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In the light clocks, time ticks via the motion of light and since speed of light is constant therefore when the clock is in motion ,the photon has to cover a greater distance by the perspective of an object at rest . So in the perspective of object in rest time ticks at slow rate but in other clocks such as mechanical clocks .time ticks via the motion of different objects not light. and the speed of the objects are not constant.so from the perspective of an object at rest time ticks at the same rate. How can be this possible as time dilation affects all clocks?

AKSHAT DIXIT
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2 Answers2

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I like this question because it contains several common misconceptions about relativity, which, if not dispelled, will hinder progress.

Misconception 1: Motion affects the internal mechanism of clock. Clocks measure time, and their function is not affected by motion.

Misconception 2: Moving clocks run slow. The clocks don't run slow, time runs slow, but there is a caveat.

Misconception 3: Time runs slow in the moving frame. Time does not run slow in the moving frame, because in the moving frame, the moving frame is at rest, so everything is normal.

For misconceptions 1-3 to be correct, there would have to be an absolute rest frame, and a major element of SR is that there is no absolute rest frame.

The point of the light clock is that it is unambiguous. Under the axiom that $c$ is constant in all reference frames.

For clarity, put the clock in frame $S$ where it measures the passage of time properly. In a frame $S'$ moving relative to $S$, the clock ticks slower. For this to be self consistent, $S'$ has to have different space-time coordinates from $S$.

Note, I didn't say which frame was moving, because it doesn't matter. There is no absolute rest frame, so it can't even be defined.

Right now, there are reference frames (say riding a straight section of the LHC, or an ultra high energy cosmic ray) that measure UTC to be ticking at nano-seconds per second (order of magnitude), and that has absolutely no affect on us.

No matter how fast another frame sees you moving, you still live in a flat Minkowski spacetime, with light pulses moving at $c$ in all direction, because you cannot move relative to space.

JEB
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  • a nice answer, well deserving of my upvote. Why do you think these misconceptions are so common? Is it something to do with the way SR is taught? – Marco Ocram Sep 04 '23 at 19:27
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    If you have the guts, you can teach people about spacetime interval and diagrams in a few hours, then derive most of the answers to common SR problems and "paradoxes" (I am coming to loathe that word!) in minutes. Unfortunately there are too many teachers attempting to shoe-horn in armfuls of unnecessary physics and /or "intuition", and YT video makers that like to present the "woo-woo" stuff badly for a laugh ;) Yep it is a circus alright. – m4r35n357 Sep 04 '23 at 19:42
  • @MarcoOcram I think the greatest offense is saying as you approach $c$, your mass diverges so that it takes infinite energy to reach $c$. This implies the moving thing is changing (and getting flat, and slowing down), which implies an absolute rest frame. All these non-Galilean effects are only our frame....the moving object doesn't care. Also, saying as you approach $c$. If I accelerate to $0.99c$ and coast...which way do I then accelerate to get closer to $c$? All directions are equivalent, because I am at rest. Hyperbolic geometry. – JEB Sep 05 '23 at 14:18
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The answer is that if you have two events that occur in the same place in one frame, then the time interval between them is always less in that frame than in any other frame in which they occur in two different places. Note it is the time interval itself that is shorter. For example, the interval might be four seconds in one frame and six seconds in the other. Any type of clock will therefore measure the time accordingly.

Marco Ocram
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