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In a closed box in inertial motion a ball bounces up and down vertically. Apart from this movement, the ball is motionless relative to the box. The trajectory of the ball seen by a stationary observer will be tilted toward the front, not vertical.

Next, we do the same experiment but with a photon. The photon is directed exactly in the same vertical direction as the ball, but as it has no mass it is not being carried away by the motion of the box, and seen from a stationary observer its path will not be tilted toward the front but vertical.

The two trajectory are not the same.If the box is absolutely motionless, seen from the interior of the box the photon will be vertical and will have the same trajectory as the ball, otherwise it will have a trajectory tilted towards the rear.

What is wrong with this reasoning?

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    $\begingroup$ Your question is unclear, but if I am following right you are mistaken about the light ray. It also follows a purely vertical path viewed from inside the box. Why should it not? $\endgroup$
    – RC_23
    Commented Apr 13, 2023 at 17:17
  • $\begingroup$ The light and the ball cannot follow the same path since the ball is carried away with the box but not the light. $\endgroup$
    – externo
    Commented Apr 13, 2023 at 17:19
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    $\begingroup$ We can always arrange both the ball and the light to have any angle we like. The entire point of relativity is that what we are seeing inside the box and what an external observer sees from the outside are not the same. That has nothing to do with "absolute motion". It is, indeed, an indication that relative motion matters. $\endgroup$
    – FlatterMann
    Commented Apr 13, 2023 at 17:39
  • $\begingroup$ From the point of view of an stationary observer, the ball will be carried by the box because it will have kinetic energy, but the ray of light will follow a path which will depend only on the angle at which it was emitted. $\endgroup$
    – externo
    Commented Apr 13, 2023 at 18:09
  • $\begingroup$ Light also has KE (kinetic energy). In fact, a photon is a quantum of KE of the electromagnetic field. But more importantly for your scenario of a ball and light bouncing in a box, light has momentum, and the motion of the ball and light both obey the law of conservation of momentum. $\endgroup$
    – PM 2Ring
    Commented Apr 13, 2023 at 19:28

3 Answers 3

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What is wrong with this reasoning?

It is based on a false assumption of how light works.

The photon is directed exactly in the same vertical direction as the ball, but as it has no mass it is not being carried away by the motion of the box, and seen from a stationary observer its path will not be tilted toward the front but vertical.

This simply isn’t how light works.

Consider, for example, the following arrangement: there is a tube, mounted vertically in the box for launching the ball in a straight line vertically. Attached parallel to this tube is another tube. This second tube has a spherical point light source in the center of a cap on the bottom end of the tube and a small hole (barely large enough that diffraction is negligible) in the center of a cap on the top end of the tube.

The ball is launched and leaves a spot on the ceiling above the launcher.

The spherical light source pulses, most of the light is absorbed by the tube, except for the light that hits the pinhole. That bit of light continues on that straight line and hits a spot right next to the mark from the ball.

The whole assembly is gently accelerated to some velocity, at which point it moves inertially. The experiment is repeated. In this frame the ball moves diagonally with the tube, travels diagonally as the room moves, and makes a mark in the same spot on the ceiling.

The spherical light source pulses, most of the light is absorbed by the tube, except for the light that hits the pinhole which is the light that moved diagonally at the correct angle. That bit of light continues on that diagonal line and hits the same spot right next to the mark from the ball.

So light does not behave as you described. There is no optical detection of absolute motion

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  • $\begingroup$ I was speaking about a photon or a laser beam, not a spherical light source. But I think I have understood : the box impart momentum to the photon, as said by PM 2Ring in a comment under the question. $\endgroup$
    – externo
    Commented Apr 14, 2023 at 10:00
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    $\begingroup$ It doesn’t matter. Both are collimated directional light sources. I chose the pinhole design because it is easier to analyze than a laser resonant cavity. If you actually analyze a laser cavity you get the same conclusion, but with a lot more work $\endgroup$
    – Dale
    Commented Apr 14, 2023 at 10:04
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If the ball and the light are directed vertically, then they only interact with the top and bottom walls. There is no difference.

If you move the box to the side, then to an observer inside the box, both the ball and the light beam appear to deflect to the side. Neither appears to move vertically any longer.

Assuming the walls are perfect reflectors, both the ball and the light when it hits the side wall will reflect back into the box. In both cases this is done by the box and the object (ball or light) exchanging momentum.

So yes, if you move the box sideways, both the ball and the light can be carried away.

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  • $\begingroup$ I think you mean to say "If you move the box to the side, then to an observer outside the box, both the ball and the light beam appear to deflect to the side." The inside observer who is not aware of any motion, sees a vertical path for both $\endgroup$
    – RC_23
    Commented Apr 13, 2023 at 18:07
  • $\begingroup$ No. I'm assuming the objects are already in motion. Accelerating the box doesn't affect the ball or the light (from the inertial observer's perspective) until the wall is pushed into their path. The box observer "feels" that a gravitational force has appeared from one side and both the ball and the light deflect due to it. $\endgroup$
    – BowlOfRed
    Commented Apr 13, 2023 at 18:19
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    $\begingroup$ Maybe it would be clearer to say ""If you accelerate the box to the side while the ball and light are in motion..." $\endgroup$
    – RC_23
    Commented Apr 13, 2023 at 18:31
  • $\begingroup$ I am not speaking about acceleration. The box is in inertial motion. $\endgroup$
    – externo
    Commented Apr 13, 2023 at 18:54
  • $\begingroup$ Then can you clarify what is meant by "carrying away the ball"? If the ball is moving vertically in the box, and the box is not accelerating, then there's nothing to carry away. $\endgroup$
    – BowlOfRed
    Commented Apr 13, 2023 at 19:32
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The easiest way to convince yourself you are wrong should be to switch the roles of the two observers. Imagine you are the stationary observer and you have light bouncing vertically up and down in a box next to you. That fits perfectly with how you believe light behaves. Now imagine how that looks to another observer coasting past you inertially- in their frame the light is following an angled path, since to them the box is on the move.

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