpart, as opposed to themselves. In this case the contractions are reversed, presumably.


Albert & Evelyn
Let's say that Albert is joined by his cousin, Evelyn, on the platform; she is there when Henry passes, traveling at an inertial speed; Albert and Evelyn are at rest relative to each other. Now, let's say that Albert and Evelyn both decide to construct a mathematical reference frame to describe the scenario, and to find out the relative motion and relevant contractions.


Albert constructs his reference frame and labels himself as "at rest"; he measures Henry's relative velocity to be something like 0.8c. He concludes time, for Henry, is dilated, or that his clock is running slower than the clock shared by Albert and Evelyn.


Now, while Albert was busy at work, so too was Evelyn; but unlike Albert, Evenlyn constructed a reference frame which labelled Henry as "at rest"; Evelyn measured her and Albert's velocity, relative to Henry, as 0.8c. Evelyn concludes that the clock herself and Albert share is running slower than Henry's i.e. that time, for Albert and herself is dilated.


Both reference frames are equally valid, and supposedly represent the exact same scenario, but they seem to be contradictory. Who is right; for whom does time run slowly; or where have I gone wrong?


It is probably worth stating that, I don't think stating that reference frames have been mixed adequately addresses the question, because both reference frames are equally valid and both Albert and Evelyn are entitled to construct them how they wish; both should accurately represent the given scenario.

Evelyn is doing her calculations in a reference frame where Henry is at rest, but making measurements in a reference frame where she is at rest. She therefore has to perform a Lorentz transformations to either relate her calculations in henry's frame to her measurements, or equivalently to relate her measurements to her calculations.

roosh

Morbert wrote: »

Evelyn is doing her calculations in a reference frame where Henry is at rest, but making measurements in a reference frame where she is at rest. She therefore has to perform a Lorentz transformations to either relate her calculations in henry's frame to her measurements, or equivalently to relate her measurements to her calculations.

She's not though; she is making her measurements in a reference frame where her, Albert, and their clock are "in motion"; as her co-ordinate labeling system reflects.

EDIT: also, won't Albert and Evelyn disagree about the simultaneity of events?

Morbert

roosh wrote: »

She's not though; she is making her measurements in a reference frame where her, Albert, and their clock are "in motion"; as her co-ordinate labeling system reflects.

EDIT: also, won't Albert and Evelyn disagree about the simultaneity of events?

She is. Her/Albert's clock is at rest with respect to her. I.e. She is making measurements in the same reference frame Albert is making measurements.

roosh

Morbert wrote: »

She is. Her/Albert's clock is at rest with respect to her. I.e. She is making measurements in the same reference frame Albert is making measurements.

She is free to define her reference frame as above, just as Albert is. In the frame, as defined by Evelyn, both Albert and the clock are also in motion, along with Evelyn; they are at rest relative to each other, because they all moving at the same velocity.

EDIT: it might be worth asking the question, is Evelyn wrong in her conclusion that her and Albert's clock is ticking slower than Henry's; or is Albert wrong that it is Henry's clock that is ticking slower?

Morbert

roosh wrote: »

She is free to define her reference frame as above, just as Albert is. In the frame, as defined by Evelyn, both Albert and the clock are also in motion, along with Evelyn; they are at rest relative to each other, because they all moving at the same velocity.

EDIT: it might be worth asking the question, is Evelyn wrong in her conclusion that her and Albert's clock is ticking slower than Henry's; or is Albert wrong that it is Henry's clock that is ticking slower?

She is not free at all. "Her" reference frame is the one which labels her as at rest. She is free to perform calculations in any reference frame she likes, but to make those calculations consistent with what she measures, she must perform the required transformations.

roosh

Morbert wrote: »

She is not free at all. "Her" reference frame is the one which labels her as at rest. She is free to perform calculations in any reference frame she likes, but to make those calculations consistent with what she measures, she must perform the required transformations.

And therein lies the implicit assumption about the intrinsic nature of motion.


The question begged from the above is, if "her" reference frame is the one which labels her as "at rest", relative to what does it label her as being at rest? Presumably the answer is relative to herself, primarily, but in this case, also, relative to the platform, Albert, and their shared clock. Of course, she is labeled as being at rest relative to these, even in her, equally valid, reference frame which labels them all as being in motion, with the same velocity, relative to Henry. Essentially, it is the motion of her and Albert's clock, relative to Henry and his, that leads her to the conclusion that their clock is ticking slower.

Indeed, neither herself nor Albert can actually measure Henry's clock, they can only make calculations about it, which leads them to certain deductions. Evelyn's perfectly valid calculations, lead her to the, supposedly, perfectly valid conclusion that her and Albert's clock is ticking slower than Henry's. This is true in all reference frames.

On the other hand Albert's perfectly valid calculations lead him to the, supposedly, perfectly valid conclusion that Henry's clock is ticking slower than their shared clock.


One of them has to be wrong, or else time dilation must be a mathematical artefact, not a physical reality.

Morbert

roosh wrote: »

And therein lies the implicit assumption about the intrinsic nature of motion.


The question begged from the above is, if "her" reference frame is the one which labels her as "at rest", relative to what does it label her as being at rest? Presumably the answer is relative to herself, primarily, but in this case, also, relative to the platform, Albert, and their shared clock. Of course, she is labeled as being at rest relative to these, even in her, equally valid, reference frame which labels them all as being in motion, with the same velocity, relative to Henry. Essentially, it is the motion of her and Albert's clock, relative to Henry and his, that leads her to the conclusion that their clock is ticking slower.

Indeed, neither herself nor Albert can actually measure Henry's clock, they can only make calculations about it, which leads them to certain deductions. Evelyn's perfectly valid calculations, lead her to the, supposedly, perfectly valid conclusion that her and Albert's clock is ticking slower than Henry's. This is true in all reference frames.

On the other hand Albert's perfectly valid calculations lead him to the, supposedly, perfectly valid conclusion that Henry's clock is ticking slower than their shared clock.


One of them has to be wrong, or else time dilation must be a mathematical artefact, not a physical reality.

She is at rest relative to the apparatus she is reading. Neither is wrong. They just need to make sure to be consistent wither coordinate labels.

roosh

Morbert wrote: »

She is at rest relative to the apparatus she is reading. Neither is wrong. They just need to make sure to be consistent wither coordinate labels.

I think you might be making an implicit assumption about what the term "motion" implies, because her co-ordinate labels are perfectly consistent. Her co-ordinate labels don't label her as "in motion relative to her apparatus", they label her as "at rest relative to her apparatus, Albert, and the platform", they label her, Albert and, critically, their clock, as "in motion relative to Henry". Albert's co-ordinate labels do the very same.

The difference is, Evelyn measures the velocity relative to Henry, while Albert measures it relative to himself and Evelyn; both are perfectly valid, and acceptable. However, this has the effect that Evelyn calculates that her and Albert's shared clock ticks slower than Henry's, while Albert calculates that Henry's clock ticks slower.

This is a contradiction, unless one of their calculations is wrong; or unless their mathematical reference frames don't correspond to the physical world.

Morbert

roosh wrote: »

I think you might be making an implicit assumption about what the term "motion" implies, because her co-ordinate labels are perfectly consistent. Her co-ordinate labels don't label her as "in motion relative to her apparatus", they label her as "at rest relative to her apparatus, Albert, and the platform", they label her, Albert and, critically, their clock, as "in motion relative to Henry". Albert's co-ordinate labels do the very same.

The difference is, Evelyn measures the velocity relative to Henry, while Albert measures it relative to himself and Evelyn; both are perfectly valid, and acceptable. However, this has the effect that Evelyn calculates that her and Albert's shared clock ticks slower than Henry's, while Albert calculates that Henry's clock ticks slower.

This is a contradiction, unless one of their calculations is wrong; or unless their mathematical reference frames don't correspond to the physical world.

You are making a mountain out of an incredibly simple molehill.

She does her calculations in a reference frame where the clock is in motion. She measures the clock in a reference frame where the clock is at rest. She must therefore perform the relevant transformations.

My advice would be to try a few practice calculations yourself.

roosh

Morbert wrote: »

You are making a mountain out of an incredibly simple molehill.

She does her calculations in a reference frame where the clock is in motion. She measures the clock in a reference frame where the clock is at rest. She must therefore perform the relevant transformations.

My advice would be to try a few practice calculations yourself.

And you are making an implicit assumption about the intrinsic nature of motion.

To say "she does her calculations in a reference frame where the clock is in motion" is to make a statement about the absolute nature of the motion, of the clock; not an absolute statement about the relative motion of the clock; relative to something else.

You should be saying she does her calculations in a reference frame where her, and Albert's, shared clock is in motion relative to Henry; but then, so too does Albert.

Evelyn measures the clock in a reference frame where their shared clock is in motion relative to her Henry; but then, so too does Albert.

Albert does his calculations in a reference frame where their shared clock is at rest relative to Albert and Evelyn; but then, so too does Evelyn.

Albert does his measurements in a reference frame where their shared clock is at rest relative to Albert and Evelyn; but then, so too does Evelyn.


The only difference is, Albert chooses to measure the velocity relative to himself, while Evelyn chooses to measure it relative to Henry; and both are perfectly entitled to do so, because Albert and Evelyn are at rest relative to themselves, while simultaneosuly being in motion relative to Henry.

It is, precisley, the choice of whom to measure the velocity relative to that affects each of their calculations; Albert calculates that Henry's clock will be ticking slower than his and Evelyn's shared clock, while Evelyn calculates that Henry's clock will be ticking faster than her and Albert's shared clock.


To suggest that Evelyn has to do a transform simply says that she has to transform her co-ordinates into Albert's, such that she will get Albert's co-ordinates i.e. she has to define her reference frame as Albert has. The implication, of course, is that her co-ordinates do not correctly describe the scenario - when, of course, they supposedly do. The only difference between her and Albert's referecne frame is who they choose to measure the velocity relative to; both are perfectly entitled to measure it as they have; the only issue is that it leads to a paradox.


Whether or not it is a mountain, or a molehill, depends on your frame of reference I guess.

Morbert

roosh wrote: »

And you are making an implicit assumption about the intrinsic nature of motion.

To say "she does her calculations in a reference frame where the clock is in motion" is to make a statement about the absolute nature of the motion, of the clock; not an absolute statement about the relative motion of the clock; relative to something else.

You should be saying she does her calculations in a reference frame where her, and Albert's, shared clock is in motion relative to Henry; but then, so too does Albert.

Evelyn measures the clock in a reference frame where their shared clock is in motion relative to her Henry; but then, so too does Albert.

Albert does his calculations in a reference frame where their shared clock is at rest relative to Albert and Evelyn; but then, so too does Evelyn.

Albert does his measurements in a reference frame where their shared clock is at rest relative to Albert and Evelyn; but then, so too does Evelyn.


The only difference is, Albert chooses to measure the velocity relative to himself, while Evelyn chooses to measure it relative to Henry; and both are perfectly entitled to do so, because Albert and Evelyn are at rest relative to themselves, while simultaneosuly being in motion relative to Henry.

It is, precisley, the choice of whom to measure the velocity relative to that affects each of their calculations; Albert calculates that Henry's clock will be ticking slower than his and Evelyn's shared clock, while Evelyn calculates that Henry's clock will be ticking faster than her and Albert's shared clock.


To suggest that Evelyn has to do a transform simply says that she has to transform her co-ordinates into Albert's, such that she will get Albert's co-ordinates i.e. she has to define her reference frame as Albert has. The implication, of course, is that her co-ordinates do not correctly describe the scenario - when, of course, they supposedly do. The only difference between her and Albert's referecne frame is who they choose to measure the velocity relative to; both are perfectly entitled to measure it as they have; the only issue is that it leads to a paradox.


Whether or not it is a mountain, or a molehill, depends on your frame of reference I guess.

If a reference frame labels something as in motion, it means it is in motion with respect to that frame of reference. Hence, it is not a statement about intrinsic motion. If Evelyn performs her calculations in Henry's frame of reference, she will need to perform a transformation to recover the measurements made from her frame of reference.

Also, all reference frames say Albert's clock is in motion, relative to Henry's.

roosh

Morbert wrote: »

If a reference frame labels something as in motion, it means it is in motion with respect to that frame of reference. Hence, it is not a statement about intrinsic motion. If Evelyn performs her calculations in Henry's frame of reference, she will need to perform a transformation to recover the measurements made from her frame of reference.

Also, all reference frames say Albert's clock is in motion, relative to Henry's.

Evelyn isn't performing her calculations in Henry's frame of reference though, she is performing her calculations in her own frame of reference; her arbitrarily constructed, and equally valid, mathematical frame of reference, labels her as "at rest relative to her and Albert's shared clock"; it also labels her, and their shared clock as, "in motion relative to Henry" - Albert's arbitrarily constructed, and equally valid, mathematical frame of reference does precisely the same.

The only difference is the, entirely arbitrary, choice of relative to whom to measure the velocity. Evelyn chooses to measure it relative to Henry, as she is entitled to do, Albert chooses to measure it relative to himself, as he is entitled to do.

This leads Evelyn to calculate that Henry's clock is ticking faster, while Albert's choice leads him to calculate that it is Henry's clock that is ticking slower.

Morbert

roosh wrote: »

Evelyn isn't performing her calculations in Henry's frame of reference though, she is performing her calculations in her own frame of reference; her arbitrarily constructed, and equally valid, mathematical frame of reference, labels her as "at rest relative to her and Albert's shared clock"; it also labels her, and their shared clock as, "in motion relative to Henry" - Albert's arbitrarily constructed, and equally valid, mathematical frame of reference does precisely the same.

The only difference is the, entirely arbitrary, choice of relative to whom to measure the velocity. Evelyn chooses to measure it relative to Henry, as she is entitled to do, Albert chooses to measure it relative to himself, as he is entitled to do.

This leads Evelyn to calculate that Henry's clock is ticking faster, while Albert's choice leads him to calculate that it is Henry's clock that is ticking slower.

"Her" reference frame is the reference frame she is at rest with respect to. It is distinct from the arbitrary reference frame she used in her calculations.

roosh

Morbert wrote: »

"Her" reference frame is the reference frame she is at rest with respect to. It is distinct from the arbitrary reference frame she used in her calculations.

By "her" [in inverted commas] reference frame, do you mean, not really her reference frame?

She is, of course, entirely free to choose how to define her [no inverted commas] arbitrary, mathematical reference frame however she chooses, as long as it reflects the reality of the physical situation. In the physical world she doesn't move relative to an imaginary, mathematical reference frame, she moves relative to physical objects; and her, arbitrary mathematical reference frame reflects this. She also performs her measurements and calculations in the physical world, at rest, or in motion, relative to physical objects; again, her arbitrary mathematical reference frame reflects the fact that she is at rest reltive to her apparatus and that her apparatus are in motion relative to Henry - in exactly the same way as Albert's does.


Her arbitrary, mathematical reference frame is solely for the purpose of helping her with her calculations, so that she can make predictions about the physical world; her arbitrary, mathematical reference frame lead her to calculate, and predict, that Henry's physical clock will be running faster than her and Albert's shared physical clock - because she arbitrarily chooses to measure velocities relative to Henry (which she is perfectly entitled to do); while Albert's calculations lead him to predict that Henry's physical clock will be ticking slower than their phyiscal clock - because he arbitrarily chooses to measure velocities relative to himself (which he is perfectly entitled to do). There is, of course, no experimental evidence of reciprocal contractions - without circular reasoning - presumably because it is a paradox, or a contradiction. Either way though, the calculation that Henry's clock will tick both faster and slower than Albert and Evelyn's shared clock, is a paradox.


I think this points to the fact that reciprocal contractions are a mathematical artefact, rather than a physical reality.

Morbert

roosh wrote: »

By "her" [in inverted commas] reference frame, do you mean, not really her reference frame?

She is, of course, entirely free to choose how to define her [no inverted commas] arbitrary, mathematical reference frame however she chooses, as long as it reflects the reality of the physical situation. In the physical world she doesn't move relative to an imaginary, mathematical reference frame, she moves relative to physical objects; and her, arbitrary mathematical reference frame reflects this. She also performs her measurements and calculations in the physical world, at rest, or in motion, relative to physical objects; again, her arbitrary mathematical reference frame reflects the fact that she is at rest reltive to her apparatus and that her apparatus are in motion relative to Henry - in exactly the same way as Albert's does.


Her arbitrary, mathematical reference frame is solely for the purpose of helping her with her calculations, so that she can make predictions about the physical world; her arbitrary, mathematical reference frame lead her to calculate, and predict, that Henry's physical clock will be running faster than her and Albert's shared physical clock - because she arbitrarily chooses to measure velocities relative to Henry (which she is perfectly entitled to do); while Albert's calculations lead him to predict that Henry's physical clock will be ticking slower than their phyiscal clock - because he arbitrarily chooses to measure velocities relative to himself (which he is perfectly entitled to do). There is, of course, no experimental evidence of reciprocal contractions - without circular reasoning - presumably because it is a paradox, or a contradiction. Either way though, the calculation that Henry's clock will tick both faster and slower than Albert and Evelyn's shared clock, is a paradox.


I think this points to the fact that reciprocal contractions are a mathematical artefact, rather than a physical reality.

I mean the reference frame she is at rest with respect to. You are ignoring the salient point: The reference frame she is performing her calculations in is different from the reference frame she is performing her measurements in. That is all there is to it.

roosh

Morbert wrote: »

I mean the reference frame she is at rest with respect to. You are ignoring the salient point: The reference frame she is performing her calculations in is different from the reference frame she is performing her measurements in. That is all there is to it.

I understand which mathematical reference frame you meant, I was just wondering why the word her was in inverted commas.



The salient point is that you are ascribing physical characteristics to something non-physical.

To say "her" reference frame is the one she is at rest relative to, not the one she is moving relative to, ascribes physical characteristics to her mathematical reference frame; it doesn't correspond to the physical world. There are aspects of her mathematical reference frame which do correspond to the physical world, but her motion relative to a mathematical reference frame isn't one of them.

In the physical world she moves relative to physical objects; in the physical world she is moving relative to Henry and his clock, and she is at rest relative to Albert and their shared clock. The same is true for Albert; and both her and Albert's arbitrary, mathematical reference frames represent this.

Evelyn performs her measurements in the physical world, where she is at rest relative to Albert, and their shared clock; Albert does the same. She also does her calculations in the physical world, where she is at rest relative to Albert and their shared clock; Albert does precisely the same. Both their arbitrary, mathematical reference frames reflect this.

Neither of them do their calculations in a mathematical reference frame; they use their arbitrary, mathematical reference frames to do calculations, and make predictions about the physical world. The only difference is the, entirely arbitrary, choice of relative to whom, to measure the velocity.


Albert arbitrarily chooses to measure the velocity relative to himself, and this leads him to calculate that Henry's physical clock will physically be ticking slower, than his and Evelyn's shared, physical clock. Evelyn arbitrarily chooses to measure the velocity relative to Henry; this leads her to calculate that Henry's physical clock will physically be ticking faster, than her and Alberts shared, physical clock.

This is a paradox.

Morbert

roosh wrote: »

I understand which mathematical reference frame you meant, I was just wondering why the word her was in inverted commas.

The salient point is that you are ascribing physical characteristics to something non-physical.

To say "her" reference frame is the one she is at rest relative to, not the one she is moving relative to, ascribes physical characteristics to her mathematical reference frame; it doesn't correspond to the physical world. There are aspects of her mathematical reference frame which do correspond to the physical world, but her motion relative to a mathematical reference frame isn't one of them.

In the physical world she moves relative to physical objects; in the physical world she is moving relative to Henry and his clock, and she is at rest relative to Albert and their shared clock. The same is true for Albert; and both her and Albert's arbitrary, mathematical reference frames represent this.

Evelyn performs her measurements in the physical world, where she is at rest relative to Albert, and their shared clock; Albert does the same. She also does her calculations in the physical world, where she is at rest relative to Albert and their shared clock; Albert does precisely the same. Both their arbitrary, mathematical reference frames reflect this.

Neither of them do their calculations in a mathematical reference frame; they use their arbitrary, mathematical reference frames to do calculations, and make predictions about the physical world. The only difference is the, entirely arbitrary, choice of relative to whom, to measure the velocity.


Albert arbitrarily chooses to measure the velocity relative to himself, and this leads him to calculate that Henry's physical clock will physically be ticking slower, than his and Evelyn's shared, physical clock. Evelyn arbitrarily chooses to measure the velocity relative to Henry; this leads her to calculate that Henry's physical clock will physically be ticking faster, than her and Alberts shared, physical clock.

This is a paradox.

It is still clear you do not understand how coordinate systems are employed in relativity. The coordinate system is arbitrary, but the apparatus she is using is at rest relative to herself, and hence coordinate measurements are taken in the frame she is at rest with respect to. This is not ascribing any ontological quality to the reference frame. It is instead a statement about consistency in handling calculations and measurement apparatus.

roosh

Morbert wrote: »

It is still clear you do not understand how coordinate systems are employed in relativity. The coordinate system is arbitrary, but the apparatus she is using is at rest relative to herself, and hence coordinate measurements are taken in the frame she is at rest with respect to. This is not ascribing any ontological quality to the reference frame. It is instead a statement about consistency in handling calculations and measurement apparatus.

Indeed, the apparatus Evelyn is using is at rest relative to herself, and Albert; but that is just half the story; Evelyn, Albert, and their shared apparatus, are also in motion relative to Henry. With the aid of her arbitrary, mathematical reference frame, Evelyn calculates that the clock which is at rest relative to herself and Albert, and which she is using to perform measurements, is ticking slower than Henry's clock.

Both Albert's and Evelyn's arbitrary, mathematical reference frames reflect that they are at rest relative to their apparatus/ The difference between the two, is who they choose to measure the velocity relative to; this affects their calculations, and,therefore, their predictions about the physical clock, which they use to perform their measurements.

Albert calculates that Henry's clock will be ticking slower, while Evelyn calculates that Henry's clock will be ticking faster.

Morbert

roosh wrote: »

Indeed, the apparatus Evelyn is using is at rest relative to herself, and Albert; but that is just half the story; Evelyn, Albert, and their shared apparatus, are also in motion relative to Henry. With the aid of her arbitrary, mathematical reference frame, Evelyn calculates that the clock which is at rest relative to herself and Albert, and which she is using to perform measurements, is ticking slower than Henry's clock.

Both Albert's and Evelyn's arbitrary, mathematical reference frames reflect that they are at rest relative to their apparatus/ The difference between the two, is who they choose to measure the velocity relative to; this affects their calculations, and,therefore, their predictions about the physical clock, which they use to perform their measurements.

Albert calculates that Henry's clock will be ticking slower, while Evelyn calculates that Henry's clock will be ticking faster.

Both Albert and Evelyn measure the velocity relative to themselves. In order to measure the velocity relative to Henry, Evelyn would have to be at rest relative to Henry.

roosh

Morbert wrote: »

Both Albert and Evelyn measure the velocity relative to themselves. In order to measure the velocity relative to Henry, Evelyn would have to be at rest relative to Henry.

I suppose if we're going to split hairs, we may as well try and be as accurate as possible and say that, what they actually measure is the relative velocity between themselves and other objects, such as Henry; they are as much measuring their own velocity relative to other objects, as they are the objects velocity relative to themselves - unless of course a different measurement would be yielded, by doing it the other way around.

They perform this measurement in a reference frame where they are at rest relative to each other, and their shared clock; but equally, they perform the measurement in a reference frame where they, and their shared clock, are in motion relative to Henry. Henry of course obtains the same measurement, so that particular minutia isn't critical.

What is critical is how they use the value for the relative velocity in their calculations; Evelyn uses it in such a way, that she calculates that Henry's clock will be ticking faster, than her and Albert's shared clock; while Albert uses it in such a way, that he calculates that Henry's clock will be ticking slower.

Morbert

roosh wrote: »

I suppose if we're going to split hairs, we may as well try and be as accurate as possible and say that, what they actually measure is the relative velocity between themselves and other objects, such as Henry; they are as much measuring their own velocity relative to other objects, as they are the objects velocity relative to themselves - unless of course a different measurement would be yielded, by doing it the other way around.

They perform this measurement in a reference frame where they are at rest relative to each other, and their shared clock; but equally, they perform the measurement in a reference frame where they, and their shared clock, are in motion relative to Henry. Henry of course obtains the same measurement, so that particular minutia isn't critical.

What is critical is how they use the value for the relative velocity in their calculations; Evelyn uses it in such a way, that she calculates that Henry's clock will be ticking faster, than her and Albert's shared clock; while Albert uses it in such a way, that he calculates that Henry's clock will be ticking slower.

Their motion relative to Henry is irrelevant. They are performing measurements using a frame of reference A. If Evelyn performs her calculations in another frame of reference , B, she must employ Lorentz transformations. This is independent of any fact about the relation between the clock and Henry. For while it is true that they are in motion, relative to henry, this does not mean they are therefore sharing the frame of reference of Henry.

More specifically, when Evelyn reads the "tick" of the clock, it is at some position x1. When she reads the "tock", indicating 1 second, it is still at position x1. This specifies the reference frame she is performing her measurements in. In this reference frame, the coordinate time is equal to the proper time of the clock. If she were performing her measurements in Henry's reference frame, then the clock would be at x1 for the tick, but not for the tock.

roosh

Morbert wrote: »

Their motion relative to Henry is irrelevant. They are performing measurements using a frame of reference A. If Evelyn performs her calculations in another frame of reference , B, she must employ Lorentz transformations. This is independent of any fact about the relation between the clock and Henry. For while it is true that they are in motion, relative to henry, this does not mean they are therefore sharing the frame of reference of Henry.

Again, you are ascribing physical characteristics to something which is non-physical.

They don't perform their measurements using a mathematical reference frame; they perform their measurements using physical instruments. They also don't perform their calculations in a mathematical reference frame, they use the mathematical reference frame as part of their calculations, and to help make predictions about the physical world.

So Evelyn doesn't perform her physical measurements using a mathematical reference frame A, and then perform her calculations in a mathematical reference frame B; she performs her measurements using physical instruments, relative to which she is at rest; while her and her physical instruments are in motion relative to Henry. She constructs a mathematical reference frame, A, which accurately refelcts this; and she uses this mathematical reference frame to assist her in her calculations; her calculations lead her to conclude that Henry's clock will be ticking faster.

Albert also performs his measurements using physical instruments, relative to which he is at rest; while he and his shared physical instruments are in motion relative to Henry. He constructs a mathematical reference frame, B, which accurately refelcts this; and he uses this mathematical reference frame to assist him in his calculations; his calculations lead him to conclude that Henry's clock will be ticking faster.

Morbert wrote: »

More specifically, when Evelyn reads the "tick" of the clock, it is at some position x1. When she reads the "tock", indicating 1 second, it is still at position x1. This specifies the reference frame she is performing her measurements in. In this reference frame, the coordinate time is equal to the proper time of the clock. If she were performing her measurements in Henry's reference frame, then the clock would be at x1 for the tick, but not for the tock.

That's not very specific at all, it's actually rather vague; you will have to clarify what you mean by "position X1".

If I'm not mistaken though, I think the point you are trying to make assumes Albert's arbitrary co-ordinates to be the valid ones, where X1 is meant to be a co-ordinate reference; of course, according to Evelyn's co-ordinate reference frame, she isn't located at X1 for the tock.

That is assuming I've understood the point you were trying to make.

Morbert

roosh wrote: »

Again, you are ascribing physical characteristics to something which is non-physical.

They don't perform their measurements using a mathematical reference frame; they perform their measurements using physical instruments. They also don't perform their calculations in a mathematical reference frame, they use the mathematical reference frame as part of their calculations, and to help make predictions about the physical world.

So Evelyn doesn't perform her physical measurements using a mathematical reference frame A, and then perform her calculations in a mathematical reference frame B; she performs her measurements using physical instruments, relative to which she is at rest; while her and her physical instruments are in motion relative to Henry. She constructs a mathematical reference frame, A, which accurately refelcts this; and she uses this mathematical reference frame to assist her in her calculations; her calculations lead her to conclude that Henry's clock will be ticking faster.

Albert also performs his measurements using physical instruments, relative to which he is at rest; while he and his shared physical instruments are in motion relative to Henry. He constructs a mathematical reference frame, B, which accurately refelcts this; and he uses this mathematical reference frame to assist him in his calculations; his calculations lead him to conclude that Henry's clock will be ticking faster.

That's not very specific at all, it's actually rather vague; you will have to clarify what you mean by "position X1".

If I'm not mistaken though, I think the point you are trying to make assumes Albert's arbitrary co-ordinates to be the valid ones, where X1 is meant to be a co-ordinate reference; of course, according to Evelyn's co-ordinate reference frame, she isn't located at X1 for the tock.

That is assuming I've understood the point you were trying to make.

Again, I am not ascribing any physical properties to coordinate systems.

http://en.wikipedia.org/wiki/Coordinate_time
http://en.wikipedia.org/wiki/Proper_time

"In the theory of relativity, it is convenient to express results in terms of a spacetime coordinate system relative to an implied observer."

So Evelyn does employ a reference frame that is different from the one she is using for calculation purposes, because, as the name implies, a reference frame is the frame of reference of an implied observer (Evelyn). Therefore, if she does her calculations in a different reference frame, she is describing the measurements from the frame of reference of a different observer. As I said before, Henry is entirely irrelevant in this problem, because even though Evelyn is at rest with respect to the clock in the reference frame of a different observer, she still measures the clock in the frame of reference of herself.

roosh

Morbert wrote: »

Again, I am not ascribing any physical properties to coordinate systems.

http://en.wikipedia.org/wiki/Coordinate_time
http://en.wikipedia.org/wiki/Proper_time

"In the theory of relativity, it is convenient to express results in terms of a spacetime coordinate system relative to an implied observer."

So Evelyn does employ a reference frame that is different from the one she is using for calculation purposes, because, as the name implies, a reference frame is the frame of reference of an implied observer (Evelyn). Therefore, if she does her calculations in a different reference frame, she is describing the measurements from the frame of reference of a different observer. As I said before, Henry is entirely irrelevant in this problem, because even though Evelyn is at rest with respect to the clock in the reference frame of a different observer, she still measures the clock in the frame of reference of herself.

According to relativity, yes, Evelyn uses a different frame of reference that is different to the one she is using for her calculations; but just because relativity says so, that doesn't necessarily make it true. Indeed, that relativity says this is the case, isn't in dispute, what is in dispute is the justification being given for it.Convenience isn't rational justification.

Evelyn doesn't employ a mathematical reference frame for her measurements; she uses the physical instruments beside her; she doesn't use other co-ordinate clocks, located at a distance from her, for her measurements either; clocks which she would have to assume are synchronised - but that is a separate matter.

It doesn't change the fact, that Evelyn calculates that her and Albert's shared clock is ticking slower than Henry's; it juts means that she calculates that all the co-ordinate clocks are also ticking slower.

Morbert

roosh wrote: »

According to relativity, yes, Evelyn uses a different frame of reference that is different to the one she is using for her calculations; but just because relativity says so, that doesn't necessarily make it true. Indeed, that relativity says this is the case, isn't in dispute, what is in dispute is the justification being given for it.Convenience isn't rational justification.

Evelyn doesn't employ a mathematical reference frame for her measurements; she uses the physical instruments beside her; she doesn't use other co-ordinate clocks, located at a distance from her, for her measurements either; clocks which she would have to assume are synchronised - but that is a separate matter.

It doesn't change the fact, that Evelyn calculates that her and Albert's shared clock is ticking slower than Henry's; it juts means that she calculates that all the co-ordinate clocks are also ticking slower.

Again, you are clearly not taking the time to understand how reference frames are employed. When Evelyn performs her calculations in a different frame of reference, she is working out what the hypothetical, implied observer would measure. This is different from what she will measure, because she and the implied observer are moving, relative to one another. It doesn't get any simpler than that.

roosh

Morbert wrote: »

Again, you are clearly not taking the time to understand how reference frames are employed. When Evelyn performs her calculations in a different frame of reference, she is working out what the hypothetical, implied observer would measure. This is different from what she will measure, because she and the implied observer are moving, relative to one another. It doesn't get any simpler than that.

I understand how reference frames are employed, it's the justification for the way in which they are employed which is being questioned.


The point is that she doesn't perform her calculations in a different frame of reference, because she doesn't perform her calculations in a mathematical reference frame, at all. She performs her measurements in the physical world, using the clock that is beside her, and at rest to relative to herself and Albert; just as Albert does. She constructs an arbitrary and imaginary, mathematical reference frame as part of her calculations; she uses this in her calculations, she doesn't perform measurements, or calculations in it.

Her calculations are indeed intended to work out what an implied observer will measure; if by implied observer you mean Henry; but the intention isn't to calculate what he will measure in a different frame of reference, the intention is to calculate what he will measure in the physical world. Indeed, she does conclude that what Henry measures will be different to what she measures; she concludes that the clock Henry uses for measurements will be ticking faster than the clock she is using; Albert also calculates that what Henry measures will be different, but he calculates that the clock Henry uses for his measurements will be ticking slower.


Graph paper
It might help to think of her mathematical reference frame in terms of graph paper; the dot that represents her on the co-ordinate reference frame doesn't actually perform measurements, or calculations, in that graph paper; the little dot that represents her is part of her calculations.

She can draw the reference frame however she pleases, on that graph paper, and use that graph paper to help her make predictions. With the aid of this graph paper she calculates that Henry's clock will tick faster than her and Albert's shared clock, which they both use for measurements, in the physical world.

With the aid of his graph paper, Albert calculates that Henry's clock will be ticking slower, than the clock he and Evelyn use to perform measurements, in the physical world.

Morbert

roosh wrote: »

I understand how reference frames are employed, it's the justification for the way in which they are employed which is being questioned.

The point is that she doesn't perform her calculations in a different frame of reference, because she doesn't perform her calculations in a mathematical reference frame, at all. She performs her measurements in the physical world, using the clock that is beside her, and at rest to relative to herself and Albert; just as Albert does. She constructs an arbitrary and imaginary, mathematical reference frame as part of her calculations; she uses this in her calculations, she doesn't perform measurements in it, or perform calculations in it.

And when she is describing what she measured, she uses her reference frame, i.e. The coordinate system that codifies what she measures.

Her calculations are indeed intended to work out what an implied observer will measure; if by implied observer you mean Henry; but the intention isn't to calculate what he will measure in a different frame of reference, the intention is to calculate what he will measure in the physical world. Indeed, she does conclude that what Henry measures will be different to what she measures; she concludes that the clock Henry uses for measurements will be ticking faster than the clock she is using; Albert also calculates that what Henry measures will be different, but he calculates that the clock Henry uses for his measurements will be ticking slower.

Graph paper
It might help to think of her mathematical reference frame in terms of graph paper; the dot that represents her on the co-ordinate reference frame doesn't actually perform measurements, or calculations, in that graph paper; the little dot that represents her is part of her calculations.

She can draw the reference frame however she pleases, on that graph paper, and use that graph paper to help her make predictions. With the aid of this graph paper she calculates that Henry's clock will tick faster than her and Albert's shared clock, which they both use for measurements, in the physical world.

With the aid of his graph paper, Albert calculates that Henry's clock will be ticking slower, than the clock he and Evelyn use to perform measurements, in the physical world.

She does not conclude this. She concludes that the hypothetical observer will measure Henry's clock as ticking faster than hers. She concludes nothing about any intrinsic, absolute "ticking rate" of clocks. The closes relativity permits is "proper ticking rate", which is defined as the ticking rate of a clock as measured by an observer colocated with the clock.

citrus burst

Roosh, I think you may have accidentally added another extra reference frame to your thought experiment. The frame where Eve performs her calculations

roosh

Morbert wrote: »

And when she is describing what she measured, she uses her reference frame, i.e. The coordinate system that codifies what she measures.

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.

Morbert wrote: »

She does not conclude this. She concludes that the hypothetical observer will measure Henry's clock as ticking faster than hers. She concludes nothing about any intrinsic, absolute "ticking rate" of clocks. The closes relativity permits is "proper ticking rate", which is defined as the ticking rate of a clock as measured by an observer colocated with the clock.

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.

roosh

citrus burst wrote: »

Roosh, I think you may have accidentally added another extra reference frame to your thought experiment. The frame where Eve performs her calculations

Hey citrus; I don't think I have, but I don't really think it would matter either way, because the reference frames are mathematical; they are imaginary.

Evelyn doesn't perform her calculations in a mathematical reference frame; the mathematical reference frame is part of her calculations; calculations which lead her to conclude that Henry's physical clock is ticking faster than her and Albert's shared clock.

Similiarly, Albert doesn't perform his calculations in a mathematical reference frame; the mathematical reference frame is part of his calculations; his calculations lead him to conclude that Henry's clock is ticking slower than his, and Evelyn's, shared clock.