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Light Clock Problem

  1. Oct 11, 2012 #1
    In a recent thread, a discussion developed on the subject of how we observe light and how this affects our understanding of SR. I called attention to the famous light clock diagrams:

    http://home.comcast.net/~peter.m.brown/sr/image_gif/sr05-im-01.gif [Broken]

    In my view, the problem here is not with the resulting formulas, nor with time dilation, nor with the assumptions of SR, but that the light clock diagrams often lead to logical paradoxes, depending on how you interpret the problem, and I believe this happens because these diagrams are paradoxical to start with, and I would like to hear other opinions on this subject.

    From where I stand, the problem with the diagrams is very simple:
    You can't detect light at a distance. Detection of EM waves (or photons) in SR is strictly a local event. You can't be aware of light moving in any direction other than straight into your eyes (or detectors). So how can a non-local observer see those light rays? They are bouncing back and forth between the two mirrors, and anywhere else.

    Suppose those are laser beams (so they don't radiate spherically). From the stationary frame, they go straight up and straight down, cross the distance between the mirrors at the speed of light and the time is proper time, so everything's fine. From the point of view of a distant observer, if you follow the logic in the diagrams, you could either deduce a change in the speed of light or time dilation. Since every experiment shows us that light always travels at c, we need time dilation to explain the angular light beams in the moving system.

    First, if you assume that light was emitted at an angle, how does the emitter know the correct angle of emission?
    Second, how can those light paths be part of anyone's data? If they reach the mirror, they don't reach the observer. We can assume that each mirror gives off a light signal every time it reflects the beam, and a local observer would measure the speed of the light as c, and no time dilation would be noticed. If a distant observer receives those light signals, than he must do the transforms with that light, and not the light that is being reflected inside the light clock. If you do that, than you will achieve the values for time dilation and length contraction before you diagram the light clock's beams, and when you finally get to diagram those beams, you will diagram them just like the local/stationary observer would.

    Light would never be diagramed at those angles and nobody would even consider that light could go above c, or that it had to experience time dilation.

    Isn't it weird to claim that the light has been time dilated? We use light to measure time dilation and length contraction on other things, so how can you time dilate the light itself?

    Here is a very thorough and standard analysis:


    I look for hearing different opinions on:

    - How can we correctly diagram undetected light like that? How does the emitter adjust the angle of emission?
    - Conversely, how can light be emitted at an angle if it's speed is not affected by the motion of the emitter?
    - Shouldn't we apply SR transforms primarily with light that is actually observed and than use that information to diagram the interior of the light clock?
    - Isn't diagraming the light clock in the moving frame like that illegal? Aren't those vectors purely imaginary?
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Oct 11, 2012 #2


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    In the rest frame of the emitter and detector the light travels vertically and hits the detector. This means that every observer will see that happening. It is an event where two worldlines intersect and is thus unchanged by any change of coordinates.
  4. Oct 11, 2012 #3
    :smile: It's not a "for real" (proper?) angle. an angle is comparative, like speed, to your point of the diagrams being diagrams. Consider the light clock isn't necessarily moving at all. :uhh:

    It's a longer distance/interval (chunk of spacetime) between events. ("ticking" of light clock, those events are what's measured)

    For the light clock observer that longer distance is "contracted" (to the obvious straight up/down "path", more specifically the "shortest" length between events), if you measure the photon on an angle...I mean traveling a longer distance/interval between events.

    From the other observers point of view, the longer distance/interval of the photon path is measured/observed as a purely length measurement.

    Observation is an event, an event pin points length/time measurements to a specific location.

    The distance/interval between those ticking event locations of the light clock can be observed as any combination of length & time measurements.

    apparently it all adds up to c, :smile: That is the continuum speeds along at c.

    Is there such a thing as "proper angles". same idea as proper time/length ect? because of RoS, I'd guess there must be. It's time/length fusion:tongue2: Where the right(angle) place & the right(angle) time meet for an event. Well now I know what angles are. :smile:

    Last edited: Oct 11, 2012
  5. Oct 11, 2012 #4


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    That would be truly amazing for a paradoxical start to yield correct formulas and correct values for time dilation. I think this is reason enough to be highly doubtful that the diagrams are paradoxical at all.

    The emitter simply follows Maxwell's equations (or QED if quantum effects are important for the emitter). The laws of Maxwell and QED are such that if the light follows a straight path in one frame then it must follow a diagonal path in another frame.

    We have good experimental reasons to believe Maxwell's equations and QED. They predict those light paths. While a particular detector may not collect data from each point along the way, the data that any detector does collect is consistent with the light paths as drawn. So why not draw them? Should we just act surprised each time that some data is collected and pretend that we don't have a good understanding of the laws that governed that data?
  6. Oct 11, 2012 #5
    It may help to imagine that the light clock is "at rest" and that you as the remote observer are passing by it... what would the diagram look like then?
    The deeper question might be why when setting out to measure time and space for things moving fast or at a distance that we would choose to use clocks and rulers when these are observed to change their times and lengths when employed in those situations... (as if we had a choice to use something else)?
  7. Oct 12, 2012 #6
    Yes, it is truly amazing, but on the other hand, we already knew what we were trying to find, this is just one more way to visualize the problem and derive time dilation. A diagram full of logical holes can still yield the correct results, if you know the results from the start and build everything around that.

    This seems to contradict one of SR postulates, that the speed (and logically direction) of light is unaffected by the motion of the emitter.

    The only workaround I see is if we always take the frame where light is detected as the stationary frame, as bahamagreen sugested. This is what actually happens in real life. A detector can't have motion relative to itself when it detects light. It is also what happens when we pick a rest frame in other SR thought problems, we take our frame as the rest frame and observe the relative positions and times of other things through light. We do the transforms with the light that reaches us from events, not with unseen light that never reaches our eyes.

    [/QUOTE]While a particular detector may not collect data from each point along the way, the data that any detector does collect is consistent with the light paths as drawn.[/QUOTE]

    Detections happen locally, just like in the diagram to the left. That's how a local observer would see the light paths, straight up and down. Are you saying that a local observer, in the stationary frame, would draw the light paths diagonally, as if he was on the moving frame, like the diagram to the right?

    An observer in relative motion wrt the light clock would not even see those light beams, so how could he diagram them? Would't he need to receive some sort of signal that tells him when a beam has been reflected from a mirror? And if so, wouldn't you have to do the transforms with these light signals in the first place? Than we would find the coordinates as seen from the light clock's frame and the light beams would be diagramed just like in the stationary frame. The final results would be exactly the same, you would still find the same value for time dilation and everything, but isn't it way more consistent and logical? Doesn't it bother you that we are trying to diagram light as "seen" by an "observer" that isn't even aware of those light beams?

    if you take the light clock system as the stationary frame, everything fits. This tells me that light is always a local event, and we should only be allowed to diagram or visualize light from a stationary frame. This would also explain why Einstein said that the speed of light was unaffected by the motion of the emitter in his 1905 paper, and only later introduced the receiver.
  8. Oct 12, 2012 #7


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    Nonsense. Speed is the magnitude of velocity, not its direction. There is no sense in which a postulate about the speed of light logically implies anything to do with its direction.

    You (and others) seem stuck on this schizophrenic idea that events can happen in one frame and not in another. A reference frame is a mathematical construct, a simple way of labeling events and directions, a coordinate system. If a detector detects light in one frame then it must detect light in all frames. Simply changing your arbitrary mathematical labeling cannot change the physical fact that the light was detected.

    Do you agree with that?
  9. Oct 12, 2012 #8
    On the first point ("undetected") I gave a counter example in that recent thread as follows:

    Once more: a cloud chamber scatters light over the whole trajectory. It is technically feasible to observe the diagram on the right with an array of close-up lateral detectors that are in rest in the "stationary" frame, and the same can also be captured far away with a CMOS camera that is mounted "in rest" in the "stationary" frame. Both diagrams are equally observable, with real data.
    As a matter of fact, SR was first of all concerned with comparing real data from real measurements, and that diagram illustrates what according to SR really can be measured.

    - https://www.physicsforums.com/showthread.php?t=620279&page=2

    And about the light angle, this was discussed for example here:
  10. Oct 12, 2012 #9
    I too would like to see the explanation as to how matter adjusts the angle of the emitted light when the light clock is made to move?

    For reference, the answer I have been given previously, is that: As far as the light clock is concerned, once it is at a steady speed, it is not moving - so the question of how the moving laser emits the light at a forward angle is irrelevant.

    To me this doesn't explain how it works. (It's a bit like answering the question of: How does gravity work? And replying: Gravity works by pulling you towards the ground.)
  11. Oct 12, 2012 #10
    Explained in the second link of post #8 :wink:
  12. Oct 12, 2012 #11
    That's a a decent take on it.

    But as far as the angle thing goes, you can't force your observation into another FoR.

    For example just because your reality shows an angled path, doesn't mean that's the reality for the light clock observer. I believe they call this "relativity", it's symmetrical just like the light clock demonstrates (when including c postulate).
  13. Oct 12, 2012 #12


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    The explanation is Maxwell's equations. Write down the equation in one frame, transform to another frame, and note two things:
    1) the transformed wave moves at an angle
    2) the transformed wave is a solution to Maxwell's equations

    Regardless of the reference frame, the emitter simply follows Maxwell's equations.
  14. Oct 12, 2012 #13
    There is nothing there "working". It is a different perspective of the two events (photon hitting top/bottom of mirror).

    This is a particularly big hurdle though; to accept two separate physical realities of the same events. Try to note the difference between the perspectives, at same time ignore the idea of light emitting at an angle as being the part of the physical events.

    Get the picture in your head that the only difference between the frames is an increase in the path/distance/interval/chunk of spacetime the photon travels. You already know that path/distance/interval/chunk of spacetime can be observed either as time or length, depending on "perspective".

    The angle is just a comparative result, while physical, is not a change in the physical light clock itself.
    Last edited: Oct 12, 2012
  15. Oct 12, 2012 #14
    It suddenly strikes me that of course this cloud chamber with glass walls can be used to better clarify that angle issue, as it was meant to bring home that this is exactly what necessarily must be measured.

    Take a light ray going straight up from bottom to top, as depicted on the left, but in a cloud chamber with glass walls, and to which we attach the label S'; necessarily scattered light from halfway up (at Y=0.5L) is also at the same horizontal position in S'.*

    However, what if this cloud chamber S' is moving at very high speed to the right as observed by a stationary system S, as depicted in the sketch on the right?

    The scattering water molecules at the bottom in S' will be detected at for example x=0 in system S.
    However, while the light moves up in S', S' moves to the right. Necessarily the scattering water molecules at 0.5L in S' are not at x=0 in S, but are slightly more to the right. And the scattered light at the top is even more to the right.

    IOW, by geometric necessity this is what must be measured in S.

    [EDIT:] I did not discuss here simultaneity; however, I think that for this picture that can only make a numerical difference, and not a qualitative one. It corresponds to physical reality (absolute, agreed by all) that S' moves like that relatively to S, with the light ray also progressing like that relative to the detectors of each. The sequence of local events as well as their respective locations is not an issue here. As a matter of fact, those are literally trajectories that can be traced simultaneously on photographic plates in S and in S'.

    * Technically the reference system S' corresponds to that cloud chamber but with infinite extensions in all directions
    Last edited: Oct 12, 2012
  16. Oct 12, 2012 #15


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    There's nothing particularly "paradoxical" about light clock diagrams. However, because they omit any discussion of the relativity of simultaneity, they aren't the whole story.

    Since not understanding the relativity of simultaneity is responsible for (at a guess) at least 90% if not more of the problems people have with understanding relativity, and most likely the feature that leads you to believe that they are "paradoxical", it's an important omission.
  17. Oct 12, 2012 #16


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    Yes, that's one of the reasons why I made the animated spacetime diagrams
    in the link provided by OP.

    I think this animation might help with the discussion of photons associated with the moving clock:
    http://physics.syr.edu/courses/modules/LIGHTCONE/LightClock/VisualizingProperTime-y-pair-A-with-photons.avi [Broken]
    Last edited by a moderator: May 6, 2017
  18. Oct 12, 2012 #17
    Yes. If a detector detects light that detection is real. It is real because light has reached the detector, it is detected by contact. This detection is not an observation from a distant observer. A distant (moving or not) observer can't see light that is in contact with the mirrors, it can only see light that is in contact with himself.

    I am not saying that the detection of light is not real from a distant (moving, in this particular case) observer, i am saying that this distant observer doesn't know that the light has been detected, he doesn't know where the light is, he is not receiving those light beams, he doesn't have any data from those light beams.
  19. Oct 12, 2012 #18
    It is at the same horizontal y position at the moment of emission. But when it is detected some x distance away, the beam has moved in the y direction. So you will have the same y coordinate, but not the same t.

    But more importantly, if the deterctors are stationary relative to the emitters, they will diagram the light as in the stationary frame. They will measure the distance between the mirrors in the stationary frame and diagram light in a straight path between them. The mirrors will not change position with time, and the time light takes to move from one mirror to the other will be in agreement with other onboard clocks, and the speed of light will remain constant.

    Now, if your detectors are receiving scattered light from a moving frame, you must apply transforms to find the distance between mirrors and the time in the primed system using the the information brought by the scattered light that actually reaches you. Only after that you will have the coordinates of the primed system (the light clock) and can begin to correctly diagram those light paths, and as a matter of fact, if you do this, they will be diagramed just like the image on the left, the stationary system. The diagram to the right, with the diagonal beams, will not be diagramed that way using real data.

    If light is reflected perpendicular to the mirror in one frame, it must do so in all frames, and if you apply SR transforms using real data, that is exactly what you will find.

    This diagram yields the correct numbers because they are arrived at by applying transforms unrealistically, after the "fact". You are applying the same transforms you would in any SR problem. But the situation in the diagram in not a real, possible, situation. You can't observe light detected at a distance, because you have not detected that light, and you have no information of that light. So you can't diagram that light. The mathematical results are the same, but the diagram is falacious, it assumes you can see light that you can't, and it puts light moving at an angle, in contradiction with any real data. No detectors on the mirrors would detect light being reflected at an angle. If they did, the light would miss the other mirror.
  20. Oct 12, 2012 #19


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    If a series of detectors is placed in a vertical line so a light on the detector is switched on when the beam passes, then the line of lights will not be vertical when observed ( photographed ?) by an observer in motion wrt the receiver/emitter.

    Isn't this the same problem that Einstein treated directly, the passenger on the moving train drops a stone and sees it fall vertically, but the observer on the platform sees the stone move in a parabola.
  21. Oct 12, 2012 #20
    1.) Principle of Relativity
    2.) Invariance of c

    As #1 says, yes the the physics are the same in both frames, this would have to include the light does not leave the emitter at an angle.

    As #2 says, the light must leave the emitter at an angle, for c to be calculated as a constant.

    While those two interpretations are at odds, it isn't a paradox. Those are perspectives from two different FoRs.

    Considering them both as simultaneous realities isn't right, they are mutually exclusive perspectives (and physical realities). Would you ever try to imagine day & night at the same time and place as a reality?
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