Special relativity: Can you explain the paradox?

[swansont]

It confuses me when an expert replies to a comment but does not refute facts stated in the comment that are clearly wrong. It seems like the expert is agreeing. I start to question my understanding (which is great when I have things wrong, but unproductive when I have it right) Above is a case in point.

 

 

 

To me this is clearly wrong. It doesn't matter who is moving, if they are moving relative to each other (toward each other), then both should be shorter to the other. If I am wrong here, please let me know and excuse this post. If I am right, why not point out the shortcoming?

 

You may have, kind of, here:

 

 

 

But, I'm not sure.... and I can easily see others being confused.

 

 

Mea culpa. I did not read the whole thing carefully; I was focusing in on 3&26 wondering who had mentioned the ladder paradox, so I shouldn't have quoted the whole statement without pointing out that there were errors. You are quite correct: each will think the other has been shortened by length contraction and that is the source of the "paradox," as it involves the doors shutting and opening. From the barn frame the ladder is shortened and quite easily fits inside, so the front door can shut before the back door is opened. But from the ladder perspective the barn is contracted and the ladder will not fit inside, so the back door must open before the front door shuts. Thus there is a straightforward example of the order of events changing depending on the frame of reference, which is driven by simultaneity being relative.

[IM Egdall]

This ladder paradox is a tricky thing. I find pictures of what's going on really help me. Take a look at:

 

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

 

From the barn's point of view (reference frame), the ladder is moving. So the ladder is contracted or shorter in length. So the ladder fits inside the barn. So both barn doors can be shut at the moment the ladder is inside the barn. And then they both open to let the ladder out.

 

But from the ladder's point of view, the barn is moving. So the barn is contracted or shorter in length. So how does the ladder fit inside this shorter barn? It doesn't in this reference frame! And in this reference frame, the shutting of the doors is not simultaneous. Einstein's relativity of simultaneity says that two events which occur at the same time for one observer do not happen at the same time for another observer in relative motion. So in the ladder reference frame, the front of the ladder goes to the back of the barn and the back door is closed. Then the back door is opened and the ladder goes through the barn. When the back of the ladder is just inside the barn, the front door is closed. Then it is opened.

 

Both doors close at the same time and then open at the same time from the barn's poiint of view. But from the ladder's point of view, the rear door closes and opens, then at a later time the front door closes and opens. So no contradiction. Einstein escapes again. Relativity of simultaneity is invoked to explain length contraction. This stuff is beautiful!

 

 

[vuquta]

I posted it, and like most of these so-called paradoxes, they really aren't it's a paradox only if one assumes simultaneity is absolute. The reason I mentioned it was to rebut the notion that the order of events couldn't differ in different frames. The ladder "paradox" is a classic example of that very thing; the order of the events, i.e. the ladder entering the barn and the doors shutting and opening, depends on which frame the observer is in.

 

No forces need be involved, though. You can look at the situation after the ladder is moving relative to the barn, and there are no accelerations to worry about.

 

Nope.

 

These observers A and B are perfectly time dilated in each direction.

 

However, by them back in one frame, we can perform the Einstein clock sync and decide which is really older. So, the method of breaking SR is to place the relativity postulate in the form of reciprocal time dilation up against the absoluteness of the frame clocks sync.

 

That flushes out the error in SR.

 

And to further this, Einstein said, "We assume that this definition of synchronism is free from contradictions".

http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

So, I did not introduce absoluteness, he did.

 

Anyway, this little exercise says the clocks sync is inconsistent with reciprocal time dilation. It is simple logic.

 

This ladder paradox is a tricky thing. I find pictures of what's going on really help me. Take a look at:

 

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

 

From the barn's point of view (reference frame), the ladder is moving. So the ladder is contracted or shorter in length. So the ladder fits inside the barn. So both barn doors can be shut at the moment the ladder is inside the barn. And then they both open to let the ladder out.

 

But from the ladder's point of view, the barn is moving. So the barn is contracted or shorter in length. So how does the ladder fit inside this shorter barn? It doesn't in this reference frame! And in this reference frame, the shutting of the doors is not simultaneous. Einstein's relativity of simultaneity says that two events which occur at the same time for one observer do not happen at the same time for another observer in relative motion. So in the ladder reference frame, the front of the ladder goes to the back of the barn and the back door is closed. Then the back door is opened and the ladder goes through the barn. When the back of the ladder is just inside the barn, the front door is closed. Then it is opened.

 

Both doors close at the same time and then open at the same time from the barn's poiint of view. But from the ladder's point of view, the rear door closes and opens, then at a later time the front door closes and opens. So no contradiction. Einstein escapes again. Relativity of simultaneity is invoked to explain length contraction. This stuff is beautiful!

 

Yes, you have a perfect solution to these paradoxes.

 

1,2 and 3) are all correct if B does not accellerate, C is acting as the rest frame and B and C are motionless relative to each other.

 

I think the problem is you're thinking if A has (v) relative to B then B has (v) relative to A and I'm saying this is wrong. This leads you to the opinion that the will both see each other as time dilated (as you said above) and this is wrong (as I understand it)

 

To simplify the problem without altering the effects

 

A accelerates (instantly) to (v) travels at (v) for one second and then decelerates (instantly) to rest again.

 

 

Here's the logic

 

A and B are motionless relative to each other (the principle of relativity says nothing is absolutely motionless BUT two things can be absolutely motionless relative to each other)

 

Now construct a frame around A and B which is absolutely at rest relative to A and B (constructing this frame is just like using a ruler to measure something and it acts as a datum)

 

Newtons law of inertia, a body at rest will remain at rest until acted upon by a force (it is essential you understand what this implies)

 

A and B are at rest therefore no forces are acting upon them

 

Apply a force to A and A only. A and A only accelerates. A and A only has (v) relative to the rest frame

 

There is no force acting upon B so B is still motionless (law of inertia)

 

Therefore A is absolutely in motion and B is absolutely at rest (within this frame of refference)

 

A's time will slow down relative to the rest frame (the rest frame is still at rest because no force has been applied to it)

 

B's time will be the same as the rest frame's because he is motionless relative to it (still no force applied to B)

 

If A is experiencing time at a slower rate than B then for whose one second does he travel at (v) for

 

He travels at (v) for one second of the rest frame (we measure against the rest frame)

 

One second in the rest frame = one second of B's time (B is motionless relative to the rest frame), BUT

One second in the rest frame < one second of A's time (A is moving relative to the rest frame)

 

So if B experiences one full second, A (whose time is slower), has not experienced one full second yet

and if A experiences one full second, B (whose time is faster), has experienced more than one second

 

They will both agree A is younger

They will both agree B is older

 

They will disagree by how much A is younger

They will disagree by how much B is older

 

Somebody posted the ladder paradox (may have been you??) but the paradox does not exist. It comes from a misunderstanding of the theory of relativity. In this paradox the ladder is both longer and shorter than the garrage and the garrage is both longer and shorter than the ladder.

 

Nonsense

 

If you apply a force to the ladder then the ladder IS moving.

 

As viewed from the garrage the ladder will appear shorter.

As viewed from the ladder the garrage will appear longer.

 

If the ladder remains at rest (ie no force applied) and you accelerate the garrage instead then

 

As viewed form the ladder the garrage will be shorter and

As viewed from the garrage the ladder will be longer

 

Your solution is not absolute.

 

A and B disagree and the clock sync resolves it.

 

Thus, under SR, there exists two conclusions where there should be one.

 

Hey, if you want to introduce a 3rd to further break SR, have at it. It is simply not necessary.

 

What folks have not realized yet with SR, if you have an absolute solution frame to frame, then you contradict the relativity postulate.

Edited September 17, 2010 by vuquta

[swansont]

Nope.

 

Yup.

 

These observers A and B are perfectly time dilated in each direction.

 

However, by them back in one frame, we can perform the Einstein clock sync and decide which is really older. So, the method of breaking SR is to place the relativity postulate in the form of reciprocal time dilation up against the absoluteness of the frame clocks sync.

 

That flushes out the error in SR.

 

And to further this, Einstein said, "We assume that this definition of synchronism is free from contradictions".

http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

So, I did not introduce absoluteness, he did.

 

Anyway, this little exercise says the clocks sync is inconsistent with reciprocal time dilation. It is simple logic.

 

This was a discussion of the ladder paradox, not your "who is older, A or B" scenario. There was no discussion of clock synchronization or time dilation.

 

 

What folks have not realized yet with SR, if you have an absolute solution frame to frame, then you contradict the relativity postulate.

 

I think everyone here realizes that there is no absolute frame in SR.

[vuquta]

vuquta, on 17 September 2010 - 04:12 PM, said:

 

What folks have not realized yet with SR, if you have an absolute solution frame to frame, then you contradict the relativity postulate.

 

 

 

 

I think everyone here realizes that there is no absolute frame in SR.

 

Well, that is not what I said.

 

I said, "What folks have not realized yet with SR, if you have an absolute solution frame to frame, then you contradict the relativity postulate".

 

For example, let's look at the relativity of simultaneity train enbankment experiment.

 

Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A. We thus arrive at the important result:

http://www.bartleby.com/173/9.html

 

Note how both frames draw the absolute conclusion the observer on the train sees the front light before the back. This is not a conclusion that is relative to the frames it is absolute for both.

 

Note, how it implies both frames agree the train observer is hastening towards the beam of light .

 

I wonder how the train taken as stationary hastens toward the light.

[losfomot]

Well, that is not what I said.

 

I said, "What folks have not realized yet with SR, if you have an absolute solution frame to frame, then you contradict the relativity postulate".

 

For example, let's look at the relativity of simultaneity train enbankment experiment.

 

 

http://www.bartleby.com/173/9.html

 

Note how both frames draw the absolute conclusion the observer on the train sees the front light before the back. This is not a conclusion that is relative to the frames it is absolute for both.

 

Note, how it implies both frames agree the train observer is hastening towards the beam of light .

 

I wonder how the train taken as stationary hastens toward the light.

 

 

It is not a conclusion that is drawn by the person on the train... it is a fact. And the person on the embankment does see the person on the train hastening toward one of the lightning flashes, so yes, if he knew SR, knew that there was no absolute frame, he could 'draw the conclusion' that the person ON the train sees one flash before the other, contrary to what he himself sees.

 

There is no 'absolute solution' here.

 

I wonder how the train taken as stationary hastens toward the light.

 

The observer on the train can take the train as being stationary. To him, he is not hastening anywhere, the light simply flashes at 2 different times. He is not agreeing about any absolute solution. He can also work out what the other observer sees, but not by saying "I'm hastening toward the light and the observer on the ground is not"... instead the train observer follows the following logic:

 

I am stationary.

 

I saw flash B first, then flash A.

 

The observer on the embankment is hastening toward flash A with just the right velocity such that they must have seen both flashes at the same time, contrary to what I saw.

[swansont]

 

 

Note how both frames draw the absolute conclusion the observer on the train sees the front light before the back. This is not a conclusion that is relative to the frames it is absolute for both.

 

 

They both have to agree on what each observer sees, because the solutions are single-valued. This is neither a flaw in nor a violation of any principle of relativity.

[vuquta]

They both have to agree on what each observer sees, because the solutions are single-valued. This is neither a flaw in nor a violation of any principle of relativity.

 

Well, when the front flash occurs, each observer are equidistant to the flash. That is a fact since both are co-located when the flash occurs.

 

Same is true for the rear flash.

 

So, we have a moving light source (which does not matter) with light flashes that are equidistant to the observer when they occur.

 

Thus, the train as stationary will conclude the flashes are simultaneous whereas the embankment will conclude they are not for the train observer.

 

It is not a conclusion that is drawn by the person on the train... it is a fact. And the person on the embankment does see the person on the train hastening toward one of the lightning flashes, so yes, if he knew SR, knew that there was no absolute frame, he could 'draw the conclusion' that the person ON the train sees one flash before the other, contrary to what he himself sees.

 

There is no 'absolute solution' here.

 

 

 

The observer on the train can take the train as being stationary. To him, he is not hastening anywhere, the light simply flashes at 2 different times. He is not agreeing about any absolute solution. He can also work out what the other observer sees, but not by saying "I'm hastening toward the light and the observer on the ground is not"... instead the train observer follows the following logic:

 

I am stationary.

 

I saw flash B first, then flash A.

 

The observer on the embankment is hastening toward flash A with just the right velocity such that they must have seen both flashes at the same time, contrary to what I saw.

 

the light simply flashes at 2 different times

 

See, this is the problem.

 

Let's just take the front flash.

 

You are claiming when M and M' are co-located, the flash in the front occurs at a closer distant to M', the moving observer than M.

 

Since the speed of light is a constant, this must be true.

 

You see, you cannot claim lightning is at a location from one frame and not at that location in another.

 

But if the lightning is closer, then both frame agree it strikes in 2 different locations.

 

Your logic does not work.

 

So, let's review, we have ONE lightning flash at ONE location that occurs when M and M' are co-located, ie at the same place.

[Janus]

Well, when the front flash occurs, each observer are equidistant to the flash. That is a fact since both are co-located when the flash occurs.

 

Same is true for the rear flash.

 

So, we have a moving light source (which does not matter) with light flashes that are equidistant to the observer when they occur.

 

Thus, the train as stationary will conclude the flashes are simultaneous whereas the embankment will conclude they are not for the train observer.

 

 

 

the light simply flashes at 2 different times

 

See, this is the problem.

 

Let's just take the front flash.

 

You are claiming when M and M' are co-located, the flash in the front occurs at a closer distant to M', the moving observer than M.

 

Since the speed of light is a constant, this must be true.

 

You see, you cannot claim lightning is at a location from one frame and not at that location in another.

 

But if the lightning is closer, then both frame agree it strikes in 2 different locations.

 

Your logic does not work.

 

So, let's review, we have ONE lightning flash at ONE location that occurs when M and M' are co-located, ie at the same place.

 

M &M' are co-located when the flashes occur in the embankment frame, they are not so in the train frame.

 

Events according to the Embankment frame:

 

 

Same events according to the Train frame:

 

 

Both frames agree that the flashes occur when the Ends of the Trains are co-located with the red dots.

 

Both frames agree that the embankment observer sees the flashes simultaneously, and what point of the train is co-located with the observer when he sees the flashes.

 

Both frame agree that the train observer sees the flashes at separate times, And what points of the embankment are co-located with the observer when he sees each flash.

 

The frames will not agree as to whether the flashes occurred simultaneously, or how far each observer was from the flash when they occurred.

[losfomot]

See, this is the problem.

 

Let's just take the front flash.

 

You are claiming when M and M' are co-located, the flash in the front occurs at a closer distant to M', the moving observer than M.

 

Since the speed of light is a constant, this must be true.

 

I don't think I'm claiming anything of the sort.

 

And if you only look at one flash, there is no simultaneity comparison. The observer on the train will see a flash hit the front of the train. The observer on the ground will see a flash hit the front of the train.

 

 

You see, you cannot claim lightning is at a location from one frame and not at that location in another.

 

 

When? They are experiencing time and space differently. When did they each see the flash? That is the point of the two flashes, to have something to make a comparison to.

 

If you only look at one flash, there is no way for the two observers to compare what they saw and see a difference.

[vuquta]

M &M' are co-located when the flashes occur in the embankment frame, they are not so in the train frame.

 

Events according to the Embankment frame:

 

 

Same events according to the Train frame:

 

 

Both frames agree that the flashes occur when the Ends of the Trains are co-located with the red dots.

 

Both frames agree that the embankment observer sees the flashes simultaneously, and what point of the train is co-located with the observer when he sees the flashes.

 

Both frame agree that the train observer sees the flashes at separate times, And what points of the embankment are co-located with the observer when he sees each flash.

 

The frames will not agree as to whether the flashes occurred simultaneously, or how far each observer was from the flash when they occurred.

 

OK, how does the train frame conclude the front flash occurs before the back.

 

We must remember, both flashes happen when M and M' are co-located.

 

Hence, both are equidistant light flashes that occir to each frame when M and M' are co-located.

 

How will you make the flahs in the front of the train emit before the back?

 

That implies if and A and A' were co-located at the flash at the same place, one would have to claim light is speeding down the x-axis whereas the other at the same place claims light is not there.

 

How do you work this out?

 

I don't think I'm claiming anything of the sort.

 

And if you only look at one flash, there is no simultaneity comparison. The observer on the train will see a flash hit the front of the train. The observer on the ground will see a flash hit the front of the train.

 

 

 

When? They are experiencing time and space differently. When did they each see the flash? That is the point of the two flashes, to have something to make a comparison to.

 

If you only look at one flash, there is no way for the two observers to compare what they saw and see a difference.

 

Yes, we are tallking about light reception.

 

Does each receive the signals differently.

 

Let's stay on the M' train frame.

 

Are they two flashes equidistant yes or no.

[swansont]

Well, when the front flash occurs, each observer are equidistant to the flash. That is a fact since both are co-located when the flash occurs.

 

Same is true for the rear flash.

 

So, we have a moving light source (which does not matter) with light flashes that are equidistant to the observer when they occur.

 

Thus, the train as stationary will conclude the flashes are simultaneous whereas the embankment will conclude they are not for the train observer.

 

 

The moving of light source doesn't matter to the observer of the light source measuring the speed of light relative to him. But it matters if he is measuring the speed of light relative to some other frame. Co-location does not imply simultaneity if the co-located points are moving with respect to each other.

[vuquta]

The moving of light source doesn't matter to the observer of the light source measuring the speed of light relative to him. But it matters if he is measuring the speed of light relative to some other frame. Co-location does not imply simultaneity if the co-located points are moving with respect to each other.

 

We are talking about the light emission as being simultaneous.

 

Let's see, if the light emission is not simultaneous between the frames, how would you possible do the original mirror experiment for LT construction? It assumes a common light emission where both clocks are set to 0.

 

Furthermore, Einstein used a common light emission to prove the consistency, which he is wrong, of SR.

 

So, you cannot say the light emission was not simultaneous to the frames at the front of the trains or your refute all of SR.

[losfomot]

Yes, we are tallking about light reception.

 

Does each receive the signals differently.

 

yes.

 

Let's stay on the M' train frame.

 

Are they two flashes equidistant yes or no.

 

In the Train frame the two flashes are 'equidistant', yes. But they are not simultaneous. They occur at different times.

 

We are talking about the light emission as being simultaneous.

 

Let's see, if the light emission is not simultaneous between the frames, how would you possible do the original mirror experiment for LT construction? It assumes a common light emission where both clocks are set to 0.

 

Furthermore, Einstein used a common light emission to prove the consistency, which he is wrong, of SR.

 

So, you cannot say the light emission was not simultaneous to the frames at the front of the trains or your refute all of SR.

 

I'm not sure I understand your position on all of this...

 

Are you trying to say that both observers will see the flashes as simultaneous, and therefore SR is wrong, or

 

are you trying to say that they won't both see the flashes as simultaneous, but SR is wrong in how it describes this.

 

 

Are you trying to understand this stuff, or

 

do you think you understand it perfectly, you're just refuting it?

 

edit - I think I found the SOURCE of your arguments.

Edited September 20, 2010 by losfomot

[swansont]

We are talking about the light emission as being simultaneous.

 

Let's see, if the light emission is not simultaneous between the frames, how would you possible do the original mirror experiment for LT construction? It assumes a common light emission where both clocks are set to 0.

 

Furthermore, Einstein used a common light emission to prove the consistency, which he is wrong, of SR.

 

So, you cannot say the light emission was not simultaneous to the frames at the front of the trains or your refute all of SR.

 

It is nonsensical to speak generally of simultaneous emission, since simultaneity is frame dependent. One must always refer to the frame in which the events are simultaneous.

 

!

Moderator Note

However, this is a thread about solutions to relativity "paradoxes," not your imagined inconsistencies in relativity. Those discussions belong in speculations

[between3and26characterslon]

Going back to an earlier argument. There is no absolute rest frame in the universe because, as was said, that would violate the principle of relativity.

 

However an inertial frame that is moving with uniform retilinear translation with respect to all other inertial frames is no different to being at rest, it's the same thing.

 

For this reason, even though coordinate system K is moving relative to all other coordinate systems, objects A and B are at rest relative to K so motion and rest are absolute within K. Whilst at rest A and B have their own coordinate systems which are inertial but when A is accelerated its coordinate system is no longer inertial.

 

I found this which explains better than I can.

 

http://www.einstein-...ights/TwinsRoad

 

 

EDIT: As for the ladders I misunderstood the scenario

Edited September 20, 2010 by between3and26characterslon

[Janus]

OK, how does the train frame conclude the front flash occurs before the back.

By the fact that the light form the front flash reaches him first and the sources of the flashes are equal distant from him

 

We must remember, both flashes happen when M and M' are co-located.

 

Hence, both are equidistant light flashes that occir to each frame when M and M' are co-located.

NO! . The only frame in which the flashes occur when M and M' are co-located is the embankment frame.

 

 

How will you make the flahs in the front of the train emit before the back?

 

In both frames, the Flashes occur when each end of the train is co-located with a spot on the embankment where the lightning strikes. These points are at the same spots of the embankment in both frames. However, The relative distance between these points and the two ends of the Train is not equal in both frames. In the embankment frame the train has relative motion and is length contracted, thus it is the contracted length of the train that fits exactly between the simultaneous flashes. However, in train frame, the train is its non-contracted proper length and it is the embankment that has relative motion and is contracted. Thus the distance between the spots on the embankment will be shorter than the length of the train. The front of the train will reach its point of the embankment where the lightning strikes before the back of the train does. Since the lightning strikes and the co-location of the ends of the train and the strike points on the embankment are all co-located, both frames have to agree to to this fact. The train frame has to conclude that the lightning strikes occured at separate times

 

That implies if and A and A' were co-located at the flash at the same place, one would have to claim light is speeding down the x-axis whereas the other at the same place claims light is not there.

 

How do you work this out?

 

 

 

Yes, we are tallking about light reception.

 

Does each receive the signals differently.

 

Let's stay on the M' train frame.

 

Are they two flashes equidistant yes or no.

 

All explained above and in the animations if you bother to study them.

[vuquta]

It is nonsensical to speak generally of simultaneous emission, since simultaneity is frame dependent. One must always refer to the frame in which the events are simultaneous.

 

!

Moderator Note

However, this is a thread about solutions to relativity "paradoxes," not your imagined inconsistencies in relativity. Those discussions belong in speculations

 

Einstein said the following.

 

At the time t'=t=0, when the origin of the co-ordinates is common to the two systems, let a spherical wave be emitted therefrom, and be propagated with the velocity c in system K. If (x, y, z) be a point just attained by this wave, then

 

From the origin of system k let a ray be emitted at the time along the X-axis to x',

 

http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

I do not mind admitting I am confused.

 

Can you explain in the two above why these statements of simultaneous emissions are false?

 

Einstein required a simultaneous emission of light for LT construction and for his "proof" of the logical consistency of SR.

 

If these are not simultaneous frame emissions as you say and they are stupid, then how can you agree with Einstein?

Edited September 21, 2010 by vuquta

[swansont]

Einstein said the following.

 

At the time t'=t=0, when the origin of the co-ordinates is common to the two systems, let a spherical wave be emitted therefrom, and be propagated with the velocity c in system K. If (x, y, z) be a point just attained by this wave, then

 

From the origin of system k let a ray be emitted at the time along the X-axis to x',

 

http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

I do not mind admitting I am confused.

 

Can you explain in the two above why these statements of simultaneous emissions are false?

 

Einstein required a simultaneous emission of light for LT construction and for his "proof" of the logical consistency of SR.

 

If these are not simultaneous frame emissions as you say and they are stupid, then how can you agree with Einstein?

 

I don't see where "simultaneous" is mentioned in either of those statements. In both cases it is made clear that the event is being observed in system K. If two events are simultaneous in K, they cannot be assumed to be simultaneous in other frames. As I said, simultaneity is frame-dependent. There's nothing here that contradicts that.

 

Edit: You appear to be using "simultaneous" to refer to a single event viewed in multiple frames. That's not simultaneity. You can arbitrarily set clocks in multiple frames to be synchronized to one event (Not multiple events, though (separated by time or space)) just as you can arbitrarily choose one point in every frame to be the origin.

[between3and26characterslon]

vuquta

 

I think you're over complicating things.

 

As viewed from the embankment both flashes occur at the ends of the train at the precise moment M and M' coincide.

 

In the time it takes light, from the front of the train, to reach M' the train has moved nearer to the flash, at the front of the train, and so M' will see that one first, simply because the light has travelled less distance.

 

So like you say he will measure the speed of light as being faster because it has travelled, from his point of view, the length of the train in less time, only he won't because of time dilation and length contraction which will exactly compensate (he can't see the train is shorter or his seconds are longer).

 

He will see both flashes occur equidistant from him, he will measure the speed of light as c but he will see one flash before the other.

 

Which is basically another way of saying what Janus said.

[vuquta]

I don't see where "simultaneous" is mentioned in either of those statements. In both cases it is made clear that the event is being observed in system K. If two events are simultaneous in K, they cannot be assumed to be simultaneous in other frames. As I said, simultaneity is frame-dependent. There's nothing here that contradicts that.

 

Edit: You appear to be using "simultaneous" to refer to a single event viewed in multiple frames. That's not simultaneity. You can arbitrarily set clocks in multiple frames to be synchronized to one event (Not multiple events, though (separated by time or space)) just as you can arbitrarily choose one point in every frame to be the origin.

 

OK, let's remove the term "simultaneous" because that is not really what I meant. I meant, when lightning strikes position A, two conditions are true.

 

1) Ma and M' are co-located.

2) At the position of the front lightning strike, I will call it A/A', both frames can sync t'=t=0 at that particular location.

 

Make sense?

 

So, when M and M' are co-located, neither frame can disagree t=t'=0 at the location of the lightning strke.

 

vuquta

 

I think you're over complicating things.

 

As viewed from the embankment both flashes occur at the ends of the train at the precise moment M and M' coincide.

 

In the time it takes light, from the front of the train, to reach M' the train has moved nearer to the flash, at the front of the train, and so M' will see that one first, simply because the light has travelled less distance.

 

So like you say he will measure the speed of light as being faster because it has travelled, from his point of view, the length of the train in less time, only he won't because of time dilation and length contraction which will exactly compensate (he can't see the train is shorter or his seconds are longer).

 

He will see both flashes occur equidistant from him, he will measure the speed of light as c but he will see one flash before the other.

 

Which is basically another way of saying what Janus said.

 

Yea, you have a very good view of the embankment frame.

 

However, we are taking the train as stationary.

 

So, it does not travel toward the light.

 

It this true, or does a rest frame travel toward a light pulse?

[swansont]

OK, let's remove the term "simultaneous" because that is not really what I meant. I meant, when lightning strikes position A, two conditions are true.

 

1) Ma and M' are co-located.

2) At the position of the front lightning strike, I will call it A/A', both frames can sync t'=t=0 at that particular location.

 

Make sense?

 

So, when M and M' are co-located, neither frame can disagree t=t'=0 at the location of the lightning strke.

 

 

Nope. The clocks are synced at the origin, not at the position of the lightning strike.

[Janus]

OK, let's remove the term "simultaneous" because that is not really what I meant. I meant, when lightning strikes position A, two conditions are true.

 

1) Ma and M' are co-located.

2) At the position of the front lightning strike, I will call it A/A', both frames can sync t'=t=0 at that particular location.

 

Make sense?

 

So, when M and M' are co-located, neither frame can disagree t=t'=0 at the location of the lightning strke.

 

The distances M-A and M'-A' are different when measured from the M' frame then they are when measured from the M frame. For instance, if the relative velocity difference between the frames is 0.5 c, and and M-A and M'-A' are both 1 km according to M, then according to M', M-A will be 0.866 km and M'-A' will be 1.15 km.

 

If M' and M are co-located at the same instant as A' and A, in the frame of M, they cannot be co-located at the same instant in the M' frame. (In the above example, they will be 0.289 km apart in the M' frame when A' and A are co-located.)

 

So if both frames agree that A'/A occurs at t=t'=0, then only one frame could say that M' and M are co-located at t=t'=0.

[ScaryPirateMan]

How does this even make sense? How can we come up with these theories? Have we even been able to reach the speed's required to take these measurements? You can say anything in theory, but please show me the applied examples. I'm sorry, non of this makes sense to me and I really want it to.

[swansont]

How does this even make sense? How can we come up with these theories? Have we even been able to reach the speed's required to take these measurements? You can say anything in theory, but please show me the applied examples. I'm sorry, non of this makes sense to me and I really want it to.

 

Yes, we have been able to reach speeds to make these measurements, since we don't rely on human perception or other poor instrumentation like that. We use e.g. atomic clocks, which are sensitive to nanosecond-level amounts of time dilation. That permits us to see relativistic effects for speeds attainable with planes, trains and automobiles.