06-05-2012, 11:35 #1 roosh Registered User   Join Date: Sep 2009 Posts: 1,977 Question on time dilation Just wondering about the following scenario. It's probably easiest to explain in the context of this explanation of Lorentz contractions 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.
06-05-2012, 14:51   #2
Morbert
Registered User

Join Date: Sep 2004
Location: What?
Posts: 3,105
Quote:
 Originally Posted by roosh Just wondering about the following scenario. It's probably easiest to explain in the context of this explanation of Lorentz contractions 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.

07-05-2012, 01:29   #3
roosh
Registered User

Join Date: Sep 2009
Posts: 1,977
Quote:
 Originally Posted by Morbert 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?

Last edited by roosh; 07-05-2012 at 05:13.

07-05-2012, 15:06   #4
Morbert
Registered User

Join Date: Sep 2004
Location: What?
Posts: 3,105
Quote:
 Originally Posted by roosh 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.

08-05-2012, 05:11   #5
roosh
Registered User

Join Date: Sep 2009
Posts: 1,977
Quote:
 Originally Posted by Morbert 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?

Last edited by roosh; 08-05-2012 at 07:22.

08-05-2012, 19:13   #6
Morbert
Registered User

Join Date: Sep 2004
Location: What?
Posts: 3,105
Quote:
 Originally Posted by roosh 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.

09-05-2012, 01:39   #7
roosh
Registered User

Join Date: Sep 2009
Posts: 1,977
Quote:
 Originally Posted by Morbert 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.

09-05-2012, 16:05   #8
Morbert
Registered User

Join Date: Sep 2004
Location: What?
Posts: 3,105
Quote:
 Originally Posted by roosh 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.

10-05-2012, 01:11   #9
roosh
Registered User

Join Date: Sep 2009
Posts: 1,977
Quote:
 Originally Posted by Morbert 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.

Last edited by roosh; 10-05-2012 at 01:14.

10-05-2012, 12:13   #10
Morbert
Registered User

Join Date: Sep 2004
Location: What?
Posts: 3,105
Quote:
 Originally Posted by roosh 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.

10-05-2012, 13:10   #11
roosh
Registered User

Join Date: Sep 2009
Posts: 1,977
Quote:
 Originally Posted by Morbert 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.

Last edited by roosh; 10-05-2012 at 13:18.

10-05-2012, 13:40   #12
Morbert
Registered User

Join Date: Sep 2004
Location: What?
Posts: 3,105
Quote:
 Originally Posted by roosh 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.

10-05-2012, 14:08   #13
roosh
Registered User

Join Date: Sep 2009
Posts: 1,977
Quote:
 Originally Posted by Morbert 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.

Last edited by roosh; 10-05-2012 at 14:30.

10-05-2012, 15:28   #14
Morbert
Registered User

Join Date: Sep 2004
Location: What?
Posts: 3,105
Quote:
 Originally Posted by roosh 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.

11-05-2012, 00:15   #15
roosh
Registered User

Join Date: Sep 2009
Posts: 1,977
Quote:
 Originally Posted by Morbert "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.

Last edited by roosh; 11-05-2012 at 05:34.