Hello , I'm not great at maths but this morning I have attempted to add some values to my question in case it was not understood .

1. Clock at relative rest

H = ~399723277m

Tick rate = 1.3 light seconds per tick

What's this H thing?

I get that it's a distance of some kind. Light, travelling at 299 792 458 m/s would take 1.3333 seconds to travel distance H.

2. Clock in relative motion

H= 299792458m

Light would take 1 second to travel that distance.

Angular path distance the light travels

d=~399723277m

Is this a light clock?

Let's assume it is. Then let's make H =299792458 m the distance between two mirrors that are stationary (on a spaceship, say). Somebody watches that spaceship fly past at speed v, and the light follows a "slanted" path as it travels between the mirrors. Then d is the "slanted" path distance, which you call "angular path distance".

So, in the spaceship rest frame, the light takes 1 second to travel between the mirrors - call that one "tick" on the spaceship, or one "spaceship tick".

In the "outside" frame, the light takes 1.333 seconds to travel between the mirrors - call that one "Earth tick".

The fact that it takes different times in the two frames is due to the assumption that the

*speed of light* is

*the same* in both frames - a fundamental assumption of Einstein's special theory of relativity.

It follows that "outside" observers say that the spaceship clock is running "slow", because 1 spaceship tick equates to 1.333 Earth ticks.

With a bit more analysis, we can determine that the speed of this spaceship, relative to the Earth, must be 0.66 c, where c is the speed of light.

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So, that's all fine. Now what?