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I want to know what are the minimal requirements for a physical system that must be satisfied in order for it to make sense to talk about time.

For example, there shouldn't be time in a system of a single free particle since nothing ever changes.

Another example - if we have two particles that move apart from each other, that distance between them is a measure for the time that passed since they left the origin. But if the particles are just rotating around their joint center of mass, the system always looks the same so there is no time. Can we have even more complicated systems that has no time?

Also, talking about a single particle or maybe even two is a bit not physical, in reality we cant have such an isolated system, so apart from theory, how would these principles apply in practice?

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    $\begingroup$ A system in which nothing changes doesn't invalidate the concept of time. A system without time is one where nothing can change. $\endgroup$ – Nuclear Wang Sep 20 '17 at 14:32
  • $\begingroup$ @NuclearWang how does it makes sense to say "such and such amount of time has paseed" if nothing cahnged? $\endgroup$ – proton Sep 20 '17 at 14:38
  • $\begingroup$ Suppose we watch a radioactive isotope to see whether it decays. After X minutes, we see that it has not. Nothing has changed in the system, but it's still very useful to know how long that invariance has lasted. You seem to suggest that a change in time must be accompanied by a change in some other quantity, which simply isn't so. Some things are constant (invariant with time), but that doesn't mean time has frozen. Zero change in time implies zero change in some other quantity, but the reverse is not true - zero change in some quantity does not imply zero change in time. $\endgroup$ – Nuclear Wang Sep 20 '17 at 15:01
  • $\begingroup$ @NuclearWang how can you even say "X minutes have passed" when all there is in the world is a single particle? maybe i miss expressed myself, i'm not saying " - zero change in some quantity imply zero change in time" but " - zero change in every quantity imply zero change in time" $\endgroup$ – proton Sep 20 '17 at 15:05
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Your argument:

there shouldn't be time in a system of a single free particle since nothing ever changes

is not securely founded. For example the stereotypical black hole, the Schwarzschild geometry, is time invariant but that does not stop us from describing it as a four dimensional geometry - one of the dimensions being time like.

I suspect you are talking about the flow of time not time itself, but this is not a concept that exists in physics. That is, the more you try and pin down what the flow of time means the more elusive it becomes. I explore this in my answer to Is there a proof of existence of time? and also in What is time, does it flow, and if so what defines its direction?.

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  • $\begingroup$ Can you elaborate about the black holes? also, it arises the questions whether a black holes is more simple then single particle (or two), which i'm not sure that makes sense to talk about $\endgroup$ – proton Sep 20 '17 at 14:37
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    $\begingroup$ @proton: an uncharged non-rotating black hole is the simplest posible structure in the universe. It is completely characterised by one variable - its mass. $\endgroup$ – John Rennie Sep 20 '17 at 14:47
  • $\begingroup$ ok, so lats say we have a black hole alone in the universe. why do we need time? $\endgroup$ – proton Sep 20 '17 at 14:49
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    $\begingroup$ @proton: because a black hole is a 4D structure $\endgroup$ – John Rennie Sep 20 '17 at 14:51

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