Is time dilation connected to particles or space around?

Question

Is kinematic time dilation considered connected to accelerated particles or the spacetime around the particles?

Answer 1

Time dilation follows from the geometry of spacetime. It arises because two reference frames which are moving relative to each other do not have a common time axis. Instead the time axis of each frame is tilted relative to the time axis of the other, the degree of tilt increasing with speed, so that a plane of constant time in one frame is a sloping slice through time in the other.

The consequence of the sloping planes of constant time is called the relativity of simultaneity, and all the effects of SR, such as time dilation, the barn paradox, the twin paradox etc, follow straightforwardly from it. Nearly all the effects have direct spatial analogies with everyday experience. There are plenty of answers on this site that explain how time dilation arises from the relativity of simultaneity. However, let me try an analogy...

Suppose you climb the stairs on a double-decker bus. In your frame of reference (the bus) you have climbed 3 metres, say. However, if the bus had been driving up a ramp, and in the time you had climbed 3m it had also gone 1m up the ramp, then to someone standing outside you would have risen 4m in total. The 3m height you have risen in your frame seems 'dilated' to the person standing outside who has seen you rise 4m. The difference arises not because the stairs of the bus have grown, or any other physical effect like that, but simply because you and the person outside use a different baseline of height. Your baseline is the bus, and that baseline is higher than the baseline of the person outside because you have gone up a ramp.

Time dilation happens in an analogous way. If you move 3 seconds through time in your frame of reference and while you are doing that, your entire frame of reference has moved up a sloping ramp of time in the other frame to a region where the local time in that frame was a second ahead, then in that other frame you will have moved forwards 4 seconds. It is not because anything has happened to your watch, but because your frame and the other frame have different baseline times.

Answer 2

Time dillation is between inertial frames.

Suppose we have a observer A travelling at 0 m/s which has a clock A and a observer B travelling at 10m/s which has a clock B.

According to obsever A the clock of observer B(clock B) will tick slower than his/her clock(clock A).

According to observer B the clock of observer A(clock A)will tick slower than his/her clock(clock B) because according to B A is moving with a velocity of 10m/s away from him/her.

Answer 3

Is kinematic time dilation considered connected to accelerated particles or the spacetime around the particles?

You could make either interpretation if you wish. The math and the experiments just tell you how much time is measured on a given clock.

However, I believe that most scientists prefer to interpret it as being connected with spacetime. Time dilation is simply one facet of spacetime having a (-+++) signature. This approach has the advantage of simplicity and predictive utility. Accepting that one simple premise leads automatically to all relativistic effects.

Associating time dilation with the particles instead requires multiple explanations, one for each type of particle, and a non-spacetime reason why they are all the same. Also, even with such an array of explanations, you would need additional explanations for all the other relativistic effects.