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In this stack about deriving Lorentz transformations, the op writes an answer where he proves the relation between time in a moving frame and regular frame but I just can't understand what the logic of it is.

What I understand this is that when the rod moves, the path is altered and hence light needs a different time to traverse it. Noting that the speed of light must be constant in all reference frames, we set a relation with Pythagoras theorem and relate the times. So, what finally concluded was that:

$$ t' = \gamma t$$

So, where exactly do the moving frames and non moving frames come in here? And, how does this extra time which light takes to cover a longer path relate to the time contraction felt by observers in different frames?

To put it short, I'm having a hard time understanding the physical outcome of the result of this derivation

Qmechanic
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tryst with freedom
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  • You refer to "the rod" without any explanation of where the rod came from or what it's doing. I can take a pretty good guess what you have in mind but your readers --- particularly when you're asking them for help -- shouldn't be forced to guess. – WillO Aug 23 '22 at 22:26

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I have seen this derivation described in terms of a clock which consists of a pulse of light which is bouncing back and forth between two mirrors. Each “tick” of the clock occurs when the pulse gets back to the bottom mirror. The clock is on the outside of a spaceship which moves past a “stationary” observer at a very high speed. As indicated, the stationary observer sees the ticks occurring more slowly than a person on the ship. Since motion is relative, the person in the ship would say that the “stationary” observer is moving, and it is his clock that is running slow.

R.W. Bird
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