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I think the pulse-clock-on-a-train model for explaining time dilation is obviously flawed. The external observer never sees the light that travels from the emitter to the mirror, and back again. Instead, he sees the omnidirectional spread of light from the source. The path used to explain the greater distance travelled is only the path of angles from which the emitted light travels to him. These are photons lost to the clock.

Replacing the clock with a bouncing ball results in the same problem. The observer only sees the light, as emitted from local light sources, that bounces to him from the ball. The ball itself did not actually travel the different path or greater distance.

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    $\begingroup$ Welcome to Physics! Can you clarify why it matters whether any photons from along the pulse's path gets to the observer on the ground? Can't the external observer infer the path taken by the pulse of light if they know how the clock works and that light travels along straight lines and reflects off of mirrors? $\endgroup$ Apr 27, 2021 at 15:59
  • $\begingroup$ It matters that the external observer can see the path of the pulse because the greater distance of the triangular path compared to the shorter one seen by the internal observer is the basis for the time dilation. I posit that the light traveled the exact same path regardless of its relative path of travel to the internal and external observers. The time the light took to make the travel will be the same, regardless. $\endgroup$
    – Daniel Lee
    Apr 27, 2021 at 16:31
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    $\begingroup$ There's a common problem that often befuddles novices. Relativity is about clocks, position, and events. That is, what happens at a particular position at a particular time as recorded by xxxxxxxxx. The problem is the xxxxxxxx. Often the language used is "observer" or even "an observer sees." But what is meant is a set of coordinates for the event, $(x,y,z,t)$ Human vision is not involved. The issue is finding a way to say that in one word. $\endgroup$
    – garyp
    Apr 27, 2021 at 16:42

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The external observer does not need to see the light in the clock. Technically no observers need to actually see the light. As long as the clock behaves as intended ("ticking" based on light bouncing back and forth) then you are good to go.

The point of the thought experiment is to take the assumption of "the speed of light is the same in all inertial reference frames" and then determine what arises from that. In other words, we just need to say "what if...". You can bring into the scenario actually seeing light as well, but, as you have pointed out, you would need to bring in further steps (how is the light getting to your eyes? How do you correct for the time it takes for light to travel from the beam to your eyes, etc.).

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – ACuriousMind
    Apr 29, 2021 at 11:21
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I cannot see the quartz crystal insight my wrist watch, but it's ok because the oscillations inside the watch are connected to the hands and I can see those. In a similar way, a light pulse clock can be furnished with a light-detector and amplifier at one of the mirrors. For example, make the lower mirror have 99% reflectivity, and have a detector pick up the remaining 1% of the pulse that goes through. This detector then emits a click, or causes a hand to rotate, or whatever.

After about 100 oscillations this clock will run down (the light pulse gets dim) so to keep it going you just launch another light pulse every 50 oscillations or so, or have a small gain medium ready to amplify the pulse, or whatever.

The above, plus some further technical details, gives a good rough-and-ready picture of how the huge 'light pulse clocks' (well laser interferometers really) used to detect gravitational waves at the LIGO and VIRGO facilities are designed. The optical configuration there is more involved but it is basically about round-trips of light and it has the means to detect and amplify the light.

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People have actually video'd light travel through gas with extremely slow motion cameras, eg. https://www.youtube.com/watch?v=EtsXgODHMWk . Now, you could say, "well, the light is traveling in gas, not a vacuum, which allows some of it to scatter" but in these thought experiments you always need to carefully isolate what are the essential features and the non essential features of the set up. Even if some of it scatters off of a small number of gas particles, you could for instance imagine that they are so diffuse that most of the photons travel through without ever coming in contact with the gas, meaning that they really are travelling in vacuum.

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If you are having difficulty in understanding the experiment, consider the following variant of it, which uses radio waves that nobody can see.

Imagine you are at rest and you fire a pulse of radio frequency directly overhead, where there is a reflecting surface a light-second away. In your hand you have a radio receiver which emits a beep when the reflected radio signal comes back to you, two seconds after you had caused it to be emitted. In your frame the light has travelled a distance of exactly two light seconds in two light seconds.

Now imagine that I was walking past you at a meter per second at exactly the moment you fired the pulse upwards. Two seconds afterwards, when the reflected pulse returns to you and is detected by the receiver you are holding, I will be two meters away from your receiver. In my frame the radio pulse has travelled more than two light seconds, since instead of travelling directly upwards and being reflected back to me, it has moved at a slight angle and been reflected back to a point two meters away. In my frame, therefore, the interval between the pulse being emitted by you and returning to your receiver must be slightly more than two seconds.

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