Trying to Understand Light in Motion: A Frustrating Puzzle

[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

 

[Dale]

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

It is not possible for these two frames to agree in this scenario because the relative motion is in the x direction and the lightning strikes are separated in the x direction. See the formula I posted earlier which clearly shows the impossibility of agreement here.

The wiki article appears to refer to the possibility of two frames moving in the x direction to agree on events separated only in y or z. That does not apply here.

 

[Doc Al]

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

In one frame the two (non causally connected) accidents may happen at the same time; but in a frame moving with respect to that one, they will not happen at the same time. You won't find them happening at the same time in two frames moving with respect to each other (along the line between the two accidents).

 

[Muphrid]

I think the problem is that you're trying to assume certain things are the same in both frames that aren't. Let's turn the problem around a little bit.

Let's say two lightning strikes hit opposite ends of a stationary platform again. Person P, stands in the middle of the platform; person T is riding a train. The strikes both hit at the same time according to person P, and at that moment, person T is in the middle of the platform (or as close as he can be while riding a train passing it by) as well.

Now, let's equip both person P and person T with two simple light sensors that tell when they have seen the light from each lightning strikes.

Person P sees both light flashes at the same time, and both his sensors light up at the same time. Now, according to person P, person T can't possibly see both flashes at the same time because T is moving forward and will catch up to the forward light pulse while running away from the backward light pulse. T will see the forward strike first, and then the backward strike.

Now, T doesn't agree on why he sees the two strikes at different times. He thinks the strikes must've happened at different times, with the forward strike first and hte backward strike second. But, he thinks person P is moving backward and that the time delay between the strikes is enough so P will still see both strikes at the same time.

In other words, P and T both believe P will see the strikes at the same time and that T will see them at different times. That is the physically meaningful statement they can make. That is what both frames agree on. Everything else, well, is relative.

 

[ghwellsjr]

Solarflare, it doesn't appear that we are making any headway with you on this issue. Perhaps it would help if we changed the scenario so that it basically happens in the reverse order.

Let's consider a totally different scenario:

We have a very long train, much longer than the length of the platform and so long we don't care where the front and rear are. But instead of just one observer, we have an observer at every window, all along the train.

Then on the ground, we have a platform of some arbitrary length. At the center of the platform, we have a flash bulb that will produce a bright flash of light sometime while the train is passing but we don't care when. Then at each end of the platform, we have a mirror placed at a 45 degree angle so that when the flash of light reaches it, it will reflect the light towards the train.

What we want to do is have whatever train observer is adjacent to the flash bulb when it flashes make note of the event. We'll call him Observer A. In a similar way, we want whichever two train observers see the light reflected off the two mirrors make note of those two events. We'll call the one toward the front of the train Observer F and the one toward the rear of the train Observer R.

Now isn't it obvious that by the time the light reaches the mirrors, the train has moved forward along with Observer A and so he will be closer to Observer F and farther from Observer R?

So now let's say that we take a video of this scenario and we play it backwards. We also pretend that Observer F and Observer R represent the ends of the train (except that now F and R are interchanged because the train will appear to be going backwards). Won't this be exactly the same scenario that we have been discussing in this thread, except that Observer A is not in the center of our now truncated train? And if Observer A sees the light from the two mirrors (which are analogous to the two lightning strikes) impenging on the flash bulb (analogous to the man in the original video) then Observer A cannot be the same as the woman on the train in the original video. In other words, if Observer A, who is not midway between Observer F and Observer R, sees the two flashes arriving simultaneously, then another observer who is midway between Observer F and Observer R cannot also see the two flashes arriving simultaneously.

Please note that this analysis does not require defining any frames of reference or synchronizing any clocks.

Does this make sense to you?

 

[solarflare]

I think the problem is that you're trying to assume certain things are the same in both frames that aren't. Let's turn the problem around a little bit.

Let's say two lightning strikes hit opposite ends of a stationary platform again. Person P, stands in the middle of the platform; person T is riding a train. The strikes both hit at the same time according to person P, and at that moment, person T is in the middle of the platform (or as close as he can be while riding a train passing it by) as well.

Now, let's equip both person P and person T with two simple light sensors that tell when they have seen the light from each lightning strikes.

Person P sees both light flashes at the same time, and both his sensors light up at the same time. Now, according to person P, person T can't possibly see both flashes at the same time because T is moving forward and will catch up to the forward light pulse while running away from the backward light pulse. T will see the forward strike first, and then the backward strike.

Now, T doesn't agree on why he sees the two strikes at different times. He thinks the strikes must've happened at different times, with the forward strike first and hte backward strike second. But, he thinks person P is moving backward and that the time delay between the strikes is enough so P will still see both strikes at the same time.

In other words, P and T both believe P will see the strikes at the same time and that T will see them at different times. That is the physically meaningful statement they can make. That is what both frames agree on. Everything else, well, is relative.

the problem is that your using the results from the platform frame to explain what the person in the train sees - they are different frames and so what the person on the platform believes the person on the train will see is not actually what they will see - for all the person on the platform knows the person on the train might be blind and won't see anything.

 

[cepheid]

I made this spacetime diagram a while ago, and I *think* it corresponds to the original scenario that is being discussed here. Maybe it will help. The "worldline" of the train (which is its path through spacetime) is clearly indicated, and it of course coincides with the t' axis:

The worldline of the photon that is coming in from the front (i.e. from the positive side) clearly intercepts the worldline of the train before (i.e. at a smaller value of t') the worldline of photon that is coming in from the rear (negative side) does.

The coordinate grid I've drawn is for the train observer, in the primed (t',x') coordinate system.

 

[Muphrid]

the problem is that your using the results from the platform frame to explain what the person in the train sees - they are different frames and so what the person on the platform believes the person on the train will see is not actually what they will see - for all the person on the platform knows the person on the train might be blind and won't see anything.

If that's what you think, you're sorely mistaken. Both observers agree on spacetime intervals. This is fundamental to the theory. Cepheid has pretty clearly shown how the points of reception are not the same. Both observers must agree on the proper time between the two reception events for the train observer--or that they're different at all.

 

[solarflare]

I made this spacetime diagram a while ago, and I *think* it corresponds to the original scenario that is being discussed here. Maybe it will help. The "worldline" of the train (which is its path through spacetime) is clearly indicated, and it of course coincides with the t' axis:

The worldline of the photon that is coming in from the front (i.e. from the positive side) clearly intercepts the worldline of the train before (i.e. at a smaller value of t') the worldline of photon that is coming in from the rear (negative side) does.

The coordinate grid I've drawn is for the train observer, in the primed (t',x') coordinate system.

this diagram says that if the stikes happen simultaneously - on the tracks - the the observer will see them simultaneously also. just at a different time.

 

[solarflare]

now look at post 49 and post 50.

 

[solarflare]

Sure. The lightning struck the ends at the same time in her frame and since they traveled the same distance they reach her at the same time. No mystery there.

the diagram shows that the lightning struck in the trains frame of reference simultaneously and also in the platform observers frame.

so according to Doc Al's statement above the train observer will see the bolts a the same time also.

 

[Doc Al]

this diagram says that if the stikes happen simultaneously - on the tracks - the the observer will see them simultaneously also. just at a different time.

The observer on the tracks will see them simultaneously, not the observer on the train.

the diagram shows that the lightning struck in the trains frame of reference simultaneously and also in the platform observers frame.

No it doesn't. The diagram shows that the flashes are not simultaneous in the train frame.

so according to Doc Al's statement above the train observer will see the bolts a the same time also.

And no again.

 

[MikeLizzi]

If anyone is interested, here is an analysis of a train/lightening problem using straightforward math, no diagrams. It's not the same as the OP original but I believe it addresses the same issues.

http://www.relativitysimulation.com/Documents/Train and Lightning.htm

 

[solarflare]

two simultaneous strikes on the train - cause - the observer on the platform to see the two strikes simultaneously because he is the same distance from each strike.

you seem to be ignoring the cause of the strikes which occur simultaneously - if they did not the man on the platform could not see them simultaneously

 

[Doc Al]

two simultaneous strikes on the train - cause - the observer on the platform to see the two strikes simultaneously because he is the same distance from each strike.

Not true. (Unless those strikes are simultaneous in the platform frame.)

you seem to be ignoring the cause of the strikes which occur simultaneously - if they did not the man on the platform could not see them simultaneously

The strikes occur simultaneously in the platform frame.

Don't keep flipping back and forth between the two physically different scenarios:
(1) The lightning strikes are simultaneous in the platform frame.
(2) The lightning strikes are simultaneous in the train frame.

They cannot both be true. Stick to scenario 1 (as in the video) until you understand it.

 

[solarflare]

the lines being drawn from the x-axis are at -4 and +4 but both are at t=0

 

[Doc Al]

the lines being drawn from the x-axis are at -4 and +4 but both are at t=0

Yes. The lightning strikes are simultaneous in the platform frame.

 

[solarflare]

there are tree different events

the first is lightning hitting the train
the second is the light getting to the observer on the platform
the third is the the light getting to the passenger

the third has nothng to do with the second just the first

 

[solarflare]

Yes. The lightning strikes are simultaneous in the platform frame.

the x-axis is the train frame because that is where the light originated from - there are two train frames - one when the lightning strikes the train and one when the light reaches the passenger

 

[Muphrid]

the x-axis is the train frame because that is where the light originated from - there are two train frames - one when the lightning strikes the train and one when the light reaches the passenger

The x-axis measures distance according to someone on a stationary platform (that is, someone standing talong the track).

The diagram is very clear. The two photons' worldlines cross the platform/track observer's worldline at the same time (as expected) but do not cross the train observer's worldline at the same time. Hence, they do not reach the train observer at the same time. They cannot be perceived simultaneously in this situation.

 

[Doc Al]

the x-axis is the train frame because that is where the light originated from - there are two train frames - one when the lightning strikes the train and one when the light reaches the passenger

No, the x-axis is the platform frame. The lightning strikes do not originate in a frame, they happen in all frames. The x' frame is the train frame.

Don't confuse events (such as: lightning striking the front of the train, lightning striking the rear of the train, light from the front of the train reaching the passenger) with frames. In this analysis there are two frames of interest: the platform frame and the train frame.