Was Einstein Wrong About Relativity of Simultaneity?

[longshinewoole]

Was Einstein Wrong?

In Chapter 9, The Relativity of Simultaneity, of Einstein’s book Relativity (http://www.marxists.org/reference/archive/einstein/works/1910s/relative/index.htm), Einstein said: “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.”

Were these words wrong?

We understand, in Einstein’s thought experiment, besides observers he also had a mid point on the long train like this: A__________M’__________B. Taking such a long train into our consideration, his words must mean: the beam of light emitted from B will reach the mid point M’ sooner than the beam of light emitted from A.

I think such a meaning is wrong; Einstein was wrong in saying it because light will cover equal distances with equal time regardless how the train is moving. Taking equal time to cover equal distance means light from B and A will reach mid point M’ simultaneously, contrary to Einstein’s words.

Furthermore, when he said “Observers who take the railway train as their reference-body……” my understanding of those words was: there is a mathematical way to support their conclusion. Since those observers and Einstein did not use mathematics to support their “…conclusion that the lightning flash B took place earlier than the lightning flash A”, I wish some one here could. Please oblige.

I am a hobby reader. I have no formal training in physics.

 

[Chris Hillman]

Suggest studying a standard textbook rather than marxists.org

Hi, longshinewoole,

Before anyone says anything I'd like to make a rather obvious suggestion. Websites like marxists.org promote political agendas and have been known to mispresent scientific knowledge in order to pursue those agendas. So I'd suggest that if you want to understand what str says, you should study a standard textbook such as Taylor & Wheeler, Spacetime Physics. If you have studied "high school geometry" (more properly, euclidean plane geometry) and "high school trigonometry" (more properly, euclidean plane trigonometry), and if you have a strong visual imagination, you can really acquire solid intuition for Minkowski geometry from Taylor & Wheeler.

Alternatively, some on-line resources are suggested in the website in my sig (see below).

(Other readers, in search of amusement, may like to compare specific misrepresentations of relativistic physics found certain creationist websites with those found in marxists.org. In some cases these sites claim to be using the same phenomena to argue for very different politicized conclusions!)

Einstein was not wrong, although these are tiny effects for velocities comparable to the speed of the TGV. But see the Hafele-Keating experiment! http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html

 

[MeJennifer]

Please verify before you make accusations

The http://www.marxists.org/reference/archive/einstein/index.htm" on Marxist.org simply contains the online book "Relativity: The Special and General Theory" written by Albert Einstein. You can even download the complete book in pdf format. Albert Einstein is simply included on Marxists.org because of his known sympathies with socialism.

Other readers, in search of amusement, may like to compare specific misrepresentations of relativistic physics found certain creationist websites with those found in Marxists.org. In some cases these sites claim to be using the same phenomena to argue for very different politicized conclusions

It is obvious that Chris Hillman did not even bother to verify that Marxists.org simply hosts the book "Relativity: The Special and General Theory" written by Albert Einstein. The website makes no comments whatsoever about the validity of the theory.

The referenced quote is accurate by the way.

It would be nice if people on this forum would refrain from making unfounded accusations, putting down people, insinuating that people are sockpuppets or that they are known crackpots. And refrain from putting down perfectly valid websites in order to self promote their own website.

 

[Doc Al]

In Chapter 9, The Relativity of Simultaneity, of Einstein’s book Relativity (http://www.marxists.org/reference/archive/einstein/works/1910s/relative/index.htm), Einstein said: “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.”

Were these words wrong?

No, of course not.

We understand, in Einstein’s thought experiment, besides observers he also had a mid point on the long train like this: A__________M’__________B. Taking such a long train into our consideration, his words must mean: the beam of light emitted from B will reach the mid point M’ sooner than the beam of light emitted from A.

That's correct.

I think such a meaning is wrong; Einstein was wrong in saying it because light will cover equal distances with equal time regardless how the train is moving. Taking equal time to cover equal distance means light from B and A will reach mid point M’ simultaneously, contrary to Einstein’s words.

Just because light takes equal time to cover equal distance doesn't mean that they arrive at the midpoint simultaneously. That would only be true if the two lights flashed at the same time. But the point of Einstein's argument is that whether the lights flash at the same time is frame dependent: train observers and embankment observers disagree.

Furthermore, when he said “Observers who take the railway train as their reference-body……” my understanding of those words was: there is a mathematical way to support their conclusion. Since those observers and Einstein did not use mathematics to support their “…conclusion that the lightning flash B took place earlier than the lightning flash A”, I wish some one here could. Please oblige.

You really need to read the entire passage, not just pick out quotes. Just prior to your quoted sentences, Einstein gives a simple argument showing that the light from B must arrive at M' before the light from A. That's the key.

There are plenty of modern, pedagogically-oriented books specifically for beginners; I recommend you get one and study it. Spacetime Physics by Taylor and Wheeler (which Chris mentioned) is one; It's About Time by N. David Mermin is another.

 

[RandallB]

longshinewoole


A__________M’__________B.


Your problem is you have not accurately represented what Einstein said in the problem. You need a Midway observer next to the train track at M. and the A & B you have listed are next to the track not on the train as well. I’m sure Einstein said the lighting strikes hit next to the track simultaneously or at the “same time” in the reference frame of A M & B. His point about simultaneity is that from the view of A’ & B’ (moving locations you do not show) the two strikes dot not happen at the same time. B’ can directly see the lighting hit the ground outside the train well before A’ sees the ground hit by the second bolt of lightning from there common frame of reference a synchronized time. Even though they can both see the observers out side also observing the same event are displaying large clocks that read the same time at both A & B.
The point is only A & B see the events as simultaneous. A’ & B’ do not! And since B’ sees the strike well before A’ and both are the same distance from M’ moving in the same frame – of course M’ will se the forward A strike before the B strike.

 

[pmb_phy]

Was Einstein Wrong?

I haven't followed this conversation regarding Einstein's errors but I do know that Einstein sure knew what he was talking about. But like all people, he was falible. There will be a new book comming out by Ohanian in a few weeks about about Einstein's mistakes. I'll be getting a chapter of it soon and can let you know more about Einstein's errors and will check to see if this is mentioned.

Pete

 

[RandallB]

I haven't followed this conversation regarding Einstein's errors but I do know that Einstein sure knew what he was talking about. But like all people, he was falible. There will be a new book comming out by Ohanian in a few weeks about about Einstein's mistakes. I'll be getting a chapter of it soon and can let you know more about Einstein's errors and will check to see if this is mentioned.

Pete

That sounds interesting.
Do you know any details like does it address Special Relativity as having errors? Doesn’t seem like Einstein could have any error there, that one seems pretty solid.

Or is it focused on GR having errors? Which might be more plausible since modern physics seems to divide between Particle Physics and Astrophysics based on QM vs. GR. Since the two theories seem to be irreconcilably different (100% particle exchanges vs. Space time warps) they cannot both be right, so one must be wrong.

For all the testing that has been done on GR I assume the argument must be a theoretical or thought proof / explanation?

Do you know any other details like Publisher or likely title? Or do they want you to just leave it as someone from Ohio.

Edit below: OOPS not "from Ohio" but the author of :

“The role of dynamics in the synchronization problem”,
by Hans C. Ohanian
Am. J. Phys. 72 (2), 141-148 (2004)

I found where Alan Macdonald of the Department of Mathematics, Luther College, Decorah IA, criticized the above paper issues about “clock synchronization”.
Which means if H. C. Ohanian is publishing the book on the same issue, it would be directed against SR. If so, it seems to me Ohanian may not be dealing with simultaneity any better than “longshinewoole”. If so I don’t see where the book will be very productive. But that’s just a guess from the journal pages. I’m sure more papers can be found but I’ll wait for the book before calling it wrong.

Longshinewoole : Just a tip - - stick with getting to really understand the point of simultaneity. It impacts every SR paradox, twins etc.
If you do not understand simultaneity; you do not understand SR. Which can only make GR near impossible.

 

[pmb_phy]

That sounds interesting.
Do you know any details like does it address Special Relativity as having errors? Doesn’t seem like Einstein could have any error there, that one seems pretty solid.

I don't know any details as of yyet. I'll have some when he sends me a chapter or two. I expect he'll have the error in Einstein's original 1905 special relativity paper. I mentioned it to him when I first noticed it several years ago. The error I speak of I recorded here
The term locally flat refers to a system of coordinates

Or is it focused on GR having errors? Which might be more plausible since modern physics seems to divide between Particle Physics and Astrophysics based on QM vs. GR. Since the two theories seem to be irreconcilably different (100% particle exchanges vs. Space time warps) they cannot both be right, so one must be wrong.

Don't know. All I know is its about Einstein's errors.

“The role of dynamics in the synchronization problem”,
by Hans C. Ohanian
Am. J. Phys. 72 (2), 141-148 (2004)

Actually the author of this paper is the same as the author of the book comming out.

Which means if H. C. Ohanian is publishing the book on the same issue, it would be directed against SR. If so, it seems to me Ohanian may not be dealing with simultaneity any better than “longshinewoole”.

Why? I've known Ohanian for many years and have read many of his texts. He's very sharp man in my opinion.

Pete

 

[RandallB]

I expect he'll have the error in Einstein's original 1905 special relativity paper. I mentioned it to him when I first noticed it several years ago. The error I speak of I recorded here
The term locally flat refers to a system of coordinates

I don't know where "here" is - I expect you had intented a link hooked to that word. You should still be able to edit the post, or PM it to me.

Why? I've known Ohanian for many years and have read many of his texts. He's very sharp man in my opinion.

As I said, (I’ll wait for the book before calling it wrong) rather than try to figure out what papers he may be including in the book. I only skimed Alan Macdonald comments on just that one paper by Ohanian. But I've never seen anything to make me question Einstein's SR. And I have seen very sharp people argue against it but always found Einstein to have been just a little sharper with his original 1905 idea.
But I'll take an open minded look at anything presented rationally.

 

[pmb_phy]

I don't know where "here" is...

Sorry for the confusion. By "here" I was referring to this forum.

But I've never seen anything to make me question Einstein's SR. And I have seen very sharp people argue against it but always found Einstein to have been just a little sharper with his original 1905 idea.
But I'll take an open minded look at anything presented rationally.

As I mentioned above there is his 1905 paper. See
http://www.geocities.com/physics_world/sr/ae_1905_error.htm

Then there is the well known error in his 1911 paper. At that time he had not thought of working spacetime curvature into such a problem. The end result was that his calculation of the deflection was off by a factor of two. He got the value correct in 1915 when he finished creating GR.

Pete

 

[RandallB]

As I mentioned above there is his 1905 paper. See
http://www.geocities.com/physics_world/sr/ae_1905_error.htm

Then there is the well known error in his 1911 paper. ... He got the value correct in 1915 when he finished creating GR.

Pete

Wow
- An argument that complains about Einstein saying “it was not good to introduce the quantity m=ym₀” (relativistic mass)
- Arguing for the use of m_rel (relativistic mass) while everyone is settled on using m₀ (intrinsic rest mass).
- And making a big deal out of a 1911 error, but corrected by Einstein in the final 1915 submission of his GR theory.

Not much to write a book about in my view.

No need for us to get into a debate – as I said I’ll wait for the book to look at it.

 

[pmb_phy]

Wow
- An argument that complains about Einstein saying “it was not good to introduce the quantity m=ym₀” (relativistic mass)
- Arguing for the use of m_rel (relativistic mass) while everyone is settled on using m₀ (intrinsic rest mass).
- And making a big deal out of a 1911 error, but corrected by Einstein in the final 1915 submission of his GR theory.

Not much to write a book about in my view.

That's because you seem to believe that is all the book is about. I was merely speculating about the kind of things that the book might contain.

Best wishes

Pete

 

[longshinewoole]

No, of course not.

That's correct.

Just because light takes equal time to cover equal distance doesn't mean that they arrive at the midpoint simultaneously. That would only be true if the two lights flashed at the same time. But the point of Einstein's argument is that whether the lights flash at the same time is frame dependent: train observers and embankment observers disagree.

You really need to read the entire passage, not just pick out quotes. Just prior to your quoted sentences, Einstein gives a simple argument showing that the light from B must arrive at M' before the light from A. That's the key.

There are plenty of modern, pedagogically-oriented books specifically for beginners; I recommend you get one and study it. Spacetime Physics by Taylor and Wheeler (which Chris mentioned) is one; It's About Time by N. David Mermin is another.

I certainly did read the whole chapter, and I found it was impossible to understand. Einstein first said: "People traveling in this train will with advantage view the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train..." Then he changed his position and said something completely on the constrary; see his words in the parenthesis such as (as judged from the embankment), and (considered with reference to the railway embankment). This of course is contrary to his opening statement: "People traveling in this train will with advantage view the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train..."

My quote "Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A." was an independent statement. Together with its follwoing sentece "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", I would say Einstein reversed back again, meaning "People traveling in this train will with advantage view the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train...".

This flipflop by Einstein gave us an impression that Einstein even did not know what he was proposing.

It seemed so far nobody could give mathematics to support that light from B will reach M' sooner than that from A.

When you said "But the point of Einstein's argument is that whether the lights flash at the same time is frame dependent: train observers and embankment observers disagree", the frame dependent nature was what the thought experiment wanted to establish by showing that lights will not arrive simultaneously at M'. Now I am asking you people use meth to show this un-simultaneous arrivals. If you cannot, then the frame dependent nature is in doubt.

 

[Doc Al]

I certainly did read the whole chapter, and I found it was impossible to understand. Einstein first said: "People traveling in this train will with advantage view the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train..." Then he changed his position and said something completely on the constrary; see his words in the parenthesis such as (as judged from the embankment), and (considered with reference to the railway embankment). This of course is contrary to his opening statement: "People traveling in this train will with advantage view the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train..."

Events can be viewed from either frame of reference. There is no contradiction in viewing events from one frame for convenience and then deducing what the other frame must see. But nowhere does Einstein contradict his statement that people traveling on the train view things from the train frame, while those on the embankment view things from the embankment frame.

My quote "Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A." was an independent statement. Together with its follwoing sentece "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", I would say Einstein reversed back again, meaning "People traveling in this train will with advantage view the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train...".

Obviously a statement beginning with "Hence..." is not an independent statement, but a deduction from previous statements.

This flipflop by Einstein gave us an impression that Einstein even did not know what he was proposing.

What flipflop?

It seemed so far nobody could give mathematics to support that light from B will reach M' sooner than that from A.

I suppose Einstein thought this example simple enough that translating it into mathematical language was unnecessary. But if you insist:

Let's examine things from the viewpoint of the embankment observers. According to them, the lights flash simultaneously and are (say) a distance L apart. Let's say that the lights both flash at time t_0 = 0 (according to embankment clocks). Let's further call the time that the light from B arrives at M' to be t_1. During that time how far did the train move? If the speed of the train is v, the distance the train moved is v*t_1. So how far did the light have to travel in getting from B to M'? Not the full length of half the train (L/2), but only a distance equal to L/2 - v*t_1, since the train (and M') moved towards B.

Of course, during that same amount time the light from A also travels the same distance. But since M' has moved a distance v*t_1 towards B, the light from from A has not yet reached M'. The light moved a distance of L/2 - v*t_1 from A, but M' is already at a distance of L/2 + v*t_1.

So it should be clear, from our analysis of events seen from the embankment, that the light from B must arrive at M' before the light from A does. Got it?

What might not be clear is the fact that EVERYONE in ANY FRAME must agree that the light from B arrives at M' first. It's a fact independent of any reference frame.

Now Einstein uses this fact to deduce that according to the train frame observers the lights did not flash simultaneously: B must have flashed before A.

When you said "But the point of Einstein's argument is that whether the lights flash at the same time is frame dependent: train observers and embankment observers disagree", the frame dependent nature was what the thought experiment wanted to establish by showing that lights will not arrive simultaneously at M'. Now I am asking you people use meth to show this un-simultaneous arrivals.

See the above.

If you cannot, then the frame dependent nature is in doubt.

Only in your mind.

 

[longshinewoole]

Events can be viewed from either frame of reference. There is no contradiction in viewing events from one frame for convenience and then deducing what the other frame must see. But nowhere does Einstein contradict his statement that people traveling on the train view things from the train frame, while those on the embankment view things from the embankment frame.


Obviously a statement beginning with "Hence..." is not an independent statement, but a deduction from previous statements.


What flipflop?


I suppose Einstein thought this example simple enough that translating it into mathematical language was unnecessary. But if you insist:

Let's examine things from the viewpoint of the embankment observers. According to them, the lights flash simultaneously and are (say) a distance L apart. Let's say that the lights both flash at time t_0 = 0 (according to embankment clocks). Let's further call the time that the light from B arrives at M' to be t_1. During that time how far did the train move? If the speed of the train is v, the distance the train moved is v*t_1. So how far did the light have to travel in getting from B to M'? Not the full length of half the train (L/2), but only a distance equal to L/2 - v*t_1, since the train (and M') moved towards B.

Of course, during that same amount time the light from A also travels the same distance. But since M' has moved a distance v*t_1 towards B, the light from from A has not yet reached M'. The light moved a distance of L/2 - v*t_1 from A, but M' is already at a distance of L/2 + v*t_1.

So it should be clear, from our analysis of events seen from the embankment, that the light from B must arrive at M' before the light from A does. Got it?

What might not be clear is the fact that EVERYONE in ANY FRAME must agree that the light from B arrives at M' first. It's a fact independent of any reference frame.

Now Einstein uses this fact to deduce that according to the train frame observers the lights did not flash simultaneously: B must have flashed before A.


See the above.


Only in your mind.

Your meth analysis was completely false. Let me redraw Einstein thought experiment.

A__________M__________B.
A__________M'__________B.

Einstein's thought experiment stupilated that lightning stuck simultaneously at both ends A and B. Further it said "Then every event which takes place along the line also takes place at a particular point of the train." Therefore the events on the embankment were designated as A and B, and the events on the train were also designated as A and B. I said this (4 events) because of the fact that a long train was used by Einstein. That is, the train has both ends. The lightning struck at both ends of the embankment, also struck at both ends of the train, resulting in A and B on the embankment as well as A and B on the train. Now as the train moved to the right, after the lightning strikes, the thought experiment should look like this:

embankment: A__________M__________B.
the train:....A__________M'__________B.

When you said "But since M' has moved a distance v*t_1 towards B, the light from from A has not yet reached M'." , the A and B in your sentence was the A and B events on the embankment, not the events A and B on the train.

M' can have motion relative to the events on the embankment, but cannot have motion relative to the
events on the train. Therefore your meth analysis was only correct provided you were talking about M' moving relative to the embankment events.

But, why there was a long train? why there were observers on the train? We must therefore obey Einstein's words "People traveling in this train will with advantage view the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train."
That is, we cannot talk about M' moving relative to the embankment events. Since you were, your meth were false.

 

[RandallB]

Your meth analysis was completely false. Let me redraw Einstein thought experiment.

A__________M__________B.
A__________M'__________B.

Einstein's thought experiment stupilated that lightning stuck simultaneously at both ends A and B. ...
...:

embankment: A__________M__________B.
the train:....A__________M'__________B.

As I said back in post 5; your still not representing what Einstein said. Where is A' and B' on the train?? As vector distances from the M's; A = -B and A' = -B' but you seem to be saying here that A = A' and B = B'. You will never get anywhere if you think that is true.

As to Einstein "flip flop" just how do you think he was saying "first from the view of the train" (train ref frame) and "then from the view of the Embankment and train stations" (station ref frame). You need to translate his statements correctly or agaiin you will not get far.

 

[Doc Al]

Your meth analysis was completely false. Let me redraw Einstein thought experiment.

A__________M__________B.
A__________M'__________B.

An event is something that happens at a particular time and place. In this scenario there are two events: a light flash at A and a light flash at B. A & B are the locations at the ends of the embankment where the events took place, not the events themselves. Note how you added labels A & B to the train, which Einstein does not do. If you wish to label the ends of the train, do it this way so no one gets confused:

A__________M__________B.
A'_________ M'__________B'.

Realize also that this diagram is drawn from the viewpoint of the embankment observers, since according to them the ends of the train (A' & B') coincided with the ends of the platform (A & B) at the exact moment that the two flashes occurred. According to the embankment observers, the events happened simultaneously at locations A & B; According to the train observers, the events occurred at the ends of the train at locations A' & B' (but happened at different times).

Einstein's thought experiment stupilated that lightning stuck simultaneously at both ends A and B.

Right: According to embankment observers.

Further it said "Then every event which takes place along the line also takes place at a particular point of the train." Therefore the events on the embankment were designated as A and B, and the events on the train were also designated as A and B.

The ends of the train are labeled A' & B', not A & B which are locations on the embankment. (Note that Einstein does not label the ends of the train at all.)

I said this (4 events) because of the fact that a long train was used by Einstein. That is, the train has both ends. The lightning struck at both ends of the embankment, also struck at both ends of the train, resulting in A and B on the embankment as well as A and B on the train.

Again, there are only two events. But both events are observed by both train and embankment observers.

Now as the train moved to the right, after the lightning strikes, the thought experiment should look like this:

embankment: A__________M__________B.
the train:....A__________M'__________B.

Again, a less confusing way of drawing this diagram (which describes what is seen by embankment observers) would be:

embankment: A__________M__________B.
the train:....A'__________M'__________B'.

When you said "But since M' has moved a distance v*t_1 towards B, the light from from A has not yet reached M'." , the A and B in your sentence was the A and B events on the embankment, not the events A and B on the train.

Again, there are only two events, not four. According to the embankment observers--who drew this diagram (a diagram drawn by the train observers would be very different!)--the events took place at A and B. (Note how M' gets closer to B and further from A.)

M' can have motion relative to the events on the embankment, but cannot have motion relative to the
events on the train.

Almost right: M' moves with respect to the embankment, not with respect to the locations A' & B' where train observers saw the events to occur.

Therefore your meth analysis was only correct provided you were talking about M' moving relative to the embankment events.

Which is exactly what I (and Einstein) was talking about. Note where I made it clear by saying:

Let's examine things from the viewpoint of the embankment observers.

But, why there was a long train? why there were observers on the train? We must therefore obey Einstein's words "People traveling in this train will with advantage view the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train."
That is, we cannot talk about M' moving relative to the embankment events. Since you were, your meth were false.

Nonsense. M' is the location of an observer on the train--of course he moves with respect to the embankment. Think of M' as a person in the middle of the moving train--embankment observers can certainly observe and study his movements over time.

Try again!

 

[longshinewoole]

Again, there are only two events. But both events are observed by both train and embankment observers...

I believe there were four events because Einstein finally concluded that: "Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa." This vice versa means there were two event A' and B' on the train and another two A and B on the embankment. Earlier he also said that "Then every event which takes place along the line also takes place at a particular point of the train." This "at a particular point of the train" must mean A' and B'. If Einstein did not show A' and B', he did show them in his statements. I would say, it was another flipflop by him.

In both cases, it means there were four events like this (if you like I shall use primed letters):

embankment...A__________M__________B.
the train....A'__________M'__________B'.

According to Einstein, "People traveling in this train will with advantage view the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train." According to such a rule, M' on the train must view A' and B', not A and B. Furthermore, when the train is a "rigid reference-body", how can people in a rigid system observe events outside of this system? To say M' view events on the embankment must be wrong.

When M' view things in his own system, he will find A' and B' happened simultaneous, namely A'M'/c = M'B'/c. Einstein's thought experiment showed simultaneity is absolute, not relative.

Even if M' is able to view things outside of his system and is able to tell which of those outside light arrives at his eyes sooner or later, this same ability must also enable him to see that he is no longer midway between A and B. As such (not located midway between A and B), he must know he could not use the sooner and later arrivals of light to conclude that A and B are not simultaneous. Let us draw this picture:

A__________M___M'_______B.

It shows, when lightning strikes happened simultaneously at A and B, M' is able to see light from B and A, but also able to tell he is no longer midway between them. If M' is a good physicist, would he say lightning did not stike simultaneously at A and B? No way.

 

[cristo]

I believe there were four events..

What is your definition of an event? What are your four events in this scenario?

 

[RandallB]

I believe there were four events because Einstein finally concluded ... I would say, it was another flipflop by him.
...
If M' is a good physicist, would he say lightning did not stike simultaneously at A and B? No way.

No, its two events seen from two reference frames give four observations,

And if M’ is such a good physicist what is the explanation for the two light flashes arriving at different times to his view when he knows that one occurred at exactly the same distance of train of car lengths ahead of him as the distance of car lengths for the one behind him. If light travels at the same speed over his distances measured the only way the two strikes could be simultaneously in the train reference frame is if the flashes did arrive together at M’.

You need to do as Doc Al suggested and try again with real numbers:

Recommend you use Speed as 0.6c with Gamma factor1.250 and dilation factor 0.800

Set t=0 for A M and B and t’ =0 for M’

Use an easy distance like 10 light seconds (that is distance not time) for B. remember A = -B.
What is the distance for A’ & B’ ?
Give us times for;
t’ at A’(when t =0 at A)= Strike time’ for A’
t’ at B’(when t =0 at B)= Strike time’ for B’

Does Strike time’ for A’ = Strike time’ for B’ ………”No Way”
just as Einsein said.

 

[curt]

Unanswered Questions

Doc Al:

You said on 06-07-2007, 10:28 AM:
“Just because light takes equal time to cover equal distance doesn't mean that they arrive at the midpoint simultaneously.”

Why wouldn’t they? Please take no offense, but that sentence doesn’t make sense. If light, from both lightning strikes, travel at the same speed, then this means they cover equal distance over equal time. That is the definition of equal speed. If they cover equal distance over equal time, then mathematically speaking, they must arrive at the midpoint simultaneously. How would they not? If they don’t, then the speed of light must be different for the 2 lightning strikes.

You said:
“But the point of Einstein's argument is that whether the lights flash at the same time is frame dependent: train observers and embankment observers disagree.”

I still don’t understand why. I read Einstein’s chapter 9. I read the postings here. But, there isn’t any logical explanation of this.

You said:
“Just prior to your quoted sentences, Einstein gives a simple argument showing that the light from B must arrive at M' before the light from A.”

How does Einstein show that light from B must arrive at M’ before the light from A? Can you elaborate or provide his explanation? I don’t see any logical explanation of this.

RandallB:

You said on 06-07-2007, 10:50 AM:
“A’ & B’ (moving locations you do not show)”
Einstein’s chapter did not mention A’ & B’. Which chapter mentions this?

You said:
“B’ can directly see the lighting hit the ground outside the train well before A’ sees the ground hit by the second bolt of lightning from there common frame of reference a synchronized time. Even though they can both see the observers out side also observing the same event are displaying large clocks that read the same time at both A & B.”

I’m not sure I understand these sentences. Can you elaborate?

You said:
“The point is only A & B see the events as simultaneous.”
Which events? I can understand if A & B see the light arrive at the M simultaneously. But, they would see lightning strikes at A & B at different times, wouldn’t they?

You said:
“And since B’ sees the strike well before A’ and both are the same distance from M’ moving in the same frame – of course M’ will se the forward A strike before the B strike.”

Which lightning strike does B’ see well before A’? The strike at B? Again, why would M’ see the A strike before the B strike? To simply say that M’ would see the A strike before the B’ strike because the train is moving, does not explain why.

Doc Al:

You said on 06-09-2007, 08:49 PM:
“Let's examine things from the viewpoint of the embankment observers. According to them, the lights flash simultaneously and are (say) a distance L apart. Let's say that the lights both flash at time t_0 = 0 (according to embankment clocks). Let's further call the time that the light from B arrives at M' to be t_1. During that time how far did the train move? If the speed of the train is v, the distance the train moved is v*t_1. So how far did the light have to travel in getting from B to M'? Not the full length of half the train (L/2), but only a distance equal to L/2 - v*t_1, since the train (and M') moved towards B.”

You said the A and B are L apart. Then you said “…full length of half the train (L/2)”. Are you saying that the length of the train is L? Did Einstein say the length of the train is L? Why would the length of the train have to be L and how is this relevant? You said “but only a distance equal to L/2 - v*t_1, since the train (and M') moved towards B.” This is really confusing and doesn’t make sense. If L is the distance between A and B and also is the length of the train, and if M and M’ coincide, then that means the middle of the train is at M’ and M when the lights from the 2 lightning strikes hit M simultaneously, which that means the light did travel the “full length of half the train (L/2)”. You said “…but only a distance equal to L/2 - v*t_1, since the train (and M') moved towards B.” Are you implying that L/2 does not equal v*t_1 just because the train is moving towards B? If so, why don’t they equal?

You said:
“But since M' has moved a distance v*t_1 towards B”

Are you implying that M’ moves? How and why? Einstein said “Let M1 be the mid-point of the distance A B”. If M’ is at the mid-point of A and B, then it’s not moving, regardless if the train moves. M’ cannot not move because A and B don’t move.

You said:
“But since M' has moved a distance v*t_1 towards B, the light from from A has not yet reached M'. The light moved a distance of L/2 - v*t_1 from A, but M' is already at a distance of L/2 + v*t_1.”

Again, this doesn’t make sense. Why hasn’t the light from A reached M’ yet if M’ coincides with M? If M’ moved away from M, then you cannot use or refer to M’. You must use N’, O’ or P’.

RandallB:

You said Today, 11:10 AM:
“And if M’ is such a good physicist what is the explanation for the two light flashes arriving at different times to his view when he knows that one occurred at exactly the same distance of train of car lengths ahead of him as the distance of car lengths for the one behind him.”

The light flashes didn’t arrive at different times. They arrived at the same time.

Einstein never mentioned A’ or B’ or that lightning stuck at the end of the trains. Adding this in confuses and invalidates the argument. Even if there were A’ or B’, lightning did not strike A’ or B’ (end of the trains), because A’ is moving towards A and B’ is moving towards B when the lightning struck A and B. When A’ and B’ reach A and B, the light from the lightning strikes reach M and M’.

Please look at my attached figures (1 to 5). In figure 1, light from A and B reach simultaneously at the mid-point. In figure 2, an observer travels towards the mid-point/intersection. The observer can be any entity (a micron?). At the intersection, can we agree that that the observer sees the lights from A and B simultaneously? (These figures are like looking from the sky downwards toward the ground.) In figure 3, instead of traveling perpendicular, the observer travels at an angle towards the intersection. Is there any reason that the observer wouldn’t see the lights from A and B simultaneously at the intersection? In figure 4, the observer travels at even more of an angle. Is there any reason that the observer wouldn’t see the lights from A and B simultaneously at the intersection? In figure 5, the observer is traveling in the same line as the light from A. Is there any reason that the observer wouldn’t see the lights from A and B simultaneously at the intersection?

To me, this Einstein argument seems to have sentences which don’t make sense or are not logical.

Do we have the George Bush/Colin Powell effect here, where most Americans believed them because of their prominence? Last month, Al Gore said that 50% of Americans still believe that Iraq is related to 9/11. Is it possible that many mathematicians/physicists skim over Einstein’s explanations because of his prominence?

I apologize if my comments came across as offensive or rude. They are not meant to be. I’m just curious, inquisitive and maybe confused.

 

[MeJennifer]

If light, from both lightning strikes, travel at the same speed, then this means they cover equal distance over equal time. That is the definition of equal speed. If they cover equal distance over equal time, then mathematically speaking, they must arrive at the midpoint simultaneously. How would they not? If they don’t, then the speed of light must be different for the 2 lightning strikes.

In the theory of relativity it is postulated that the speed of light is the same for all inertial observers. Light, in the theory of relativity has no frame of reference, in other words light has no speed with respect to absolute space. The speed of light in the theory of relativity is measured only in relation to inertial bodies that have mass.

Some people simply do not like that and prefer a different ontology. For instance the Lorentz ether theory produces identical numerical results as special relativity.

But since this is the relativity forum, which is intended to help people in understanding this theory, there is not much of a point arguing for alternative theories here.

 

[Doc Al]

I believe there were four events because Einstein finally concluded that: "Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa." This vice versa means there were two event A' and B' on the train and another two A and B on the embankment.

The two events in this scenario are the lightning strikes at each end of the train. There are only two events, viewable by all observers whether on the train or on the embankment. (The entire point of this discussion is that different observers can see the same events happening at different times!) Note that it is you, not Einstein, who refers to A' and B' as events.

Earlier he also said that "Then every event which takes place along the line also takes place at a particular point of the train." This "at a particular point of the train" must mean A' and B'. If Einstein did not show A' and B', he did show them in his statements. I would say, it was another flipflop by him.

Note the careful use of "at a particular point". A' and B' are particular points--the ends of the train--not events. (Sounds like you are the one flipflopping words around. ) There are just two events: Embankment observers would naturally say that these events occurred at locations A and B with respect to the embankment; Train observers would naturally say that these same events--the lightning strikes--occurred at locations A' and B' with respect to the train.

In both cases, it means there were four events like this (if you like I shall use primed letters):

embankment...A__________M__________B.
the train....A'__________M'__________B'.

Nope. Just two events described by different sets of observers.

According to Einstein, "People traveling in this train will with advantage view the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train." According to such a rule, M' on the train must view A' and B', not A and B. Furthermore, when the train is a "rigid reference-body", how can people in a rigid system observe events outside of this system? To say M' view events on the embankment must be wrong.

Again, an event is just something that happens at a particular place and time. It is viewable by anyone. Of course, different observers will use their own reference frame and clocks to describe the place and time that the event occurred.

When M' view things in his own system, he will find A' and B' happened simultaneous, namely A'M'/c = M'B'/c. Einstein's thought experiment showed simultaneity is absolute, not relative.

All you've stated here is that according to the train observers, the light travels the same distance in the same time to reach M'. This is true! But it does not imply that the flashes occurred simultaneously (which would not be true). (Think about it: Alice and Bob each live 10 miles from their office and travel at the same speed. Do they arrive at work at the same time? Only if they leave home at the same time!) The entire point of this exercise is that the light from each flash does not reach M' at the same time.

Even if M' is able to view things outside of his system and is able to tell which of those outside light arrives at his eyes sooner or later, this same ability must also enable him to see that he is no longer midway between A and B. As such (not located midway between A and B), he must know he could not use the sooner and later arrivals of light to conclude that A and B are not simultaneous.

But M' knows exactly where the flashes occurred--according to his reference (the train, of course) they occurred at A' and B', the ends of the train! (Anyone can verify this--the lightning made black burn marks on the train and the embankment.) He couldn't care less what reference frame the embankment observers use.

So, using his own train-based reference frame and clocks, he is forced to conclude that the flashes must have occurred at different times (since the light took the same time to reach him, having traveled the same distance). So he must conclude that the flash at B' occurred first, followed by the flash at A'.

It shows, when lightning strikes happened simultaneously at A and B, M' is able to see light from B and A, but also able to tell he is no longer midway between them. If M' is a good physicist, would he say lightning did not stike simultaneously at A and B? No way.

All the train observers have to go by is their own observations. They measure the location of the events (the lightning strikes) with respect to the train. Everyone agrees that the light from the two flashes arrives at M' at different times. But each frame will disagree as to why that is.

The embankment frame says: The light arrived at M' at different times because M' was moving towards one flash and away from the other.

The train frame says: The light arrived at M' at different times because the lightning struck at different times.

 

[RandallB]

Doc Al: You said
“Just because light takes equal time to cover equal distance doesn't mean that they arrive at the midpoint simultaneously.”

Why wouldn’t they? Please take no offense, but that sentence doesn’t make sense.

Ther could arrive at the same time if they start at different time could they.

RandallB: You said
“A’ & B’ (moving locations you do not show)”
Einstein’s chapter did not mention A’ & B’. ..
.
You said ..“The point is only A & B see the events as simultaneous.”

Which events? I can understand if A & B see the light arrive at the M simultaneously. But, they would see lightning strikes at A & B at different times, wouldn’t they?...

? the entire problem is based on two simultaneously lightning strikes at A & B while A' is at A and B' is at B.

Einstein used the term "Train" { view, pespective, measure, or whatever } for anything ?' ie. t' A' B' M' whatever'

Einstein used the term "Embankment" { view, pespective, measure, or whatever } for anything ?* ( where * means NO PRIME MARK) ie. t A B M whatever*

Have you worked the simple problem in post #20.

 

[Doc Al]

Doc Al:

You said on 06-07-2007, 10:28 AM:
“Just because light takes equal time to cover equal distance doesn't mean that they arrive at the midpoint simultaneously.”

Why wouldn’t they? Please take no offense, but that sentence doesn’t make sense. If light, from both lightning strikes, travel at the same speed, then this means they cover equal distance over equal time. That is the definition of equal speed.

So far, so good.

If they cover equal distance over equal time, then mathematically speaking, they must arrive at the midpoint simultaneously. How would they not? If they don’t, then the speed of light must be different for the 2 lightning strikes.

Nope. See my response to this very point in my last post.

You said:
“But the point of Einstein's argument is that whether the lights flash at the same time is frame dependent: train observers and embankment observers disagree.”

I still don’t understand why. I read Einstein’s chapter 9. I read the postings here. But, there isn’t any logical explanation of this.

You said:
“Just prior to your quoted sentences, Einstein gives a simple argument showing that the light from B must arrive at M' before the light from A.”

How does Einstein show that light from B must arrive at M’ before the light from A? Can you elaborate or provide his explanation? I don’t see any logical explanation of this.

I gave a detailed mathematical description of things in an earlier post--please reread it.

Doc Al:

You said on 06-09-2007, 08:49 PM:
“Let's examine things from the viewpoint of the embankment observers. According to them, the lights flash simultaneously and are (say) a distance L apart. Let's say that the lights both flash at time t_0 = 0 (according to embankment clocks). Let's further call the time that the light from B arrives at M' to be t_1. During that time how far did the train move? If the speed of the train is v, the distance the train moved is v*t_1. So how far did the light have to travel in getting from B to M'? Not the full length of half the train (L/2), but only a distance equal to L/2 - v*t_1, since the train (and M') moved towards B.”

You said the A and B are L apart. Then you said “…full length of half the train (L/2)”. Are you saying that the length of the train is L? Did Einstein say the length of the train is L? Why would the length of the train have to be L and how is this relevant?

I was, as requested, giving a mathematical description of the situation. I used L to represent the distance between the ends of the embankment: A & B. (It's also the length of the train as measured by embankment observers.)

You said “but only a distance equal to L/2 - v*t_1, since the train (and M') moved towards B.” This is really confusing and doesn’t make sense. If L is the distance between A and B and also is the length of the train, and if M and M’ coincide, then that means the middle of the train is at M’ and M when the lights from the 2 lightning strikes hit M simultaneously, which that means the light did travel the “full length of half the train (L/2)”. You said “…but only a distance equal to L/2 - v*t_1, since the train (and M') moved towards B.” Are you implying that L/2 does not equal v*t_1 just because the train is moving towards B? If so, why don’t they equal?

L/2 is the distance between M and B; v*t_1 is the distance light has to travel in getting from B to M'--it's certainly not equal to L/2! M' moves! (According to the embankment observers, at least--which is what we are talking about.)

You said:
“But since M' has moved a distance v*t_1 towards B”

Are you implying that M’ moves? How and why? Einstein said “Let M1 be the mid-point of the distance A B”. If M’ is at the mid-point of A and B, then it’s not moving, regardless if the train moves. M’ cannot not move because A and B don’t move.

M' is the midpoint of the train. Of course it moves. (Don't confuse M' with M.)

You said:
“But since M' has moved a distance v*t_1 towards B, the light from from A has not yet reached M'. The light moved a distance of L/2 - v*t_1 from A, but M' is already at a distance of L/2 + v*t_1.”

Again, this doesn’t make sense. Why hasn’t the light from A reached M’ yet if M’ coincides with M? If M’ moved away from M, then you cannot use or refer to M’. You must use N’, O’ or P’.

M only coincides with M' at one particular instant. The train is moving! And the entire point is to show that light arrives at M' at different times--of course I can refer to M'.

I urge you, if you are seriously interested in this topic, to get and study one of the books mentioned at the end of post #4. Each of them is vastly superior--pedagogically speaking--to Einstein's popular book.

 

[curt]

Unanswered Questions

Everybody,
Thanks for replying.

MeJennifer,

I wasn’t trying to argue that the speed of light is different for the two lightning strikes from A and B. Doc Al said “Just because light takes equal time to cover equal distance doesn't mean that they arrive at the midpoint simultaneously.” I was arguing that they must arrive at the midpoint simultaneously if the speed of light from A and B are the same.

Doc Al,

You said “The entire point of this exercise is that the light from each flash does not reach M' at the same time.” and “Everyone agrees that the light from the two flashes arrives at M' at different times. But each frame will disagree as to why that is.” I still did not read any explanation as to why or how the lights from A and B reached M’ at the different times. If M’ coincides with M, how and why did the lights right M’ at different times?

You said in post #25: “Nope. See my response to this very point in my last post.” My apologies, but I don’t see your response to my point.

You said “I gave a detailed mathematical description of things in an earlier post--please reread it.” My apologies again. I’ve read every one of your posts. Are you referring to post #14? If so, I had argued the math in your post.

You said “v*t_1 is the distance light has to travel in getting from B to M'--it's certainly not equal to L/2!” Why not? Even if M’ moves, we are referring to M’ when it coincides and is at M, which is the mid-point of A and B. We are not referring to M’ when it is physically closer to A or B. M’ coincides with the physical mid-point of M.

So, if we refer to M’, like you are, then M’ is referring to the physical mid-point of M. Therefore M’ is equi-distance from A and B, is it not?

Have you looked at my attached diagram (figures 1 to 5) and associated explanation in post #21? Do you agree or disagree with it?

RandallB,

You said “Ther could arrive at the same time if they start at different time could they.” I don’t understand this sentence. Can you elaborate?

You said “the entire problem is based on two simultaneously lightning strikes at A & B while A' is at A and B' is at B.” Where did Einstein mention A’ and B’? If A’ is at A and B’ is at B, are you implying that the train is the same length as the distance from A to B? If so, why? What relevance does this have?

If you say at A’ is at A and B’ is at B, then the answer to your question “What is the distance for A’ & B’ ?” in post #20, is A’ = -B’, where A’ – B’ = 10 light seconds of distance. If I have this wrong, please explain.

If A’ – B’ = 10 light seconds = A – B, then Strike time’ for A’ = Strike time’ for B’. If I have this wrong, please explain.

Have you looked at my attached diagram (figures 1 to 5) and associated explanation in post #21? Do you agree or disagree with it?

 

[nrqed]

Doc Al:

You said on 06-07-2007, 10:28 AM:
“Just because light takes equal time to cover equal distance doesn't mean that they arrive at the midpoint simultaneously.”

Why wouldn’t they? Please take no offense, but that sentence doesn’t make sense. If light, from both lightning strikes, travel at the same speed, then this means they cover equal distance over equal time.

True

That is the definition of equal speed. If they cover equal distance over equal time, then mathematically speaking, they must arrive at the midpoint simultaneously.

Only assuming that they were emitted at the same time . Of course, if two light signals are emitted at different times, even though they cover equal distances in equal times, they will not arrive at the midpoint simultaneously.

This is one fo the key points of special relativity: the concept of simultaneity is relative. So two events which occur at the same time in one frame will not occur simultaneously in another frame moving relative to the first one.

This is a common source of confusion for people learning SR: they run into all sort of apparent paradoxes because they implicitly use an absolute time by implying that if two events are simultaneous in one frame, they are simultaneous in all frames.

However, the point of this gedanken experiment is to show that if the speedof light is an invariant, the concept of simultaneity is frame dependent!.

The steps are:

Let's assume that the two events are simultaneous in the frame of the embankment.

Then, looking at the situation from the point of view of the embankment, it is obvious that the beam of light from the front of the train will reach the
middle of the train before other light beam. This is obvious because the middle of the train is moving toward the beam of light traveling toward the left (emitted at B) while it's moving away from the beam emitted at A. Since the speed of light is not infinite, ithe middle of the train will meet the light emitted at B before being reached by the beam of light emitted at A. Even in Galilean physics this conclusion would be the same so there is nothing strange about that.

Therefore, someone standing at the middle of the train will see the light flash from the front before the light flash from the back. But since even in the frame of the train, the two lightning impacts occur at the same distance, and light still travels at c, the person in the middle of the train concludes that the lightning impact at the front of the train must have occurred before the impact at the back as measured in the frame of the train .

So there you have it: the two impacts were simultaneous in the frame of the embankment but not in the frame of the train.

One thing that is interesting to ponder is what would be the difference in a Galilean/Newtonian context. well, first of all, time si absolute so the two events would also be simultaneous in the frame of the train. But how would that come about? It's just that speed of light is also relative, in classical physics. So if the two beams of light have the same speed in the frame of the embankment, they would not have the same speed in th eframe of the train. The person at the middle of the train would *still* see the light coming from B before the light coming from A, but the first beam would be traveling faster as well. Taking this difference of speed into account, the observer at the middle of the train would have to do some calculation (so in a sense, the example is more complicated in the Newtonian context!) and would find, lo and behold, that the two lightning impacts actually occurred at the same time even in the frame of the train (the difference of speed of the two light beams would compensate exactly the difference of arrival time).

You said:
“But the point of Einstein's argument is that whether the lights flash at the same time is frame dependent: train observers and embankment observers disagree.”

I still don’t understand why. I read Einstein’s chapter 9. I read the postings here. But, there isn’t any logical explanation of this.

Do you follow my example?

You said:
“Just prior to your quoted sentences, Einstein gives a simple argument showing that the light from B must arrive at M' before the light from A.”

How does Einstein show that light from B must arrive at M’ before the light from A? Can you elaborate or provide his explanation? I don’t see any logical explanation of this.

I tried to explain this above.

Hope this helps

Patrick

 

[Doc Al]

I wasn’t trying to argue that the speed of light is different for the two lightning strikes from A and B. Doc Al said “Just because light takes equal time to cover equal distance doesn't mean that they arrive at the midpoint simultaneously.” I was arguing that they must arrive at the midpoint simultaneously if the speed of light from A and B are the same.

Did you read post #23?

Doc Al,

You said “The entire point of this exercise is that the light from each flash does not reach M' at the same time.” and “Everyone agrees that the light from the two flashes arrives at M' at different times. But each frame will disagree as to why that is.” I still did not read any explanation as to why or how the lights from A and B reached M’ at the different times. If M’ coincides with M, how and why did the lights right M’ at different times?

Where did you get the impression that M' and M coincide except for a passing moment? M' only coincides with M at the moment (according to embankment clocks) that the lightning strikes the ends of the train and platform. By the time the light from B reaches M', M' has moved closer to B (according to embankment observers).

You said in post #25: “Nope. See my response to this very point in my last post.” My apologies, but I don’t see your response to my point.

Again, did you read post #23?

You had said (in post #21):

If they cover equal distance over equal time, then mathematically speaking, they must arrive at the midpoint simultaneously. How would they not? If they don’t, then the speed of light must be different for the 2 lightning strikes.​

I answered this exact question in post #23. (Please read it!) In a nutshell, according to the train observers the light does travel equal distances in getting to M'. That just means it takes equal time for each light beam to reach M'. But the light would only arrive at M' simultaneous if--according to the train observers--the lights flashed simultaneously. Which they do not.

The light does reach the midpoint of the embankment at the same time--but M' is long gone by then.

You said “I gave a detailed mathematical description of things in an earlier post--please reread it.” My apologies again. I’ve read every one of your posts. Are you referring to post #14? If so, I had argued the math in your post.

Your arguments do not hold up, as I described earlier.

You said “v*t_1 is the distance light has to travel in getting from B to M'--it's certainly not equal to L/2!” Why not? Even if M’ moves, we are referring to M’ when it coincides and is at M, which is the mid-point of A and B. We are not referring to M’ when it is physically closer to A or B. M’ coincides with the physical mid-point of M.

Imagine that there is a person riding the train at its midpoint--location M'. We want to know when the light hits that observer, when it reaches point M'. And that point moves!

So, if we refer to M’, like you are, then M’ is referring to the physical mid-point of M. Therefore M’ is equi-distance from A and B, is it not?

If M' and M coincided there would be little point in having separate symbols for each. M' is equidistant from the ends of the train--points A' and B'. Of course, due to our arrangement, M' happens to coincide with M at the moment the lights flash--according to the embankment observers.

Have you looked at my attached diagram (figures 1 to 5) and associated explanation in post #21? Do you agree or disagree with it?

You are illustrating a different scenario than the one we are discussing, so I don't see the point. Does the light arrive at the same time at the midpoint of the embankment (point M)? Of course! Can you arrange for a moving observer to pass through that point exactly at the right moment? Sure! Will that observer see the light arrive at the same time. Of course! But that's not the situation we are discussing. In our scenario, the lightning hits the ends of the train and platform together--not so in yours.

 

[complexchaos]

Math

Your meth analysis was completely false. Let me redraw Einstein thought experiment.

A__________M__________B.
A__________M'__________B.

Einstein's thought experiment stupilated that lightning stuck simultaneously at both ends A and B. Further it said "Then every event which takes place along the line also takes place at a particular point of the train." Therefore the events on the embankment were designated as A and B, and the events on the train were also designated as A and B. I said this (4 events) because of the fact that a long train was used by Einstein. That is, the train has both ends. The lightning struck at both ends of the embankment, also struck at both ends of the train, resulting in A and B on the embankment as well as A and B on the train. Now as the train moved to the right, after the lightning strikes, the thought experiment should look like this:

embankment: A__________M__________B.
the train:....A__________M'__________B.

When you said "But since M' has moved a distance v*t_1 towards B, the light from from A has not yet reached M'." , the A and B in your sentence was the A and B events on the embankment, not the events A and B on the train.

M' can have motion relative to the events on the embankment, but cannot have motion relative to the
events on the train. Therefore your meth analysis was only correct provided you were talking about M' moving relative to the embankment events.

But, why there was a long train? why there were observers on the train? We must therefore obey Einstein's words "People traveling in this train will with advantage view the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train."
That is, we cannot talk about M' moving relative to the embankment events. Since you were, your meth were false.

There is one fundamental tenant of Special Relativity that I feel is either being completely ignored or misunderstood. And that is the fact that the speed of light is invariant. This means that the speed of light appears to be the same regardless of what frame of reference you are in.

An example of this would be if you were to shoot a light beam at your annoying friend who was moving .99 times the speed of light relative to you, even though it may seem that he has effectively slowed down the speed of light intuitively (you could use a Galilean Transformation and assume the light is approaching him at (c-.99c). How ever the speed of light is constant so he sees it approaching him at the speed of light too.

To take this effect into account, one must apply a Lorentz transformation to change reference frames.

Written with four vectors it is given by:

|ct'| = |Y -BY| |ct|
|x' | = |-BY Y| |x |, (matrix notation)

where Y= 1/sqr(1-B^2) and B= v/c, v is the velocity of the new reference frame, x and t are are the space time coordinates before the transformation and the x' and t' are after the change in reference frame.

When you consider two points in time and space you get:

|c(t'2 - t'1)| = |Y -BY| |c(t2 - t1)|
| x'2 - x'1 | = |-BY Y| | x2 - x1 | (matrix notation)

Now let's assume that you have two events occurring at a separated distance simultaneously. This means that t2 - t1 = 0. We now have:

c(t'2 - t'1) = -BY(x2 - x1).

Since the two events are separated by a distance (ie. x2 - x1 is not 0). Then the separation in time of the events in the new reference frame is not 0.

Simultaneity is only frame dependent if the events are separated in space.

There you have it, since the events on the train were separated by a distance, then simultaneity is completely relative.

I hope that math is sufficient for you, as it is relatively simple and straight forward.

If you need more help on Lorentz transformations, please look them up. They follow directly from the fact that the speed of light is constant in all reference frames.

By the way, I'm not sure why you keep using the word meth instead of math. Unless I have misunderstood your meaning.

 

[complexchaos]

Please look at my attached figures (1 to 5). In figure 1, light from A and B reach simultaneously at the mid-point. In figure 2, an observer travels towards the mid-point/intersection. The observer can be any entity (a micron?). At the intersection, can we agree that that the observer sees the lights from A and B simultaneously? (These figures are like looking from the sky downwards toward the ground.) In figure 3, instead of traveling perpendicular, the observer travels at an angle towards the intersection. Is there any reason that the observer wouldn’t see the lights from A and B simultaneously at the intersection? In figure 4, the observer travels at even more of an angle. Is there any reason that the observer wouldn’t see the lights from A and B simultaneously at the intersection? In figure 5, the observer is traveling in the same line as the light from A. Is there any reason that the observer wouldn’t see the lights from A and B simultaneously at the intersection?

It depends, in your diagram, on which event the observer is trying to observe, and what direction the observer is traveling in, but not what its position is.

If you are talking about an event that is occurring in the same place. Then every figure in you diagram will see them occurring at the same time.

However if you are talking about two events occurring in the stationary frame at the same time, but different places. Then the answer is different. As long as the observer is traveling with some component in the direction of separation, then the events will occur at different times. To calculate the sloped observer path, a four vector in x, y must be used.

Lorentz transformations are the key to understanding the confusion in the wake of special relativity. They are derived very simply from the invariance of the speed of light as verified by Michelson and Morley. Once you apply them to any situation, much of the confusion is gone. It is a powerful reductionist approach to the very confusing situations in Relativity.

To me, this Einstein argument seems to have sentences which don’t make sense or are not logical.

Do we have the George Bush/Colin Powell effect here, where most Americans believed them because of their prominence? Last month, Al Gore said that 50% of Americans still believe that Iraq is related to 9/11. Is it possible that many mathematicians/physicists skim over Einstein’s explanations because of his prominence?

This is not necessarily true. This problem is from special relativity. Einstein had little to no prominence when he came out with his theory, and so blind acceptance was not much of an issue. Einsteins ideas actually came under tremendous scrutiny, and many experts on physics (especially those with different theories) criticized him heavily.

However, his theory withheld the scrutiny, and is now widely accepted. I find it very hard to believe that something as simple as simultaneity in special relativity can be wrong and be so widely accepted for so long (especially by todays quantum physicists, who can't deal with the idea of no simultaneity).

I hope i was clear on everything.

I would have shown you some math to convince you, but I am new here and I am very bad at printing Math is ASCII. You would think that they would have some simple equation editors in a physics forum site.

 

[longshinewoole]

The two events in this scenario are the lightning strikes at each end of the train. There are only two events, viewable by all observers whether on the train or on the embankment. (The entire point of this discussion is that different observers can see the same events happening at different times!) Note that it is you, not Einstein, who refers to A' and B' as events.

Note the careful use of "at a particular point". A' and B' are particular points--the ends of the train--not events. (Sounds like you are the one flipflopping words around. ) There are just two events: Embankment observers would naturally say that these events occurred at locations A and B with respect to the embankment; Train observers would naturally say that these same events--the lightning strikes--occurred at locations A' and B' with respect to the train.

Einstein said:
"People traveling in this train will with advantage view the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train."

The words "also takes place" in the second sentence obviously says there are events taking place on the train.

If there are only two events A and B on the embankment, he must say "Then every event which takes place along the line will NOT take place at a particular point of the train."

If there are only two events A and B, then his experiment should look like this:

embankment: A_________M_________B.
the train...:__________M'__________.

Then how could he use that "vise versa"?

Now you said "But M' knows exactly where the flashes occurred--according to his reference (the train, of course) they occurred at A' and B', the ends of the train!" To me you were saying the samething as Einstein did: events taking place on the embankment also take place on the train. Due to the movement of the train, will a total of 4 events be created?

Now you said this: "All the train observers have to go by is their own observations. They measure the location of the events (the lightning strikes) with respect to the train. Everyone agrees that the light from the two flashes arrives at M' at different times. But each frame will disagree as to why that is."

If what the train observer observed was the light from A' and B' [according to his reference (the train, of course) they occurred at A' and B'], how could they agree that the light from A' and B' arrives at DIFFERENT TIMES? To this question of mine, I request you use methematics to show how "they measure." Don't use affirmative but ambiguous sentences such "Everyone agrees that the light from the two flashes arrives at M' at different times." Ambiguous because the phrase "two flashes" could mean either A and B, or A' and B'.

 

[complexchaos]

If there are only two events A and B on the embankment, he must say "Then every event which takes place along the line will NOT take place at a particular point of the train."

Einstein does not say that the events occur on the embankment, there are obviously only two events and they are viewed in two different frames of reference.

The people on the embankment will see two events and the people on the train will see the same two events, just in a different way.

This question seems to be more about semantics than it does about the actual essence of Einsteins theory. I believe this forum was entitled "Was Einstein Wrong?". Did you mean in this particular thought experiment, or with the concept of simultaneity in general?

I showed in my previous posts why simultaneity is relative, is that not enough?

 

[pervect]

A few comments: I've noticed that a lot of people have a hard time of grasping or accepting the concept of the relativity of simultaneity.

I gather this has been also noted in the literature, for instance
] "The challenge of changing deeply held student beliefs about the relativity
of simultaneity" [/url]

I think there have been many other papers on this and related topics (about how to teach relataivity) as well, though Scherr seems to have done more work with actual students than some of the other papers I remember reading.

I've been looking for websites that take approaches inspired by Scherr's work. While I have found one

http://webphysics.davidson.edu/physlet_resources/special_relativity/

it seems clunky. For instance, if the student clicks on the first lesson, and hits play, nothing happens. Furthermore, if he reads further, and clicks on "Synchronization procedure A", and THEN hits play, nothing APPEARS to happen, but the example is actually proceeding - just at a snail's pace.

However, if the student or reader (including some of the participants in this thread) did have the patience to work through all of the examples in order, I have a feeling that they might learn something. (I would omit Synchronization procedure A, for all but the most patient, however! The only point of this applet is to point out that you can synchronize clocks by hand-carrying them at a very low velocity, but that this process takes a considerable amount of time.)

The logic is all there, along with the graphics (though the later are somewhat clunky). It starts out with a disucssion of how, experimentally, one actually synchronizes clocks, moves to the distinction between what one "sees" directly and the coordinates one gives to an event, and finally presents the space-time diagrams of the train platform experiment along with a parallel animated pictorial representation.

One might wish that they, in addition to the above discussion how one synchronizes clocks, that they discussed WHY one synchronizes clocks - i.e. points out that satisfying Newton's laws requires that one measure velocities with properly synchronized clocks. This doesn't seem to be directly discussed in Scherr's research, however. It could be said that it's obvious, but a lot of things covered are very obvious .

The fundamental idea is (IMO) that the logical chain of how and why relativity requires one to abandon absolute synchronization be presented in a very complete, detailed, and thorough manner, even though it does make the presentation move at a snail's pace. Otherwise the old ideas are not really completely eradicated, but sill present, waiting to reappear and cause errors to be made.

Anyway, there's a fair amount of material there, and it's inspired by some actual research on how students learn, so it might be helpful to the really motivated.

I'm still looking for a better (free) visual presentation of the same material, however.

 

[cristo]

The words "also takes place" in the second sentence obviously says there are events taking place on the train.

You still appear to be highly confused by the meaning of the word "event." There are multiple posts above telling you that there are not four events; there are merely two events observed in two different reference frames. This, to me, seems to be your most fundamental confusion.

I would have shown you some math to convince you, but I am new here and I am very bad at printing Math is ASCII. You would think that they would have some simple equation editors in a physics forum site.

There is-- LaTex is enabled. Use the tags [ tex] and [ /tex] around your maths (without the spaces). There is a thread at the top of the tutorial forum if you get stuck.

 

[longshinewoole]

You still appear to be highly confused by the meaning of the word "event." There are multiple posts above telling you that there are not four events; there are merely two events observed in two different reference frames. This, to me, seems to be your most fundamental confusion.

I don't think I was onfused by the meaning of the word event. It was Einstein who said so: events which take place on the line also take place at a particular place on the train.

Besides, Einstein also used "vise versa" to imply that there were 4 events. If there were no events on the train, how could he said vise versa?

Let me temporarily agree to your "two event" idea. Then Einstein's thought experiment would look like this:

Embankment:A__________M__________B.
The train moved...:_________M'__________.

M' is no longer midway between A and B. Light from B of course will reach M' sooner than that from A. Can M' conclude (from this different arrivals of light) that the 2 events A and B not simultaneous?

No way.