Trying to Understand Light in Motion: A Frustrating Puzzle

[Doc Al]

we must only conclude that if we assume that the speed of light is not the same relative to everything.

if we conclude that the light will arrive at her at different times - then we are saying that we can add and subtract the trains speed from that of the speed of light. but relativity says that we cannot because light travels at the speed of light relative to the trains motion

You misunderstand the meaning of the 'constant speed of light'. As I said earlier, any observer will measure the speed of light to be c with respect to their own frame, regardless of their motion relative to some other frame. The platform observers will see that the closing rate of the middle of the train and the light flash from the front of the train to be equal to 'c + v' (and 'c - v' for the light flash from the rear of the train). But note that both train and platform observers see the light flashes travel at speed c with respect to themselves.

Note further that the 'closing rate' is not really the speed of anything. It's just the rate that things approach each other as seen by someone else.

 

[Doc Al]

if the lightning stikes the train at the same time in platforms frame and the observer on the platform is equidistant from the strikes then the strikes must be at the same time in the passengers frame also.

Having you been following the discussion? That's not true. Where's your logic?

 

[Dale]

if the lightning stikes the train at the same time in platforms frame ... then the strikes must be at the same time in the passengers frame also.

No, regardless of which scenario you are considering, the lightning strikes can only be simultaneous in at most one of the frames, not both. This is what is meant by the relativity of simultaneity.

 

[solarflare]

what you are doing is overlapping the platforms frame of reference with the passengers frame of reference -

if the platform observer sees the two strikes hit the train at the same time and he is equidistant from each strike then they MUST strike at the same time in the passengers frame also. if they strike at the same time in the passengers frame then she must see them strike at the same time also.

 

[Doc Al]

what you are doing is overlapping the platforms frame of reference with the passengers frame of reference -

Why in the world do you think that? According to the platform frame, the passenger is moving to the right (say) at speed v and the light is moving to the left at speed c (of course). So it's just simple arithmetic to realize that they approach each other at a rate of 'c + v'. All measurements were made in the frame of the platform.

if the platform observer sees the two strikes hit the train at the same time and he is equidistant from each strike then they MUST strike at the same time in the passengers frame also.

Well, no. Just the opposite. (Just repeating the same thing louder will not make it true. Why not read an introductory treatment of relativity where this is all layed out in explicit detail?)

if they strike at the same time in the passengers frame then she must see them strike at the same time also.

That part is true. "If" is the key word here.

 

[ghwellsjr]

Solarflare, you've got the cart before the horse. Instead of thinking in terms of whether the lightning strikes are actually at the same time, you need to realize that we can't tell if they are at the same time or not unless we apply a definition of time for remote events. Einstein's definition is that if they are both an equal distance away from you and you see them at the same time, then the remote times are the same. That's part of the definition of a Frame of Reference. So if the passenger sees them at the same time, then the remote times are the same in her reference frame. On the other hand, if the man sees them at the same time and he is equally distant from them, then in his reference frame, the remote times are the same.

Now if you start out by simply saying, two lightning strikes occur at the same time and both are equal distant from the man and the woman and ask will they see them at the same time, we have no way to answer that question because you haven't stated which reference frame you mean when you say "at the same time". So if you say it's the man's reference frame, then, lo and behold, he sees them at the same time because that is how we define "at the same time". If instead, you say it's the woman's reference frame, then she sees them at the same time because that is how we define "at the same time".

And it doesn't matter if you use wire or light signals, they both take the same time to propagate information. So in post #26, you are asking an ambiguous question. You have to tell us what you mean by the lightning strikes occurring at the same time. If you say it is in the train's reference frame, then the lights come on together. (Or you could tell us that they come on together and then we will know that it's the train's reference frame in which the strikes occurred simultaneously. On the other hand, if you say it is in the platform's reference frame, then the lights will not come on together.

So the answer to your question is that you have to tell us the answer and then we'll tell you the answer right back. There is no other way.

 

[solarflare]

how can the platform observer be equidistant from the stikes but that they do not hit at the same time?

 

[solarflare]

light travels at the same speed - he sees the strikes hit the train - the light travels the same distance to his eyes - therefore they must have hit at the same time in the passengers frame also- the only way it could not happen is if the platform observer was not equidistant

 

[Doc Al]

how can the platform observer be equidistant from the stikes but that they do not hit at the same time?

Whenever you make a statement about the lightning strikes, get in the habit of say which frame sees the lightning strikes as simultaneous. Otherwise we'll just keep going in circles.

If the lightning strikes simultaneously in the platform frame, then the flashes will hit the platform observer at the same time. But if the lightning strikes simultaneously in the train frame, then the flashes will hit the platform observer at the different times. (Remember that they are moving with respect to each other. And that each sees the light traveling at the same speed.)

 

[solarflare]

the point is that by saying the observer on the platform is equidistant from the flashes implies that the strikes must happen at the same time in both frames.

 

[ghwellsjr]

how can the platform observer be equidistant from the stikes but that they do not hit at the same time?

If we knew, apart from Einstein's arbitrary postulate that light travels at c in all directions for any inertial observer, then we could never conclude that they hit at the same time. We cannot measure the time it takes for light to traverse from a remote location to us. We can only declare it to be whatever value (within reason) that we want. Each frame of reference makes a different declaration based on the inertial state of that reference frame and they end up with incompatible differences in the timing of the remote events. The train's frame asserts one definition for the remote timing of the strikes and the platform's frame asserts a differnet definition. That's why we need to state which definition we are using when we say "at the same time" or we have no way of knowing. Nature won't disclose anything more specific to us. There is no "actual" time that we can discover or measure.

 

[Doc Al]

the point is that by saying the observer on the platform is equidistant from the flashes implies that the strikes must happen at the same time in both frames.

Please explain your reasoning. We've certainly explained the reason why that's not true several times.

Sounds like you just want to stick with your 'common sense' notions that relativity has shown to be incorrect.

 

[Muphrid]

how can the platform observer be equidistant from the stikes but that they do not hit at the same time?

Let's go back to the math and then figure out what the intuition should be. Let's, again, simplify the problem by considering the lightning strikes being equidistant for the platform observer and then ask what the passenger perceives as their distances. Again, ${e^x}' = \gamma (e^x - \beta e^t)$. Clearly, then, the distance the train observer perceives to the front flash is $(d e_x) \cdot (\gamma [e^x - \beta e^t]) = \gamma d$, and minus that for the other flash.

I admit, I'm straining a little to make sure I get the physical interpretation of this right, but I believe the way you should think of this is as follows: according to the observer on the train, the platform is length-contracted, so for the train observer to believe both flashes came from the same distance away, he has to believe they originated at different times. The front flash comes earlier, so according to the train observer the train is not yet 50% of the way through the platform.

Short version: the "moving" observer perceives one flash has having occurred before the other, so because he's moving, he's in two different places for the repsective detections. This is how he can believe his distance to the respective flashes is the same in both cases--he's not measuring with respect to a single location.

 

[solarflare]

if the strikes at exactly the same time happen in the trains reference frame at t=0 and the observer is 1 light second away from the centre of train then at t=1 he will see the flashes hit.

do you agree with that?

 

[Muphrid]

No, the entire point is that the stationary observer will perceive the two flashes occurring at two different times. I've gone to great lengths to explain why that happens. Please tell me what you find confusing about that explanation.

 

[ghwellsjr]

if the strikes at exactly the same time happen in the trains reference frame at t=0 and the observer is 1 light second away from the centre of train then at t=1 he will see the flashes hit.

do you agree with that?

If you mean that the light from the two strikes arrive simultaneously at the center of the train at t=0 when the passenger sees them simultaneously (this is after the two strikes occurred) and the platform observer is 1 light second away, then, yes, at t=1 he will see the reflected light from those two events also at the same time. But this has nothing to do with all the prior discussion in this thread.

If this isn't what you mean, then you're going to have to spell out in detail what you mean in each post because otherwise everyone will interpret what you are saying differently.

Actually, I'm sure this isn't what you mean but I can't tell so I'm just taking a shot in the dark.

 

[solarflare]

Example: You and I are exactly 1 mile from the same point and we travel exactly at the same speed. Do we necessarily arrive at that point at the same time? Of course not: I started off at 1pm and you started off at 1:15pm. We only arrive at the same time if we left at the same time.

if we set off at the same time and was moving at the same speed -would we both be 1 mile away from that same point at the same time?

 

[Doc Al]

if we set off at the same time and was moving at the same speed -would we both be 1 mile away from that same point at the same time?

If we started from the same point, sure. (Assuming we went straight, of course.)

 

[solarflare]

when you watch the video at 28 seconds the train is paused to show the motion of the light from the two strikes. clearly the light is coming from the two ends of the train to his eyes. the video is agreeing with what I am saying. by saying that the light that hit the train at the same time gets to the platform observer at different times means that you will disagreeing with the video.

 

[Dale]

the point is that by saying the observer on the platform is equidistant from the flashes implies that the strikes must happen at the same time in both frames.

The strikes cannot happen at the same time in both frames. See:
http://en.wikipedia.org/wiki/Relativity_of_simultaneity
$$\Delta t'=\gamma (\Delta t - v \Delta x / c^2)$$
Since both v and Δx are nonzero then it is impossible for Δt and Δt' to both be zero.

 

[Doc Al]

when you watch the video at 28 seconds the train is paused to show the motion of the light from the two strikes. clearly the light is coming from the two ends of the train to his eyes. the video is agreeing with what I am saying. by saying that the light that hit the train at the same time gets to the platform observer at different times means that you will disagreeing with the video.

Uh, no. The video has the light hit the train at the same time according to the platform frame and thus the flashes reach the platform observer at the same time. (The flashes reach the passenger at different times.)

 

[solarflare]

yes and because he is equidistand from each end then the flashes must have come from the train at the same time

 

[solarflare]

you are saying that if he sees the flashes at the same time then the flashes occur at different times - but if he is equidistant from the falshes then that would mean light traveled at different speeds to reach his eyes at the same time

 

[Doc Al]

yes and because he is equidistand from each end then the flashes must have come from the train at the same time

If the lightning strikes occur at the same time according to platform clocks (as in the video), and at the moment of the strikes the platform observer is equidistant from the ends of the train, then the flashes will reach him at the same time.

The flashes will reach the middle of the (moving) train at different times.

you are saying that if he sees the flashes at the same time then the flashes occur at different times - but if he is equidistant from the falshes then that would mean light traveled at different speeds to reach his eyes at the same time

No, the flashes will reach the woman (train passenger) at different times, who therefore concludes that according to her train clocks the lightning strikes were not simultaneous. It is a basic principle of relativity that the light travels at the same speed with respect to all observers.

 

[Chestermiller]

If the two lightning strikes hit the ends of the train at the same time, as reckoned from the platform observer's frame of reference, then the two flashes will not arrive at the same time in the train rider's frame of reference, even though the distances between the rider and each of the two flashes as measured on the train were the same. If there were a train rider positioned at the front of the train and another train rider positioned at the rear of the train, then according to their synchronized clocks, the train rider at the front of the train would measure the flash at his location to occur at an earlier time than the train rider at the rear of the train. So the rider at the center of the train would have to reckon that the flash from the front of the train occurred first, followed by the flash from the rear of the train (if the speed of light is the same in all directions in his frame of reference).

Now, let's consider the opposite situation.

If the two lightning strikes hit the ends of the train at the same time, as reckoned from the train rider's frame of reference, then the two flashes will not arrive at the same time in the platform guy's frame of reference, even though the distances between the platform guy and each of the two flashes as measured on the ground were the same. If there were a platform guy positioned exactly at the location of the front lightning strike and another platform guy positioned at exactly the location of the rear lightning strike, then according to their synchronized clocks, the platform guy at the location of the front lightning strike would measure the flash to occur at a later time than the platform guy at the location of the rear lightning strike. So the guy at the center of the platform would have to reckon that the flash at the rear of the train occurred first, followed by the flash at the front of the train (if the speed of light is the same in all directions in his frame of reference).

Chet

 

[solarflare]

Why in the world do you think that? According to the platform frame, the passenger is moving to the right (say) at speed v and the light is moving to the left at speed c (of course). So it's just simple arithmetic to realize that they approach each other at a rate of 'c + v'. All measurements were made in the frame of the platform.


Well, no. Just the opposite. (Just repeating the same thing louder will not make it true. Why not read an introductory treatment of relativity where this is all layed out in explicit detail?)


That part is true. "If" is the key word here.

so what your saying is that they do strike at the same time but because she has forward momentum she sees the front stike first and the back strike second?

 

[solarflare]

Whenever you make a statement about the lightning strikes, get in the habit of say which frame sees the lightning strikes as simultaneous. Otherwise we'll just keep going in circles.

If the lightning strikes simultaneously in the platform frame, then the flashes will hit the platform observer at the same time. But if the lightning strikes simultaneously in the train frame, then the flashes will hit the platform observer at the different times. (Remember that they are moving with respect to each other. And that each sees the light traveling at the same speed.)

here you say that if they strike in the trains frame the flashes will reach him at different times

 

[Doc Al]

so what your saying is that they do strike at the same time but because she has forward momentum she sees the front stike first and the back strike second?

No, they strike at the same time in the platform frame. You've got to remember that saying 'at the same time' is meaningless unless you specify according to what frame.

here you say that if they strike in the trains frame the flashes will reach him at different times

Right! If the strikes occur simultaneously in the train frame, they occur at different times in the platform frame.

 

[solarflare]

but how can light from the trains frame that travels the same distance from each end not reach the platform frame at the same time.

you have to apply the same maths to the platform frame as you do to the passengers frame.

 

[solarflare]

here is what i think happens - the two observers see the same thing - they both see the two bolts hit simultaneously - but they will disagree on the time that the two bolts hit. the passenger might say they hit at 3:00 and the platform observer might say they hit at 3:01

they agree on what happened but they disagree on when it happened

 

[Chestermiller]

here is what i think happens - the two observers see the same thing - they both see the two bolts hit simultaneously - but they will disagree on the time that the two bolts hit. the passenger might say they hit at 3:00 and the platform observer might say they hit at 3:01

they agree on what happened but they disagree on when it happened

No. If the two strikes occur at the same time according to the set of synchronized clocks in the platform frame of reference, then they will be observed to occur at different times according to the set of synchronized clocks in the train frame of reference. If there are actually observers from each of the two frames of reference present at the locations of the lightning strikes when they hit, and if the 4 observers at these locations (2 on the platform and 2 on the train) write down on pieces of paper the times on their clocks that the two strikes hit, the times written down on the platform observers' pieces of paper will be identical to one another; the times written down on the train observers' pieces of paper will not be identical to one another. According to the team of observers on the train, the clocks on the platform are out of synchronization, and according to the team of observers on the platform, the clocks on the train are out of synchronization.

 

[Doc Al]

but how can light from the trains frame that travels the same distance from each end not reach the platform frame at the same time.

For the same reason that light from each end of the train (simultaneously emitted in the platform frame) can arrive at the middle of the train at different times.

you have to apply the same maths to the platform frame as you do to the passengers frame.

Exactly! You must apply the same math and the same rules for all frames. But what you cannot do is just ASSUME that the lightning strikes are simultaneous in both frames. (If you do, you'll contradict the basic assumption that the speed of light is the same for everyone.)

So don't keep flipping back and forth between two physically different scenarios. Pick one scenario, such as the lightning strikes being simultaneous in the platform frame (as in the video) and analyze it properly.

 

[Doc Al]

here is what i think happens - the two observers see the same thing - they both see the two bolts hit simultaneously - but they will disagree on the time that the two bolts hit. the passenger might say they hit at 3:00 and the platform observer might say they hit at 3:01

they agree on what happened but they disagree on when it happened

They do agree on what happened, but not in the way that you think.

Since the lightning bolts hit simultaneously in the platform frame, we can mathematically deduce that the flashes must arrive at the middle of the train at different times.

The train observers agree of course. But the train observers also say that the lightning strikes were not simultaneous according to their clocks. Furthermore, they claim that the clocks on the platform are not synchronized.

Simultaneity is frame dependent, just like length and clock rates.

 

[Dale]

Let's try it this way. Given that there are two lightning flashes and an inertially moving observer which sees both flashes at the same time, and given that the light from the flashes travels at c, under what conditions did the flashes occur simultaneously? The condition is that the observer must be equidistant from the flash points at the time he receives the light.

This can be true in at most one frame. In other frames the observer will have moved off center.

 

[solarflare]

According to the special theory of relativity, it is impossible to say in an absolute sense whether two distinct events occur at the same time if those events are separated in space, such as a car crash in London and another in New York. The question of whether the events are simultaneous is relative: in some reference frames the two accidents may happen at the same time, in other frames (in a different state of motion relative to the events) the crash in London may occur first, and in still other frames the New York crash may occur first. If the two events are causally connected ("event A causes event B"), then the relativity of simultaneity preserves the causal order (i.e. "event A causes event B" in all frames of reference).

http://en.wikipedia.org/wiki/Relativity_of_simultaneity

this states that in some reference frames the two accidents may happen at the same time. yet you claim that it is not possible for two frames to agree