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I Independence of speed of light and velocity of source

  1. Mar 7, 2016 #1
    I've been attempting to learn special relativity, but I've encountered a stumbling block.

    I understand that the speed of light is independent of the speed of the source of the light (similar to how sound waves travel at a speed that is independent of the speed of the energy source of those waves).

    I also understand that the speed of light is invariant across and within all inertial frames of reference.

    My question deals with the first property.

    In many thought experiments, e.g. involving moving light clocks (where a photon is bouncing up and down against two horizontally moving mirrors that are separated by a vertical distance), the key motif of the Lorentz transformation (1/√(1-v2/c2)) can be derived by analyzing the geometry of the path of the photon as seen by two observers in different inertial frames, one of which is the same frame as the light clock.

    To an observer in the same inertial frame as the clock, the photon bounces up and down, but to an observer in a stationary inertial frame (relative to the clock), the photon will take a longer, zig zag path through space.

    What bugs me is that this thought experiment seems to violate the independence of the speed of light from its source. The very fact that the photon is taking a zig zag path through space, as seen by the stationary observer, suggests that the photon is inheriting the velocity of the clock.

    The only way that the experiment makes sense to me is if the photon itself is aimed at an angle in anticipation of the mirrors' future position. But if this is the case, the examples we are given never make this explicit.

    Can anyone deconfuse me?
     
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  3. Mar 7, 2016 #2

    Orodruin

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    You really should be talking about a "light pulse" here and not about photons. Photons are a further development into quantum field theory and not the little balls you are likely having in mind.

    Anyway, it is not moving with the velocity of the clock. It is moving at the velocity c. It has the same velocity component as the clock in the direction of motion, but this is also true in the clock rest frame.

    This is a rather obvious thing, and it is also true in the rest frame. The pulse needs to be aimed at where the mirror will be or it will not be reflected. In the rest frame, this means orthogonal to the mirrors. Transforming to a frame where the clock moves, it is at an angle.
     
  4. Mar 7, 2016 #3
    Thanks for the reply, Orodruin.


    Good to know. Light pulse it is.

    Let me see if I'm understanding:

    From the clock's frame, the speed of the light pulse is c. The vertical component of the velocity is c, and the horizontal component is 0. Is this correct?

    It certainly wasn't obvious to me. The same issue arises in Feynman's description of the Michelson-Morley experiment. Nothing is mentioned about how the angle of the beam splitting mirror (B) and the reflecting mirror (C') must be subtly adjusted depending upon the velocity of the apparatus. In multiple videos (e.g. see the 3:07 mark of this video, or 3:35 mark of this video), the mirrors are aligned such that a light pulse would be reflected orthogonal to the direction of motion (i.e. straight up and down), rather than at an adjusted angle to account for the motion.

    I think I'm still not grasping something obvious here. Here's another thought that just occurred to me, and makes me think I'm still misunderstanding something, and perhaps it will help someone debug my thinking process.

    Couldn't you use the deflection angle as an indication of your absolute velocity through space?

    If I'm in a spaceship, and I have no idea how fast it's moving, I could aim a light pulse, directly upwards at the ceiling, and if it hits a spot directly above the source, then I can infer that I'm stationary. If it hits a spot to the left or right of the source, then I can infer my absolute velocity.
     
  5. Mar 7, 2016 #4

    Orodruin

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    No. As long as you share the rest frame with the clock you need to aim orthogonally to the mirrors. The angle is frame dependent. This is nothing but aberration.
     
  6. Mar 7, 2016 #5
    I'm not understanding how this makes sense. I thought that the speed of light is independent of the velocity of the source.

    If I'm in a uniformly moving spaceship, and I throw a ball up to the ceiling, it will hit a spot that is directly above me. This is because the ball has inherited the velocity of the spaceship. I thought that light does not inherit the velocity of the source. Yet if a light pulse hits the spot directly above me, doesn't that mean that the horizontal component of the light's velocity inherited the horizontal component of the spaceship's velocity?
     
  7. Mar 7, 2016 #6

    Ibix

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    The speed of light is always c. Its direction can be different as viewed in different frames. One way to think about it is to think about how the light source works. Old school, this was a lump of some hot material which emits light, with a slit in front of it. But in the frame where the apparatus is moving, the slit isn't in front of where the hot material was when the light was emitted. Thus light must come out on the diagonal. But it still comes out at speed c.
     
  8. Mar 7, 2016 #7

    Ibix

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    The speed is independent. The velocity is not. People are sometimes casual about the distinction.
     
  9. Mar 7, 2016 #8
    Interesting!

    So for this to work (in the slit case), the light pulse is more of a point source, where the pulse is spreading in all directions, right?
     
  10. Mar 7, 2016 #9
    So the horizontal component of the light pulse is inherited, and the vertical component adjusts so that the sum of the velocity components, when viewed from both observers, are each c.

    In the case where the direction of vehicle motion is parallel to the direction that the light pulse is aimed, none of the velocity is inherited, as this would violate the causal speed limit of the universe.

    Am I on the right track?
     
  11. Mar 7, 2016 #10

    Orodruin

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    It is.

    It does. But you are only talking about the horizontal component of a signal that was sent in the vertical direction in your frame. The speed of light is not about components, it is about the overall speed.

    Only in the very special case when the light is emitted orthogonal to the direction of motion. You may want to look up light aberration.
     
  12. Mar 7, 2016 #11
    Ah, when you said aberration earlier, I thought you meant my statement was an aberration! I just looked up light aberration and it seems to get at the heart of my question, thank you. I'll study the issue further and post back to see if I grasp it.
     
  13. Mar 7, 2016 #12
  14. Mar 7, 2016 #13

    Janus

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    Try looking at it like this.
    You and your spaceship are stationary when you perform your toss. Of course, you expect the ball to go straight up and come straight down relative to you and your ship. Now imagine a second ship which is moving uniformly with respect to yours. He is watching you toss the ball. The fact that he is moving with you will have no effect on the path of the ball. However, the path the ball takes as measured by him, relative to his own ship, will be a zig-zag. His motion relative to you causes him to see the path you see as straight up and down as being at an angle. But motion is relative. There is no test that can tell us which of the two ships is "really" moving. We can just as easily say that it is the second ship that is "stationary" and the first ship is moving. The observer in the second ship can toss a ball up in the air and have it come straight back to him, while you see it as traveling in a zig-zag. The idea that either ship has an absolute motion and is the one that is 'really" moving becomes meaningless. This is just simple Galilean relativity. It makes no difference which ship we consider as moving, we get the same end results. he only reason to assign motion to one ship over the other is a matter of convenience. (If I'm considering the path of my own ball, it is more convenient to consider myself at rest than moving.)
    The difference between Galilean relativity with the ball and SR with light is that, with the first, not only does the path the ball take differ between the observers, but so does it speed. For the observer for which the ball travels at an angle, its speed is also greater. It travels a longer path but does it faster so both observers agree on how much time it took from leaving the hand to returning to the hand, but in the second case, the speed of the light is not different for the two observers and thus the second observer measures the light as taking a longer time to travel a longer path. (In SR, the ball doesn't quite behave the same way as it does for Galileo either. Its speed is greater for the observer that sees it travel the longer path, but just not by as much, so the ball still takes a greater time to complete its path for this observer than it does for the person who tossed it.)
     
  15. Mar 7, 2016 #14
    Yes I understand all this. The problem is that, according to Feynman, at the time of Michelson and Morley, the independence of the speed of light relative to its source was thought to be a property that would allow a way to cheat Galilean invariance. So invoking Galilean invariance does not answer my question, as Galilean invariance itself assumes that everything within an inertial frame inherits the inertia of that frame.


    Wow, you and I went through a very similar thought process. It's heartening to know I'm not alone in asking this question. I was beginning to question my sanity (I had recently posed this question to stackexchange and got nothing useful there). Nugatory's answer is interesting, but it begs the question: Michelson and Morley did not know about time dilation and the relativity of simultaneity, so why did they expect the angle of the light pulse to be deflected? I suppose one answer is that they were aware of light aberration, yet did not understand the cause of it.

    Based on reading through your thread, pixel, it seems that there are two classes of explanation:

    1) taking a naive view of photons as a single particle, a photon does indeed inherit the velocity of the source, but the speed of the photon will always be c. This isn't very satisfying: if the direction of emission is parallel to the direction of movement, then the velocity of the source isn't inherited.

    2) relativity of simultaneity means that a beam of light aimed upwards will act exactly like a phased array would in classical mechanics.
     
  16. Mar 7, 2016 #15

    PAllen

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    Are you missing that MM expected that speed of detector through aether did affect observed lightspeed, while motion of emitter did not? Also, that aberration WAS expected. It occurs for raindrops and sound, so of course for their model of light. The precise form direction change between frames they expected would be that of a directed sound beam. Also, note that they didn't expect to detect absolute motion. Instead, they would detect motion through aether, a hypothetical material medium, like air, about whose remarkable properties (based on speculation), much had been written.
     
    Last edited: Mar 7, 2016
  17. Mar 7, 2016 #16
    as measured from within the apparatus or from without? (assuming the latter could be measured)

    But the aberration of raindrops can be explained by simple Galilean invariance, where the speed of the raindrops is inherited from the speed of the inertial frame (similar to a bouncing ball in a car).

    Right, they expected to detect motion relative to the aether.
     
  18. Mar 7, 2016 #17

    PeroK

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    It seems to me you began with a minor misunderstanding based on little more than a semantic confusion over the words speed, velocity and independent, but now you have got yourself in a real old tangle and confusion of ideas.
     
  19. Mar 7, 2016 #18
    Quite possibly. I understand the difference between velocity and speed, but perhaps I've inadvertently made assumptions about Michelson and Morley's interpretation of the independence of the speed of light vs the independence of the velocity of light.

    I'm still confused.

    I'm perfectly willing to accept that light aberration is real. What I don't yet understand is how Michelson and Morley reconciled aberration of light with the independence of the speed of light, before they understood special relativity.
     
  20. Mar 7, 2016 #19

    Ibix

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    They expected light to behave like sound. They expected it to travel at c with respect to the aether, but at a different speed with respect to any object in motion with respect to the aether. This is just as sound travels. Any observer stationary with respect to the air will measure sound passing at 330m/s. Any observer moving at 10m/s with respect to the air will measure a speed between 320m/s and 340m/s depending on the direction of travel of the sound wave.

    You get a form of aberration here, too. As someone noted above, all objects get some form of aberration when viewed from a moving frame. This is one way of looking at why a vertically falling raindrop makes a diagonal streak on a moving car window.
     
  21. Mar 7, 2016 #20
    Thanks Ibix, I think this is key. If I can understand how sound waves experience aberration (as PAllen also mentioned), then I think I will be completely satisfied.

    So, to test my understanding:

    Suppose we have a speaker shaped like a rectangular box. The membrane of the speaker is aligned such that when the speaker is stationary with respect to the air, the sound waves it generates progagate in a direction orthogonal to the length of the box.

    Now suppose the speaker moves at a velocity (v) relative to the air, in a direction is parallel to the length of the box. Now, if it generates an impulse sound wave, will a stationary observer see that wavefront propagate at an angle?
     
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