Two lightnings that happen at the same time, a train and a passanger

[Nikitin]

allright, I'm finishing up my final Gymnasium physics course and the weirdest chapters (QM and Einstein) are at the end.

So here is a book-example I don't understand:

Lightning strikes at point A and B at the same time (if an outside observer is watching). Between A and B is a train moving at a constant speed in the direction AB. An observer M is sitting right in the middle of the train, ie right in the middle of A and B.

The observer measures that he light coming from B reaches him before the light from A.

OK this is weird. I thought that that speed of light is always c to whoever the observer is. So since the light from A and B is approaching the dude at the same speed, shouldn't the light from A & B reach him at the same time?

If the observer sees the light from B first, this would mean that the observer's relative speed to the light from B is > C.

 

[Doc Al]

The observer measures that he light coming from B reaches him before the light from A.

Note: Everyone (even the outside observer) agrees that light reaches M at different times.

OK this is weird. I thought that that speed of light is always c to whoever the observer is. So since the light from A and B is approaching the dude at the same speed, shouldn't the light from A & B reach him at the same time?

Only if the light starts out at the same time, which is the point. According to the train observers, the lightning strikes were not at the same time. Simultaneity is frame dependent.

 

[Nikitin]

What? Really? I am so confused, why? Is this just some excuse used to claim that c is always constant?

 

[Nikitin]

also can you help me with some math? how do I turn t₀²(1 - c²/v²) to the lorentz factor? I don't know how to convert (1 - c²/v²)^-1 into (1 - v²/c²)

 

[Doc Al]

What? obviously the light starts out at the same time..?? how can this be possible lol

The lightning strikes at the same time according to the outside observer on the tracks. But if we assume that light travels at the same speed in every frame, train observers are forced to concluded that the lightning struck B before it struck A.

 

[Nikitin]

so this is just an excuse to say that c is always constant?

well we know how that cern thing went...

 

[Doc Al]

so this is just an excuse to say that c is always constant?

No, it's a consequence of c being invariant. (And overwhelmingly supported experimentally.)

well we know how that cern thing went...

I assume you're joking.

 

[Nikitin]

OK, can you help me with post #4?

thanks for ur patience btw, I really appreciate the help

 

[Doc Al]

also can you help me with some math? how do I turn t₀²(1 - c²/v²) to the lorentz factor? I don't know how to convert (1 - c²/v²)^-1 into (1 - v²/c²)

Where is this coming from?

In any case:

(1 - c²/v²) = - (c²/v²)(1 - v²/c²)

 

[Nikitin]

well the book says

2) t² = c²t₀²/(c²-v²)

==> 3) t = t₀/sqrt(1 - v²/c²)

I don't get how they went from 2 to 3

 

[Doc Al]

well the book says

2) t² = c²t₀²/(c²-v²)

==> 3) t = t₀/sqrt(1 - v²/c²)

I don't get how they went from 2 to 3

t² = c²t₀²/(c²-v²)

t² = t₀²/(1-v²/c²)

Got it? (Divide top and bottom of the fraction by c².)

 

[Nikitin]

Oh oops thanks lol

 

[Nikitin]

I got another problem, pls help: Inside a spaceship passing Earth at 0.6c, time goes slower inside the ship from the POV of earth. But, from the spaceship's POV the Earth is moving backwards at 0.6c so the Earth is the one whose time is slowing down?

The book claims this isn't a contradiction.. but how?

 

[Erland]

I've said it before and I say it again: I don't like this example. I only get confused when I think of it. But there is a simpler example which demonstrates the relativity of simultaneity. I quote myself from another post:

"... imagine a light being turned on in the middle of the train. The light reaches the front and the back of the train simultaneously, according to an observer on the train. But according to an observer on the embankment, the light will reach the back of the train before it reaches the front of the train, because according to such an observer, the light that reaches the back of the train will have traveled a shorter distance than the light that reaches the front of the train, since train is moving, according to this observer."

 

[Erland]

I got another problem, pls help: Inside a spaceship passing Earth at 0.6c, time goes slower inside the ship from the POV of earth. But, from the spaceship's POV the Earth is moving backwards at 0.6c so the Earth is the one whose time is slowing down?

The book claims this isn't a contradiction.. but how?

I think it is easier to see this if we think of a train instead of a spaceship. Again, I refer to another post of my own, where I try to explain this:

https://www.physicsforums.com/showthread.php?t=468826

 

[Nikitin]

So if the Earth gets accelerated so much that it catches up to the spaceship and moves parallel to it at the speed 0.6c, Earthlings who launch themselves in rockets and visit the spaceship find out that the spaceship guys are old?

That.. can't be possible?

 

[Erland]

So if the Earth gets accelerated so much that it catches up to the spaceship and moves parallel to it at the speed 0.6c, Earthlings who launch themselves in rockets and visit the spaceship find out that the spaceship guys are old?

That.. can't be possible?

As far as I undertand it, it will be as you write (provided that the rockets you mention have much smaller velocities than 0.6 c) because Earth is the body which accelerates in this case.

And well, I guess it wouldn't be possible to accelerate the Earth to the speed 0.6 c.

 

[2clockdude]

Simultaneity is frame dependent.

But how can simultaneity be frame dependent when events themselves are frame independent? In other words, since events occur independently of any coordinates or frame, i.e., since events occur in only one way, simultaneity cannot be frame dependent.

I agree that light from events can reach observers in different frames differently, but what the heck has this got to do with the events themselves? I would say that it has everything to do with said observers physically separating during the observation, but nothing to do with how the events themselves actually occurred.

What say you?

 

[Erland]

But how can simultaneity be frame dependent when events themselves are frame independent? In other words, since events occur independently of any coordinates or frame, i.e., since events occur in only one way, simultaneity cannot be frame dependent.

In SR. time is just a coordinate. The phenomenon is analogous to the following: If we rotate a cartesian coordinate system in the plane, two points which had the same x-coordinate before the rotation will have unequal x-coordinates after the rotation.

 

[DaveC426913]

But how can simultaneity be frame dependent when events themselves are frame independent? In other words, since events occur independently of any coordinates or frame, i.e., since events occur in only one way, simultaneity cannot be frame dependent.

I agree that light from events can reach observers in different frames differently, but what the heck has this got to do with the events themselves? I would say that it has everything to do with said observers physically separating during the observation, but nothing to do with how the events themselves actually occurred.

What say you?

Two events are separated by spacetime (otherwise there's only one event). How much time they are separated by is dependent on the observer's frame of reference.

 

[2clockdude]

Two events are separated by spacetime (otherwise there's only one event). How much time they are separated by is dependent on the observer's frame of reference.

Your "time" is a coordinate value, but all physical phenomena are
completely independent of coordinates, because Nature quite clearly
doesn't need or use coordinates. Coordinates are merely tools of
description, and artifacts related to the choice of coordinates cannot
affect physical phenomena, only the _description_ of them.

Events can occur physically in only one way, regardless of how some
set of silly observers views the events by using light rays from them
or by using coordinates. Events can be either truly simultaneous or
not, and in Einstein's train example, he assumed that they were truly
or absolutely simultaneous. Why, then, did not both observers see
them as they really were? The only way that observers can actually
see how the events actually occurred is by placing truly synchronous
clocks _at_ the events. This is not done in relativity theory, is it?

 

[Erland]

Events can be either truly simultaneous or
not, and in Einstein's train example, he assumed that they were truly
or absolutely simultaneous. Why, then, did not both observers see
them as they really were? The only way that observers can actually
see how the events actually occurred is by placing truly synchronous
clocks _at_ the events. This is not done in relativity theory, is it?

How do you define "truly simultaneous events" and "truly synchronous clocks"?

It seems that you believe that there exists an "absolute time" which is independent of all observers. It doesn't.

 

[DaveC426913]

The only "truly"* simultaneous events are events that occur coincident in both space and time.

(*is there another kind? falsely simultaneous?)

Now, how one distinguishes two events that are in the same spatial location at the same time is a tricky one.

Events can be either truly simultaneous or
not, and in Einstein's train example, he assumed that they were truly
or absolutely simultaneous.

No, he does not.

There is no such thing as absolute simultaneity in Einstein relativity.

In fact the relativity is short for 'relativity of simultaneity'. That is the central postulate of Einstein, from which all other phenomena are derived.

Why, then, did not both observers see
them as they really were? The only way that observers can actually
see how the events actually occurred is by placing truly synchronous
clocks _at_ the events. This is not done in relativity theory, is it?

It cannot be done.

There is no such thing as "really".

You are espousing Newtonian physics, which has been deprecated in favour of Einsteinian physics, as it better describes the universe we observe.

 

[DrGreg]

Your "time" is a coordinate value, but all physical phenomena are
completely independent of coordinates, because Nature quite clearly
doesn't need or use coordinates. Coordinates are merely tools of
description, and artifacts related to the choice of coordinates cannot
affect physical phenomena, only the _description_ of them.

Events can occur physically in only one way, regardless of how some
set of silly observers views the events by using light rays from them
or by using coordinates.

All true.

Events can be either truly simultaneous or not,

Not true, and you haven't given any argument why it should be.

and in Einstein's train example, he assumed that they were truly
or absolutely simultaneous.

Also not true.

In special relativity, two events can be related in one of three ways:

1. if they have timelike separation, it is possible to travel from one to the other slower than the speed of light; an inertial observer will take the maximum time to travel, other observers will take a shorter time, but the time is never zero
2. if they have null separation, it is possible to travel from one to the other in a straight line at exactly the speed of light;
3. if they have spacelike separation, it is impossible to travel from one to the other; different inertial observers will disagree over whether they took place at the same time or not, or what order they occurred in

All observers (i.e. all coordinate systems) agree over which of the three types of separation applies to a given pair of events, whatever else they may disagree over.

Simultaneity is a coordinate-dependent property: it is simply the equality of two time coordinates. In general relativity, you are free to choose pretty much any coordinate system you like. The coordinates are just a set of 4 labels you apply to each event. In special relativity we deliberately restrict ourselves to using coordinate systems in which the speed of light is always the same value c. One we have adopted that constraint, we cannot also impose a constraint of simultaneity being absolute as those two constraints are not compatible with each over (as the train-lightning thought experiment shows).

 

[pervect]

It's convenient to think of "simultaneity" as being an artifact of perception.

The short way to show this is to use the Einstein definition of simultaneity, which defines simultaneity in a specific frame as being defined by the midpoint method. You place a pair of stationary clocks at two different locations, and you synrhonize them via a signal emitted at the midpoint. The two events where the synchronizing signal reaches each clock are considered to be simultaneous.

That definition is all you need to show that simultaneity is relative in special relativity where the speed of light is always constant.

You can spend / waste a lot of time trying to come up with some "better" definition of simultaneity, the consequence of any "better" method would be to induce a perferred frame. But no experimental result has ever shown any reason to prefer one frame over another.

You could perhaps pick some particular frame by fiat and declare it to be "the one and true perferred frame", but if you actually try to calculate in it, you'll find it inconvenient to say the least.

For instance you could write down a Lagrangian using the generalized coordinates (I've done it, but I've never seen a published paper taking this approach). You'll find that the derived momenta in this formalism are not proportional to velocity, however, in the low velocity limit.

Basically, making Newtonian physics work in the low-velocity limit demands Einstein's clock synchronization procedure, which demands that the notion of simultaneity be frame-dependent.

 

[Dale]

Coordinates are merely tools of
description, and artifacts related to the choice of coordinates cannot
affect physical phenomena, only the _description_ of them.

This is a key point. Since simultaneity means simply that $t_a=t_b$ you know immediately that simultaneity cannot affect physical phenomena, only the description.

 

[Saw]

This is a key point. Since simultaneity means simply that $t_a=t_b$ you know immediately that simultaneity cannot affect physical phenomena, only the description.

I would even go a little further. Strictly speaking, simultaneity does not describe (in a discrepant manner) the events, but the measurements that each observer carries out in order to solve the problems associated to those events. For example, "did the guys at the front at the back of the train get light signals emitted from the mid-point simultaneously?".

We say that, in the train frame, the signals were simultaneous. But what this describes, to be accurate, is that that those light signals have returned to the train-mid point simultaneously, the go-and-return trip has ben measured and hence it has been established that half of that time is the one that each of the front and back clock should read when they received their respective signals.

Similarly, we say that in the ground frame the said signals were not simultaneous. But actually, to be more precise, what we are describing here is that the signals did not return at the same time to the person who was standing in the ground by the train mid-point when they were emitted. That is why she did not set the ground clocks that were aligned by the train front and train back clock when they were illuminated, to read the same time.

That is semantics, yes, but helpful, I think. The descriptions are different but only because the described facts or events are different.

But what when it comes to describing the same events? Then both frames agree on the same words and descriptions. For example, how many times can the person at the back of the train scratch his nose in the time interval between receiving his or her signal and the one reflected from the front of the train? By applying the proper time formula, both frames reach the same conclusion and describe this event in a homogeneous manner.

 

[2clockdude]

Originally Posted by 2clockdude
Events can be either truly simultaneous or not,

Not true, and you haven't given any argument why it should be.

The argument was given. It is the fact that events occur independently of frames and their clocks combined with the fact that relative simultaneity exists only when these clocks are used. The opposite of relative time is absolute time, so that exists when the other does not. But there is more to the simultaneity story; see below.

Originally Posted by 2clockdude

and in Einstein's train example, he assumed that they were truly or absolutely simultaneous.

Also not true.

You are wrong, and it's because you failed to read the whole train example story. I am not here to educate, but I will take the time to ask you what this phrase from that story means: "able meteorologist."

In special relativity we deliberately restrict ourselves to using coordinate systems in which the speed of light is always the same value c. One we have adopted that constraint, we cannot also impose a constraint of simultaneity being absolute as those two constraints are not compatible with each over (as the train-lightning thought experiment shows).

There is no evidence that light's one-way speed per two same-frame clocks is c in all frames. But there is evidence from Einstein himself that is not c in all frames when truly or absolutely synchronous clocks are used. Again, I am not here to educate, but look at Einstein's equation w = c - v at http://www.bartleby.com/173/7.html where he said that "The velocity of propagation of a ray of light relative to the carriage thus comes out smaller than c."

As promised above, here is the rest of the simultaneity story:
The only "proof" or "evidence" of the relativity of simultaneity is the train example.
However, it is easy to show that this example has nothing to do with the relative simultaneity of events.

Einstein believed that observers' different views of light rays from events say something about the events' occurrence times. It is easy to agree with Einstein when two events are involved because this makes it difficult to see what is really happening. However, if we look at only one event, e.g., the right-hand lightning strike, then we can clearly see Einstein's mistake.

Let's label the right-hand lightning strike event E. Let the rail observer be R, train observer be Tf, and an added rearward-moving train observer Tr.

-------------Tr--------R---------Tf-----------E
---------light<--------------------------------

The forward-moving train observer (Tf) sees the light ray before R, and Tr sees the ray after R. (These are absolute before-and-after's because these are three light-like events.) For example, Tf sees the ray at 11am, R sees it at noon, and Tr sees it at 1pm. (There are no clocks in the train example, but we can use these times to help us visualize the example. They merely echo the fact that the events have absolute before-and-after's.)

However, the observers now know that Einstein's view is false because a single event cannot occur at different times; that is, the observers must reject Einstein's belief that different views of a light ray from an event say something about the time of the event itself.

Why do the observers see the light ray arrive differently? The cause is simply the observers' physical separations. If the observers separate during the experiment, then the light ray must reach them differently, and this clearly has nothing to do with the time of the lightning event or simultaneity.

Here is Einstein's conclusion regarding his train example:
"Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event." http://www.bartleby.com/173/9.html

But we have found that seeing light rays from events differently says nothing about events' occurrence times or the RoS, but merely says that the observers were in different locations. The observers do disagree, but not about time or simultaneity, only about the light ray arrivals.

 

[Janus]

The argument was given. It is the fact that events occur independently of frames and their clocks combined with the fact that relative simultaneity exists only when these clocks are used. The opposite of relative time is absolute time, so that exists when the other does not. But there is more to the simultaneity story; see below.



You are wrong, and it's because you failed to read the whole train example story. I am not here to educate, but I will take the time to ask you what this phrase from that story means: "able meteorologist."





There is no evidence that light's one-way speed per two same-frame clocks is c in all frames. But there is evidence from Einstein himself that is not c in all frames when truly or absolutely synchronous clocks are used. Again, I am not here to educate, but look at Einstein's equation w = c - v at http://www.bartleby.com/173/7.html where he said that "The velocity of propagation of a ray of light relative to the carriage thus comes out smaller than c."

How ironic that you accuse someone above of not having read the whole example, when you yourself obviously didn't read the whole section that you are quoting above. The quote comes from a part where he is discussing the state of physics before Relativity and is pointing out what,at the time, seemed a incompatibility between the propagation of light and the principle of Relativity. He then goes on later on the same page to state
"in reality there is not the least incompatibility between the principle of relativity and the law of propagation of light, " Put another way, he is giving a little background before going on to present his theory. He is not arguing for the statement you quoted. He hasn't even gotten to presenting his argument yet.

As promised above, here is the rest of the simultaneity story:
The only "proof" or "evidence" of the relativity of simultaneity is the train example.
However, it is easy to show that this example has nothing to do with the relative simultaneity of events.

Einstein believed that observers' different views of light rays from events say something about the events' occurrence times. It is easy to agree with Einstein when two events are involved because this makes it difficult to see what is really happening. However, if we look at only one event, e.g., the right-hand lightning strike, then we can clearly see Einstein's mistake.

Let's label the right-hand lightning strike event E. Let the rail observer be R, train observer be Tf, and an added rearward-moving train observer Tr.

-------------Tr--------R---------Tf-----------E
---------light<--------------------------------

The forward-moving train observer (Tf) sees the light ray before R, and Tr sees the ray after R. (These are absolute before-and-after's because these are three light-like events.) For example, Tf sees the ray at 11am, R sees it at noon, and Tr sees it at 1pm. (There are no clocks in the train example, but we can use these times to help us visualize the example. They merely echo the fact that the events have absolute before-and-after's.)

However, the observers now know that Einstein's view is false because a single event cannot occur at different times; that is, the observers must reject Einstein's belief that different views of a light ray from an event say something about the time of the event itself.

Why do the observers see the light ray arrive differently? The cause is simply the observers' physical separations. If the observers separate during the experiment, then the light ray must reach them differently, and this clearly has nothing to do with the time of the lightning event or simultaneity.

Here is Einstein's conclusion regarding his train example:
"Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event." http://www.bartleby.com/173/9.html

But we have found that seeing light rays from events differently says nothing about events' occurrence times or the RoS, but merely says that the observers were in different locations. The observers do disagree, but not about time or simultaneity, only about the light ray arrivals.

You are missing the whole point of the exercise. The railway observer sees the from both flashes simultaneously. and because he is halfway between the strike points, he can conclude that the strikes took place simultaneously.

He will also note that the train observer sees one flash before the other. (The train observer will be next to different points of the tracks when each flash reaches him).

Now, as you noted a single event can only occur once, so the train observer must also agree that he was next to two different points of the track upon seeing each flash and thus agrees that he sees the flashes at different times.

However, the train observer sits at the midpoint of the train, and the lightning strikes hit the end of the train. Due to the invariance of the speed of the light, the flashes approaching from each end of the train have to travel at the same speed relative to him as determined from his frame. If the light from the rear of the train approaches at 300,000 km/sec, and the light from the front of the the train approaches at 300,000 km/sec and the distances from from the observer to the two ends are equal, and he sees the flashes at different times, then he must conclude that the strikes occurred at different times.

The fact that the train observer see the flashes at the "same time" as the embankment observer is a red herring.

In fact, we can rearrange the experiment so that both observers do see the flashes at the same time. by changing the scenario so that the flashes arrive at the embankment observer at the same time as he is next to the train observer, like this:

[URL]http://home.earthlink.net/~jparvey/sitebuildercontent/sitebuilderpictures/train1.gif[/URL]

The expanding circles represent the flashes.

Again, according to the embankment observer, the flashes both occur simultaneously and he sees them simultaneously.

The train observer also sees them simultaneously. However, he is moving with respect the embankment. Thus he will be closer to one lightning strike than the other when the strikes occur.

Again, since the speed of light must be constant for him, the light from the strikes expand out as even circles from points that maintain a constant distance from himself. (while the points on the embankment where the strikes occurred move away from these centers. )

Thus this is what happens according to the train observer:

[URL]http://home.earthlink.net/~jparvey/sitebuildercontent/sitebuilderpictures/train2.gif[/URL]

In order for him to see both flashes at the same time and at the same time as the embankment observer, the strikes that caused them have to occur at different times.

Thus even though both observers see the flashes simultaneously, One concludes that they originated at the same time and the other that they originated at different times

 

[Dale]

The argument was given. It is the fact that events occur independently of frames and their clocks combined with the fact that relative simultaneity exists only when these clocks are used.

Your premise, "events occur independently of frames", does not imply your conclusion. So it cannot be considered as an argument for your conclusion.

However, the observers now know that Einstein's view is false because a single event cannot occur at different times

Sure it can, even non-relativistically. For instance, I regularly schedule events which occur at 11:00 am my time and 5:00 pm in my German colleague's time. There is nothing wrong with me assigning a time coordinate of 11:00 and someone else assigning a time coordinate of 5:00 to the same event. A single event can occur at different times in different frames. That is basic everyday non-relativistic physics.

 

[2clockdude]

How ironic that you accuse someone above of not having read the whole example, when you yourself obviously didn't read the whole section that you are quoting above. The quote comes from a part where he is discussing the state of physics before Relativity and is pointing out what,at the time, seemed a incompatibility between the propagation of light and the principle of Relativity. He then goes on later on the same page to state "in reality there is not the least incompatibility between the principle of relativity and the law of propagation of light, " Put another way, he is giving a little background before going on to present his theory. He is not arguing for the statement you quoted. He hasn't even gotten to presenting his argument yet.

I have read the whole example many times. Of course it is pre-SR. Perhaps this is a way to get you to see the real story here: Why or how did the embankment observer get c for light's one-way speed in a pre-SR setting? (To be specific, this was before E-synch.)

However, the train observer sits at the midpoint of the train, and the lightning strikes hit the end of the train. Due to the invariance of the speed of the light, the flashes approaching from each end of the train have to travel at the same speed relative to him as determined from his frame.

Again, it may help if I pin you down to one question, namely, can you show one-way light speed invariance on paper? (You must use at least two frames, and in order to clearly differentiate them, you must use a single light source, because otherwise you are just repeating a single frame case. One source usage is justified by the fact of light's source independent nature.)

 

[Erland]

I have read the whole example many times. Of course it is pre-SR.

But you wrote before:

But there is evidence from Einstein himself that is not c in all frames when truly or absolutely synchronous clocks are used. Again, I am not here to educate, but look at Einstein's equation w = c - v at http://www.bartleby.com/173/7.html where he said that "The velocity of propagation of a ray of light relative to the carriage thus comes out smaller than c."

Since you now say you understand that it is pre-SR, and thus that Einstein didn't really claim it is true, this example does NOT give any "evidence from Einstein himself that is not c in all frames when truly or absolutely synchronous clocks [whatever that may be] are used."

So, you are contradicting yourself.

can you show one-way light speed invariance on paper?

It cannot be "shown on paper". It follows from the Special Relativity Principle and the assumption that the light speed is constant in at least one inertial frame. Both these are experimentally verified facts.

 

[Erland]

It follows from the Special Relativity Principle and the assumption that the light speed is constant in at least one inertial frame. Both these are experimentally verified facts.

I should add that the Michelson-Morley experiment clearly shows that the measured light speed is independent of the motion of the observer, since the Earth is moving in opposite directions at opposite times of the year.

If the speed of light is frame dependent, how can you then explain the outcome of this famous experiment, 2clockdude?

 

[harrylin]

I've said it before and I say it again: I don't like this example. I only get confused when I think of it. But there is a simpler example which demonstrates the relativity of simultaneity. I quote myself from another post:

"... imagine a light being turned on in the middle of the train. The light reaches the front and the back of the train simultaneously, according to an observer on the train. But according to an observer on the embankment, the light will reach the back of the train before it reaches the front of the train, because according to such an observer, the light that reaches the back of the train will have traveled a shorter distance than the light that reaches the front of the train, since train is moving, according to this observer."

Although I don't find Einstein's example confusing, I fully agree that the variant with one light source in the middle of the train is much easier to follow - very much preferable.

Perhaps the best way to teach this is to first present that simpler variant as problem 1a, and then switch to Einstein's variant as 1b, to check that 1a was fully understood.

 

[2clockdude]

Since you now say you understand that it is pre-SR, and thus that Einstein didn't really claim it is true, this example does NOT give any "evidence from Einstein himself that is not c in all frames when truly or absolutely synchronous clocks [whatever that may be] are used."

So, you are contradicting yourself.

If someone had just been kind enough to have answered my query "Why or how did the embankment observer get c for light's one-way speed in a pre-SR setting? (To be specific, this was before E-synch.)," then you would know that Einstein himself talked about absolutely synchronous clocks. This is not a forbidden topic.

Let me answer my own question. The only way that any observer in any frame could possibly get the result c for light's one-way speed prior to E-synch would be by using absolutely synchronous clocks in a frame that is at absolute rest.

As for your above, Einstein claimed that the carriage observer got c - v for the departing light ray's speed, whilst the railway observer got simply c, and both of these results were fully in the context of classical physics, where only truly synchronous clocks were used.
Also, as I said, both results were in the pre-SR, pre-E-synch era.

As I said earlier, Einstein even used absolutely synchronous lightning strikes in his train example. This is proved by his phase "able meteorologist," given at the start of the example, where it belongs. http://www.bartleby.com/173/8.html

Einstein also talked about truly synchronous clocks immediately following the "able" phrase. He was talking about light's one-way speed, and he said this:

“Your definition would certainly be right, if I only knew that the light by means of which the observer at M perceives the lightning flashes travels along the length A —> M with the same velocity as along the length B —> M. But an examination of this supposition would only be possible if we already had at our disposal the means of measuring time. It would thus appear as though we were moving here in a logical circle.”

The pertinent phrase here is "the means of measuring time." This can only mean one thing - truly or absolutely synchronous clocks. Einstein had to admit that he did not possesses the means of measuring time. He did not know how to truly synchronize a pair of clocks. (Of course, he could not prove the negative that such clocks cannot exist, but he hated such clocks because he knew that they could detect absolute motion by measuring the one-way speed of light. This is why he wanted to discard such clocks, and to replace them with clocks that he hoped would get only c invariantly.)

I was not by any means contradicting myself. The example does give "evidence from Einstein himself that is not c in all frames when truly or absolutely synchronous clocks [whatever that may be] are used."

After using the bogus train example to convince himself that simultaneity was "relative," Einstein then felt like he could at last toss aside those "nasty" truly synchronous clocks, and replace them with his (incredibly-more-nasty-really) asynchronous clocks, which he tried to force to get c invariantly, but this cannot be done, not even on paper.

Here is Einstein's proud abandonment of truly synchronous clocks (a move that he "cleverly" disguised as "we must discard the assumption of absolute time") :
"Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance, i.e. that it is independent of the state of motion of the body of reference. But we have just seen that this assumption is incompatible with the most natural definition of simultaneity; if we discard this assumption, then the conflict between the law of the propagation of light in vacuo and the principle of relativity (developed in Section VII) disappears."

Einstein thought that absolutely synchronous clocks (absolute time) would violate the principle of relativity by detecting absolute motion; however, anyone who knows what this principle really says would laugh at Einstein's "violation" claim. The PR allows any and all laws that may be found, and says nothing about what the laws can or cannot be used for. The PR is actually a meta-law, a law about laws, and says that all inertial observers must find the same general laws. Contrary to Einstein (re his c - v example), this is exactly what happens when truly synchronous clocks are used to measure the one-way speed of light; i.e., the one-way law for all observers is w = c +/- v. Of course, as Einstein saw, each frame's observers will get their very own little result, such as w = c - v for the carriage observer, and w = c for the railway observer, whose absolute speed in space was of course zero (v = 0). Note carefully that the one-way law fully satisfies the PR, but can still be used to detect absolute motion. (But this makes perfect sense because truth cannot possibly conflict with truth - that is. truly synchronous clocks cannot possibly conflict with a true principle (the PR). Albert should have known better, but the might Michelson-Morley experiment did him in. He "read" that null result as "null results all the way down!")

I hate to be the bearer of bad news (for SR proponents), but there was never any need for special relativity, none at all. Absolute time (or absolute synchronization) does NOT in any way "violate the principle of relativity"; there was never any need to try to force poor clocks to "always get c"; indeed, as I can show, this "c invariance" cannot happen either on paper or experimentally. On the other hand, as Einstein himself had to admit, if we use absolutely synchronous clocks, then we can have both absolute time and absolute motion detection.

I should add that the Michelson-Morley experiment clearly shows that the measured light speed is independent of the motion of the observer, since the Earth is moving in opposite directions at opposite times of the year.

If the speed of light is frame dependent, how can you then explain the outcome of this famous experiment, 2clockdude?

As John Wheeler pointed out, said experiment did not even close the round-trip case, much less the one-way case. Wheeler noted that physical length contraction (à la Mr. Lorentz) was the proper physical explanation for the MMx null result, but this would not stop the Kennedy-Thorndike experiment from getting a positive result. (This, btw, proves that there was no aether involved, and that the MMx did not "do away with the aether.") Wheeler went on to say that time dilation (physical clock slowing) could explain the KTx result.

Now let's look back at your (Erland's) innocuous-looking phrase "the measured light speed is independent of the motion of the observer," and let's think a bit about that word "measured." Hmmm... Let's combine both round-trip experiments. Now we have a clock that is slowed, and a ruler that is contracted, or at least we have no proof that these distortions are not present during the measurement. If one uses distorted instruments, then one should expect invalid results. Yes, the so-called "null result" was an invalid result - it does not reflect the reality that even light's round-trip speed would vary with frame velocity if undistorted instruments were used.

And now let's look at the one-way case. There are still only two kinds of instruments involved, namely, rulers (or rods) and clocks. However, the addition of a second clock makes all the difference because even tho Nature can cause a null result in the round-trip case by slowing clocks and contracting rulers, She cannot possibly cause a one-way null result because She cannot reach down and set our clocks. Indeed, as I hinted at above, not even man (read "Einstein") can cause a one-way null result, not even on paper.

If you believe that a one-way null result can happen, then show us how. It ain't possible.