# Einstein's train/embankment thought experiment as an example of backward causation

1. Apr 9, 2009

### pLatOscLoSET

Here is a link to the text, chapter 9... page 30:

So I have been analyzing this thought experiment from a causal perspective and have found it to be quite unsatisfactory. The role that lightning plays is key and that is where I will start. How is the experience "it is lightning" possible? Allow me to derive a causal chain in order to illustrate this. First, their must be a material event, an atmospheric discharge of electricity(doe), an emission of light, a subsequent absorption of light by the optical system of the observer, and that data/information is then organized by the mind into the experience(eol). So we have:

doe > emission > absorption > eol

we can combine the emission and absorption events into a singular causal process so that we have:

doe > e/a > eol = a > b > c

So the distilled version of this thought experiment is that there are two observers, one located at m', moving with some velocity on the train, and one perpendicular to m, at rest on the embankment. Now at the moment that the embankment observer has the experience "it is lightning", Einstein freezes the action and explains to us that m' naturally coincides with m, and that if the train didn't have the velocity it did, the light emitted from places A & B would be absorbed by the observers optical system at m' in a manner that would allow him experience stroke A & B simultaneously. So the causal chain you must extract from Einstein is:

eol > e/a > eol = c > b > c

How can the the embankment observer have the experience "it is lightning" before light is emitted from places A & B? Another way of putting it is, does he have the same experience twice?

2. Apr 9, 2009

### JesseM

Re: einstein's train/embankment thought experiment as an example of backward causatio

I don't follow. Why do you think that Einstein's statement implies that causal chain? He's just saying that if m' remained at the same position as m, then the light from both flashes would reach both m and m' at the same moment. But in fact m' does not remain at the same position as m, instead m' is moving towards the position of flash B, so the light from that flash will reach m' first. Nothing about this implies any weird causality.

Perhaps some numbers would help? Suppose in the embankment frame, the embankment observer m is at rest at position x=0 lights-seconds, and at t=0 seconds lightning flash A strikes at positions x=-16 l.s. and lightning flash B strikes at position x=16 l.s. Also suppose that the train is moving at 0.6c (it's one of those new maglev trains!) in the +x direction, and at t=0 m' is also at position x=0 l.s. So, the light from flash A will reach m at x=0 l.s. at the same time the light from flash B reaches his position--he'll see both at t=16 s. However, since m' is moving towards the position of B, he'll see flash B a bit earlier--at t=10 s, the light from flash B will have reached x = 16 - 10 = 6 l.s., and m' will also be at 6 l.s. because he's moving at 0.6c, so he'll see flash B at t=10 s. Meanwhile the light from flash A won't reach him until t=40 s, because at that moment the light from flash B will have reached x = -16 + 40 = 24 l.s., and at 0.6c m' will also be at x = 40*0.6 = 24 l.s.

So, in summary, if we use the coordinates in the embankment frame, both lightning strikes occur at t=0 s, the light from both flashes reachs m simultaneously at t=16 s, while the light from flash A reaches m' at t=10 s and the light from flash B reaches him at t=40 s. Do you see any causality problems with these numbers?

edit: Perhaps your mistake is here:
Einstein does not say that at the moment the embankment observer experiences the lightning, m' is at the same position as m; rather, he says that m' is at the same position as m at the same time the strikes actually happen in the rest frame of the embankment observer m. This observer m won't actually see the light from the flashes until later, as you can see is true in my numerical example above.

Last edited: Apr 9, 2009
3. Apr 9, 2009

### pLatOscLoSET

Re: einstein's train/embankment thought experiment as an example of backward causatio

First, let me thank you for your response. I have a few points of contention, but allow me to make only one in this post.

If you refer back to the text, Einstein makes it very clear that when m and m' naturally coincide the judgment, in regards to the flashes of lightning occurring, is made from the embankment. How can one make a judgment about something he has not experienced yet? Judgment entails an eol... not a doe.

Respectfully...jpb

4. Apr 9, 2009

### JesseM

Re: einstein's train/embankment thought experiment as an example of backward causatio

No, you're misreading it, at the moment m and m' coincide, m is not yet aware that the flashes have occurred, although m will retrospectively say that the flashes were simultaneous with the event of m and m' coinciding in his own coordinate system (i.e. he will assign all three events the same t-coordinate). That's one of the features of how inertial frames work in relativity, you may retrospectively say two events occurred simultaneously even if you were not aware of one event until well after you became aware of the other event. For example, if in 2009 according to my clock I observe the light from an event 2 light-years away according to my measurements, and in 2017 I observe the light from an event 10 light-years away, I will retrospectively say both these events occurred simultaneously in 2007 in my frame, since the light from the first event must have been in transit for 2 years in my frame while the light from the second event must have been in transit for 10 years in my frame.

If you still think Einstein was saying m was actually aware of the flashes at the moment m' was next to him, can you quote the specific sentence or paragraph that makes you think this?

5. Apr 9, 2009

### Al68

Re: einstein's train/embankment thought experiment as an example of backward causatio

I don't follow, either. Einstein doesn't imply that any judgment is made in advance by the observers. The embankment observer just combines the fact that the flashes of light were observed by him simultaneously with the fact that they were equidistant from him to conclude the strikes were simultaneous in his frame. He can then account for the light transit time to conclude that the strikes were simultaneous with m' passing m in his frame.

Which means that the train observer will not observe the flashes simultaneously, and since the strikes were also equidistant from the train observer in his frame, they were not simultaneous in his frame.

No judgments are made by the observers in advance. They simply set up the scenario as described, record the results, and make the judgments later.

6. Apr 9, 2009

### pLatOscLoSET

Re: einstein's train/embankment thought experiment as an example of backward causatio

Sure... here's the link again:
Chapter 9, page 31 and I quote:

"Just when the flashes(as judged from the embankment) of lightning occur, this point M' naturally occurs with point M, 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 posses this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A & B would reach him simultaneously, i.e. they would meet just where he is situated. 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 ahead of the beam of light coming from A."

I look forward to your interpretation. Respectfully...jpb

Last edited: Apr 9, 2009
7. Apr 9, 2009

### JesseM

Re: einstein's train/embankment thought experiment as an example of backward causatio

Yes, as judged in the embankment frame, the two flashes of lightning occur simultaneously with M' and M lining up. This does not mean M actually saw them at the same moment M' was next to him. Similarly, in my example, I judged that in my rest frame, the two events occurred simultaneously in 2007, even though I (a particular observer at rest in this frame) saw them in 2009 and 2017 respectively (a different observer at rest in the same frame might see the same two events at different times, but would still judge that both happened in 2007 once he corrected for light travel times).

Last edited: Apr 9, 2009
8. Apr 9, 2009

### pLatOscLoSET

Re: einstein's train/embankment thought experiment as an example of backward causatio

What is the point then of referring to a particular frame of reference for a judgment to be made? Of course they are simultaneous. The whole point of the experiment is to demonstrate that the experience of simultaneity is dependent on the observers state of motion with respect to those events. By your reasoning, we must consider them simultaneous with respect to the train also because in retrospect the observer at m' should take into account increased and decreasing distance due to his velocity relative to places a & b where the lightning occurs. The embankment observer just happens to be at rest. If you put him in motion along with train it doesn't mean doe wasn't simultaneous it just means both of their eol's wouldn't be. Respectfully...jpb

9. Apr 9, 2009

### JesseM

Re: einstein's train/embankment thought experiment as an example of backward causatio

Only in that frame, not in other frames.
No, you're missing the whole point of the thought-experiment, which is that if each observer retroactively assigns a time to the events based on the assumption that the light traveled at c in their own frame, they will disagree about whether the events occurred simultaneously or not. The train observer m' defines the position of the flashes not by where they occurred relative to the track (a sort of ruler at rest in the embankment frame), but where they occurred relative to the train (a ruler at rest in the train frame). Remember, m' is at the exact midpoint of the train, and the two flashes occurred right next to either end of the the train. So in the frame of m', the two flashes occurred at equal distances from himself, and so the only way for him to explain the fact that the light from flash B reached him before the light from flash A, taking into account his assumption that the light traveled at c in both directions in his frame, is for him to conclude that flash B actually occurred at an earlier time than flash A in his frame. Here an analogy would be if I see an event in 2009 which occurred 2 light-years away according to my measurements, and then in 2010 I see an event which occurred 2 light-years away in the opposite direction in my frame--I must conclude that in my frame these events occurred non-simultaneously, the first in 2007 and the second in 2008.
In relativity there is no absolute truth about who is at rest and who is in motion, it all depends on your frame of reference: in the embankment frame, the embankment observer is at rest and the train observer is in motion, but in the train frame, the train observer is at rest and the embankment observer is in motion. All inertial frames are considered equally valid in relativity, and the laws of physics work the same way in each one, including the fact that in each frame the speed of a light beam is always c as measured in terms of that frame's distance/time. The train thought-experiment shows that one consequence of the assumption that both beams of light move at c in both frames is that the two frames must disagree about simultaneity.

10. Apr 9, 2009

### Al68

Re: einstein's train/embankment thought experiment as an example of backward causatio

The distances from m' to the front and rear of the train (a & b) do not change. In the frame of the train, the location of the strikes are equidistant to m'. That's the whole point, since the strikes are at the same distance from m', and the flashes are not observed simultaneously by m', then the strikes were not simultaneous in the train's frame.

Sure m' could take into account his velocity relative to the embankment locations of the strikes, but that would only show that the strikes were simultaneous in the frame of the embankment, and we already knew that. The whole point of the story is that in the frame of the train, the strikes are at equal distances from m' (front and back of the train) and are not observed simultaneously, so they did not occur simultaneously.

Edit: Oops, JesseM beat me to it again. :shy:

11. Apr 9, 2009

### pLatOscLoSET

Re: einstein's train/embankment thought experiment as an example of backward causatio

So it seems we will definitely disagree as to the correct interpretation of the thought experiment. That's fine, but to not let this dissolve into a war of words, I am going to draw some logical conclusions from your initial calculations.

Before I begin let us assume that that places A & B, where the doe occurs, form 2 vertices of an equilateral triangle where the position of the embankment observer is the third. From your calculations it takes 16 s for the light to travel to m'. So I must conclude that because the distance from A or B to the embankment observer is twice the distance from A or B to m', it would take 32 seconds from the moment the doe occurs for him to have his eol. If this is correct than I would be forced to conclude that the embankment observer, because of the continued forward motion of the train, would perceive flash B to be striking the body of the train and flash A to not be in contact with the train at all. In effect you would have the train and flash B in a superposition of states. This is relativity not quantum mechanics. respectfully...jpb

12. Apr 9, 2009

### JesseM

Re: einstein's train/embankment thought experiment as an example of backward causatio

It's not as if this is really open to debate, your interpretation is incompatible with the whole theory of SR while mine is not. Also the train thought-experiment has been repeated by many different authors in many different textbooks, all of them interpreting it the way I have; I'm sure you could find plenty of examples from during Einstein's lifetime, surely he would have corrected them if they misunderstood his meaning.
I don't understand, why would it be a triangle? All of these events occur along a single straight line, it's a one-dimensional problem. Realistically I suppose the embankment observer would have to be offset slightly to avoid getting run over by the train, but it's an idealized problem, and in any case we can assume this offset is negligible compared to the distance between A and B rather than large as would be the case if it were an equilateral triangle.
Why would you conclude this? I never said anything about an equilateral triangle, and in fact my numbers make clear that I intended m to be at the midpoint of the line between A and B:
If the strikes occur at t=0 and the light from the strikes reaches m at t=16 in his frame, and m was at position x=0 while the strikes were at positions x=-16 and x=16 in his frame, obviously I intended for m to be at the midpoint of the line connecting the two strikes, whereas you seem to be assuming for no good reason that m was at a different position on the y-axis than the strikes were (specifically your assumption of an equilateral triangle implies that if the strikes happened at y=0, then m was positioned at y = $$\sqrt{32^2 - 16^2} = \sqrt{768}$$ = 27.7128). We could assume this if you want to, but the numbers would obviously have to be different than they were in my problem.
You seem to be weirdly conflating the time m sees the light from the strikes with the position the train actually is at that time in his frame. Given your assumptions, it's true that he'd see the strikes at t=32, but at that moment he would also see that the train's back end was at the position of strike A (x=-16, y=0) and the train's front end was at the position of strike B (x=16, y=0)--the light from the events of the train's ends reaching these two positions would just be reaching his eyes at t=32 even though they "really" happened much earlier. And of course at t=32 the train has "really" moved on in his frame, and the back end is "really" at x=-16 + 0.6*32 = 3.2 while the front end is "really" at x=16 + 0.6*32 = 35.2, but he can't actually see the instantaneous position of the train in his frame at t=32, because the light from the train takes some time to reach his eyes just like the lightning flashes. And if you're interested in when events "really" happened in his frame rather than when he sees them, then of course the strikes themselves "really" happened at time t=0 rather than t=32 in his frame, so that's the time you should be calculating the "real" position of the two ends of the train.

Last edited: Apr 9, 2009
13. Apr 9, 2009

### pLatOscLoSET

Re: einstein's train/embankment thought experiment as an example of backward causatio

So up to this point we have considered everything with reference to our embankment. Our embankment observer is at rest, our track is at rest, our lightning strokes are at rest, everything is at rest except for the train, basically the world is at rest and the train is in motion. So knowing that motion is relative, can we perform this experiment in an inverse manner. What I mean by that is, can we say that the train is at rest and the world is in motion?

14. Apr 9, 2009

### Al68

Re: einstein's train/embankment thought experiment as an example of backward causatio

Absolutely. If we have two lightning strikes at either end of the train that are simultaneous in the train's frame (to m'), then the strikes would not be simultaneous in the frame of the embankment (to m). In the frame of the embankment, the strike at the rear of the train occurred before the strike at the front, in this case.

15. Apr 9, 2009

### JesseM

Re: einstein's train/embankment thought experiment as an example of backward causatio

Yes. Assume the train observer m' uses a primed system of coordinates, and that he's at x'=0, y'=0 in his system. The train was 32 light-seconds long in the embankment frame, but this must be shorter than the length of the train in its own rest frame due to length contraction; in the train's own rest frame it must be $$32/\sqrt{1 - 0.6^2}$$ = 32/0.8 = 40 light-seconds long in the train's rest frame. So, the back end of the train is at x'=-20, y'=0 and the front end is at x'=20, y'=0.

That takes care of where the strikes occur in the train observer's frame, but how about the time of each strike? Well, let's assume that m' is next to m at t'=0 in the train frame, since this event happened at t=0 in the embankment frame. From my numbers, we know that in the embankment frame, the light from strike B reached the train observer m' at t=10, and the light from strike A reached m' at t=40. These are the times in the embankment frame, but we know that the clock of the train observer m' is slowed down by a factor of 0.8 in the embankment frame, so the light from B reaches m' at t'=10*0.8=8, and the light from A reaches m' at t'=40*0.8=32. If the distance between m' and each strike was 20 light-seconds in the train frame, then if we assume the light travels at c in the train frame, then each strike must have happened 20 seconds prior to m' seeing them--strike B must have happened at t'=8-20=-12 seconds, and strike A must have happened at t'=32-20=12 seconds.

Another way to arrive at these figures would be to use the Lorentz transformation which tells us how to transform between two inertial frames; if we know the coordinates x,y,z,t of an event E in the first (unprimed) frame, and there's another (primed) frame whose origin is moving at speed v along the x-axis of the unprimed frame, with the origins of the two frames lining up at t=0 and t'=0, then the coordinates of event E in the primed frame are given by:

$$x' = \gamma*(x - vt)$$
$$y' = y$$
$$z' = z$$
$$t' = \gamma*(t - vx/c^2)$$
with $$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$

In this case we have v=0.6c, so $$\gamma = 1/0.8 = 1.25$$. So for example, if we knew strike A occurred at x=-16, y=0, z=0 and t=0 in the unprimed embankment frame, the coordinates in the primed train frame must be:

x' = 1.25*(-16 - 0.6*0) = -20
y' = 0
z' = 0
t' = 1.25*(0 - 0.6*-16) = 12

And strike B occurred at x=16, y=0, z=0, t=0 in the unprimed embankment frame, so the coordinates in the primed frame are:

x' = 1.25*(16 - 0.6*0) = 20
y' = 0
z' = 0
t' = 1.25*(0 - 0.6*16) = -12

So, you can see that this agrees with the previous analysis.

16. Apr 9, 2009

### Staff: Mentor

Re: einstein's train/embankment thought experiment as an example of backward causatio

The http://en.wikipedia.org/wiki/Minkowski_space#Causal_structure" is frame invariant. This means that a cause preceeds its effect in all reference frames. Although the order of spacelike separated events is different in different reference frames such events cannot be causally related so you cannot get backwards causation.

Last edited by a moderator: Apr 24, 2017
17. Apr 9, 2009

### pLatOscLoSET

Re: einstein's train/embankment thought experiment as an example of backward causatio

Thanks for all your detailed responses. My last point was not as clear as I would have liked it to be, so let me restate it. There is going to be some need for translation on your parts so bear with me and see if you make out what I'm trying to say.

So from the embankments frame, nothing is moving but the train, but when I think in terms of the trains frame, everything is moving, the observer, places A & B where the lightning occurs, M, etc. Now if I truly switch to the train's frame it seems to me that its false when Einstein concludes with... "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 ahead of the beam of light coming from A" What I mean by this is that if we really put our self in the train and declared ourselves to be at rest, then we wouldn't be hastening towards the beam of light coming from B, and riding ahead of the beam of light coming from A, B would be hastening towards us and A would be riding away from us. The light sources, places A & B, would be in motion... not us. Hopefully you can translate what I am trying to say. respectfully...jpb

18. Apr 9, 2009

### matheinste

Re: einstein's train/embankment thought experiment as an example of backward causatio

Hello pLatOscLoSET

Quote:-
-----The light sources, places A & B, would be in motion... not us. Hopefully you can translate what I am trying to say. respectfully...

The points of light emission can be considered at rest in every frame.

Matheinste.

19. Apr 9, 2009

### pLatOscLoSET

Re: einstein's train/embankment thought experiment as an example of backward causatio

Hi matheinste,

I agree... the point of emission would... but not the place of emmission(source)

20. Apr 9, 2009

### JesseM

Re: einstein's train/embankment thought experiment as an example of backward causatio

The two strikes were instantaneous events rather than persisting objects which have a well-defined position at different times, so each frame defines the positions of the strikes A & B relative to landmarks at rest in that frame. So in the embankment frame, the position of the strikes can be defined in terms of where on the tracks they occurred, but in the train frame, the position is defined in terms of where on the train they occurred (the ends of the train). Thus in the frame of the train-observer m', he is not moving towards or away from the position where the strikes occurred in his own frame.
Yes, but Einstein only said "considered with reference to the railway embankment", making clear that he was considering things in the embankment frame in that sentence, he didn't say that m' was "hastening towards the beam of light coming from B" in any absolute sense, and indeed he isn't in the train rest frame (in the train rest frame, it is m that is hastening towards the beam coming from A). But all frames always agree on predictions about events which coincide at a single localized point in time and space, like the reading on a given observer's clock when a certain beam of light hits him, so it's perfectly valid to use the embankment frame to predict that the light from B will hit m' before the light from A hits him, and once you've concluded that's true, you can be sure it must also be true in the train rest frame.