Exploring the Speed of Light in Deep Space: A Scenario on a Space Station

[zoobyshoe]

I don't see ythe problem here, the confusion here is 1 sec for who? and 300,000 km, in whose reference frame? It's clear that the person on the rocket ship who measures the distnace to the spacestaion to be 300,000 km when the light is emitted, will measure the time taken for that light to cover that distance will be 1 second. It doesn't need any calculations or any thought experimnets to prove as it's a postulate of special relativity.

True, a postulate is a postulate. However, in this case, going by the postulate leads to a situation where there is no Relativity of Simultaneity. Going by the postulate, Einstein's observer on the train should see both light flashes as simultaneous. Einstein says he won't, however.

 

[jcsd]

No, it's not inconsistent with the relativity of simulatneoty I think what you're missing is what the observer on the space station sees:

When the light is emitted, the rocket is approximately 340,000 km away, when it arrives at the rocket it is approximately 170,000 km away as viewed by the space station, and thus took approximately 0.6 secs to arrive at the rocket. You cannot ignore the fact that length and time change with reference frame when comparing the two examples.

 

[Doc Al]

There is no mixup: they are identical. The lighning flashes are simultaneous, not to the embankment in general, but at one specific spot: the exact midpoint M between point A and point B. Einstein: "When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A---->B of the embankment."

You are mixed up. In Einstein's example, the lightning flashes are simultaneous in the frame of the embankment. I have no idea what you mean by simultaneous at one specific spot.

This mid-point M corresponds to the distance 300,000 kms from the space station in my rocket example because the light is emitted, in the train scenario, exactly at the moment the observer on the train is at the mid-point M between the two points.

In Einstein's example the midpoint M is a fixed distance from the source B in the embankment frame. So, by analogy, your rocket frame corresponds to the embankment frame. (Sort of.) You've gotten them mixed up.

The observer continues to move and encounters the flash from B before the flash from A by his own reckoning not as seen from the embankment. The flash he perceives from point B corresponds to the flash from the space station as my rocket approaches it, (or it approaches my rocket if you want to define it that way) and the flash from point A corresponds to the flash from the space station as I am moving away from it (or it away from me).

The moving train corresponds to your space station frame. At least it would if your example were comparable to Einstein's, but it's not.

The mid point M in the train scenario corresponds to the distance 300,000 kms in the rocket scenario because it is the same distance in the example where the station is approaching me, and also in the example where the station is moving away from me. In both cases the station emits light when the distance bewteen the station and my ship is 300,000 kms.

It would make more sense if there was a moving observer at that midpoint. But there isn't is there?

To make this as clear as possible let's say that when the distance between point A and point B in the train scenario was measured it proved to be exactly 600,000 kms. The midpoint, therefore, is located 300,000 kms from both A and B. Any value for the distance will do as long as point M is exactly midway between A and B. Using 300,000 kms helps you to see how the rocket example is the same as the train.

The example with the train is very clear. What's not clear is what it has to do with your rocket? If the "rocket" is the midpoint, where's the moving train that passes by at just the right moment?

In Einstein's example any observation anyone on the embankment might have about what the observer on the train sees is unimportant, and Einstein doesn't even mention it. What is important about any person on the embankment is that they will see the flashes of light from both directions at exactly the same time. That is important because Einstein wants to contrast it with what the observer on the train will see.

No, Einstein uses the observations from the embankment to conclude draw conclusions about what actually happens and what the train sees. He deduces from what the embankment must see that the light reaches the moving train at different times. (Both frames agree with this.) And then the observers on the train use that fact to deduce that those lights cannot have been flashed simultaneously.

It is important to note that when the flashes occur, the observer on the train is located at the midpoint M between the two flashes.

Careful! To the observer on the train the flashes do not occur at the moment he passes the midpoint--they can't, since they happen at different times. Only from the embankment are the flashes observed to be simultaneous.

However, he moves away from that spot before the flashes arrive. The result is that he detects flash B before flash A, in spite of the fact he was at the midpoint when they occured!

It would be a contradiction to the basic assumption of the invariant speed of light if this were true. But it's not. In his frame, the flashes did not occur when he was at the midpoint.

By this reasoning, I would not detect the light beam from the space station, emitted when the distance between my rocket and the station was 300,000 kms, to be 1 sec, in any case of relative motion toward or away from the station (or it toward or away from me) By Einstein's reasoning, I will detect it in less than a second when the distance between my ship and the station is closing at .5c, and I will detect it in some time greater than 1 sec. when the distance between my ship and the station is widening at .5 c.

Your reasoning is incorrect, as I have explained. Don't blame Einstein.

Again, If I detect it to be 1 sec coming or going Einstein has no basis upon which to build his case for what he calls The Relativity of Simultaneity.

Sorry, but you don't seem to understand Einstein's argument. And, on top of that, you are misapplying Einstein's argument in comparing it to your rocket example.

I recommend that you work to understand Einstein's simple argument for the relativity of simultaneity. Maybe this will help: https://www.physicsforums.com/showpost.php?p=229410&postcount=2

 

[plover]

I did this in my post above

If we substitute the situation where the space station is approaching me (from my perspective) for the situation where the observer on the train is approaching the flash of light from point B, you can see that Einstein would not reakon the time between the flash and when I detect it to be one second, rather, less than a second.

Likewise, if we substitute the situation where the station is moving away from me for the situation where the observer on the train is moving away from the flash of light at point A, you can see that Einstein would not reakon the time between the flash of light and when I detected it to be one second, but something greater than one second.

Ok, I see that you want to set stations as being at the points A and B on the train tracks. As Doc Al noted, you have to be careful here. To fill out the analogy, we can stick someone else in a rocket that's half way between the stations, and at rest with respect to the stations. We'll call this observer X. Now, the original specification of the scenario is that the flashes are simultaneous in X's reference frame - not yours.

Suppose you have a long rigid filament stretched out to the front and back of your rocket to correspond to the rest of the train. X says that each station emitted a flash at the same moment that you passed him, and that this is the same moment as the ends of the filament passed the stations.

Now remember, since you're in motion with repect to X, the filament appears length contracted to X. In your frame of reference the filament is not length contracted. Thus if X says that the length of the filament corresponds to the distance between the two stations, then to you, the filament must have a length that is greater than that, and therefore if each flash originates just as the end of the filament passes the station, then to you the flashes could not have originated simultaneously.

(See also below for warnings about the observer on the train regarding themself as being in motion.)

I didn't respond to the bulk of your post because it started with the false premise that the observer in the rocket corresponded to someone on the embankement in Einstein's version. That is false.

The bulk of my post contains no direct comparison to the rocket scenario. Its logic can be analyzed without reference to any outside analogy.

This is false. The quote from Einstein does not contain any predictions by one observer about what another will see.

The form that Einstein's argument takes over the course of the essay is to present the conclusions that can be drawn by a person on the embankment, and to show which common assumptions must be discarded in order to remove apparent contradictions that arise. It is not until the later sections of the essay (starting in Ch 11) that he starts showing what removing these assumptions implies for how time and space measurements differ for the observer on the train compared to the person on the ground.

You quote:

Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A.​

Note that the "hastening towards" and "riding ahead" going on here are "considered with reference to the railway embankment". Remember - an observer on the train must regard the train as being at rest. An observer in special relativity can never describe themself as "hastening" or "riding" anywhere!

The quote continues:

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.
​

These statements are a conclusion (note the "hence") that can be drawn by the observer on the embankment (X) about what the observer on the train (Y) will see.

Thus Einstein is noting that X can conclude from his own space and time measurements that Y will see the photon from B before seeing the photon from A, but there is nothing that yet describes how time and space are arranged from Y's perspective.

One thing to keep in mind here is that observers in any inertial reference frame will agree on the order of events for any given spatial coordinate in other reference frames (thus both X and Y will agree on the order of events that each will see as X occupies a specific coordinate in X's reference frame and Y occupies a specific coordinate in Y's reference frame. What observers disagree on is whether events that are separated spatially in both frames are simultaneous (a difference which can lead to changes in the overall order of events depending on the particular reference frame).

 

[zoobyshoe]

No, it's not inconsistent with the relativity of simulatneoty I think what you're missing is what the observer on the space station sees:

In the Einstein train scenario transferred to space, there is no observer at the space station. Nothing observed by any observer in the space stations inertial frame is of importance except to confirm, I suppose, that the observer in the rocket is located at exactly 300.000 kms from the station when the station emits light. We really don't need an observer for that because Einstein stipulates it.

When the light is emitted, the rocket is approximately 340,000 km away...

I have no idea where you are getting 340,000 km. It is stipulated that when the light flashes the observer in the rocket is 300,000 away from the station. It is a stipulation in both Einstein's train scenario (the observer on the train is at the midpoint when the light flashes) and the rocket scenario.

You cannot ignore the fact that length and time change with reference frame when comparing the two examples.

We can't take length and time dilation into account at all yet. Einstein is setting up his case for the existence of time dilation with this very scenario. Relativity of Simultaneity preceeds time and length dilation. He must first demonstrate Relativity of Simultaneity, in order to show why there is a need for time and length dilation. No Relativity of Simultaneity, no different reckoning of time in different reference frames.

Somehow, the postulate that light always propagates at c in all reference frames has gotten in the way of The Relativity of Simultaneity. I am surprised. This is passing strange.

 

[zoobyshoe]

Now remember, since you're in motion with repect to X, the filament appears length contracted to X.

This filament and midpoint observer are completely unnecessary since Einstein stipulates that the flashes occur when the train observers position coincides with the midpoint between A and B. Also, as I pointed out to jcsd, at this point we aren't concerned with any time or length dilations. We have no need of them. They are immaterial to his point.

The form that Einstein's argument takes over the course of the essay is to present the conclusions that can be drawn by a person on the embankment,

In this chapter Einstein's point is to show there will be a difference of perception of when the flashes of light occur between the two reference frames: the moving train, and the embankment. He is not describing the embankment observers notion of what the observer on the train will see. He describes what the embankment observer will see, and separately, what the train observer will see. Neither speculates about what the other sees.
You quote:

The quote continues:

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.
​

These statements are a conclusion (note the "hence") that can be drawn by the observer on the embankment (X) about what the observer on the train (Y) will see.

I am astonished that you can accurately quote him as saying "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," and maintain he is talking about something an observer on the embankment is speculating about. Are you just yanking my chain?

Thus Einstein is noting that X can conclude from his own space and time measurements that Y will see the photon from B before seeing the photon from A, but there is nothing that yet describes how time and space are arranged from Y's perspective.

If what you just said here were true Einstein would have had no reason to write this chapter and call it The Relativity of Simultaneity. Where's the story, if all we're talking about is what the embankment observer sees vs what he thinks the train observer sees?

Back to the problem: If the calculation of 1 sec, 150,000 km for one flash, and 1 sec 450,000 km for the other flash is correct, then: 1 sec = 1 sec, and both the train observer and the embankment observer detect the flashes to be simultaneous. This leads to the conclusion there is no Relativity of Simultaneity. How can that be?

 

[jcsd]

In the Einstein train scenario transferred to space, there is no observer at the space station. Nothing observed by any observer in the space stations inertial frame is of importance except to confirm, I suppose, that the observer in the rocket is located at exactly 300.000 kms from the station when the station emits light. We really don't need an observer for that because Einstein stipulates it.

Clearly the train scenario relies on two different inertial observers, otherwise the relativity on simultaneity cannot be demonstrated. Indeed if we're only talking about 1 inertial observer we needn't really bring in relativity to such a simple problem as long as we remember than the speed of light for that inertial observer will be c.

I have no idea where you are getting 340,000 km. It is stipulated that when the light flashes the observer in the rocket is 300,000 away from the station. It is a stipulation in both Einstein's train scenario (the observer on the train is at the midpoint when the light flashes) and the rocket scenario.

A got the the figures of 340,000 and 170,000 by simply applying a Lorentz transformation to the 4-vector postion of the space station a) when the light is emitted b) when it arrives. I think this is the vital point that you're missing that the distance between the rocket and the space station are NOT the same for the two different observers.

We can't take length and time dilation into account at all yet. Einstein is setting up his case for the existence of time dilation with this very scenario. Relativity of Simultaneity preceeds time and length dilation. He must first demonstrate Relativity of Simultaneity, in order to show why there is a need for time and length dilation. No Relativity of Simultaneity, no different reckoning of time in different reference frames.

No time dialtion and length contraction do not require the relativity of simultaneity to be demonstarted, they can be demonstrated with two events that have a definite ordering in 2 different reference frames. Indeed in the situation we describe there is no need to consider the relativity of simulatenoty (and if there was it would arise naturally out of considering time dialtion and length contraction) as both observers observe the light to be emitted before it hits the spaceship.

Somehow, the postulate that light always propagates at c in all reference frames has gotten in the way of The Relativity of Simultaneity. I am surprised. This is passing strange.

It doesn't get in the way it is easy to demonstare that both situations are consistent with relativity.

 

[zoobyshoe]

Clearly the train scenario relies on two different inertial observers,

Agreed.

otherwise the relativity on simultaneity cannot be demonstrated.

Indeed if we're only talking about 1 inertial observer we needn't really bring in relativity to such a simple problem as long as we remember than the speed of light for that inertial observer will be c.

Right.

Lets ask though, if we need an observer at the space station? What would the space station correspond to in Einsteins's train scenario? It would correspond to point A or point B. These are the points at which the lightning hits the tracks. As space stations they are the points at which light is emitted. Did Einstein put any observers at points A or B? He did not. This is why I said we don't need an observer at the space station.

We do need an observer in the space station's inertial frame, though, as you pointed out. Where do we put him? Where did Einstein put him? At point M, the mid point between lightning flash A and lightning flash B.

What is that observer going to see? We don't have to calculate this or figure it out in any way. Einstein has carefully controlled everything in order that the observer at point M sees the two flashes of light as simultaneous. That is: he has carefully measured the distance from point A--->M and from B---->M, and determined them to be the same, and then he has stipulated that light will always travel at the same speed, regardless of direction of travel.

Because the two distances the light will travel are the same, and because light has been stipulated by Einstein to always travel at the same speed, there is no doubt whatever that the light from both lightning strikes will arrive at point M simultaneously.

That is why I said we don't need an observer at the space station: for the same reason we don't need an observer at the points where lightning strikes the rails. Einstein didn't have any observers at the point where lightning struck the rails. Why do we need anyone at the space station?

As for the observer who is at point M I said "We don't really need an observer for that because Einstein stipulates it." This was not incorrect. I am saying that Einstein has controlled all the conditions so carefully that there is no doubt about what an actual person at point M will see. He can't see anything but simultaneous flashes of light from A and B. That being the case, we don't actually have to station a person there to know what he'd see.

So we don't need an observer at the space station, and we have taken care of what the potential observer at point M (which would be a point 300,000 km from the space station on the rockets path in that example) will see by stipulation. There we have our two different inertial frames: one observer on the train, and one at point M.

I'll stop here to see if you understand and agree or disagree.

 

[jcsd]

Agreed.


Right.

Lets ask though, if we need an observer at the space station? What would the space station correspond to in Einsteins's train scenario? It would correspond to point A or point B. These are the points at which the lightning hits the tracks. As space stations they are the points at which light is emitted. Did Einstein put any observers at points A or B? He did not. This is why I said we don't need an observer at the space station.

By saying that the light strikes simulatenously on the tracks he tacitly includes an observer in the rest frame of the tracks.

We do need an observer in the space station's inertial frame, though, as you pointed out. Where do we put him? Where did Einstein put him? At point M, the mid point between lightning flash A and lightning flash B.

It's not of great import where the obsrever is spatially locatedd as where only in differences in distances and times rather than definign a co-ordinate system.

What is that observer going to see? We don't have to calculate this or figure it out in any way. Einstein has carefully controlled everything in order that the observer at point M sees the two flashes of light as simultaneous. That is: he has carefully measured the distance from point A--->M and from B---->M, and determined them to be the same, and then he has stipulated that light will always travel at the same speed, regardless of direction of travel.

Because the two distances the light will travel are the same, and because light has been stipulated by Einstein to always travel at the same speed, there is no doubt whatever that the light from both lightning strikes will arrive at point M simultaneously.

That is why I said we don't need an observer at the space station: for the same reason we don't need an observer at the points where lightning strikes the rails. Einstein didn't have any observers at the point where lightning struck the rails. Why do we need anyone at the space station?

As for the observer who is at point M I said "We don't really need an observer for that because Einstein stipulates it." This was not incorrect. I am saying that Einstein has controlled all the conditions so carefully that there is no doubt about what an actual person at point M will see. He can't see anything but simultaneous flashes of light from A and B. That being the case, we don't actually have to station a person there to know what he'd see.

So we don't need an observer at the space station, and we have taken care of what the potential observer at point M (which would be a point 300,000 km from the space station on the rockets path in that example) will see by stipulation. There we have our two different inertial frames: one observer on the train, and one at point M.

I'll stop here to see if you understand and agree or disagree.

Ok, so the obsrever at M is tin the rest frma eof the space staitons right? and in the rest frame of the space staions the two flashes are emitted simulatneously? As I said before though the observer at M will be 340,000 km from the two space stations due to the effects of length contraction. Or are you changing it now so that in the space stations' rest frame rtaher than the rocket's the distance is 300,000 km. It cannot be the same for both observers.

 

[zoobyshoe]

Ok, so the obsrever at M is tin the rest frma eof the space staitons right?

Right.

and in the rest frame of the space staions the two flashes are emitted simulatneously?

Absolutely. That's the way Einstein worked so hard to set it up.

As I said before though the observer at M will be 340,000 km from the two space stations due to the effects of length contraction.

Confusion. The observer at M is the one in the rest frame of the stations. He is at the mid point between the stations. The stations are 600,000 km apart. Therefore the observer at M is always located 300,000 km from both stations in the station's rest frame. (M stands for midpoint)

The observer in the rocket/train is the one in relative motion to the stations. He is different than the observer at M. We shouldn't refer to the guy in the rocket as "the observer at M."

Or are you changing it now so that in the space stations' rest frame rtaher than the rocket's the distance is 300,000 km. It cannot be the same for both observers.

I haven't changed any distance or anything else. What, in fact, I have done is to forget that at .5c the observer on the train will not see the 300,000 km distance as 300,000 kms, and I have erroneously referred to it as 300,000 even when speaking about his perspective. Sorry for that confusion.

Now, my reading of the Einstein leads me to conclude that he believes there is an instant in time when both the observer on the rocket/train and the observer at point M will agree that the observer on the rocket/train is located at point M and that it is at this instant the lights flash. I am not completely sure, but I get the impression that you have an objection to this, and that you don't think there can be an instant where both observers agree that the observer on the rocket is at point M. Do you have such an objection?

 

[plover]

[The Einstein quotes in the following are taken from Chapter 9 of the essay Relativity: The Special and General Theory.]
​

When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A--->B of the embankment.

[§ 1]
This reiterates the definition of simultaneity given in Ch 8. As stated here, it uses observations taken at M as an indicator to define simultaneity specifically for events at A and B and only in the embankment frame. Under the definition of "'time' in physics" given in Ch 8, we may also say that any observer who shares the embankment frame (i.e. is at rest with respect to the observer at M) will agree that the flashes are simultaneous in that reference frame by making use of clocks or of some other suitable extension to the mechanism established in the footnote to Ch 8.

But the events A and B also correspond to positions A and B on the train.

[§ 2]
This could be confusing. Let's call the points on the train A' and B' to distinguish them from the points A and B on the embankment.

Further quotes from the Einstein essay are edited to reflect this change.

Let M' be the mid-point of the distance A'--->B' on the traveling train.

[§ 3]
Let's have a diagram:

[motion of train]________---->
[train ] ... ==== A'======= M'======= B'==== ...
[ground] ... ____ A _______ M _______ B ____ ...

Just when the flashes [as judged from the embankment] of lightning occur, this point M' naturally coincides with the point M ...

[§ 4]
The footnote interpolated here in brackets is not strictly necessary as there is only one reference frame (i.e. the embankment frame) for which we have established that the flashes are simultaneous, and thus only one reference frame in which the phrase "Just when the flashes ... occur" has any meaning.

In particular, we have no basis to assert that the three events - 1) flash at A, 2) flash at B, and 3) M' passes M - are simultaneous to an observer in the reference frame of the train.

There are two sets of events that can be asserted as simultaneous in both frames as they have been defined as such -- this definition being possible because the events occur (for the purposes of the argument) at the same location.

The first set is: 1) flash at A, 2) A' passes A.
The second set is: 1) flash at B, 2) B' passes B.

There is, of course, one other set of events which we can assert are simultaneous in the embankment frame: 1) flash from A arrives at M, and 2) flash from B arrives at M. (This assertion follows from the mechanism through which simultaneity of events separated in space was defined.)

...but it moves towards the right in the diagram with the velocity v of the train. If an observer sitting in the position M' in the train did not possesses this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated.

[§ 5]
So, an observer in the reference frame of the train moves with the same velocity as the train, and consequently such an observer cannot be in the frame of the embankment.

Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A.

[§ 6]
Since the observer on the train at M' (the "he" of the preceding quote) is not at rest with respect to the observer at M (i.e. not at rest in the embankment frame), the observer at M will say that the observer at M' moved toward B during the period when light from the flashes was traveling from A and B to M, and thus that the observer at M' was moving toward the flash from B and away from the flash from A.

Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.

[§ 7]
Therefore, the observer at M may conclude, since the flash from B passed M' sometime before reaching M, and the flash from A will pass M' sometime after reaching M, an observer positioned at M' will witness the flash from B prior to witnessing the flash from A.

And if the preceding conclusion about an observer at M' is true, then, using the same procedures from Ch 8 mentioned above, the following conclusion may be made about any observers in the reference frame of the train:

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.

[§ 8]
Or in other words, events (separated in space) that are determined to be simultaneous by observers in the frame of the embankment could not be determined to be simultaneous by observers in the frame of the train.

If one were to work through all these steps again, only exchanging the assumption that the flashes are simultaneous in the embankment frame for the assumption that the flashes are simultaneous in the frame of the train, the complementary conclusion would be reached: that events (separated in space) that are determined to be simultaneous by observers in the frame of the train could not be determined to be simultaneous by observers in the frame of the embankment.

These two complementary conclusions comprise the definition of Relativity of Simultaneity given by Einstein. In his words:

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity).

Zoobyshoe:

[§ 9]
I don't know what upsets you about this argument. At this point in history, however, trying to proclaim this argument to be false falls under the rubric of "Extraordinary claims require extraordinary proof".

I doubt that a comparison with the rocket scenario that you worked out is useful - nobody giving answers in the early part of this thread was limiting themselves to the assumptions employed by Einstein in Ch 1-9 of this essay, they were employing whatever knowledge of Special Relativity seemed appropriate. So it is likely that whatever conclusions you have made about the rocket scenario would need to be rejected on the same basis that you reject any mention of length contraction.

I will point out that it was not until post #43 of this thread that you made it explicit enough (at least to me - I can't be sure of what Doc Al and jcsd were thinking, but from their answers I doubt the assumption was clear to them either) that the reason that you insist that the person in the rocket should correspond to the observer on the train is that because the stations are emitting the photons and the lightning strikes the ground in the embankment frame, the stations need to be in the embankment frame.

It is not actually relevant what frame the photon emitters are in, what matters is that the observer in the embankment frame at M sees the flashes at the same moment. The constant velocity of light makes the velocity of the source irrelevant (and the reference frame of the source irrelevant) to when the flashes arrive at M. In addition, Einstein gives this as an empirical result in Ch 7.

It is much more important to have a thorough and explicit listing of the assumptions that are made about each frame. And to make sure that knowledge gained with reference to one frame is not applied to the other in unwarranted ways.

 

[zoobyshoe]

Plover,

Excellent, excellent breakdown of the train scenario! You are an extremely patient, persistent, and articulate poster.
Good to have you here.

You have pointed out that the observer on the embankment will suppose the observer on the train sees one flash before the other. However, there is doubt in my mind as to whether you think Einstein is asserting that the man on the train will see one flash of light before the other in his reference frame on the train.

His wording is iffy at many points, but since he comes to the conclusion "Events which are simultaneous with reference to the embankment are not simultaneous with respect to thr train, and vice versa (relativity of simultaneity)." it seems unbelievable to me that he could only be talking about what the observer on the embankment thinks the observer on the train might be experiencing. If he were, why would he go on to conclude "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 time." It would make no sense whatever for him to draw that conclusion unless he believed an actual observer seated on the train would actually see one flash before the other.
-------
It never occurred to me that the flashes could come from the ends of the train just as well as from fixed points on the rails, but now that you point it out, I see that it is another valid possibility.
---------
I'm not claiming Einstein's argument is false.

Janus, Doc Al and you answered my questions about the rocket in such a way that it seems to me the observer on the train will see the flashes of light as simultaneous. If there is anything about the train scenario that I failed to carry over to the rocket questions, I am still not aware of what it was. If there is a different method that should be used to calculate how much time the man on the train will judge to have elapsed between the instant he is at the midpoint and when he detects the light and what should be used to determine the time that will elapse for the rocket man between the instant he hits the 300,000 km mark and when he detects the light, I will be very surprised: all the distances and speeds are the same.


I don't object to length contraction or time dilation being brought in if it can be used to explain that the observer on the train will see one flash of light before the other. He seemed to be on his way to use it to say something about how the rocket looks to station.
-------
I've reread your explanation of the reason the observer on the train might see one flash before the other. It is quite interesting, but is dependent on point M of the track and point M' of the train not actually corresponding when the light flashes for it to work. That would be fine except Einstein is, it seems to me, explicit about the fact that point M' of the train must correspond to point M of the embankment when the flashes occur. (I don't know why he even bothers to mention what the ends of the train are doing when he is so exacting in his description of the midpoints lining up.) It seems to me he is trying very hard to describe a situation exactly like what would happen if a rod sticking out from the outside of the train beside the observer on the train were to trip a switch located at point M on the embankment causing the flashes (the signal getting from the switch to the lights instantaneously, by magic, of course). Does that not seem to be the case to you?

 

[jcsd]

Right.

Absolutely. That's the way Einstein worked so hard to set it up.

Confusion. The observer at M is the one in the rest frame of the stations. He is at the mid point between the stations. The stations are 600,000 km apart. Therefore the observer at M is always located 300,000 km from both stations in the station's rest frame. (M stands for midpoint)

The observer in the rocket/train is the one in relative motion to the stations. He is different than the observer at M. We shouldn't refer to the guy in the rocket as "the observer at M."

I haven't changed any distance or anything else. What, in fact, I have done is to forget that at .5c the observer on the train will not see the 300,000 km distance as 300,000 kms, and I have erroneously referred to it as 300,000 even when speaking about his perspective. Sorry for that confusion.

Right so that is cleared up.

Now, my reading of the Einstein leads me to conclude that he believes there is an instant in time when both the observer on the rocket/train and the observer at point M will agree that the observer on the rocket/train is located at point M and that it is at this instant the lights flash. I am not completely sure, but I get the impression that you have an objection to this, and that you don't think there can be an instant where both observers agree that the observer on the rocket is at point M. Do you have such an objection?

The problem is time is relative, there will be an instant in M's refernce frame where the rocket ship is at M and there will be an instant in the rocket ship's frame when he is at M. The problem is at the instant in M's frame that the rocket ship is at M this will be the instant the two lights flash, BUT in the rocket ship's frame at the instant that he is at M, one of the lights will already of flashed and the other light will not of yet flashed.

 

[Doc Al]

Janus, Doc Al and you answered my questions about the rocket in such a way that it seems to me the observer on the train will see the flashes of light as simultaneous.

I'm still not seeing how you conclude this based on what we have explained. You are drawing a confused analogy between Einstein's train and your rocket.

But in any case, I'd still like to know what you think is wrong with the simple calculation, done by the folks in your rocket, that shows that according to the rocket clocks the light takes 1 second to reach them from the time it leaves the station. You agree that the rocket frame has measured the distance from the station to the rocket to be 300,000 km at the time of emission, right? (That's given in the problem.) And you must also agree that the rocket frame observes the light to travel towards the rocket at speed c, right? (That's a postulate of relativity.) Since all measurements are made in the same frame, the conclusion follows from D = VT: The time (measured by rocket clocks) must be 1 second. There is no need whatsoever to invoke any measurements made in other frames. But you must think something is wrong with this calculation. What is it?

I've reread your explanation of the reason the observer on the train might see one flash before the other. It is quite interesting, but is dependent on point M of the track and point M' of the train not actually corresponding when the light flashes for it to work.

Einstein's conclusion is that it physically impossible for that condition to be satisfied.

That would be fine except Einstein is, it seems to me, explicit about the fact that point M' of the train must correspond to point M of the embankment when the flashes occur.

What Einstein arranges is that M' pass by the midpoint M exactly at the moment that the lights go off according to the embankment clocks. How can this be arranged? Imagine three synchronized clocks in the embankment frame: at A, M, and B. Exactly when those clocks each read 12:00 noon, the lights will flash. So M' is to pass M exactly when the M' clock reads 12:00 noon. That's the scenario.

Einstein argues that the observers on the train must conclude that according to their own clocks, those clocks on the embankment must not be synchronized because those flashes could not have occurred simultaneously at the moment M' passed M according to observations made on the train.

 

[Janus]

Maybe the attached images will help.

Let's assume that you have two space stations and a rocket. the rocket is traveling from one space station to another. Leading and trailing the rocket is a line that extends an equal distance in both directions. on the end of each line is a device that will trigger a flash of light from each station as it passes the station. The length of the lines are such that, from both station's frame of reference, each end of a line touches a station when the rocket is midway between the stations (first image of the attachment).

Now let's look at the same situation from the frame of the rocket. Length contraction has shortened the distance between the stations, so now the ends of the lines extend past the stations positions when the rocket is at the midpoint. (second image) Since the stations will not emit the flashes of light until triggered by the ends of the line(the ends of the line physically trigger the flash), they do not do so when the rocket is at midpoint (according to the rocket).

Instead we see what is shown in the next two images. First the leadiing end of the wire triggers a flash from the station ahead of the rocket, and then sometime later, the trailing end of the line triggers the station behind the rocket.

Thus the events of the station emitting the flashes are simultaneous in the station frame, but not simultaneous in the rocket frame.

 

[plover]

Now let's look at the same situation from the frame of the rocket. Length contraction has shortened the distance between the stations, so now the ends of the lines extend past the stations positions when the rocket is at the midpoint. (second image)

Note also that it is the station frame where the length of the line corresponds to the distance between stations. Since the station frame sees the line as length contracted, the rocket frame, in addition to measuring the distance between stations as shorter, also measures the line to be longer.

 

[Janus]

Note also that it is the station frame where the length of the line corresponds to the distance between stations. Since the station frame sees the line as length contracted, the rocket frame, in addition to measuring the distance between stations as shorter, also measures the line to be longer.

Yep. Exactly so.

 

[zoobyshoe]

Maybe the attached images will help.

The situation you describe is extremely interesting, and I find it to be an excellent lesson in length contraction. I haven't had much occasion to think about the length contraction of something large as viewed from something small. I've really only thought about it in terms of Einstein's measuring rods getting shortened. So, by using this example of the ship with filaments you and Plover have gotten me thinking about how, when a ship is traveling at an appreciable fraction of c the very length of the distance it is traveling shrinks from its perspective.

Thank you for putting the graphics together. They, and your verbal description, are quite clear; easy to follow.

However, as I said to Plover when he brought this up, I don't think this particular example can be used to account for why Einstein maintains the observer on his train will see one flash before the other. The reason is that in your example he will not be at point M when the flashes occur, but somewhere else. Einstein is particularly specific in pointing out that the observer on the train will be at point M when the flashes occur: "Let M' be the mid-point of the distance A--->B on the traveling train. Just when the flashes of lightning occur (as judged from the embankment) this point M' naturally coincides with the point M, but it moves toward the right in the diagram with the velocity v of the train."

And if we're in any doubt as to which rest frame Einstein means when he says M' coincides with [/i]M[/i], he makes it specifically clear that he means, at that instant,
in both rest frames:"If an observer sitting at M' in the train did not possesses this velocity, then he would remain permantly at [/M] and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated."

In the scenario with the filaments, if the observer at M' "did not possesses this velocity then he would remain permanently at"...some point before M.

The fact the light rays would reach him simultaneously if he did not possesses this velocity should be completely convincing proof that Einstein wants him at M when the lights flash, and then wants him to clear out before the light arrives.

Doc Al asserts that Einstein later concludes this condition cannot be fullfilled. That would be a critical, crucial piece of information for me, but I don't know where to look for it. It isn't in that particular chapter. If Einstein says somewhere that his set up isn't workable, I can stop worrying.

I suggested a means to plover whereby this condition could be fullfilled, to my satisfaction anyway (he hasn't given his reaction) which would be to have a rod sticking out of the side of the train right where the train rider is seated. This rod would make contact with a switch located at point M on the embankment. The switch, when thrown by the rod would send an impulse (of magic, instantaneous energy) to the lights at A and B causing them to flash. In this way, we should be able to be assured that M' is at M when the lights flash.

 

[jcsd]

Zoobyshoes the flashes CANNOT occur simulatnously in both rest frames, indeed in the situation described, no flashes will occur whilst the spaceship is at M', it's fairly trivial to prove this.

The problem is essientially one dimeionsal so if we set that the flashes occur at t = 0 and set M as the x = 0 of our co-ordiante system and L the distance from M to the spacesations (in the rest frame of M) then we get the following (x,t) co-ordinates for the situation as described by M as the flashes occur:

M = (0,0) A = (L,0) B = (-L,0)

but in the rest frame of M':

M' = (0,0) A' = (γL,-γβL/c) B' = (-γL,γβL/c)

Therefore the only way that the lights can be emitted simulatenously in bothe refebrce frames is if L = 0 or the relative velocity, u = 0

 

[zoobyshoe]

jcsd,

I'm sorry but I can't follow your last post. I think what you might be doing is setting it up with an x,y,z, and a t (for time) coordinate. I am aware this can be done but I have never done it, and can't follow your logic. (I have worked only with x,y,z coordinates.)

If you are trying to demonstrate that the two observers will not agree about when the flash occurred in units of time according a clock one or another has, that I can accept, provisionally.

Likewise, if one catches a glimpse of the others watch he will suppose the others watch is running slow.
------
What is your assessment of what will happen in the situation where the rod triggers the flash, as I described to plover and Janus?
-----------
Incidently, you keep turning it into a pair. It's just one shoe.

 

[jcsd]

jcsd,

I'm sorry but I can't follow your last post. I think what you might be doing is setting it up with an x,y,z, and a t (for time) coordinate. I am aware this can be done but I have never done it, and can't follow your logic. (I have worked only with x,y,z coordinates.)

The event M is when the spaceship is at the midpoint between the two spacesations I have defined this as happening in the rest frame of M at t =0 and and at point x=0, simlairly I defined the events A and B as the two flashes of light being emitted which also happen at in the rest frame of M at t = 0 (i.e. in this rest frame all 3 events are simultaneous) and at x = L and x = -L respectively.

I then applied a Lorentz transformation to find out what is happening in the rest frame of the spaceship and arrived at the above co-ordinates telling be that none of the evnts are simultaneous in this rest frame (γ and β are 1/√(1 - u^2/c^2) and u/c respectively where u is the relative velocity of the spaceship.[/quote]

If you are trying to demonstrate that the two observers will not agree about when the flash occurred in units of time according a clock one or another has, that I can accept, provisionally.

Likewise, if one catches a glimpse of the others watch he will suppose the others watch is running slow.

Yep that's what I'm trying to show, but remember , assuming all clocks are 100% accuarte, no clock is better than any other clock, so both are objectively measuring the 'real distance' in time between the events.
------

What is your assessment of what will happen in the situation where the rod triggers the flash, as I described to plover and Janus?

It's pretty much the same situation as the events will still have the same spacetime coordinates
-----------

Incidently, you keep turning it into a pair. It's just one shoe.

I'll try to remember.

 

[zoobyshoe]

The event M is when the spaceship is at the midpoint between the two spacesations I have defined this as happening in the rest frame of M at t =0 and and at point x=0, simlairly I defined the events A and B as the two flashes of light being emitted which also happen at in the rest frame of M at t = 0 (i.e. in this rest frame all 3 events are simultaneous) and at x = L and x = -L respectively.

OK, I follow this.

I then applied a Lorentz transformation to find out what is happening in the rest frame of the spaceship

I think I follow this. Let me check. You are saying you have shifted your perspective to that of the ship and applied the Lorentz transformation to find out what the observer on the ship will say about the timing of the flashes?

and arrived at the above co-ordinates telling be that none of the evnts are simultaneous in this rest frame

(γ and β are 1/√(1 - u^2/c^2) and u/c respectively where u is the relative velocity of the spaceship.

I recognise a Lorentz transformation in all this Greek. Don't know what &gamma and &beta, mean. "&radic" looks like it must mean "square root".

The results you gave earlier:

M = (0,0) A = (L,O) B = (-L,O)

M' = (0,0) A' = (?L, -??L/c) B'= (-?L, ??L/c)

show there is a difference, but I need a bit of an explanation. The parentheses each contain two coordinates. For M and M' are these x and t, respectively? For A and A', and B and B' these are length and time respectively? Also, I don't understand the signifigance of the question marks in the parentheses.

Yep that's what I'm trying to show, but remember , assuming all clocks are 100% accuarte, no clock is better than any other clock, so both are objectively measuring the 'real distance' in time between the events.

OK, you made a point of saying this, so I know it's important to your explanation, but I'm not sure what the phrase "`real distance´ in time" means. I´d appreciate it if you would expand a bit so I don´t miss the signifigance.

 

[Doc Al]

Einstein is particularly specific in pointing out that the observer on the train will be at point M when the flashes occur: "Let M' be the mid-point of the distance A--->B on the traveling train. Just when the flashes of lightning occur (as judged from the embankment) this point M' naturally coincides with the point M, but it moves toward the right in the diagram with the velocity v of the train."

Right. Note that Einstein explicitly says "as judged from the embankment".

And if we're in any doubt as to which rest frame Einstein means when he says M' coincides with M, he makes it specifically clear that he means, at that instant,
in both rest frames:"If an observer sitting at M' in the train did not possesses this velocity, then he would remain permantly at M and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated."

There is no question that M' passes M at the the exact moment that the lights flashed according to the M-frame observers. Of course, both frames agree that the coincidence of M and M' happens "at the same instant". How could it be otherwise?

The fact the light rays would reach him simultaneously if he did not possesses this velocity should be completely convincing proof that Einstein wants him at M when the lights flash, and then wants him to clear out before the light arrives.

Right. M' passes M just as the lights flash according to the M frame.

Doc Al asserts that Einstein later concludes this condition cannot be fullfilled. That would be a critical, crucial piece of information for me, but I don't know where to look for it. It isn't in that particular chapter. If Einstein says somewhere that his set up isn't workable, I can stop worrying.

Perhaps I wasn't clear. What I thought you were saying is that M' and M must coincide at the exact moment that the flashes are emitted according to both frames. This is, of course, impossible. (After all, as Einstein shows, the M' observers do not agree that the lights flashed at the same time.) All Einstein requires is that M' pass M just when the embankment frame says the lights flash.

I suggested a means to plover whereby this condition could be fullfilled, to my satisfaction anyway (he hasn't given his reaction) which would be to have a rod sticking out of the side of the train right where the train rider is seated. This rod would make contact with a switch located at point M on the embankment. The switch, when thrown by the rod would send an impulse (of magic, instantaneous energy) to the lights at A and B causing them to flash. In this way, we should be able to be assured that M' is at M when the lights flash.

I assume you are joking. If we start allowing magic, instantaneous messaging between the midpoint and the lights at A and B, then we have left the realm of physics. The way to set it up is as I already described. Three clocks (at A, M, and B) in the embankment frame, synchronized. Prearrange that when the clocks strike a certain time (say 12 noon) the lights will flash. Just have M' pass M exactly when the clock at M reads 12 noon.

 

[jcsd]

OK, I follow this.
I think I follow this. Let me check. You are saying you have shifted your perspective to that of the ship and applied the Lorentz transformation to find out what the observer on the ship will say about the timing of the flashes?

Yep.

I recognise a Lorentz transformation in all this Greek. Don't know what &gamma and &beta, mean. "&radic" looks like it must mean "square root".

The results you gave earlier:

M = (0,0) A = (L,O) B = (-L,O)

M' = (0,0) A' = (?L, -??L/c) B'= (-?L, ??L/c)

That is odd, you should be able to see the html chartacters: here it is again in latex (also it's a zero not an 'O'):

$$M = (0,0)$$
$$A = (L,0)$$
$$B = (-L,0)$$

$$M' = (0,0)$$
$$A' = (\gamma L,\frac{-\gamma\beta L}{c})$$
$$B' = (-\gamma L,\frac{\gamma\beta L}{c})$$

Where:

$$\beta = \frac{u}{c}$$

$$\gamma = \frac{1}{\sqrt{1 - \beta^2}}$$

Where u is the relative velcoity of the spaceship to the space station

show there is a difference, but I need a bit of an explanation. The parentheses each contain two coordinates. For M and M' are these x and t, respectively? For A and A', and B and B' these are length and time respectively? Also, I don't understand the signifigance of the question marks in the parentheses.

What I've done is basically create a co-ordinate susyetm the co-ordinates for each event are (x,t) where x is the distance from the midpoint of the space station (i.e. x = 0 at M) and t is the difference in time from when the spaceship and M occupy the same spot (i.e. t = 0 as the spaceship arrives at M)

OK, you made a point of saying this, so I know it's important to your explanation, but I'm not sure what the phrase "`real distance´ in time" means. I´d appreciate it if you would expand a bit so I don´t miss the signifigance.

The significance is that both distance and time are not absolute.

 

[Janus]

I suggested a means to plover whereby this condition could be fullfilled, to my satisfaction anyway (he hasn't given his reaction) which would be to have a rod sticking out of the side of the train right where the train rider is seated. This rod would make contact with a switch located at point M on the embankment. The switch, when thrown by the rod would send an impulse (of magic, instantaneous energy) to the lights at A and B causing them to flash. In this way, we should be able to be assured that M' is at M when the lights flash.

I hope you realize that introducing a method of instantaneous transmission violates the very principles we are trying to clarify. The best we could do is place such rods an equal distance ahead of and behind the train rider, space so that when form the rider's perspctive, these rods trigger switches at the stations themselves which initiate the the flashes at each station.

This just gives us the reverse situation as we had in the last set of images I made.

This time, from the embankment frame, the ends where the poles don't even reach to the stations when the ship is at the midpoint. (image 2)

So the sequence from the embankment would go like this:

First the trailing station is switched on (third image) and then the leading station is triggered (fourth image).

Thus taking both this and the earlier attachment into account, one sees that the stations can either flash simultaneously in the station frame and not so in the train frame, or they can flash simultaneously in the train frame, but not in the station frame. But they cannot flash simultaneously in both frames. (assuming that each staion is only triggered once)

 

[syano]

This was a really interesting article to read!

May I ask if the same thing would occur if someone threw a ball (traveling 299,999.99 km per second) at the ship instead of sending a light beam towards it? If the ship was 299,999.99 km away from the station and the ship was moving away from the station at 150,000 km per second, (or the station was moving away from the ship at 150,000 km per second) would the ball take 1 second to reach the ship (relative to the observer on the ship) or would it take well over one second?

 

[Doc Al]

May I ask if the same thing would occur if someone threw a ball (traveling 299,999.99 km per second) at the ship instead of sending a light beam towards it? If the ship was 299,999.99 km away from the station and the ship was moving away from the station at 150,000 km per second, (or the station was moving away from the ship at 150,000 km per second) would the ball take 1 second to reach the ship (relative to the observer on the ship) or would it take well over one second?

Same thing. It would take about 1 second (according to observers on the ship) for the ball to reach the ship, assuming that the speed of the ball is 299,999.99 km/s with respect to the ship and that the distance of 299,999.99 km is as measured by the ship. (We'll ignore any difficulties involved in actually throwing a ball with that speed.)

Even if that speed was the speed of the ball with respect to the space station, it would turn out that the speed as seen by the ship would still be pretty close to c. (See relativistic addition of velocities.)

 

[zoobyshoe]

Right. Note that Einstein explicitly says "as judged from the embankment".

Noted.

There is no question that M' passes M at the the exact moment that the lights flashed according to the M-frame observers. Of course, both frames agree that the coincidence of M and M' happens "at the same instant". How could it be otherwise?

Super!

Perhaps I wasn't clear. What I thought you were saying is that M' and M must coincide at the exact moment that the flashes are emitted according to both frames. This is, of course, impossible. (After all, as Einstein shows, the M' observers do not agree that the lights flashed at the same time.) All Einstein requires is that M' pass M just when the embankment frame says the lights flash.

What I am saying is that there is an instant when M' and M coincide in time and location, and they would both agree such an instant existed. (This, I believe, is how jcsd has set up his coordinate system. M = (0,0) and M' = (0,0) ).
In the M frame (embankment) the flashes of light are emitted at t=0.

However, at t=0 neither M nor M' knows the light has been emitted. Only Einstein and we know that.

The way to set it up is as I already described. Three clocks (at A, M, and B) in the embankment frame, synchronized. Prearrange that when the clocks strike a certain time (say 12 noon) the lights will flash. Just have M' pass M exactly when the clock at M reads 12 noon.

Your clocks will do wonderfully, thanks.

 

[zoobyshoe]

here it is again in latex

Ok. This is much better. Thank you for translating it to LaTex.

What I've done is basically create a co-ordinate susyetm the co-ordinates for each event are (x,t) where x is the distance from the midpoint of the space station (i.e. x = 0 at M) and t is the difference in time from when the spaceship and M occupy the same spot (i.e. t = 0 as the spaceship arrives at M)

Clear. I will plug the .5 c into these and try to make sure I understand what they are saying. Thanks.

 

[zoobyshoe]

I hope you realize that introducing a method of instantaneous transmission violates the very principles we are trying to clarify.

At some point in the future I might like to start a thread exploring what criteria must be met by a given suggested gedanken fiction for it to be acceptable. That is moot now since I don't need it any more. Doc Al's three clocks, and 12 noon stipulation work fine.

 

[plover]

Good to have you here.

Thanks.

(You got to love a place where you can get respect for waxing excruciatingly pedantic on a passage from Einstein... )

Note on the following:
For the sake of syntactic (and my own) sanity, I'll refer to [post=251281]my prior post[/post] analyzing the Einstein passage as EP (for Einstein Post). I've added section numbers to it, and the notation EP(n) indicates section n of the post.​

You have pointed out that the observer on the embankment will suppose the observer on the train sees one flash before the other. However, there is doubt in my mind as to whether you think Einstein is asserting that the man on the train will see one flash of light before the other in his reference frame on the train.

The short answer: yes, I do think Einstein is asserting that. (I can also agree that the degree to which EP(7) makes that explicit is less than absolute. )

His wording is iffy at many points,

I agree, it has its ambiguous spots. It would be good if we could know whether it was Einstein or the translator who is responsible for that. Unfortunately, I don't know German. Anyone out there want to comment on the translation of Ch 9 of Einstein's book?

but since he comes to the conclusion "Events which are simultaneous with reference to the embankment are not simultaneous with respect to thr train, and vice versa (relativity of simultaneity)." it seems unbelievable to me that he could only be talking about what the observer on the embankment thinks the observer on the train might be experiencing.

Einstein is making a much stronger statement than this. The underlying logic of the argument for the paragraph analyzed in EP is (as I read it):

Given the rigorous way in which the circumstances have been defined, what conclusions must an observer on the embankment at M deduce about the experience of an observer on the train at M'?​

(The conclusion in this case being, of course, the sentence you just quoted: "Events which ... (relativity of simultaneity).")

I'm not claiming Einstein's argument is false.

I did not really expect that you were. But given the number of threads around here called "Special Relativity Must Die" or some such, I thought it best to make completely sure...

I don't object to length contraction or time dilation being brought in if it can be used to explain that the observer on the train will see one flash of light before the other.

This is not the impression I received from your comments in [post=250589]post #41[/post]. Thus the method of EP was to try to use only the premises that Einstein used up through Ch 9 to make the argument. While Einstein doesn't say anything that conflicts with relativity, he does introduce common sense notions and later discards them when they are no longer tenable in the framework he is unfolding, and this might lead to points where certain types of comparisons become muddy.

I've reread your explanation of the reason the observer on the train might see one flash before the other.

Which one are you referring to? The train version in [post=249898]post #25[/post] of the thread, or the rocket/filament one in [post=250351]post #39[/post]? (The arguments in these are the same but the context might affect something.)

[It] is dependent on point M of the track and point M' of the train not actually corresponding when the light flashes for it to work.

How so?

That would be fine except Einstein is, it seems to me, explicit about the fact that point M' of the train must correspond to point M of the embankment when the flashes occur.

EP(4) addresses this.

(I don't know why he even bothers to mention what the ends of the train are doing when he is so exacting in his description of the midpoints lining up.)

I suspect that one reason that Einstein chooses a train as the vehicle (no pun inten... oh, who am I kidding?) for his argument is that, as an object that both moves and extends a considerable distance along the line of its motion, it corresponds well to an entire axis of a second reference frame, and thus makes the idea of a moving system of coordinates less abstract than would a moving object that functions in a more point-like way in the imagination.

As the quote preceding EP(1) shows (and Ch 8 goes over in more detail), the point M is not determined a priori but is constructed as part of the mechanism for determining the simultaneity of the flashes at A and B. Similarly, the points A' and B' are used to fix the point M'.

Note that A' and B' are defined in reference to the embankment frame. A' is the point in the train frame that happens to coincide with A when the flash takes place at A. B' is defined similarly.

It seems to me he is trying very hard to describe a situation exactly like what would happen if a rod sticking out from the outside of the train beside the observer on the train were to trip a switch located at point M on the embankment causing the flashes (the signal getting from the switch to the lights instantaneously, by magic, of course). Does that not seem to be the case to you?

As Einstein sets up this example, the point M as I pointed out above, is determined by the points A and B. So if anything it is like the flashes cause someone to be magically teleported to M (ploink!) in order to determine whether or not they were simultaneous.

In the interest of annoying or appeasing everyone evenly (as the case may work itself out), I will suggest that it was injudicious to introduce magical phenomena into a physics discussion that is treating the foundation of relativistic time effects, and which currently seems to turn on the confusion caused by minute differences in definition of terms (and especially when the phenomena introduced are not accompanied by appropriate sound effects); and on the other hand, I will also suggest that commenters could cut some slack for the use of what was essentially (and syntactically marked as) a rhetorical device, and one which, by its own rules (and considered as an "as if"), is not technically incorrect.


(Continued in next post - broken up due to length restriction.)

 

[plover]

(Continued from previous post.)

However, as I said to Plover when he brought this up, I don't think this particular example can be used to account for why Einstein maintains the observer on his train will see one flash before the other. The reason is that in your example he will not be at point M when the flashes occur, but somewhere else.

This is an example of why I think that the answers from early in this thread (while correct) may be misleading if introduced to this stage of Einstein's argument.

One thing that needs to be agreed upon is the purpose of Ch 9. I have stated in a couple of places (in slightly different terms) that I believe that the intent is to show what may be deduced about the perception in the train reference frame of events determined to be simultaneous in the embankment frame.

The emphasis of this needs to be changed slightly however: the perceptions that are being examined in the train reference frame are restricted to temporal perceptions. Thus, while a fully worked out framework for Special Relativity offers the result, there is no mention made, or circumstances implied as to spatial relationships as perceived in the train reference frame.

There are several spatial relationships established over the course of the passage, but each is described from the embankment frame. These are (see also EP(4)):

• A' coincides with A at the moment of the flashes.
• B' coincides with B at the moment of the flashes.
• M' coincides with M at the moment of the flashes.
• M' is somewhere to the right of M at the moment it passes the flash from B, and somewhere further to the right when the flash from A passes it.

As noted in EP(4) the only frame for which "the moment of the flashes" is defined is the embankment frame. Indeed the conclusion of the argument is that the phrase "the moment of the flashes" turns out to be nonsensical in the train frame.

To make the complaint that an observer at M' "will not be at point M when the flashes occur" is to anticipate the argument by using an assumption about time in the train frame as a premise rather than a conclusion.

And if we're in any doubt as to which rest frame Einstein means when he says M' coincides with [/i]M[/i], he makes it specifically clear that he means, at that instant, in both rest frames:"If an observer sitting at M' in the train did not possesses this velocity, then he would remain permantly at [/M] and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated."

There is a moment when M and M' coincide.

In each reference frame it happens at the particular moment when the two points coincide (however that moment is defined by clocks located in the respective frames).

The two points do not continue to coincide because they are in different frames.

In the embankment frame, that moment also happens to be the one when the flashes occur. There is nothing in the sentence you quote that warrants saying anything about the flashes in the train reference frame. The path of the argument is, in fact, to lead you to the conclusion that our knowledge about the flashes in the embankment frame forces the conclusion that they will not be considered simultaneous in the train frame.

At this stage of the argument, there is no point where the position of the observer at M' can be defined - as considered from the train reference frame - when either flash occurs.

The only point under consideration is whether our knowledge of the simultaneity of the flashes in the embankment reference frame allows us to maintain that they will also be simultaneous in the train reference frame. And of course, as it turns out, we may not maintain that.

In the scenario with the filaments, if the observer at M' "did not possesses this velocity then he would remain permanently at"...some point before M.

I find this and the points following it rather confusing. Perhaps you could restate them in terms of my comments above. (Some point "before" M? While such must have occurred, it is not mentioned anywhere in the argument.)

 

[zoobyshoe]

Plover,

We are definitely at odds about what Einstein has set up in terms of where M' is when the flashes occur, whose perspective is the one he wants us to be aware of in any given sentence, and the function of A' and B' of the train.

Consider the first sentence of the chapter:

"Up to now our considerations have been referred to a particular body of reference, which we have styled a "railway embankment".

By "our considerations" he means his own and his reader's.
He goes on from here to "refer" his and his readers considerations from the view of someone on the railway embankment to that of someone on the train. From this point on, we are in the train frame of reference, except where otherwise noted.

There is no double imagining going on: we are not imagining ourselves to be in the frame of the embankment imagining the frame of the train. We are in one or the other, according to where he asks us to be, but never in one imagining the other.
-------
Also: he never says that A' and B' "coincide" with events A and B. He uses the word "correspond":

"But the events A and B also correspond to positions A and B on the train. Let M' be the mid-point of the distance A---->B. Just when the flashes (footnote: As judged from the embankment) of lightning occur, this point M' naturally coincides with the point M..."

And he uses the word "coincides" when speaking of the relationship of M to M'. So, "correspond" and "coincide" are not describing the same thing, although I am not at all certain what relationship he means to imply when he uses "correspond". This is where he is "iffy".
-------------------

This sentence is explicit and crucial:

"If an observer sitting in the position M' of the train did not posses this velocity, then he would remain permanently at M', and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated."
That sentence refers to the reference frame of the train. Einstein is speaking to us concerning a point he wants us to understand about the reference frame of the train.

The couple times he deviates from the reference frame of the train are specified: once with the words in parentheses "(considered with reference to the railway embankment)" and another time with a footnote.

 

[zoobyshoe]

$$\beta = \frac{u}{c}$$

$$\gamma = \frac{1}{\sqrt{1 - \beta^2}}$$

Where u is the relative velcoity of the spaceship to the space station

Because I am a math and latex basket case you will, I am sure, be a sport and not make viscious fun of me for approaching this "trivial" problem at a ponderously slow pace.

For $$\beta$$ I get: .5

u = .5 c = 150,000 km/s

$$\beta = \frac{u}{c}$$ therefore $$\beta$$ = 150,000/300,000 = .5


For $$\gamma$$ I get: 1.1543958

.5² = .25

1- .25 = .75

$$\sqrt{.75}$$ = .8660254

1/.8660254 = 1.1547005 = $$\gamma$$

So, before I proceed, would you be kind enough to glance at this and make sure I've gotten this far correctly using .5c as the ships speed.

Thanks

 

[Doc Al]

So, before I proceed, would you be kind enough to glance at this and make sure I've gotten this far correctly using .5c as the ships speed.

Looks good to me.