I was reading The Black Hole War, by Leonard Susskind, when I came across a section describing the moving and relative bending of time. If time is a property of the movement of all matter in relation to one another, would time cease to exist if all movement stopped? Is this absolute zero?
The question is a classical one in philosophy of time, whether time is only due to events happening (the reductionist view) or independently of events (the Platonist view).
In modern physics (or at least general relativity) the answer is presumably close to the Platonist view, in that space-time is regarded as a primary "thing". There are points of space-time forming a manifold regardless of the presence of matter or its changes. Time is after all just another direction in this framework.
At absolute zero most but not all motion is gone: everything is at its ground state, but there are processes like quantum tunnelling that can happen anyway: some change is possible.
The real time-freeze would be moving at the speed of light: no change seems to be possible for a system moving along a null-geodesic (until it hits something).
If time is a property of the movement of all matter in relation to one another, would time cease to exist if all movement stopped?
Consider the Schwarzschild (exterior) solution to Einstein's field equations.
(1) there is no matter anywhere, anywhen so literally nothing is moving.
(2) the geometry is static (independent of time)
Yet, in this spacetime, time exists and there is a causal structure, i.e., time-like, light-like, and space-like geodesics.