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B On light clocks and reference frames

  1. Nov 4, 2015 #1
    I had this questioning about the light clock on another thread, and DaleSpam suggested that I open my own thread, so here it is.

    I was asking if the light clock mind experiment was not contradicting the reference frame principle.

    I added that to my drawings:
    And DaleSpam answered this:
    So here is my answer Dale:
    It seems to me that the relativity principle would prevent an observer on one of the two mirrors from being able to measure that longer echo time because the clock used to measure it would also be slowed by the motion, and in the same proportion as the echo time. So how would it be measured? Another question: for the same observer to measure a longer echo time, the light ray has to travel at an angle to the motion, in such a way that if it was a laser beam, it would have to be aimed at the future position of the mirror, which seems to contradict the reference frame principle, because by definition, a reference frame is considered at rest.
     
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  3. Nov 4, 2015 #2

    Janus

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    Your figure 2 is incorrect.
    If A fires a light pulse( or laser) at a right angle to its relative motion with respect to B at the moment that A and B are aligned (as shown in the diagram), the pulse will miss B. In order for a light pulse fired from A to hit B, it must be fired before A and B are at right angles to each other as measured relative to there motion, and at an angle less than 90 degrees from the direction of A's motion. In other words, If we consider A as moving and B as stationary, A still has to aim its light in a way as to lead B in order to hit it, just like in the situation where we consider B moving and A stationary.

    In the same vein, in the third figure, the light pulse/laser will hit B regardless of whether or not we regard A and B as moving or not. It seems to me that in both these cases you are treating light like it moves with respect to some absolute fixed reference frame, and this is not the case.

    That's basically the whole point. You have two light Clocks, A and B each with an observer that measures how long it takes for the light to bounce between the mirrors. Observer A notes that it takes 1 microsecond for the light to make the round trip between the mirrors of his light clock. He also notes that the light bouncing back and forth between the mirrors of Clock B, which has a relative velocity of ~0.87c to him, has to follow a diagonal path that it twice as long, and at the same speed as the pulse bouncing between the mirrors of his clock. Thus the light bounces back and forth between his light clock for every one time it does for Clock B and takes 2 microseconds to make one round trip. The Observer with clock B, which is identical to clock A, measures light as moving at the same speed relative to his clock as A's observer measured light moving relative to Clock A. Thus B measures 1 microsecond for the light to make the round trip between the mirrors. Thus he measures the same time period (light bouncing between the mirrors of clock B as taking half as long as A measured that same light as taking. The two observers measure the same time interval as having different lengths. This is time dilation. In addition, According to observer B, it is the light traveling between the mirrors of Clock A that follows the longer diagonal path and takes longer to make a round trip between the mirrors, and it is Clock A that ticks slower than Clock B. In other words Observer A says clock B ticks slower than his clock and Observer B says clock A ticks slower than B's clock.

    Again, you are misinterpreting the behavior of light here and trying to affix its motion to some absolute frame.

    You cannot use the behavior of light to determine whether you are moving or not in an absolute sense.

    For example, say you have two observers, again A and B, and they are moving relative to each other and meet at some point. At the instant of their meeting a flash of light is emitted from that spot. If you are observer A, you will measure the following: The light Flash will expand outward from you at c with you remaining at the center of the flash and B will be moving away from the center of the flash. However according to B, the light flash expands outward from him at c with himself staying at the center, while A moves away from the center of the flash.

    This is what Einstein means with his second postulate which says:

    The speed of light in vacuum has the same value c in all inertial frames of reference.

    He means as measured relative to the inertial frame from which it is being measured.
     
  4. Nov 4, 2015 #3
    Hi again Janus. I read your article on time: very well written. You're puzzling me here though. I thought that, if the direction of a light ray had to stay independent from the motion of the source, and if that ray had to hit the target at 90 degrees, it necessarily had to be fired at 90 degrees too, thus at the vertical to the observer. What do you mean exactly? Can you develop a bit please?

    Fig. 3 is a clone of the light clock, which is not supposed to need an absolute reference frame. Like the clock, it shows light traveling at an angle to hit the target, but in addition, it also shows how aberration and doppler effect would affect the beam.


    I thought that two observers moving in the same reference frame would experience the same time flow, that their two clocks would stay synchronized, and you seem to say the contrary. You're puzzling me again. Maybe I don't understand exactly what you mean.
     
  5. Nov 4, 2015 #4

    Dale

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    It would be measured by a system of synchronized clocks that are at rest relative to each other (but not at rest relative to the light clock). This is what is meant by time dilation. You are correct that it is not detected by observers on the mirrors.
     
  6. Nov 4, 2015 #5
    Hi again Dale! Do you mean that the clock on the mirror would not record the dilation, in such a way that if we would reunite it with those that were not traveling, it would have stayed synchronized with them? Doesn't it contradict the reason why the Hafele/Keating experiment was made, which was to prove that the clocks would really be affected?
     
  7. Nov 4, 2015 #6

    Dale

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    I was talking only about a light clock moving inertially in flat spacetime. Once you start talking about non inertial clocks or about curved spacetime then a different approach is simpler. Light clocks are pretty much only useful for understanding inertial motion in flat spacetime.
     
  8. Nov 4, 2015 #7

    Mister T

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    If those directions are the same, then yes. But if they're perpendicular, then no. If they were in perpendicular directions in every frame you could use that notion to identify a special frame, distinguishing it from all others. Imagine the interior of a passenger train where a Point F on the floor is directly below a point C on the ceiling. We check that it's directly below by connecting C and F with a straight line, and making sure that line is perpendicular to the level floor. We then shoot a laser beam from F towards C and it hits C. Now we move the train in the usual way that trains move, which is in a direction parallel to the floor of the train. With the train in motion we repeat the shooting of the laser beam, from F towards C. But by the time it gets there it will miss C if its path remains perpendicular to the floor. It would have to move along a diagonal path to hit C. Thus we could use this experiment to determine whether the train was moving or not.

    This would be a method to distinguish between a state of rest and a state of uniform motion, violating the Principle of Relativity, something no one has yet figured out a way to do despite numerous attempts.

    What's really going on here was explained by Galileo in the 1600's. Stand still and toss a ball directly upward. It's path is a straight line. Now do the same while standing on a moving train. Again the ball goes up and down along a straight and vertical line. But to an observer on the ground watching you through a window in the train car, the ball's path is a parabola. So, which is the ball's "true path"? The straight line or the parabola? The answer is that there is no "true path". The path depends on your frame of reference.

    As you move horizontally and launch something vertically it stays above its source regardless of the state of (uniform horizontal) motion of the source, but the only way that can happen is if its path has different shapes in different frames of reference.
     
  9. Nov 5, 2015 #8
    Me too, but if the accelerations that the two clocks would have to suffer to be reunited was exactly the same, which is virtually possible if they both travel half the distance to get together, they should stay synchronized. And if there is no way for the observer on the mirror to measure the dilation even if one second is longer, it seems to me that there would be no dilation recorded once the clocks would get together. For instance, whatever the length of those seconds, if one of the clocks indicates 10 seconds, the other will also indicate ten seconds.
     
    Last edited: Nov 5, 2015
  10. Nov 5, 2015 #9
    Hi MT,

    At fig.2, the source is considered in motion and the observer at rest, and the ray is fired at a vertical to the observer. Once light is sent, its is expected to go straight line, so if it is fired in the direction of the observer, it is expected to hit the target, no?

    A good way to test the direction of light for two bodies in the same reference frame would be with using the moon as a target while the source would be traveling around the earth at the same speed and in the same direction than the moon, but the beam would then have to stay as thin as it is when it gets out of the laser, which is unfortunately not the case. But even if the result showed that the beam is missing the target, it would not change the data from the experiments on relativity, and it seems to me that it would not change the postulates of relativity either. Fig. 3 shows that, to hit the observer, the beam should also be sent to its future position, but it also shows that aberration would change its real direction, in such a way that the observer would see the source as if it was at a vertical to him, which is exactly what moving in the same reference frame is supposed to mean. This way, and as you point out, there would be no true observable path for light either, even in the same reference frame, but then, would the light clock still be a good explanation of what is really going on with clocks in motion?
     
    Last edited: Nov 5, 2015
  11. Nov 5, 2015 #10

    Dale

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    If they have to suffer any acceleration then they are not inertial.

    That said, if two non inertial clocks start at rest relative to some inertial frame and afterwards undergo equal and opposite accelerations, then they will read the same when reunited. In the inertial frame where they were originally at rest, they will at all times be equally time dilated and therefore remain synchronized with each other (equally desynchronized from the reference frame).
     
  12. Nov 5, 2015 #11

    Janus

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    While the speed of light is independent of the motion of the source, the direction and thus the velocity will depend on the motion of the source. And when I say motion I mean relative motion. So If the source is moving relative to any particular frame call it frame 1, and fires a photon at an angle which, as measured by itself,, was at a right angle to the relative motion, then, as measured in frame 1 the photon will travel at an angle less than 90 degrees relative to the motion of the source. Look at it this way. What would happen if, in figure 1, the light is aimed at point B ( where the observer is when the light is fired) rather than B'? The light will miss the observer because he will have moved to B' in while the light arrives at B. This is exactly the same situation as fig 2, with the difference that in figure 2 we are looking at the scenario from the perspective of the observer instead of the source. The point is that you cannot get different results just by switching viewpoints. Your interpretation of how light works in these situations is mistaken.
    Any aberration or Doppler effect only exists in the frame that the light clock is moving with respect to. As far as the light clock itself is concerned there is no aberration or Doppler effect. And by this, I don't mean that the aberration/Doppler effect was canceled out, but that it never existed. Again, there is no difference in figure 3 if we consider it as the viewpoint of an observer "at rest" with the light clock moving, or as the viewpoint of an observer moving past a light clock that is itself is at rest. In the second case, the observer would see an aberration and Doppler effect in the light, just like in the first case, but the light clock still wouldn't, and it would be a little silly to attribute this to the idea that somehow this was due to some cancelling out. In this, and any situation all that matters is the relative motion between the two frames, not which one we consider moving or at rest.
    Two observers at rest with respect to each other measure the same time rate. But in this instance, we are dealing with two clocks that are not at rest with respect to each other. Observer A and his light Clock at at rest with respect to the same reference frame and measure time the same as each other. Observer B and his light clock are at rest with respect to another reference frame and measure time the same. However, these two reference frames are in motion with respect to each other. Thus is A's rest frame, B is moving, and In B's rest frame, A is moving. And clocks moving with respect to each other do not measure time the same.

    No, as explained above
    Your example of the Moon and a source traveling around the Earth is a bad one. It involves circular motion, which is accelerated motion, and quite frankly, until you clear up your confusion of how light behaves under non-accelerated conditions, it is best that you stay clear of accelerated motion examples.
    (For an example what I mean, if you consider things from the perspective of the source traveling around the Earth, the Laser it emits would not follow a straight line but would appear to curve.) You are also not clear by what you mean by the source and Moon moving at the same speed. Do you mean that the Moon is directly overhead at all times relative to the source, in which case, their "speed" is not the same. The Moons travels at ~1 km/s in its orbit. A source traveling around the Earth and keeping the Moon overhead would only be moviing at 17 meters/sec.

    The better example is two spaceships traveling side by side with their engines shut off. Ship A fires a Laser at Ship B. You seem to be under the impression that in order for A to hit B, that A has to aim ahead of B, But because of aberration and Doppler effect, B will see the light coming directly from A. But this is a violation of the principle of Relativity and the postulates of Special Relativity. This is because A has to change his aim depending on whether We consider A and B as moving or not. If A and B are "At rest" he aims straight across, if they are "moving" he has to aim at some other angle. This implies a "preferred rest frame", the one where A can aim straight across and hit B. There is no such frame. The only thing that determines where A has to aim in order to hit B is the relative motion between A and B, and not any perceived shared motion of A and B.
     
  13. Nov 5, 2015 #12

    Janus

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    You have to be real careful dealing with acceleration. If Clock A and Clock B both accelerated in opposite directions at the same rate and for equal times, then drifted for some time, came to a stop, accelerated towards each other and then can to a stop when they met up with each other, then yes, they would show the same time when they meet up, providing Everything about their trip is symmetrical, including the time they drift. But they will read a different time from Clock C that stays at the start and end point.

    But then consider the following scenario: The accelerations remain the same. They both accelerate for the same time and the same rate when leaving, turning around and stopping, so that the acceleration experienced by both clocks during the trip are identical. However, Clock B drifts for twice as long as Clock A. This means that Clock B returns to Clock C first and has to wait for Clock A to return. When Clock A returns, the two clocks compare readings. Clock A will read less time than Clock B, Even though they both experienced identical acceleration during their respective trips.
     
  14. Nov 5, 2015 #13
    I agree with your reasoning Janus, and I also agree that testing relativity with the moon experiment that I suggested would be a bit difficult to make, but I guess it would also be difficult to synchronize the speed and direction of two spaceships even if we had a beam that would stay thin enough for us to be able to measure with sufficient precision the direction it had in the beginning.

    I agree, but then it follows that the time measured by the observer on one of the mirrors will be as dilated as the light clock itself, so that he will not be able to register the dilation even if it happens for real, and because of aberration, he will not be able either to measure the direction of the ray even if it also happens for real. In that sense, two bodies moving in the same reference frame would only be a particularity, not a reference as the name suggests, because choosing that situation as a reference means considering that light goes straight line for real between two bodies in that particular situation, which would not be the case. On the other hand, if this can be proven with maths, then it means that a very thin light ray would miss the target if aimed at the actual position of a body moving in the same reference frame as the source. Again, I think that it would not contradict the postulates of relativity, but I'm not a specialist. Would it?
     
    Last edited: Nov 5, 2015
  15. Nov 5, 2015 #14
    Maybe you misinterpreted drawings 1 and 2, because they are symmetrical and they give exactly the same result for doppler effect and for the apparent direction of the ray, except that it is a relativistic doppler effect for fig. 2 whereas it is a direct one for fig. 1.

    That's the question I was asking Dale. Lets see... First postulate: it doesn't seem to change the laws of physics, does it? Second postulate: it doesn't seem to change the way light would travel between bodies in motion, namely it would still have the same speed, but as I said, I might be wrong. What do you think? Now, how could it violate the relativity principle if, by chance, the postulates were perfectly respected?
     
  16. Nov 5, 2015 #15

    Janus

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    You are still struggling under the misconception that there is an absolute reference by which motion can be measured. When you talk about the observer not being able to measure the time dilation he is undergoing, You are treating things like his absolute motion with respect to "space" has some effect that causes time dilation to effect him. That time dilation is due to some outside influence acting on him and his clock due to his motion with respect to "space".

    This is not what time dilation is. Time dilation is the difference in time measured between frames that are moving relative to each other. Time dilation is what you measure happening to a clock that is moving with respect to you. And, If that clock is moving with respect to you, you are moving with respect to that clock, and thus that clock measures time dilation as happening to you. Time dilation is always something happens to "the other guy" and never applies to yourself.
     
  17. Nov 5, 2015 #16

    Mister T

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    That's not what the first postulate implies, states, or means. Changing the laws of physics is not the same as demonstrating that the laws of physics are different in different inertial reference frames.

    What we're referring to as the Principle of Relativity is the first postulate. For the reasons we've stated, the scheme you propose would allow someone to distinguish between a state of rest and a state of uniform motion. That is sufficient to violate the first postulate and negate the analysis of the light clock.

    Even if you could do both of those things, you'd still be lacking an explanation of how it is that the analysis of the light clock yields a result that matches the way real clocks behave.
     
  18. Nov 5, 2015 #17
    On the contrary, the way aberration and doppler effect would be nullified in fig. 3 shows that there would be no way to differentiate between rest and uniform motion even if light would behave that way for two bodies in the same reference frame. It thus seems to me that the only difference would be that a light ray would miss the target if sent directly to the actual position of the observer. Since that possibility is almost impossible to experiment, the only way to test it is to check if it respects the postulates. It certainly respects the way light is expected to move once it has been emitted, and I think that the laws of physics would stay the same in all inertial frames too, but what about c? Would it always be measured the same by any observer? I think so, but what about you?

    When I suggest that the observer's clock on one of the mirrors will run as slow as the light clock itself, I am referring to the same external observer for both of them, one that is considered at rest while the clocks are considered moving.
     
    Last edited: Nov 5, 2015
  19. Nov 5, 2015 #18

    Dale

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    Correct.

    However "happens for real" is usually an indication of someone thinking in terms of an absolute reference frame.


    You lose me here. What are you referring to by "it also happens"

    The "two bodies moving" scenario from the earlier posts involved non inertial motion. So you could not use those two bodies to divine an inertial frame.

    However, if you were to consider two bodies moving inertially with the same velocity, those would be acceptable for defining an inertial frame.

    It would help if you would be explicit about whether you are considering inertial or non inertial motion.


    Light travels in straight lines in inertial frames. It's path in non inertial frames may be bent. It isn't clear which you are asking about.
     
  20. Nov 5, 2015 #19
    If I was thinking in those terms, I would also think that the speed of light would not be the same for all observers, and its not the case.

    I was just examining aberration and doppler effect for two bodies in the same reference frame: with relativity, the two properties are linked, so if doppler effect was unobservable even if it existed, then it should be the same for aberration.

    I was just looking for a way to compare the two clocks, and unfortunately, there is no other way than to change their direction and speed.

    I am always discussing the light clock mind experiment, whose mirrors are considered in the same reference frame, but which is considered moving with respect to a distant observer. If we imagine light traveling longer between the mirrors, and if we imagine the clock getting late compared to the observer's clock because of that, then we must also consider that light is really traveling this way, but without an observer aboard being able to observe the direction of the ray, and this is exactly what my drawings show. In fact, I am only applying aberration and doppler effect to the light clock, but I never saw this idea elsewhere, so I am uncertain that I am aloud to do that. Am I?
     
  21. Nov 5, 2015 #20

    Mister T

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    Do you know how a light clock at rest will behave? There's an observer there, also at rest, and we know what he'll see.

    But we don't know how a light clock in motion will behave because an observer at rest is not aboard.

    I think I'm finally starting to see what you're saying.
     
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