What's wrong with this so-called paradox?

[Strange]

I made no such claim.

 

Then maybe you need to explain what you mean more clearly because I obviously don't understand. Even after reading it again. You appear to be saying that Newton's laws of motion are not invariant with respect to location or speed. So what do you really mean?

[Robittybob1]

Instead of dealing with photons deal with balls and no wind resistance. If a ball was from thrown the ends of the train would the balls reach the center at the same time? "yes" if thrown from within the moving train but "no" if they were thrown at the same time from the right position on platform into the moving train. But if the train was stationary at the platform they would. So the situation is different if the train is moving.

Photons fired from two flashlight devices equidistant from the center of the platform (flash occurs when the train is dead center), so light would travel the length of the train at the same rate whether inside the train or outside of it. So when the middle of the train aligns with the center of the platform and the lights flash so that light can both move inside the train (shines through front and back windows as well as along the platform, the observer will see the lights flash at the same time but the person in the train I believe will see the light from the front of the train first.

Because light is only traveling at c it didn't matter if the flashlights were on the train or the platform.

Could you see the logic of this? You asked me to explain it but you have not commented. I know it changes things around a bit.

Edited January 31, 2015 by Robittybob1

[MigL]

Don't want to wade into studiot's and Strange's discussion, but as for the OP...

 

Syncronization is equivalent to simultaneity. So just like simultaneity it is not valid across frames .

Things can only be syncronized within a frame.

[Robittybob1]

Don't want to wade into studiot's and Strange's discussion, but as for the OP...

 

Syncronization is equivalent to simultaneity. So just like simultaneity it is not valid across frames .

Things can only be syncronized within a frame.

A flashlight goes off on the far rear corner of the train and light from that goes along the train on the inside and along the outside.

Does the wavefront of light travel side by side both inside and out?

But as the observer inside the train is moving forward with the light front, he won't be seeing the flash at the same time as the observer on the platform, will he?

And if there were two flashlights attached to the train that go off so that the platform observer sees them simultaneously the observer on the train will see the front flash before the rear flash. Agree or disagree?

The observer in the train will not believe they went off simultaneously, but it can be explained if he realises he is moving forward and light travels at c to both observers.

[Strange]

But as the observer inside the train is moving forward with the light front, he won't be seeing the flash at the same time as the observer on the platform, will he?

 

That is a problem right there: what does "at the same time" mean when people are in different frames of references? That is why you need to be very careful when posing questions.

 

 

And if there were two flashlights attached to the train that go off so that the platform observer sees them simultaneously the observer on the train will see the front flash before the rear flash. Agree or disagree?

The observer in the train will not believe they went off simultaneously, but it can be explained if he realises he is moving forward and light travels at c to both observers.

 

Correct.

Edited February 1, 2015 by Strange

[Robittybob1]

 

That is a problem right there: what does "at the same time" mean when people are in different frames of references? That is why you need to be very careful when posing questions.

 

 

Correct.

In this case the event is synchronized by the two observers passing each other, middle of the train meets middle of platform, or done by timing devices equidistant from the center.

[Janus]

In this case the event is synchronized by the two observers passing each other, middle of the train meets middle of platform, or done by timing devices equidistant from the center.

Synchronized how? Let's say that each frame has its own set of clocks each synchronized according to that frame. Now the two observers pass each other at the moment their clock's read 12 noon. According to each observer all the other clocks in his frame also read 12 noon at that same instant. However, each observer will also note that the clocks in the other frame not not all read 12 noon. Clocks in one direction will read earlier than 12 noon and clocks in the other will read later. The further apart the clocks, the larger the difference.

 

For example, in the platform frame the midpoint observer notes that his and the midpoint train observer's clock reads 12 noon at the time of there passing. There are also two clocks 10 km to either side of him sitting on the embankment, that he has synchronized to his own. The midpoint train observer also has clocks spread out along his train that he has synchronized to his clock. If the Embankment clocks record the reading of the train clock directly opposite it when it itself reads 12 noon, they will record the following:

The platform clock and the clock of the midpoint observer on the train will read 12 noon.

The clock 10 km in the direction of the train's travel will read 12 noon and the clock directly opposite on the train will read sometime before 12 noon.

The clock 10 km in the other direction will read 12 noon and the clock directly opposite it will read sometime after 12 noon.

 

If we switch to the trains frame:

 

The mid point of the train clock and the platform clock will both read 12 noon.

The clock x number of cars towards the front of the train will read 12 noon and the embankment clock directly opposite it will read sometime after 12 noon.

The clock x number of cars towards the rear of the train will read 12 noon and the embankment clock directly opposite it will read sometime before 12 noon.

[Robittybob1]

Synchronized how? Let's say that each frame has its own set of clocks each synchronized according to that frame. Now the two observers pass each other at the moment their clock's read 12 noon. According to each observer all the other clocks in his frame also read 12 noon at that same instant. However, each observer will also note that the clocks in the other frame not not all read 12 noon. Clocks in one direction will read earlier than 12 noon and clocks in the other will read later. The further apart the clocks, the larger the difference.

 

For example, in the platform frame the midpoint observer notes that his and the midpoint train observer's clock reads 12 noon at the time of there passing. There are also two clocks 10 km to either side of him sitting on the embankment, that he has synchronized to his own. The midpoint train observer also has clocks spread out along his train that he has synchronized to his clock. If the Embankment clocks record the reading of the train clock directly opposite it when it itself reads 12 noon, they will record the following:

The platform clock and the clock of the midpoint observer on the train will read 12 noon.

The clock 10 km in the direction of the train's travel will read 12 noon and the clock directly opposite on the train will read sometime before 12 noon.

The clock 10 km in the other direction will read 12 noon and the clock directly opposite it will read sometime after 12 noon.

 

If we switch to the trains frame:

 

The mid point of the train clock and the platform clock will both read 12 noon.

The clock x number of cars towards the front of the train will read 12 noon and the embankment clock directly opposite it will read sometime after 12 noon.

The clock x number of cars towards the rear of the train will read 12 noon and the embankment clock directly opposite it will read sometime before 12 noon.

That surely can't be right. if all the train clocks are reading identical times, and all the platform clocks are reading identical times, if at the mid point both agree it is 12:00 then I can't see why at each point along the train a clock there won't read exactly the same time as one on the platform opposite it.

Edited February 1, 2015 by Robittybob1

[studiot]

The end clocks on the moving train can't be opposite the platform clocks in either frame since the train appears shortened in the platform frame.

Edited February 1, 2015 by studiot

[Janus]

The end clocks on the moving train can't be opposite the platform clocks in either frame since the train appears shortened in the platform frame.

It is perfectly possible for things to be set up so that the ends clocks of the train and the platform clocks align in either frame ( you just have to have a train with a proper length such that its length contracted length is equal to the proper distance between the platform clocks), they just can't be made to align in both frames. This is why I specified that there was a string of clocks in the train frame. The clocks that are opposite the embankment clocks when the embankment frame clocks read 12 noon in the platform frame, are not the same pair of clocks that read 12 noon in the train frame when I made the comparison from that frame.

 

Now the readings on any two clocks as they pass each other will be agreed upon by both frames. If an embankment clock notes that as it reads 12 noon, the train clock passing it reads 11:59, that same train clock will note that when it reads 11:59, the embankment clock it is passing reads 12 noon.

 

That surely can't be right. if all the train clocks are reading identical times, and all the platform clocks are reading identical times, if at the mid point both agree it is 12:00 then I can't see why at each point along the train a clock there won't read exactly the same time as one on the platform opposite it.

That's the whole point behind the Relativity of Simultaneity. Events that are simultaneous in one frame (all the clocks in that frame reading 12 Noon), are not simultaneous as measured from the other train. Thus the platform frame will not measure all the clocks in the train frame as all reading the same time, even though they do in the train frame. Until you can wrap your head around this concept, you will have no chance what-so-ever of ever coming to grips with Relativity.

[StringJunky]

...Until you can wrap your head around this concept, you will have no chance what-so-ever of ever coming to grips with Relativity. Reality.

[Robittybob1]

The end clocks on the moving train can't be opposite the platform clocks in either frame since the train appears shortened in the platform frame.

Some say Length Contraction is not physical others do, so at the moment why do you need length contraction, and besides when was the synchronization was done? Some say before others say after the train accelerated.

It is perfectly possible for things to be set up so that the ends clocks of the train and the platform clocks align in either frame ( you just have to have a train with a proper length such that its length contracted length is equal to the proper distance between the platform clocks), they just can't be made to align in both frames. This is why I specified that there was a string of clocks in the train frame. The clocks that are opposite the embankment clocks when the embankment frame clocks read 12 noon in the platform frame, are not the same pair of clocks that read 12 noon in the train frame when I made the comparison from that frame.

 

Now the readings on any two clocks as they pass each other will be agreed upon by both frames. If an embankment clock notes that as it reads 12 noon, the train clock passing it reads 11:59, that same train clock will note that when it reads 11:59, the embankment clock it is passing reads 12 noon.

 

That's the whole point behind the Relativity of Simultaneity. Events that are simultaneous in one frame (all the clocks in that frame reading 12 Noon), are not simultaneous as measured from the other train. Thus the platform frame will not measure all the clocks in the train frame as all reading the same time, even though they do in the train frame. Until you can wrap your head around this concept, you will have no chance what-so-ever of ever coming to grips with Relativity.

Am I allowed to say I think you misunderstood me? We now have multiple observers and multiple clocks, all the clocks on the moving train read the same time, and all the clocks on the platform have the same time. So if the center points both agree it is 12:00 each opposing clock set should be agreeing with each other.

 

I understand no one will agree as to the time of a particular event, but we are NOT describing the event, but just saying the opposing clocks will all agree at 1 time only and thereafter won't agree any more.

[studiot]

 

Janus

It is perfectly possible for things to be set up so that the ends clocks of the train and the platform clocks align in either frame ( you just have to have a train with a proper length such that its length contracted length is equal to the proper distance between the platform clocks), they just can't be made to align in both frames.

 

I didn't say otherwise, but since that was not a permissible setup I did not consider it.

 

Perhaps didn't make a very full statement, which led to misunderstanding.

 

All three train clocks are specified to be in physical and temporal alignment at rest and side by side with the three platform clocks at the start of the experiment.

 

However this leads directly to the issue Strange and I have been discussing.

 

Two light signals travelling at (obviously) the same speed for different times (measured in the same frame) must perforce have travelled different distances to arrive together at the same point. It would be perverse to measure the times in one frame and the distances in another.

Equally clearly if they travelled for different times and arrived at some point together, they cannot have started at the same time in that frame.

Edited February 2, 2015 by studiot

[phyti]

It's a question of simultaneity. Maybe I wasn't clear in #14.

The clocks are synchronized in the ship/train at rest, which is equivalent to ground time.

When the ship is moving relative to the ground, its axis of simultaneity is skewed (at an angle in a spacetime graphic).

If the viewer on the ship polls the end clocks with light, the clocks will return different readings. Per SR the viewer must establish a relative synchronization of of the end clocks using light signals. The procedure is described in the beginning of the 1905 paper.

[whiskers]

Hi - here is related simple example, still a bit counterintuitive to me.

* Train A and Train B are traveling on the same track at the same velocity and agree that their clocks are synchronized.

* They have agreed to both exert thrust X at what they both agree is clock time Y which will accelerate them both.

* They find after the thrust event at time Y that their clocks no longer appear to be synchronized.

[xyzt]

Hi - here is related simple example, still a bit counterintuitive to me.

* Train A and Train B are traveling on the same track at the same velocity and agree that their clocks are synchronized.

* They have agreed to both exert thrust X at what they both agree is clock time Y which will accelerate them both.

* They find after the thrust event at time Y that their clocks no longer appear to be synchronized.

...because they applied the thrust synchronously in THEIR co-moving place but NOT in ANY other frame.

[whiskers]

...because they applied the thrust synchronously in THEIR co-moving place but NOT in ANY other frame.

Yes so they get more and more out of synch with repeated thrusts, and this becomes analogous to an accelerating spaceship where the clock at the rear and the clock at the front are running at different rates, as near as they can tell.

[md65536]

Yes so they get more and more out of synch with repeated thrusts, and this becomes analogous to an accelerating spaceship where the clock at the rear and the clock at the front are running at different rates, as near as they can tell.

Which I think is equivalent to two clocks at different gravitational potentials in a uniform gravitational field, which also run at different rates relative to each other.

Edited February 9, 2015 by md65536

[phyti]

Some say Length Contraction is not physical others do, so at the moment why do you need length contraction, and besides when was the synchronization was done? Some say before others say after the train accelerated.

Am I allowed to say I think you misunderstood me? We now have multiple observers and multiple clocks, all the clocks on the moving train read the same time, and all the clocks on the platform have the same time. So if the center points both agree it is 12:00 each opposing clock set should be agreeing with each other.

 

I understand no one will agree as to the time of a particular event, but we are NOT describing the event, but just saying the opposing clocks will all agree at 1 time only and thereafter won't agree any more.

In the M frame, the train is moving to the right, with the viewer T at center, and B and F back and front emitter/detectors. B and F emit simultaneous signals in the M frame, which are simultaneous with the ends of the train, but will not arrive simultaneously for T.

In the process of accelerating to a constant speed, the T frame has an altered symmetry. If T polls the F and B clocks, B’ and F’, they show different values. This is a consequence of light propagation speed being constant in space. If T synchs the clocks to his center clock, according to the SR convention, then he has “relative simultaneity”, and perceives B’ and F’ as simultaneous. Notice the path lengths are equal, but out of synch, depending on their origin. Simultaneity is a function of speed, not a property of the frame.

[whiskers]

To understand how truly strange length contraction is, you have to contemplate the "ladder paradox"

https://en.wikipedia.org/wiki/Ladder_paradox

 

At the beginning it is easy to forget that length contraction is so closely related to the relativity of simultaneity - there's no separating them.

 

It might be easier to remember this if you think of the object as moving or changing. Let's say that for a viewere on the train, a red book pops into existence in his hand, and then gradually turns greener, then disappears. From a perspective of a viewer on the station, here is what is determined to be the order of events:

 

* the part of the book towards the back of the train pops into existence

* parts of the book forward from there appear until the frontmost part of the book has popped into existence

 

* the part of the book towards the back of the train starts to turn green

* then parts of the book forward from there turn greener until the frontmost part of the book has turned green

 

* the part of the book towards the back of the train pops out of existence

* then parts of the book forward from there disappear until the frontmost part of the book has disappeared

 

When you think of a relatively stable object such as a train, a spaceship, or a ladder experiencing "length contraction" it is easy to forget this at first and it can be confusing.

[whiskers]

(oh also forgot to state the obvious: the viewer in the station will determine that the book - during that period of time it is all present - will appear to be shorter in the direction of motion than the observer in the train does)

[pavelcherepan]

1) Does the middle clock stop?

2) What is the correct line of reasoning leading to this conclusion?

3) What is the fault in the reasoning presented in post#1? Note this is the reasoning, not the statement of conditions.

 

Of the three questions the first one is now answered, yes the clock stops.

 

To answer the second and third it is good to point out that analysis and calculations are best done entirely in a single frame of reference and that this is possible in this case since the three clocks are in a common frame.

Mixing information from different frames so easily leads to incorrect conclusions (I'm sure we've all done it).

 

At this point it would be nice to hear from gib65

 

I might be all wrong but I see the situation as follows (and correct me if I'm wrong):

 

1) The train is at rest and clocks are synchronized

2) The train starts accelerating. Let's assume the acceleration is constant. Then by the equivalence principle of GR we can imagine both clocks and the middle observer being suspended at the same height above the gravitating mass that's big enough to account for the proper acceleration as can be measured by the accelerometer that the middle observer has on him/her (let's assume he/she does).

3) Both the front, rear and middle clocks will experience gravitational time dilation, but as the acceleration is the same for all of them all three clocks will still be synchronized. At the same time they (clocks) will be going slower compared to assistants' clocks who are outside and not experiencing any acceleration.

4) As acceleration finishes the train is again back to an inertial frame but the three clocks on the train and the ones that assistants have on them are still de-synchronized

5) Flashes occur at the both end of train. As the c is constant in any inertial reference frame, the middle observer will see flashes happen simultaneously.

6) If the middle observer had a spectrometer on him/her and analyzed light from both flashes he/she would see that the light coming from the front of the train has been shifted towards blue side of spectrum and the light coming from the back is red-shifted due to him/her moving towards or away from the respective source.

7) Now for the outside observers. Let's assume the train now is far enough from them that we can neglect the difference in distances that light has to travel to them from the front and rear of the train, respectively. Then they will see flashes happen simultaneously and being shifted depending on the direction the train is travelling relative to them.

8) After the experiment is finished the train decelerates to initial rest situation and as they move to the same reference plane as assistants are in, their clocks are coming back in synch. Outside observers and the middle observer compare notes and find out that they have different times recorded for the flash of the central clock while all clocks seem to be synchronized now.

 

That's my reasoning, seems very similar to the twins paradox if I'm not terribly wrong somewhere.

 

Correction: At the end of the experiment clocks on the train and clocks that assistants had may or may not be synchronized depending on how long the train has been travelling in an inertial frame at a speed close to the speed of light. If we assume that the light emission for both clocks is linked to an accelerometer so that the flash occurs exactly when the acceleration finishes and that receival of both flashes by the central observer triggers deceleration back to stationary, then in the end of the experiment clocks on the train and assistants' clocks will still be showing different times but the difference will be minute.

 

If, on the other hand, the train spends significant amount of time travelling at close to the speed of light than de-synchronization will be noticeable.

Edited March 8, 2015 by pavelcherepan

[studiot]

 

studiot

3) What is the fault in the reasoning presented in post#1? Note this is the reasoning, not the statement of conditions.

 

gib65 post#1

But for anyone not on the train (like your two assistants who also observed the stop-clocks being synchronized), the middle stop-clock should not stop because even if the flashes of light are emitted at the same time, the front flash will reach the middle stop-clock before the rear flash. After getting off the train once it stops, bringing the middle stop-clock with you, and rendezvousing with your assistants, what will they see?

 

If everyone has to observe the same events happening, then either a) everyone has to observe that the stop-clock indeed stopped, in which case your assistants would have to conclude that the flashes went off at different times (even though they observed the stop-clocks being synchronized), or b) everyone has to observe that the stop-clocks did not stop, in which case you would have to conclude that the flashes went off at different times (even though you observed the stop-clocks being synchronized).

 

Which will happen? And whatever the answer to this is, what does this imply about the timing of events that are initially synchronized?

 

 

Good morning, pavel.

 

I am not sure why you have resurrected this thread, but the answer to what was wrong with the original reasoning is simple.

 

Inappropriate mixing of information from different frames.

 

There is one and only one frame in which the centre clock can count simultaneity.

That is its own frame.

The whole train, and everything on it including the end clocks, remain in the frame of the centre clock for the entire experiment. The OP took pains to establish that the transfer of the end clocks from the centre has insignificant effect.

 

Other observers, not any the train, will see the simultaneity differently, ie they will not see it simultaneous, from their point of view (frame).

 

The error in the reasoning is thinking that they should see the flashes as simultaneous in their frame, instead of applying relativity of simultaneity, which is, of course, what they should do to obtain the correct answer.

[pavelcherepan]

Sorry about necroposting but it was just very interesting and i failed to notice the last post date.

 

Thanks for the explanation too.

[md65536]

 

2) The train starts accelerating. Let's assume the acceleration is constant. Then by the equivalence principle of GR we can imagine both clocks and the middle observer being suspended at the same height above the gravitating mass that's big enough to account for the proper acceleration as can be measured by the accelerometer that the middle observer has on him/her (let's assume he/she does).

I don't think that's correct. I think by the equivalence principle you could have the clocks in a uniform gravitational field but at different heights (ie. different gravitational potentials) corresponding to their different x positions on the train. Therefore if you do set up the train so that it accelerates uniformly for some time, you still have the clocks ticking at different rates according to GR and can end up out of sync depending on the rest of the setup. As studiot mentioned, this might not describe the original setup.

 

 

Edit: Just thinking to myself... I understand the instinct to put the clocks at the same height around a massive body in order to get the same field strength, but that's the wrong way to think about it. A uniformly accelerating train is like a uniform gravitational field. It will still take effort to "climb" your way from the back of the accelerating train to the front. The effort is proportional to distance climbed. Equivalently it takes effort proportional to distance climbed, to climb out of a gravity well with a uniform field. The location on the train and in the equivalent gravitational field matters.

Edited March 9, 2015 by md65536