Today Special Relativity dies

[Alkatran]

Case #7

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Alright, let's do this then.

Case #7

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We are watching from a frame at rest. The emitter is moving. The time it takes for light to reach the observer is distance/c (since we are at "rest" compared to them) You could say we are in the observer's frame.

Case #7

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Same thing as moving towards.

Case #7

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Alright, so now the observer is moving and we have SWITCHED FRAMES. We are now observering from the emitters frame and not the observers! This is why you get the same results.

 

[wespe]

Step 4 and 5. DOES matter where the OBSERVER moves. the light will NOT hit the observer at the same time.

I admit you had me confused for a while.

Ok, combine step 2 and 3. There are actually two emitters. They emit light when they meet. The two emitted light beams go side by side, they can be considered one. Note that the emitters are separating.

(o)___________________<-a.b->

But you can't combine step 4 and 5. If you do, the emitters would not be separating and there would be two observers. In short, they are two different perspectives so you can't combine them like that.

 

[Doc Al]

time still frame dependent

Step 1, 2, and 3. doesn't matter where the emitters move, the light will hit the observer at the same time.

Step 4 and 5. DOES matter where the OBSERVER moves. the light will NOT hit the observer at the same time.

I'm not sure what your point is, since in your last two steps you change to a different observer! Of course different frames measure different times.

Call your observer A. If the light flashes from a distance L (as measured by A) then A will observe that the light takes the same time to reach him, regardless of the relative motion of A and the light source.

Your steps 1, 2, and 3 seem to take a view from A's frame. But steps 4 and 5 take a view from a frame in which A is moving. Of course that frame will measure different times. It should be no surprize to you by now that time measurements are frame dependent.

 

[ram1024]

Case #7
Step: 1

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in this setup, we have but one emitter and one observer. keeping it simple-like. In all cases the emitter is going to emit a pulse of light on the first "frame" of the setup. assume uniform motion (no acceleration).

emitter stays the same place towards the observer.

Step: 2

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emitter moves towards the observer.


Step: 3

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emitter moves away from observer.

This is simply a demonstration of what you're saying that light doesn't care what its source does, right? In all 3 cases light would reach the observer at the same time if the first "frame" were synchronized.

now we're going to do what you guys do to things...

Step 4:

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Step 5:

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we're going to take the same set ups from above and simply CHANGE the relative motion so that the emitters are stationary and the observer is the one that's moving. this shouldn't change ANYTHING as far as you guys see it right? these cases should be EXACTLY the same as the ones above, we just changed perspective...

http://home.teleport.com/~parvey/train1.gif

http://home.teleport.com/~parvey/train2.gif

Your steps 1, 2, and 3 seem to take a view from A's frame. But steps 4 and 5 take a view from a frame in which A is moving. Of course that frame will measure different times. It should be no surprize to you by now that time measurements are frame dependent.

that is exactly why picture 2 is NOT the same situation as picture 1. :surprise:

 

[geistkiesel]

Alright Ram, you disagree with the pictures because of the non-simultanity. But remember that picture with space distorted through time? (It was UP (ahead) in the direction of movement, and DOWN (back) the other way) Guess what that means? The train experiences certain "spaces" before an unmoving observer (the ones ahead of the train), but it also experiences certain ones AFTER (the events behind the train). Do you get how that can both perceive them as different YET??

There is simple resolution to this. If you say that the moving observer will detect photons emitted simultaneously in a stationary platform as not being emitted simultaneously in the moving platform. This is a definition of lost simultaneity.

Here is your physical problem.In the stationary frame the photons were emitetd simultaeously. There is no ionstance of time where there were not two photons moving fronm their respective sources.

SR says, that photon B is emitted before photon A, which means the photons did not exist as a pair for a t > 0. There is no SR postuilates that will surpress the existence of the photons emitted simultaneously in the stationary by virtue of measuring the arrival times on the moving frame. Nor does SR provide for 'gost emitters' that would allow for the delayed emission of photons in the moving frame that have already been emitted. simultabneously in he stationary frame. The mere fact that SR predicts the photons were not emitted simultaneously is proof of the intrinsic error and fault and uselessness of SR.

Another problem: The arrival times of the photons will always be sequential in the moving frame, but this has nothing to do with SR. Use red ants or Camarros moving at a constant speed and you will always get sequential arrival times. It is silly beyond conmprehension to have any simultabneous arrival of photons, red ants or Camarros once the midpoint of the photons has been moved. Silly. Silly. Silly.

However, one may work backward from the arrival times and determine if the photons were emitted simultaneously using time and velocity data of the moving frame.

 

[geistkiesel]

I'm not sure what your point is, since in your last two steps you change to a different observer! Of course different frames measure different times.

Call your observer A. If the light flashes from a distance L (as measured by A) then A will observe that the light takes the same time to reach him, regardless of the relative motion of A and the light source.

Your steps 1, 2, and 3 seem to take a view from A's frame. But steps 4 and 5 take a view from a frame in which A is moving. Of course that frame will measure different times. It should be no surprize to you by now that time measurements are frame dependent.

You are assuming time dilation and SR. You also assume frame switching and claim moving frames and stationary frames can b e exchanged for mahematical purposes. Hiowever, trains and stationary platform are not pohysically switchable. It is the trains that are seen to accelerate and move, never the stationary platforms. You people are confused.

How are you going to handle the fact that photons emitted simultaneously in a stationary frame are determined to have been emitted sequentially in the moving frame. The latter tells us that there was some t > 0 when both photons had not been emitted, yet the photons had been emitted in the stationary frame simultaneously. Where was the non-emitted photon when the emitted photon was existing by itself?

 

[Doc Al]

You are assuming time dilation and SR. You also assume frame switching and claim moving frames and stationary frames can b e exchanged for mahematical purposes. Hiowever, trains and stationary platform are not pohysically switchable. It is the trains that are seen to accelerate and move, never the stationary platforms. You people are confused.

You have a long road to travel before you understand Galilean relativity, never mind Einsteinian relativity. Baby steps!

How are you going to handle the fact that photons emitted simultaneously in a stationary frame are determined to have been emitted sequentially in the moving frame. The latter tells us that there was some t > 0 when both photons had not been emitted, yet the photons had been emitted in the stationary frame simultaneously. Where was the non-emitted photon when the emitted photon was existing by itself?

That's only a problem for those old-fashioned folks who still think that simultaneity is absolute. But it's not!

 

[geistkiesel]

Take case two. Suppose each clock is reset to zero when the photons are emitted simultaneously in the picture frame.

Now, note the times at which each clock receives the others photon; they will be different. (as can easily be shown in the picture frame)


If the photons were emitted simultaneously in the clock frame, then the clocks would be synchronized in the clock frame. Furthermore, it takes the same time for the photon to get from A to B as it does from B to A. (Remember that the clocks are stationary in their rest frame!) Thus, the clocks must read the same time when they receive the other's photon.

Since the clocks, in fact, do not read the same time when they receive the other's photon, we conclude that the photons were not emitted simultaneously in the clock frame.

You are clock smart and physics crazy.

If photons are emitted simultaneously in the stationary plartform and are ultimately determined to have been emitted sequentially in the moving frame then there is some time t > 0 that one of gthe photons did not exist. The stationary frame proves the photons were emitted simultabeously there. The stationary frame observed two photons emitted into the universe at all times.

You would have us believe that measuring from a moving platform allows the supression of the existence of photons already emitted?

The moving observer comes along and determines that no, first there was one emitted photon, then later there was another emitted photobn. You just don't have a physical basis to make the assumption of a loss of simultaneity when you require the suppression and later emission of photons that were already emitted in the stationary frame.

Where was the non emitted photon in the moving frame when the emitted photon existed by itself?

As Grounded's posts show, time
dilation and frame shrinking is due to an error of emitting the addition of the velocity of the observer wrt the photon light source. This occurs as when counting the passing "wave lengths" the observer will count fewer/time than if she had included her own velocity, assuming she is moving against the stream form the source. So no wonder one always measures c from any inertial frame.

 

[geistkiesel]

Reality, in SR, is worldlines living in space-time.

Observers don't have their "own reality"; they just measure reality differently.

You mean the reality of suppressing and reviving photons that had already been emitted in the stationary frame? This is the result is it not when you say what was simultaneous in the stationary platform is not simultaneous in the moving frame? B emitted befoe A?

You keep forgetting Grounded's posts that show the intrinsic error in Sr by the lack of adding the observers velocity wrt the source of the photons. So easy to forget isn't it?

 

[ram1024]

omg don't distract MY Doc Al! :D

 

[geistkiesel]

all the clocks are synchronous in the stationary "picture-frame" as hurkyl would call it.

we're determining simultaneity/detection times for the observers which i believe to be immutable (meaning that no matter what frame you choose to look at there will never be a frame where events happening to one observer will change order)

in case 1 we're assuming the train is stationary (i know nothing can be truly stationary in SR, calm down let's not get bogged down)

in case 2 we're moving the train, but because it's a relativistic inertial frame we should get the same results as in case 1 right?

in case 3 we're moving the observer, we SHOULD get a different result than in step 2, right?

that was the main focus of this "gedankenexperiment". Hurkyl caught on a bit too quickly and foiled my plans, and now i can't get anyone to admit where they stand on any of the cases :D

You shouldn't listen to Hurkyl. He is a professional confuser. He will keep you off guard as much as possible.

If and observer and a midpoint in a stationary frame are colocated for an ionstant, it is ludicrous to think the photon heading to th emidpoint fopr a simultabneous arrival there will also arrive simultabneously at the point that had been colocated bu that has now moved. Yet this is how SR defines loss of simultabeity. There is no "speed of light " implications in the scenario just discussed.Absolutely none.

You have him right here Ram1024. Ask how can two photons emitted simultaneously suddenly change to one photon emitted, then later, another photon emitted? First there were two photons in the universe, then by some fancy mathematics, one photon gets suppressed in a ghost state until the moving observer is ready to let the photon into her reality.

All this time the photons are speeding toward the midpoint of the sources.

 

[Doc Al]

case #7 again

we're going to take the same set ups from above and simply CHANGE the relative motion so that the emitters are stationary and the observer is the one that's moving. this shouldn't change ANYTHING as far as you guys see it right? these cases should be EXACTLY the same as the ones above, we just changed perspective...

Still not getting your point. What do you mean "shouldn't change anything"? If you change frames, you have changed the time measurement.

Of course, what I THINK you are struggling with is this: If all we did was change perspectives, then nothing should change right? Well, for that observer (A?) in your diagrams NOTHING HAS CHANGED. It's only us, the outside observers who have changed our perspective and thus our time measurements.

Time measurements ARE a matter of perspective (in a sense). So if you are talking time, then perspective matters. Just like if you are talking about what you see, then it matters where you stand.

Of course if you are thinking: Something's funny here. How can REALITY change if all I'm doing is changing perspective? Ah... now you're beginning to see the light? ( ) In relativity (and in the real world) time and distance are frame dependent--but there are quantities that are not frame dependent! In some sense those quantities are more "real" that our frame-dependent times and distances. The "real" physical laws governing the world can't be frame dependent, right? Right! That's the entire point of SR. That's why physical laws must be "Lorentz invariant".

that is exactly why picture 2 is NOT the same situation as picture 1. :surprise:

If by "picture" you mean those animations, then OF COURSE they are different--they are views from different frames. But note that the physical reality--the fact that the lights meet the train at the same time & place--is still true in both views!

 

[ram1024]

if in order to make light constant you need to break other "Reality" laws such as Simultaneity, Absolute time, Absolute space, and True universal rest, then i don't need it.

show me the data. you guys messed up your calculations somewhere down the line

 

[geistkiesel]

Yes, it doesn't matter whether the sources are tied to the train or not, because speed of light is independent of its source.

So, what is the difference between your case #2 and #3?

The difference is: in case #2, the photons are emitted simultaneously relative to the emitters (which means also relative to the man). In case #3, the photons are emitted simultaneously relative to the emitters (as you said this is always the case), therefore they cannot be emitted simultaneously relative to the man. See, it matters in which frame they are emitted simultanously. So how do we know in which frame? It is the frame that the clocks (tied to the emitters) were synchronized in. And how were they synchronized? By sending two light signals to the emitters from the midpoint in that frame. Naturally it follows that: after this synchronization, simultaneous light signals will be received at the same time only at the midpoint in that frame (not some other frame where the midpoint moves [is somewhere else when the photons meet]).

Pure SR scientific smog. How can two photons emitted simultaneously in one frame, now turn into photons emitted sequentially when observed in a moving frame? What law of physics are you using to say that a photon once emitted into the universe, is now suppressed from existience because the moving observer's mathematics tells her that is the reality? There must be a time in the moving frame, some t > 0 when there was only one photon in the universe if Sr is true. A photon in the universe is what is meant by "emitted", as in "emitted simultaneously".

You've still got the trap of mathematics tied aound your neck I see. You shuld try studying physics.

Grounded's posts have negated all your assumptions regarding time and space dilations. Why do you persist?

 

[ram1024]

keep in mind that light speed is also governed by that Maxwell equation you brought up earlier Permitivity and Permeability or whatever.

nowhere in that equation does it say "perspective". . .

 

[Doc Al]

if in order to make light constant you need to break other "Reality" laws such as Simultaneity, Absolute time, Absolute space, and True universal rest, then i don't need it.

Whose "laws" are those? You're living in the past, man.

show me the data. you guys messed up your calculations somewhere down the line

Are you joking? We have libraries of data! All of modern physics is based upon SR. Entire fields of physics would make no sense without it. It's been tested so many times that it's hard to take these threads seriously.

 

[Doc Al]

keep in mind that light speed is also governed by that Maxwell equation you brought up earlier Permitivity and Permeability or whatever.

nowhere in that equation does it say "perspective". . .

Right! Light speed is something that is NOT a matter of "perspective". It's an invariant.

 

[Doc Al]

geistkiesel confused? Could it be?

You shouldn't listen to Hurkyl. He is a professional confuser.

I wouldn't want to take anything away from Hurkyl's professional rep, but you must admit that you are pretty easy to confuse.

 

[ram1024]

Right! Light speed is something that is NOT a matter of "perspective". It's an invariant

it's completely perspective.

take for a moment everything we KNOW to be real, distances, time, simultaneity. these are things we use every day.

how often do we travel at significant "relativistic speeds" ?

never.

so postulating that doing so would make distance/time/simultaneity UNreal is completely unreasonable.

let's work from reality for a moment and move in the right direction this time. from what we know of reality, what can we deduce from experiments calculating light speed as constant.

A. people don't know how to calculate it correctly
B. their perceptions get screwed up
C. they have no idea what "frame" they're working in <a laughable excuse, as the rest of the world works in the "reality frame">
D. the data is wrong
E. probably all of the above.

put lightly, what good does it do ANY of us to say something is 50 light years away if when we go to travel that distance our years aren't the same, nor is the distance that light travels in a year the same BECAUSE our years are different?

 

[Doc Al]

take for a moment everything we KNOW to be real, distances, time, simultaneity. these are things we use every day.

how often do we travel at significant "relativistic speeds" ?

never.

so postulating that doing so would make distance/time/simultaneity UNreal is completely unreasonable.

So we're back to stating that "relativity can't be true because it contradicts what I know is true from common sense". (Of course, relativity is perfectly consistent with your actual everyday experience--since our speeds are so low, the "strange" SR effects aren't evident.)

The most we can do in a thread like this is explain what relativity says and show why it's not contradictory with itself or anything you've actually observed. So if you want to understand relativity, then fine. But if all you want to do is deny relativity, then ... :zzz:

 

[Hurkyl]

I was trying to make things easy for you. But... if you insist on accelerating the train, just be sure to do it right. Accelerate each piece of the train uniformly (according to observers on the train) so that each piece is always moving together according to observers on the train. Do this right and the train will be accelerated and the clocks will not be affected (as far as folks on the train can tell).

That's not quite correct; the observers on the train will still observe the front clock running fast and the back clock running slow. Heuristically, recall that in an accelerated frame, clocks in the direction of acceleration run fast, and clocks on the other side run slow.

As a concrete example, consider this case.

The (x,t) coordinates of the left edge of the train is given by:
x = 1s * c * cosh (tau / 1s)
t = 1s * sinh (tau / 1s)

And the right edge is given by
x = 2s * c * cosh (tau / 2s)
t = 2s * sinh (tau / 2s)

You can check that:

tau is the proper time along these worldlines.
The lines of simultaneity for the observers at each end are lines that pass through the origin.
The train always has length (1s * c) according to the observers. (as measured along a line of simultaneity)
The right clock always reads twice the left clock. (again, according to the lines of simultaneity)


In general, analyzing from a stationary frame, if the train is accelerated towards the right, and you choose two pairs of events that train observers think occur at the same time, then the left edge will have a greater space displacement and lesser time displacement than the right edge; the proper time experienced by the left edge cannot be as much as that of the right edge.

 

[Hurkyl]

take for a moment everything we KNOW to be real, distances, time, simultaneity. these are things we use every day.

how often do we travel at significant "relativistic speeds" ?

never.

so postulating that doing so would make distance/time/simultaneity UNreal is completely unreasonable.

This seems exactly backwards to me. We never travel at significant "relativistic speeds", so we most certainly don't "KNOW" anything about it.


The only reason we assumed what we "KNOW" about slow speeds carries over to fast speeds was because there was no reason to think otherwise. With the advent of Maxwell's equations and Special Relativity, now there is reason to think otherwise.

At the current juncture in time, there has never been any experimental evidence that what we "KNOW" about slow carries over to fast... and overwhelming evidence that SR is correct. The unreasonable thing is to cling to prerelativistic assumptions.

put lightly, what good does it do ANY of us to say something is 50 light years away if when we go to travel that distance our years aren't the same, nor is the distance that light travels in a year the same BECAUSE our years are different?

It doesn't. But it does do good to say something is 50 light-years away according to a specified coordinate chart.

 

[Doc Al]

accelerating that train

That's not quite correct; the observers on the train will still observe the front clock running fast and the back clock running slow. Heuristically, recall that in an accelerated frame, clocks in the direction of acceleration run fast, and clocks on the other side run slow.

This is why I didn't want to introduce acceleration, since the final reading of those clocks will depend on how you do it. I was envisioning a step-by-step process where a small thrust is given to each part of the train simultaneously (according to the rest frame of the train). Each small thrust must be given at the same time in the current rest frame of the train. If you do that, wouldn't you agree that observers on the train would always measure the proper length of the train to be unchanged and the clocks would still be synched? Meaning: fire off that light in the middle and both clocks would still read the same time when the photons hit. Am I wrong?

In general, analyzing from a stationary frame, if the train is accelerated towards the right, and you choose two pairs of events that train observers think occur at the same time, then the left edge will have a greater space displacement and lesser time displacement than the right edge; the proper time experienced by the left edge cannot be as much as that of the right edge.

I think in your example you've accelerated the train uniformly according to the rest frame of the track. In which case, yes, the clocks would lose synch even in their own final rest frame.

 

[geistkiesel]

So we're back to stating that "relativity can't be true because it contradicts what I know is true from common sense". (Of course, relativity is perfectly consistent with your actual everyday experience--since our speeds are so low, the "strange" SR effects aren't evident.)

The most we can do in a thread like this is explain what relativity says and show why it's not contradictory with itself or anything you've actually observed. So if you want to understand relativity, then fine. But if all you want to do is deny relativity, then ... :zzz:

Prove it. Do you understand the request? Prove it? Where is the missing photon?

Show from the postulates of SR that where two photons are emitted simultaneously in a stationary frame that a moving frame observer will observe or determine, the photons were emitted sequentially, non-simultaneously, and explain where the photon that was second to appear was wrt the stationary frame, the moving frame the universe?

Are the photons in the stationary frame the same photons in the moving frame?

DOc Al why don't you stop your clowing and posturing, it isn't close to physics and it isn't even in the same zip code as funny.

 

[geistkiesel]

keep in mind that light speed is also governed by that Maxwell equation you brought up earlier Permitivity and Permeability or whatever.

nowhere in that equation does it say "perspective". . .

Keep in mind that using Maxwell's equations and disregarding the observers speed wrt the source of the EM radiation will result is the sillinness that the speed of light is constant when measured in all inertial framess. Light slows down mass shrinkles, loss of simultaneity, siliness in the universe. RAM1024 you must read grounded's papers again, and learn them. Everything you have been saying will glow like a warm ray of peace at last.

 

[geistkiesel]

Whose "laws" are those? You're living in the past, man.

Are you joking? We have libraries of data! All of modern physics is based upon SR. Entire fields of physics would make no sense without it. It's been tested so many times that it's hard to take these threads seriously.

When did you decide that including the observers velocity was not required? Include the observer's velocity and your precious constant speed of light will remain subject to the obvious that the relative velocity of the speed of light is easily measured.

Doc Al's physics is measured in the width of his smirk.

 

[geistkiesel]

Still not getting your point. What do you mean "shouldn't change anything"? If you change frames, you have changed the time measurement.

Of course, what I THINK you are struggling with is this: If all we did was change perspectives, then nothing should change right? Well, for that observer (A?) in your diagrams NOTHING HAS CHANGED. It's only us, the outside observers who have changed our perspective and thus our time measurements.

Time measurements ARE a matter of perspective (in a sense). So if you are talking time, then perspective matters. Just like if you are talking about what you see, then it matters where you stand.

Of course if you are thinking: Something's funny here. How can REALITY change if all I'm doing is changing perspective? Ah... now you're beginning to see the light? ( ) In relativity (and in the real world) time and distance are frame dependent--but there are quantities that are not frame dependent! In some sense those quantities are more "real" that our frame-dependent times and distances. The "real" physical laws governing the world can't be frame dependent, right? Right! That's the entire point of SR. That's why physical laws must be "Lorentz invariant".

If by "picture" you mean those animations, then OF COURSE they are different--they are views from different frames. But note that the physical reality--the fact that the lights meet the train at the same time & place--is still true in both views!

Your changing perspectives is a ruse. You switch views when it would be a physical impossibility to do that in a real physical situation. You are dummer than a fence post if you believe that your precious mathematical models are not subject to limitations. Just because your math says it can be done does not prove it is physically possible. Trains move, stationaary platforms are stationary throughout the course of events. Change you perspective and the physics will follow? Is this the secret of SR?

You people are going to be chewing on Grounded's thesis for quite a spell.

When a moving frame observer determines simultanously emitted photons in a stationary frame were sequentially emitted in the moving frame, then where did the nonemitted photon go, or where was it when the photons were sequentially emitted in the moving frame? You must simply signore the stationary platform as nonexistent and the only reality left for consideration is the one your moving observer perceives?

 

[geistkiesel]

Right! Light speed is something that is NOT a matter of "perspective". It's an invariant.

Regardless of ME measuring the relative speed of light in all inertial frames will provide just that: A Constant speed of light and an observer moving wrt the photon source velocity. The speed of light is invariant but the measurement of the speed of light is limited only by the imagination of experimental physicists.

 

[Doc Al]

Prove it. Do you understand the request? Prove it? Where is the missing photon?

You are the one claiming to have lost a photon. What did you do with it? And where were the photons before you turned on the light?

Show from the postulates of SR that where two photons are emitted simultaneously in a stationary frame that a moving frame observer will observe or determine, the photons were emitted sequentially, non-simultaneously, and explain where the photon that was second to appear was wrt the stationary frame, the moving frame the universe?

Again? Do you even bother to read what I've written in all the threads we've been through? (I know you don't understand it, but at least make an effort to read it.) Read through them again. You'll see that I've calculated exactly where everything is according to everyone. I'm not going to do it again, until YOU give it a try.

Are the photons in the stationary frame the same photons in the moving frame?

Not sure what you're asking here. The photons just are; they don't belong to a frame. Instead of photons, we'd be better off thinking of pulses of light (containing many photons). These pulses emanate from the light sources and can be detected in either frame. (Obviously, M' detects different photons than M. But don't get hung up on that detail. Consider them as both viewing the same pulses of light.)

DOc Al why don't you stop your clowing and posturing, it isn't close to physics and it isn't even in the same zip code as funny.

You know nothing about physics, poor geistkiesel.

 

[Hurkyl]

If you do that, wouldn't you agree that observers on the train would always measure the proper length of the train to be unchanged and the clocks would still be synched? Meaning: fire off that light in the middle and both clocks would still read the same time when the photons hit. Am I wrong?

Yah... I started considering the situation earlier when Ram considered synching the clocks then accelerating the train. I could quickly see that it was obvious that the answer depends on how you do it, so I wondered just how you would have to do it to keep the clocks synched in their own frame.

Doing all of the analysis in the stationary frame, if the train is accelerated towards the right, then no matter how the train gets acceelrated, if I consider two points that correspond to the same time in the train's frame, the right point has a greater temporal displacement and a lesser spatial displacement than the left point. Thus, if compute the proper time difference for each of the ends, the right end must have experienced more proper time than the left end.


For my example, if we switch to units where c = 1 (for simplicity), we consider the case where the left edge of the train lies along the worldline:

r(tau) = < cosh tau, sinh tau >

(exercise: check that tau is, indeed, the proper time along the worldline)

The velocity is given by

v(tau) = < sinh tau, cosh tau >

Thus, for the observer on the left edge his line of simultaneity corresponding to his proper time a is parallel to

< cosh a, sinh a >

because this is the unit vector orthogonal to v(a). The line is given, parametrically, by:

l(d) = r(a) + d < cosh a, sinh a>
= <cosh a, sinh a> + d <cosh a, sinh a>
= <(d+1) cosh a, (d+1) sinh a>

where d is the proper distance along the line of simultaneity. (aka the distance measured by the observer on the left edge of the train)

Setting d = 1 (corresonding to the train being constant length) and letting a vary gives us the worldline of the right edge:

r(s) = <2 cosh s, 2 sinh s>

A little calculus shows us that s is twice the proper time for the right edge.


In summary, according to the observer on the left edge of the train, the length of the train remains constant, but the clock on the right edge is running at double speed.


On a side note, the class of worldlines:

r(tau) = <k cosh (tau / k), k sinh (tau / k)>

has the property that each of them remain unchanged by any Lorentz boost that fixes the origin; in particular, these (and their translates) are the worldlines of observers that feel a constant acceleration.

 

[Janus]

if in order to make light constant you need to break other "Reality" laws such as Simultaneity, Absolute time, Absolute space, and True universal rest, then i don't need it.

Your loss.

You know, there is a group of people who refuse to consider breaking the "Reality" law of a true universal direction of up and down, They are called the "Flat Earth Society".

Actually that last one, 'True universal rest", is funny, since it hasn't been considered a "law of Reality" since the time of Galileo.

 

[ram1024]

Doing all of the analysis in the stationary frame, if the train is accelerated towards the right, then no matter how the train gets acceelrated, if I consider two points that correspond to the same time in the train's frame, the right point has a greater temporal displacement and a lesser spatial displacement than the left point. Thus, if compute the proper time difference for each of the ends, the right end must have experienced more proper time than the left end.

the only reason you would think that because your measure of simultaneity is wholly derived from observation impact.

to make it simple, an acceleration from the right just creates more distance covered in comparison to the non-accelerated train. it's this distance that must be accounted for in determining this "reality" compared to the previous non-accelerated one.

the "point of simultaneity" shifts to the left, the clocks don't lose their synchronization, light speed doesn't change, just you're moving at a different speed toward the light and it is intercepted faster.

no length contraction, no "lost simultaneity", no time dialation.

just a change in relative perspective easily corrected using the proper mathematics.

SR is ridiculous :zzz:

 

[Hurkyl]

the only reason you would think that because your measure of simultaneity is wholly derived from observation impact.

No, the reason I think that was because I was applying (Minowski) geometry.

 

[ram1024]

Actually that last one, 'True universal rest", is funny, since it hasn't been considered a "law of Reality" since the time of Galileo

yet true relative rest DOES exist, we use it daily. something CAN exist completely stationary relative to something else.

the universe as a whole is comprised of every object within it. at any given instant if you averaged the locations of every atom/molecule/lepton/quark/whatever within the universe you would get the universal center. it is a consensus point where everything in the universe takes motion about that axis. anyone with omniscient information would agree with you.

Relative to that location exists universal rests. determined purely on a mathematical basis.

 

[ram1024]

No, the reason I think that was because I was applying (Minowski) geometry.

but the path you took to your conclusion was towards SR. you had other options. your calculations did not retain simultaneity at the center of the train, so immediately you jumped to the conclusion that simultaneity was at fault.