# Simultaneity Train Example

1. Jan 23, 2010

### danielatha4

The train example discussing non-simultaneity that I'm sure most of you have heard of:

However, wouldn't the passenger see the strikes of lightning at the same time? As she is in an inertial reference frame and is equi-distance from the front and back?

Last edited by a moderator: Sep 25, 2014
2. Jan 24, 2010

### Staff: Mentor

The light would only reach the passenger in the middle of the train at the same time if the lightning struck the ends of the train at the same time according to the frame of the train. But it doesn't.

3. Feb 21, 2010

### stevmg

Yes it does

4. Feb 21, 2010

### stevmg

Doc Al -

Why aren't the lightning strikes to the train at the same instant?

5. Feb 21, 2010

### Staff: Mentor

What makes you say that? Did you watch the video?

6. Feb 21, 2010

### Staff: Mentor

At the same instant according to who?

Whether the lightning strikes are simultaneous depends on the frame making the observations. You are told that the strikes are simultaneous according to the frame of the platform observers. Per relativity and the invariant speed of light, the strikes cannot be simultaneous according to the frame of the train observers. (That's actually explained in the video, if I recall.)

7. Feb 21, 2010

### JesseM

One key point to understand is that in relativity all frames must agree about local events which occur at a single point in space and time. So, you can't have a situation where one frame predicts that two light rays hit an observer at the same moment in time and another doesn't, because this would involve a disagreement about local events (imagine that the observer has a bomb with light detectors on either side that will cause the bomb to explode if light hits both detectors within a very short time window--if different frames could disagree on whether the bomb exploded or not, that would essentially make different frames into parallel universes rather than just different ways of assigning space and time coordinates to events). That means that if the ground frame predicts the light hits the observer at the center of the train at different moments, then the train rest frame must say the same thing. But how can this be, given that both strikes happened at the same distance from the observer at the center of the train in the train rest frame, and the observer is at rest in this frame? The answer is that the strikes must have occurred at different times in this frame, so even though the light from each strike takes the same amount of time to reach him after the moment the strike occurred, since the strikes happened at different moments the light from each strike reaches him at different moments too.

8. Feb 21, 2010

### stevmg

Doc Al -

That's where my hangup is...

In the video it is NOT explained why the lightning strikes on the train are at different times than from the platform. It is stated that they are different but not explained why. It is a tautology - a supposition is presumed true and then is proven true because it was "true" from before (the assumption.) Look at the video again - look for the explanation of why the strikes are different and there is none.

I appreciate your help in understanding this - don't get me wrong.

9. Feb 21, 2010

### stevmg

Jesse M -

"One key point to understand is that in relativity all frames must agree about local events which occur at a single point in space and time. So, you can't have a situation where one frame predicts that two light rays hit an observer at the same moment in time and another doesn't, because this would involve a disagreement about local events (imagine that the observer has a bomb with light detectors on either side that will cause the bomb to explode if light hits both detectors within a very short time window--if different frames could disagree on whether the bomb exploded or not, that would essentially make different frames into parallel universes rather than just different ways of assigning space and time coordinates to events). That means that if the ground frame predicts the light hits the observer at the center of the train at different moments, then the train rest frame must say the same thing."

From here on you lost me - make the sentences short, sweet and keep the references aligned:

"But how can this be, given that both strikes happened at the same distance from the observer at the center of the train in the train rest frame, and the observer is at rest in this frame? The answer is that the strikes must have occurred at different times in this frame, so even though the light from each strike takes the same amount of time to reach him after the moment the strike occurred, since the strikes happened at different moments the light from each strike reaches him at different moments too"

10. Feb 21, 2010

### stevmg

Wait a minute - Jesse M - I am getting it half way.

Usin Einstein's example precisely as he states it, with reference to the ground, the light arrives at the center observer on the train at different times and WON'T explode the bomb. So, if we posited that the if the light flashes hit the observer at the same time in the frame of reference of the train, then we would have a contradiction (or "parallel universes" as you called it.) as the bomb would explode in that frame but not in the ground frame.

According to Einstein's example in section 9, it is agreed that acording to the ground frame, the flashes do not meet at the same time at the midpoint because of the motion of the train, so they likewise cannot do it in the train frame (here, that would mean that they left points A' and B' at different times in the train frmae.

I now have it half way - now I have to go and get it the full way.

I think it may be possib;e to show this by application of goods old Hugo Lorentz. Have to work on it.

Any help?

11. Feb 21, 2010

### Staff: Mentor

Watch it one more time. The person on the platform deduces (correctly) that the light from the two flashes reaches the person in the center of the train at different times. This is a fact that everyone must agree on, including observers on the train. (This is what JesseM was explaining.)

And if the light reaches the observer at the center of the train at different times, then the lightning flashes must have hit the train ends at different times (according to train observers) since the light travels the same distance from each end. (If the flashes were simultaneous according to train observers then the light would have reached the middle of the train at the same time--but we know it doesn't.)

12. Feb 21, 2010

### JesseM

Yes, exactly. But then, why do you say you only have it "half way"? It sounds like you got it. I'll try spelling out the steps in the argument in more detail, maybe it'll help:
1. In the ground frame, the light from the flashes reaches the observer M at the midpoint of the train at different moments. Since this is a local event, it must be true in the train frame too.
2. In the ground frame, the two lightning strikes happened right next to either end of the train. Since these are local events, the strikes must happen at either end of the train in the train frame too.
3. The observer M is equal distances from either end of the train, and in the train frame he isn't moving. Since the strikes happened at either end of the train (2), both strikes happened at an equal distance from M in the train frame.
4. In the train frame, the light from both strikes must travel towards M at c. Since the strikes happened the same distance from M and M isn't moving in the train frame (3), that means that the time for the light to get from the position of each strike to M must be the same. For example, if it's 3 light-seconds from M to either end of the train in the train frame, then the time between a strike and the light from that strike reaching M must be 3 seconds in the train frame.
5. If there's the same amount of time (in the train frame) between the event of each strike and the event of the light from that strike reaching M's eyes (4), and yet the light reaches M's eyes at different times (1), then the strikes themselves must have happened at different times in the train frame.

13. Feb 21, 2010

### grav-universe

Let's say that according to an observer in the center of a platform, lightning strikes occur on each side of the platform simultaneously and the light from each strike travels at c to meet the observer in the center at the same time. This is a given since it is how the scenario is set up. Now let's say that we are travelling toward the platform, so from our perspective, the platform is moving toward us. According to us, then, the light from the strikes also travels at c in both directions toward the center of the platform, but since the platform is also travelling toward us, the light from the strike on the furthest side of the platform takes a greater time to reach the center since the center of the platform is also moving away from the strike as the strike catches up to it, so has a further way to go overall. The strike from the closest side takes a lesser time to reach the center since the center of the platform moves toward the light from the strike on that side as the light moves toward it also, so has a lesser distance to go overall. Therefore the light from the strike on the closest side of the platform will reach the center in a lesser time than that from the furthest side from our perspective. All observers must agree, however, that the light from both strikes coincide in the center of the platform at the same time. That means that according to our perspective, in order for the light from both strikes to meet in the center, the strike on the furthest side of the platform must occur first, then the strike on the closest side a short time later, so not occuring simultaneously from our point of view.

What might confuse the issue somewhat in the video is that the lightning strikes occur at the front and back of the boxcar simultaneously according to the platform observer, so one might think that means they strike the front and back of the boxcar simultaneously to the boxcar observer as well since it is the boxcar they are striking after all. But that would only be true if the platform observer and boxcar observer had the same idea of simultaneity, which they don't. If the strikes occur simultaneously to the boxcar observer, they would not occur simultaneously to the platform observer, and vice versa. Another way to picture it is to see that the lightning could just as easily strike the ground next to the boxcar instead of the boxcar itself. The platform observer would still see the lightning strikes occur in the same places as the front and back of the boxcar simultaneously. The boxcar observer, while also seeing the lightning strikes occur at the front and back of the boxcar, would not say, however, that they occurred simultaneously, but that the lightning struck in the front first, then the back.

Last edited: Feb 21, 2010
14. Feb 21, 2010

### TcheQ

I thought this video was a little clearer.

2:00-2:20

Pay attention to what happens with the expanding yellow circles

Last edited by a moderator: Sep 25, 2014
15. Feb 21, 2010

### danielatha4

I think Stevmg said it perfectly. The video makes it seem as though the observer observes the passenger to see the front strike first (which maybe he does) but because of his reference frame it is concluded that in her reference frame she sees the flashes not simultaneously??

What DocAl initially said makes sense too:

"The light would only reach the passenger in the middle of the train at the same time if the lightning struck the ends of the train at the same time according to the frame of the train. But it doesn't."

But why doesn't it? according to the train frame. the video lends no credibility as to why the train passenger wouldn't see them at the same time, other than: that's the way the observer on the platform sees it. Is this credible?

16. Feb 21, 2010

### E=mc^84

Hi, you should watch this clip: http://www.youtube.com/watch
v=uJFUmBUwZjg&feature=related This explains simply that it is the act of moving away from a light beam that slows down time so the light beam can catch up. So, from the reference frame of the train the light beam in which the train is approaching is "seen" first because the light beam at the end of the train has to "catch up" with the train, so the observer on the train will the 2 simaltaneous flashes happen at different times.

17. Feb 21, 2010

### TcheQ

It's hard to 'think' relativistic without diagrams. The whole point is that a different timeline of events are observed depending on where you are due light having to travel further/shorter distances.. If we use "according to the frame of the train" we assume the train is at rest for that calculation, which would mean the observer according to us travels at speed. But it is the reverse of this in the 'actual' situation.

One thing they don't explicitly mention is that the first bolt the person in the train sees is blue, while the second is red. The observer in the train would, if they had a sensitive enough detector with them, be able to calculate their speed from the redshift+blueshift of the light spectrum.

18. Feb 21, 2010

### E=mc^84

your right, they should aplly the doppler effect to more visual diagrams ;)

19. Feb 22, 2010

### JesseM

Since she sees them non-simultaneously in spite of the fact that they happened at equal distances from her, that means that in her reference frame they happened non-simultaneously. Keep in mind that seeing events simultaneously is distinct from them happening simultaneously in your frame. For example, if in 2010 I see the light from an event 5 light-years away in my frame, and in 2015 I see the light from an event 10 light-years away in my frame, then in my frame both events happened simultaneously in 2005.
Yes, it was part of the starting premise of the problem that the lightning strikes happened simultaneously in the platform frame, and you can use that to conclude that in the platform frame the light must hit the train-observer at different times. And as I said above, all frames must agree on local events, so the train frame must predict the light hit the train observer at different times too. Of course you'd be free to imagine a different case where the strikes happened simultaneously in the train frame and thus their light hit the train-observer simultaneously, but this would be a physically different situation that isn't compatible with the premises that were used to define the physical facts of this problem.

Last edited: Feb 22, 2010
20. Feb 22, 2010

### stevmg

Sports Fans...

I didn't mean to create such a furor. I will now go and review all the videos.

As I said in my last answer to JesseM, I will try to "work it out" with Hugo Lorentz - the evil genius who concocted all this business and created all this confusion yet he was right, as far as I know.

Has Loretz (or Einstein) ever been disproven empirically. I have seen enough "garbage" on the Internet with fantastic "thought experiments" and logic which states that Simple Relativity is wrong. Since I couldn't follow the original logic by Lorentz or Einstein I surely couldn't follow the so-called arguments these other individuals used.

Finally, is there any other explanation for e = mc^2? I can derive it from momentum and work and wind up with the equation:

e = mc^2 + (1/2)mv^2 + ... (trial "tails" to an infinite series based on the biomial expanion) but I get no intuitive "feel" to the e = mc^2 part.

21. Feb 22, 2010

### stevmg

To summarize -

The train observer "sees" the lightning strike from the front earlier than the one from the back. So, this sequence must be the same in all time frames. The central point of reference is the train observer herself (as depicted in the video).

Even though this satisfies the concept by JesseM as no parallel but different universes there appears to be a contradiction in the times of the train frame. If one had atomic clocks all along the train synchronized together and atomic clocks on the ground synchronized together, one would still assume that the time in the front of the train the same as the back of the train. If one were to synchronize the train such that the lightning strikes would occur when the two observers passed each other, it would appear that the flashes would emanate at the same time and reach the on board observer at the same time as the speed of light is constant within the train and the distance covered - front and back is the same to the observer in the train. At the instant of the lightning strikes the time in the front of the train would be the same as in the back of the train with reference to the train so the observer would see both flashes simultaneously.

Rather than using words, one might be best served by using Lorentz to explain this as words are just confusing.

22. Feb 22, 2010

### JesseM

Do you understand that because of the relativity of simultaneity, clocks that are synchronized in one frame are unsynchronized in another? Specifically, if the clocks at rest at either end of the train are at synchronized in the train frame and a distance X apart in that frame, then in the ground frame where the train is moving at speed v, the two clocks are out-of-sync by vX/c^2 (the time on the trailing clock will be ahead of the time on the leading clock).
But because of the relativity of simultaneity, the notion that the strikes happened "when the two observers passed each other" has no frame-independent meaning. After all, "when the two observers passed each other" is equivalent to "the event of each strike happens simultaneously with the the event of the two observers passing each other", but because of the relativity of simultaneity, events at different locations which occur simultaneously in one frame occur non-simultaneously in other frames. And that's exactly what this thought-experiment is intended to show--that if we want to require that the speed of light be c in both frames, there's no way of avoiding the conclusion that the two frames disagree about whether the two strikes were simultaneous!
But the point of the thought-experiment is to show conceptually how the relativity of simultaneity follows from the basic postulates of relativity without having to go through the trouble of deriving the full Lorentz transformation from the two postulates. Of course if you already have the Lorentz transformation, it's quite trivial to show that events which are simultaneous in one frame are non-simultaneous in another. For example, say that in the unprimed frame event #1 happens at coordinates (x=0, t=0) and event #2 happens at coordinates (x=X, t=0). Since both these events happen at t=0, they are simultaneous in this frame. But now use the Lorentz transformation to see what coordinates each of these events will have in the primed frame and see what happens...the Lorentz transformation equations are:

x' = gamma*(x - vt)
t' = gamma*(t - vx/c^2)
with gamma = 1/squareroot(1 - v^2/c^2)

Last edited: Feb 22, 2010
23. Feb 22, 2010

### grav-universe

It's even simpler than involving the Lorentz transforms. All we really need to know is that light travels at c to all observers regardless of the motion of the source. So let's say the platform has a width of d_p and that the light from the strikes is seen simultaneously by the platform observer. So the time the light takes to travel from each side of the platform according to that observer in the center is just t_p = (1/2 d_p) / c. Now let's look at what the train observer sees with a relative speed of v. From the perspective of the train, the platform has a width of d_t and the light from each side of the platform is still measured to be travelling at c, but the center of the platform is also moving at v while the light travels to the center of the platform as well. The time the light takes to travel from the lightning strike on the furthest side of the platform to the center while the center of the platform also moves away from the light over the same time at v is c t_f = 1/2 d_t + v t_f, t_f = (1/2 d_t) / (c - v). The time that the light takes to travel from the lightning strike on the closest side of the platform while the center of the platform also moves toward the light over the same time at v is c t_c = 1/2 d_t - v t_c, t_c = (1/2 d_t) / (c + v).

So while the light takes the same amount of time to travel from each side of the platform to the center according to the platform observer, according to the passenger on the train it takes longer for the light to travel from the furthest side while the center moves away from the light than it takes to travel from the closest side as the center of the platform moves toward the light from that side. However, all observers must agree that both rays of light will coincide in the same place at the center of the platform, so in order for this to occur, then according to the passenger on the train, the lightning must strike on the furthest side first since it takes longer for the light to travel to the center, then the lightning strikes on the closest side a time of tl = (1/2 d_t) / (c - v) - (1/2 d_t) / (c + v) = (1/2 d_t) [(c + v) - (c - v)] / [(c - v) (c + v)] = (1/2 d_t) [2 v] / (c^2 - v^2) = d_t v / (c^2 - v^2) later according to the passenger's clock, so that both rays of light will coincide in the center of the platform.

Last edited: Feb 22, 2010
24. Feb 22, 2010

### stevmg

To JesseM

Actually that does it (I'm almost there again) as you stated (I cannot as yet wrap my brain around it) that the lead clock is "behind" the trailing clock even though all these clocks on the train are in the same time frame. Accepting that I can understand what this is all about.

I cannot see (and you will not be able to explain to me as I am too stupid) any deeper than this but I DO appreciate the time you spent trying to enlighten me. You did get me to a higher level but I will never get any further than this.