High School "Forced Conclusion" in Train-Embankment Experiment

[PeterDonis]

I have done so.

No, you haven't. You've explained why the frequency shift would be measurable. You have not explained why the frequency shift would affect the speed of the light beams, or how any such effect could possibly be consistent with the assumptions that Einstein made in constructing the thought experiment.

This is no different than pointing out that Maxwell's demon uses energy to open and shut the door.

It is quite different. The point in the Maxwell's Demon case is that the demon's entropy (not energy) must be included in the analysis. But there is no analogous point here.

My understanding is that the different frequencies of the light beams would suggest to the passenger that there are differences in the relative velocities of the light-sources and the passenger relative to one another

Of course. Nobody is disputing that. But that is not sufficient to support the claim you are making.

the passenger might in fact be moving toward one light-beam and away from the other light-beam

No. Motion relative to the light beam is not the same as motion relative to the source of the light beam. In fact, if the speed of the light beam is constant for all observers, regardless of the motion of the source, then the concept of "motion relative to the light beam" does not even make sense, since any such "motion" would have to change the speed of the light beam, and that is impossible by hypothesis.

 

[Nugatory]

2. To Dale's point about distances, if we call the passenger's position "P," then the distance P-A and P-B are equal only at the time of the "actual" events A and B. By the time the light-beams hit the passenger, P-B is smaller than P-A. This is by definition.

The distance the light travels is the distance between where it is emitted (the position of A or B at the moment of emission) and where it is received (the position of the passenger's eyes at the moment of reception). The movement of A or B before and after the moment of emission is irrelevant to the calculation of that distance, as is the movement the passenger before and after the moment of reception. Once you have that distance, you divide it the speed of light to get the time that it took the light to cover that distance.

Einstein does assume (and discusses the assumption earlier) that if the light took x seconds to cover the distance, and reached the passenger's eyes at time T, then it was emitted at time T-x.

 

[PeterDonis]

I was only pointing out the relative velocity of the recording device relative to the origin-loci (space coordinates) of events A and B

There is no such thing. An object can have a velocity relative to another object, but it cannot have a velocity relative to a space coordinate, because "a space coordinate" is frame-dependent. When each light flash is emitted, two objects are spatially co-located: the point on the embankment where the lightning strikes (this is what you are considering the "source" of the light beam) and the corresponding end of the train (front for B, rear for A). Each of these are objects--one is moving relative to the train passenger and one is not. But neither of them are a "space coordinate".

if we call the passenger's position "P," then the distance P-A and P-B are equal only at the time of the "actual" events A and B. By the time the light-beams hit the passenger, P-B is smaller than P-A. This is by definition.

This is true, but it does not affect the calculation of the time it takes the light beam to travel. Once again, the relevant speed is the speed of the light beam relative to the receiver, not the speed of the light source relative to the receiver. The latter cannot possibly affect the time it takes the light to travel. Only the former can, and you have already admitted that the speed of the light beam is $c$ relative to the receiver.

he would be almost compelled to conjecture about his movement relative to the points of origin of the light-beams between the time that the events occurred and the time that the light-beams arrived at his detector, and to speculate about whether his own movement was what accounted for the difference in arrival-time of the light-beams.

No, he wouldn't, because the motion of the light sources relative to the receiver after the beams are emitted can't possibly affect the time the beams take to travel. Only the motion of the light beams themselves relative to the receiver can. See above.

 

[Dale]

2. To Dale's point about distances, if we call the passenger's position "P," then the distance P-A and P-B are equal only at the time of the "actual" events A and B. By the time the light-beams hit the passenger, P-B is smaller than P-A. This is by definition.

This doesn't make any sense. A and B are events, not objects. The distance at a different time is not even defined.

This is not very difficult to work out mathematically.

Given event A which occurs at time and location $(t_A,x_A)$ , then the second postulate says that light emitted from A will be received at all the events $(t,x)$ such that $(x-x_A)^2=c^2 (t-t_A)^2$. In a spacetime diagram this figure is called a lightcone. If you have an inertial observer, O, then their worldline can be written $x=v_O t+d_O$. With very little effort you can find the intersection of any given worldline and any given light cone, specifically if $d_O=0$ and R is the event of the intersection then $(t_R,x_R)=\left(\frac{c t_A+x_A}{c+v_O},\frac{v_O(c t_A+x_A)}{c+v_O}\right)$.

So, if you are given the second postulate and $\{t_R,x_A,v_O\}$ then you can uniquely solve for $t_A$. Since the solution is unique you are indeed "forced to conclude" the value of $t_A$

The first postulate says that all of these equations hold in every frame. By simply applying these equations for two emission events and two observers under the conditions given for the problem you determine that the two observers will disagree whether or not the emission events were simultaneous.

 

[Ian432]

No, he wouldn't, because the motion of the light sources relative to the receiver after the beams are emitted can't possibly affect the time the beams take to travel. Only the motion of the light beams themselves relative to the receiver can. See above.

1. By definition, the motion of the receiver relative to the light sources after the beams are emitted directly affects the sequence with which the beams hit the passenger (B first, A second). I think we agree on that.
2. I am not claiming anything about the time it took the beams to travel. I am making a very limited claim about what the passenger is forced to conclude, or not.

There is no such thing. An object can have a velocity relative to another object, but it cannot have a velocity relative to a space coordinate, because "a space coordinate" is frame-dependent. When each light flash is emitted, two objects are spatially co-located: the point on the embankment where the lightning strikes (this is what you are considering the "source" of the light beam) and the corresponding end of the train (front for B, rear for A). Each of these are objects--one is moving relative to the train passenger and one is not. But neither of them are a "space coordinate".

This is perplexing, to be sure, and it probably requires me to restate things. The passenger is not moving relative to the front or rear of the train. The passenger is moving relative to points B and A on the embankment, but the passenger does not perceive those points. Instead, the passenger perceives only photons arising from two events. Those two events occurred at the moment that the front and rear of the train were aligned with points B and A on the embankment. The photons that arose from event B arrive at the passenger's receiver before the photons that arise from event A, because the passenger is moving toward... the photons that were emitted from event B, and away from the photons that were emitted from event A. The passenger notes that the frequencies of the photons from B are higher than the frequencies of the photons from A. The passenger deduces that he could be moving toward the B photons and away from the A photons.

When I say that the passenger is moving "toward the photons," I mean "the passenger is moving with a velocity directly opposite to the velocity of the B photons, and directly in line with the velocity of the A photons." That should help clarify things.

The distance the light travels is the distance between where it is emitted (the position of A or B at the moment of emission) and where it is received (the position of the passenger's eyes at the moment of reception). The movement of A or B before and after the moment of emission is irrelevant to the calculation of that distance, as is the movement the passenger before and after the moment of reception. Once you have that distance, you divide it the speed of light to get the time that it took the light to cover that distance.

I believe the above reply to PeterDonis is sufficient but please let me know if not. My understanding is that the movement of the passenger in relation to points B and A on the embankment is actually critical to this entire discussion as it is the origin of the difference in arrival-time of the light beams at the passenger's receiver.

 

[Ian432]

Dale, I am humbled by your facility with equations--I am very sorry to say I cannot follow you. Please see my reply to PeterDonis, above, where I amend my statement about A, B, and my previous belief about the non-existent "space-coordinates" of the events. I am not trying to avoid argument--I can step logically through a verbal explanation--but I am simply on a different wavelength from you and cannot wrap my mind around equations.

 

[Ibix]

My understanding is that the movement of the passenger in relation to points B and A on the embankment is actually critical to this entire discussion as it is the origin of the difference in arrival-time of the light beams at the passenger's receiver.

The other way to look at it is that it is the embankment observer's motion with respect to the train that is critical to why he receives the pulses simultaneously even though they were not emitted simultaneously. You keep writing as if velocity were some kind of absolute thing. It's not. In the train frame the train is not moving. What velocity it has in any other thread is irrelevant.

 

[Nugatory]

My understanding is that the movement of the passenger in relation to points B and A on the embankment is actually critical to this entire discussion as it is the origin of the difference in arrival-time of the light beams at the passenger's receiver.

The passenger's movement is essential to the result, because the thought experiment is only interesting if the passenger's position relative to the embankment is not constant. However, once we know that the passenger is at a given point at a given time, we can calculate the distance between that point and the point where a flash of light was emitted without further considering the passenger's movement.

 

[Orodruin]

I am not trying to avoid argument--I can step logically through a verbal explanation--but I am simply on a different wavelength from you and cannot wrap my mind around equations.

This put you at a far greater disadvantage than you might imagine. In order to understand relativity, you will need to deal with the equations. If you do not, you are not learning relativity, you are learning about relativity. The words that are used by people here to describe what they are doing most often have a precise mathematical interpretation, one which you seem to lose on interpretation - such as that of what an event is.

You can conclude absolutely nothing from the Doppler shift unless you specify the state of motion of the sources when they emit the light. Regardless, this is not needed for the relativity of simultaneity, which you obtain anyway.

 

[Dale]

I am not trying to avoid argument--I can step logically through a verbal explanation--but I am simply on a different wavelength from you and cannot wrap my mind around equations.

For future reference, if you mark a thread as "intermediate" then it is an indication to us that you are seeking an explanation at an undergraduate college level. This would certainly include algebra based math, and probably even calculus or some differential equations. If you want no math then you should mark the thread as "basic".

Are you comfortable with geometry? Draw three parallel vertical lines such that the outer two lines are equidistant from the center line. Pick a point on the center line and draw a 45° line down and right until it intersects the right line. From the same center-line point draw a second 45° line down and to the left until it intersects the left line.

Do you agree that you are forced to conclude that the left and right intersections are on the same horizontal line?

Now, erase the diagonal left line, pick a different center line point and draw, a 45° diagonal left line from that new point.

Do you agree that you are forced to conclude that the left and the right intersections are on different horizontal lines?

 

[Ian432]

The other way to look at it is that it is the embankment observer's motion with respect to the train that is critical to why he receives the pulses simultaneously even though they were not emitted simultaneously.

The simultaneity of the emission of the light flashes, with respect to the embankment, is a given in Einstein's original thought experiment. As an extension, we can say that these light-flashes would not have been color-shifted relative to one another, in relation to the observer on the embankment.

You can conclude absolutely nothing from the Doppler shift unless you specify the state of motion of the sources when they emit the light. Regardless, this is not needed for the relativity of simultaneity, which you obtain anyway.

I am not aiming to conclude anything from the Doppler shift, nor am I aiming to say that the Doppler shift is at all necessary for the relativity of simultaneity.

I am simply posing a very limited challenge to Einstein's statement that the passenger "must come to the conclusion" that the light flash at B took place before the light flash at A. I am saying that, by giving the passenger the opportunity to see the color-shift in the light, we are allowing him to challenge the supposition that event B occurred before event A, an act that would lead him away from Einstein's "conclusion."

One observation I will make at this late stage in the thread is that Einstein did not actually use the term "passenger" in the particular statement I'm quoting. His actual words were: "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." It may be that "taking the train as a reference-body" precludes the act of recording the color-shift in the light, and allowing it to serve as an additional data-point to be considered (along with the speed of light and the timing of arrival of the light). But I have yet to hear a good explanation about why anything would preclude a observer who is taking the train as a reference-body from knowing, at the time of arrival of the light-beams, that they were color-shifted relative to one another. So as far as I can tell, the challenge still stands.

 

[Ian432]

Do you agree that you are forced to conclude that the left and the right intersections are on different horizontal lines?

Yes, I agree.

 

[Herman Trivilino]

Given that light has a constant speed, I do understand why a reasonable passenger would arise at the conclusion that event B happened before event A, if the passenger only understood that he was "equidistant" from both events, and that a beam of light from B reached him before a beam of light from A.

Good, then you agree with the conclusion.

But if the passenger was also given information about the significant color-shift differences in the light beams, he would be almost compelled to conjecture about his movement relative to the points of origin of the light-beams between the time that the events occurred and the time that the light-beams arrived at his detector, and to speculate about whether his own movement was what accounted for the difference in arrival-time of the light-beams.

It makes no difference. Imagine instead that the flashes of light arriving at the center of the train car left, not from the train platform, but from the train itself. For example, have lamps mounted on the front and back walls of the train car. The lamps send out a flash of light when struck by lightning.

In other words, the Doppler shift, as others have pointed out, is not relevant.

 

[Dale]

Yes, I agree.

In a spacetime diagram an event is represented by a point, an object at rest is represented by a vertical line, an object traveling at c is represented by a line at 45°, and events which are simultaneous are located on the same horizontal line.

Do you see the mapping between the elements of the train scenario and the geometry?

 

[PeterDonis]

By definition, the motion of the receiver relative to the light sources after the beams are emitted directly affects the sequence with which the beams hit the passenger (B first, A second). I think we agree on that.

No, we aren't. I agree that the detected Doppler shift of the beams is correlated with the sequence in which the beams reach the passenger--if one beam is blueshifted and the other is redshifted, the blueshifted beam reaches the passenger first and the redshifted one reaches him second, and the time delay between the beams, as received by the passenger, is correlated with the magnitude of the blueshift/redshift. But correlation is not causation; and your "directly affects" implies causation.

One way of putting the claim you are making is that, from the passenger's point of view, the presence of the above correlation makes it possible that there is causation involved, i.e., that the detected Doppler shift does cause the different arrival times of the beams at the passenger. And this possibility is why the passenger is not "forced" to Einstein's conclusion that the beams were emitted at different times relative to the passenger.

However, this claim requires the additional assumption that the Doppler shift can affect the speed of the light beam relative to the receiver; but, as you have already agreed, that is not possible, because the speed of the light beam relative to the receiver is always $c$, regardless of any other factors. So it is not possible that the Doppler shift causes the different arrival times of the beams, because it is impossible for the Doppler shift to affect the speed of the beams. So the alternative you are proposing is not in fact an alternative. That is why the passenger is indeed forced to Einstein's conclusion.

The passenger is not moving relative to the front or rear of the train.

Agreed.

The passenger is moving relative to points B and A on the embankment, but the passenger does not perceive those points. Instead, the passenger perceives only photons arising from two events.

Agreed.

Those two events occurred at the moment that the front and rear of the train were aligned with points B and A on the embankment.

More precisely: at the event where the "front" light beam is emitted, the front of the train is co-located with point B on the embankment; and at the event where the "rear" light beam is emitted, the rear of the train is co-located with point A on the embankment. But these are two distinct events, and there is no assumption that they occur at the same moment.

The photons that arose from event B arrive at the passenger's receiver before the photons that arise from event A

Agreed.

because the passenger is moving toward... the photons that were emitted from event B, and away from the photons that were emitted from event A.

No. If this were true, then the speed of the photons from B, relative to the passenger, would be higher than the speed of the photons from A, relative to the passenger. But that is not the case; both sets of photons are moving at $c$ relative to the passenger, as you have already agreed. So it is not possible that the difference in arrival times is due to any difference in the motion of the passenger relative to the photons, compared to the motion of the embankment relative to the photons.

In fact, considering the embankment here makes this point even sharper: for your logic here to make sense, it would have to be the case that the embankment is somehow "at rest" relative to the photons (since an observer at rest relative to the embankment observes no Doppler shift in either light beam). But this is obviously false: the photons move at $c$ relative to the embankment. It is true that the embankment is at rest relative to the sources of the photons; but the state of motion of something relative to the sources is not the same as the state of motion relative to the photons themselves.

When I say that the passenger is moving "toward the photons," I mean "the passenger is moving with a velocity directly opposite to the velocity of the B photons, and directly in line with the velocity of the A photons."

No, this doesn't make sense. See above.

It may be that "taking the train as a reference-body" precludes the act of recording the color-shift in the light

No, it doesn't. There is nothing preventing an observer at rest on the train from measuring the Doppler shift of light signals. The point you are missing is that the Doppler shift of the light tells you nothing about its speed, because, as you have already agreed, its speed is the same for all observers, regardless of the motion of the source. The Doppler shift tells you about the speed of the source relative to the receiver, but, as I said above, the crucial speed is the speed of the light beam relative to the receiver, and that is unaffected by the Doppler shift, or indeed by anything.

 

[Ibix]

The simultaneity of the emission of the light flashes, with respect to the embankment, is a given in Einstein's original thought experiment. As an extension, we can say that these light-flashes would not have been color-shifted relative to one another, in relation to the observer on the embankment.

In my first post in this thread I showed that your "extension" is false.

If the light sources are mounted on the train then the train observer sees them non-shifted and non-simultaneous and the embankment observer sees them shifted and simultaneous.

If the light sources are mounted on the embankment then the train observer sees them shifted and non-simultaneous and the embankment observer sees them non-shifted and simultaneous.

As I pointed out in my first post you can run these experiments in parallel. The only thing the Doppler shift tells you is whether the light source was on motion relative to the receiver. It tells you nothing else.

 

[PeterDonis]

As I pointed out in my first post you can run these experiments in parallel.

More than that, you can run another set of experiments in parallel: experiments in which the lightning flashes are arranged such that they are simultaneous according to the train observer, but not according to the embankment observer. And in this case, as well, you can arrange for the nonzero Doppler shift to be observed by either observer, without changing the relative simultaneity of the flashes. So all of the possible combinations of (simultaneity, shift) can be physically realized, demonstrating conclusively that the simultaneity and the Doppler shift are completely uncoupled, causally speaking.

 

[Ibix]

More than that...

Indeed. And then, just for fun, you can mount lamps on carts on a parallel track moving with arbitrary velocity, timed so that they roll past the platform ends just as the train ends pass. Then you can have completely arbitrary Doppler shifts and pick who gets to receive pulses simultaneously.

 

[Ian432]

Ibix, PeterDonis, and MisterT, OK...given how doppler shifts work, I believe your examples (and yes Ibix you did post this much earlier in your 4-lamp example) would indeed defeat my proposed challenge, since I have to accept that the doppler shift will only take place if the source and receiver of the waveforms are moving relative to one another. This assumes that placing the lamps inside the carriage does not fundamentally alter the terms of the original experiment (and there seems to be a unanimous consensus that it does not). The nature of light continues to make absolutely no intuitive sense to me. Frustrating. On the other hand, I now understand the relationship between physics and beer-drinking a whole lot better than I did before...

Dale, I will work on the spacetime diagram issue a bit more, and will look it up in other threads, where it has probably been discussed more thoroughly.

Thanks very much everyone for your excellent thoughts and input.

 

[PeterDonis]

The nature of light continues to make absolutely no intuitive sense to me.

That's true of anyone when they start to study SR. Our intuitions simply don't cover the case of light, since the ordinary velocities that our intuitions evolved to deal with are so small compared with the velocity of light.

 

[Dale]

The nature of light continues to make absolutely no intuitive sense to me. Frustrating.

Honestly it took me 7 years of sporadic effort to intuitively grasp SR. What finally did it for me was the spacetime geometry stuff I was mentioning above. Do a little reading about spacetime diagrams, four vectors, and the spacetime interval.

 

[peety]

It seems that a lot of these lengthy discussions are held up because of the temptation to slip out of the agreed frame of reference.
Imagine (classical physics) a flight attendant on a plane is pushing a trolley forwards and at the same time moving a pot backwards. We are asked to calculate the speed of the pot. It would be absurd to analyse this without specifying a frame of reference. Relative to the trolley it's moving slowly backwards, relative to the plane forwards, relative to the Earth quickly backwards, relative to the sun (to continue using this precise technical language) very fast who knows where. The analysis completely breaks down if we move the goal-posts.
The nice thing about this is that you work out the speed but don't argue about the time. Bring a light beam into the discussion and we've got to calculate time as well as velocities.

 

[georgir]

the passenger is moving toward... the photons that were emitted from event B, and away from the photons that were emitted from event A

Think about what you are saying here. In the frame of reference of the passenger, he is not moving, by definition. Here lies the key to the tent, as they say...