On Einstein's explanation of the invariance of c

Discussion in 'Pseudoscience Archive' started by RJBeery, Dec 8, 2010.

  1. RJBeery Natural Philosopher Valued Senior Member

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    First of all, I'm not questioning Relativity in any way here, and I understand that when Physicists (such as Einstein) try to explain complex subjects to the general public sometimes the explanation is less than ideal for the sake of simplicity. I test my knowledge of Relativity by subjecting it to different scenarios, and I cannot decide where the problem lies in the one I describe below. My question has to with Einstein's train and the two flashes of lightning...the passenger at the midpoint of the flashes concludes that they were not simultaneous because he does not see them strike simultaneously. The embankment observer concludes that the passenger makes this claim because, after the strikes occur, the passenger travels toward one of the flashes while travelling away from the other which means their distance of travel is not the same.

    Fine.

    Replace the lightning with a strobing street lamp that emits a single photon (or two, if you wish - one towards the passenger and one towards the observer), and you would get the same result. Now, put those street lamps on the train...now neither party can make the case that the passenger is riding toward one light source and riding away from the other!

    Something is amiss here, because in my mind both parties would concur that the flashes were simultaneous.

    Here are my first thoughts:
    1. Equivalency. We are neglecting the equivalency of earth/train movement. If we consider that the earth is moving beneath the stationary train, then the embankment observer would be travelling toward the train's rear street lamp making him claim that the flashes were not simultaneous.
    2. Redshifting. Maybe the longer wavelength of the train's front street lamp photon results in the observer's photon detector clicking at different times for the photon's arrivals. Is there some EM principle that makes a photon's detection in a distance less than its wavelength impossible? (My instinct says yes)
    3. Something else I haven't thought of.
    #1 doesn't seem right to me in the same way the Einstein's explanation didn't seem right. I don't like the "moving toward the light source" concept. #2 would be great, but I have no idea if redshifting could fully account for the effects in consideration. Maybe someone has a #3? :idea:
     
  2. prometheus viva voce! Moderator

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    Not to do with the train thought experiment, but the invariance of the speed of light comes from Maxwell's equations. In vacuum one can show that Maxwell's equations imply that the electric and magnetic field satisfy the wave equation

    \(\nabla^2 \phi = \frac{1}{v^2} \frac{\partial^2 \phi}{\partial t^2}\)

    where v is the speed of wave propagation. In this case \(v = c = \frac{1}{\sqrt{\mu_0 \epsilon_0}\) which is a constant, ie Maxwell's theory of electromagnetism implies electromagnetic waves move at constant speed. Einstein's big leap was to realise that a constant speed is a relative concept, and special relativity essentially covers the consequences of light moving at a constant speed with respect to any observer.
     
  3. RJBeery Natural Philosopher Valued Senior Member

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    Yeah this is why the "moving towards a light source" explanation has always bothered me a bit. It implies an "absolute point in space" from which we are postulating the photon was emitted, and we are travelling towards it. If we can close the distance gap to shorten a photon's travel time then we can also increase the distance gap to lengthen it, which contradicts the concept that you cannot affect the propagation velocity of light no matter what you do. "You want to slow light down? Run away from it!"
     
  4. AlexG Like nailing Jello to a tree Valued Senior Member

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    I'm missing something here. If we increase the distance, and increase the travel time, how does that change the velocity?
     
  5. RJBeery Natural Philosopher Valued Senior Member

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    After the photon is released I'm confused on how we can make statements like "moving away from it" and "moving towards it" without affecting c. Stand on the corner, 1 mile away from a street lamp. Send a friend on a very fast motorcycle with a flashlight past the street lamp, both of which are flashed at that time. How do you claim that you are "increasing the distance" between you and the flashlight's photon (just because the source is moving away from you) while the same cannot be said about the distance between you and the street lamp's photon?
     
  6. kurros Registered Senior Member

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    I'm not sure what you are asking here, it doesn't matter how fast the sources are moving relative to you, their light still travels at c relative to you, so once the light leaves the source you can't tell how fast the source was moving (unless you know what frequency of light it was supposed to emit, because the light will be red/blue shifted and you can work out the source velocity from this; this doesn't change the light's velocity though).
     
    Last edited: Dec 8, 2010
  7. Janus58 Valued Senior Member

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    You can't. But Einstein's train example doesn't say that either. It says that in the frame of the embankment an observer will see the rain moving towards one flash and away from the other. This causes one flash to reach the train observer before the other.
    When you switch to the train's frame, the observer must agree that the flashes arrived at different times. (for him ot say otherwise would lead to a physical contradiction.) And since the lightning struck the ends of the train, and he is at the midpoint of the train, he must conclude that in his frame the lightning strikes were not simultaneous.
     
  8. AlexG Like nailing Jello to a tree Valued Senior Member

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    But we're not increasing the distance between you and the flashlight's photon. The source is moving away from you, but the photon, at the instant it is emitted, is moving towards you at c.

    We can move toward the photon, or away from it, and not effect the speed of the photon relative to ourselves due to the Lorentz transformations, which effect both distance and time.


    I was thinking of starting a thread on what it is about relativity which makes it so hard to grasp. I think it's the dual implications of there not being an absolute frame of reference, and c being constant in ALL reference frames.

    Ludwik Silberstein, during one of Arthur Eddington's lectures said "Professor Eddington, you must be one of three persons in the world who understands general relativity." Eddington paused, unable to answer. Silberstein continued "Don't be modest, Eddington!" Finally, Eddington replied "On the contrary, I'm trying to think who the third person is."
     
  9. RJBeery Natural Philosopher Valued Senior Member

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    If you agree that the flashlight and the street lamp photons will reach the corner by-stander at the same time, then put the corner by-stander and the street lamp on a train, give the flashlight to the embankment observer, and have him flash the light as he passes the street lamp at the end of the train. Equivalency claims this is the same experiment, yet now Einstein would apparently claim that the passenger is "increasing his distance" between the flashlight and himself, thereby increasing the traveling time of the flashlight's photon.

    Janus, did you read my OP? Please do so as I try my best to spell out the issue I'm having with the train analogy there.
     
  10. kurros Registered Senior Member

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    Sure this is the same experiment, the same thing would happen. The ordinary train experiment is different to this though. In that experiment you have two flashes coming from different spatial positions, in your experiment they come from the same place. If there is no spatial separation between the flashes and one observer sees them as simultaneous then there is no disagreement between them and other observers about their simultaneity, because the flashes are effectively the same spacetime event.

    This is all about simultaneity, it isn't really about "increasing your distance" from the source, except indirectly.
     
  11. RJBeery Natural Philosopher Valued Senior Member

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    Just a reminder: I'm not refuting Relativity!

    OK, that being said, take the normal train experiment but replace the flashes with street lamps. Now, also put a street lamp at the front and rear of the train. When the train's lamp passes the embankment lamp, have them both flash. Will the embankment observer still claim that the passenger is travelling "away" from the rear flashes and "toward" the front ones? This is more directed to AlexG but anyone is free to answer.
     
  12. kurros Registered Senior Member

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    Sure, I didn't think you were.

    Ok, so let me try to get this straight. You have a train, with lamps on it at either end, and it is passing a platform, also with lamps at either end? Say spaced the same as the rest separation of the lamps on the train? And that say in the frame of the platform observer the lamps on the platform flash simulaneously at the moment the front train lamp passes the front platform lamp?

    And just to point it out, the rear train lamp, say it also appears to flash simultaneously with the others to the platform observer, will not be aligned with the rear platform lamp at this time, because the train is length contracted according to the platform observer. And the observer on the train will see different things: he will agree that the front lamps flashed simultaneously, but the rear lamps will both flash at two different times. I'm not sure which direction the shift is, but the wonderful lorentz transformations will tell us:

    \(t'=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}(t-vx/c^2)\)

    so this is transforming from the platform frame to the train frame, which is moving in the +x direction at speed v. Both rear flashes occur at some negative x value (let us put x=0, t=0 as the position and time of the front lamp flashes in the platform frame). It doesn't matter where the observers in each frame are, they will all (within some frame) deduce the same thing once they figure out how long it took the light to reach them etc.

    So anyway, say the rear train lamp is \(q\) metres from the front lamps, and the rear platform lamp is \(w\) metres from the front lamps, with \(w>q\). They are in the negative x direction from the front lamps so their platform-frame positions are \(-q\) and \(-w\).

    Now, in the platform frame everything flashed at once, so \(t=0\), giving us

    \(t'=\gamma(-vx/c^2)\) (i replaced the factor at the front with gamma, it is just some number between zero and 1 which just scales things, it won't change our qualitative results)

    From this, since \(x=-q\) (or \(-w\)) we see that the train observer sees the rear lamps flash after the front ones, and later again for the one further from the front lamps (\(w\), the rear platform lamp). Because t' is positive that is and the train observer saw the front lamps flash at t'=0.
    Ok one more clarification, I say "sees" but I really mean "deduces that". Obviously what observers actually see depends on where they are positioned in the frame relative to the lamps, but what they deduce is independent of that, within a reference frame.

    Ok I guess this isn't quite your question, I guess you want to think of a way of understanding why this is. I'll have to think some more about that...
     
    Last edited: Dec 8, 2010
  13. ScribJellyDonut Registered Senior Member

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    It's funny you should say this because from what I read about Einstein [and I could be wrong] is that he actually got inspiration for relativity by observing trains and their velocities relative to one another - or something to that effect.

    Anyhow I tried to quickly read over your post but it doesn't seem intuitive what you are trying to say without studying the words. Maybe post a diagram. It doesn't have to be neat you could draw it up in paint, but it would really help out. People loathe trying to draw meaning by reading a jumble of words that could easily be misconstrued, where a few words and a diagram would make things crystal clear. You might think diagrams are more geared towards younger readers and that anyone versed in the subject should understand. However, from my experience even complex scientific documents will be supplemented with figures, tables, and equations.
     
  14. RJBeery Natural Philosopher Valued Senior Member

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    Hey no sweat bro, please think it out so you can explain it to me. I think I understand things completely and then I go and over think something, confusing myself...

    I think the answer lies in length contraction, as you mentioned, Kurros. If the train is 1 mile (yes, I'm a Yankee) long, stationary, then it will be less than 1 mile long to the observer. Let's say the observer knows about Relativity, and places street lamps at "just the right spots" such that, from his perspective, the train's lamps and the street lamps all flash in such a manner that they reach him simultaneously. He is standing in the center of both street lamps, which are separated by a distance less than 1 mile, remember.

    The problem I'm having here is that, because the respective train and embankment lamps are local to each other, everyone must agree that they flash simultaneously! I'm bumping into a contradiction here, unless I can use Einstein's hokey "moving away from the light source" explanation which is demonstrably false.
     
  15. kurros Registered Senior Member

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    Ahh, well this is not quite the case. In that situation everyone will agree that each lamp in the pairs of lamps flashed simultaneously, but not that the front and rear pairs flashed simultaneously. The train observer will say that the front pair flashed before the rear pair. Which makes sense, because the train has a longer rest length than the platform, so there is no way both pairs can align simultaneously in the train frame, and since everyone agrees that the lamps in a pair flash when they are aligned it follows that they align at different times for different observers.
     
  16. RJBeery Natural Philosopher Valued Senior Member

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    Yes, when I wrote "simultaneously" I only meant pair-wise, not necessarily all 4 of them together.

    So...let me think out loud here...the train's passenger sees the embankment as contracted. Therefore the front pairs of lights flash, then presuming all 4 are flashing simultaneously for the embankment observer, the rear lamps would flash together but later than the front ones for the passenger.

    Tentatively, I'm going to say I'm OK with this. It sounds like the problem in Einstein's explanation was in the use of translational movement relative to a light source as a substitute for length contraction. It appears he broke his own rule while reaching out to us laymen:
    :D
     
  17. Neddy Bate Valued Senior Member

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    Einstein's explanation is simpler, because it demonstrates the relativity of simultaneity without invoking any other relativistic effects, (such as length contraction).

    I can say that now, but when I first read it, I was even more confused than you! :p
     
  18. Janus58 Valued Senior Member

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    Wrong. As long as the photons from the street lights reach the embankment observer at the same time, they will reach the train observer at different times, it does not matter whether or not the streetlamps were on the train or on the embankment.
    You seem to be hung up on the idea of the "source" and misconstruing the meaning of the word. In this case, the "source" is not the physical object that produced the light, but the center of the expanding light sphere. So for the any observer, the source is the point relative to himself from which the light was emitted. So if you put the lights on the train, the train moves with respect to the sources, as measured from the frame embankment, despite the fact that the train does not move with respect to the lamps in either frame.
    No, which one we consider moving makes no difference in the example. The fact that the embankment observer sees the flashes simultaneously and that he is at the midpoint between the flashes are the initial conditions for the example. In other words, it is agreed upon that the flashes are simultaneous for the embankment, and then from this starting point we try to determine whether this is true for the train also.
    You could pick two events that are simultaneous in the train frame which would not be so in the embankment frame, but at least one of them would have to be a different event.
    Actually Einstein doesn't talk about "moving towards the source" in the way you are thinking about it, but instead he talks about moving with respect to the light itself.
     
  19. quadraphonics Bloodthirsty Barbarian Valued Senior Member

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    Both parties always concur that the flashes are simultaneous in the rest frame of the light source, and not other moving frames. This holds regardless of whether the light source is on the ground or the train. The equivalency explanation is exactly the right one here - I'm not sure what the problem is?
     
  20. Janus58 Valued Senior Member

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    Here's a pair of animations that illustrate the example:

    Embankment frame:
    [​IMG]

    Train Frame:
    [​IMG]

    There's no problem with his explanation, its just that people come into it with preconceived notions.
     

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