I've been reading up on the arrow of time and there is one thing that is being omitted from every explanation that I've found: time flow.

I am rewording this question to make it clearer. From the entropy definition of arrow of time $Δt=f(ΔS)$, where $S$ is entropy. But thermodynamically, $$ΔS=Q*(1/T_2-1/T_1),$$ where $T_1$ and $T_2$ are temperatures. Temperatures need to be integrated over volumes, but in equilibrium cases, which is what interests us, we can speak of the temperature at a point, $T_1(x,y,z)$ and $T_2(x,y,z)$. So we get

$$Δt(x,y,z)=f(ΔS(x,y,z)). $$

Obviously, function ΔS(x,y,z)!=const. Let's just take (x1,y1,z1) in vacuum and (x2,y2,z2) in the center of the Sun.

On the other hand, we observe that Δt is NOT dependent on (x,y,z) within an inertial reference frame.

That gives our function f very peculiar properties - it is actually an orthogonolizing transformation of spacetime that somehow cancels out spatial irregularities of entropy flow and creates uniform time flow out of it.

I have not found any satisfactory explanations or theories about f and its physical nature. Can someone enlighten me?


closed as unclear what you're asking by Danu, ACuriousMind, Kyle Kanos, user36790, Gert Dec 19 '15 at 3:26

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  • $\begingroup$ Your question amounts to asking "What determines the length of an object? (length of a measuring rod)" $\endgroup$ – skullpetrol Dec 19 '15 at 1:11
  • 2
    $\begingroup$ What is a "rate" of flow of a quantity if not its time derivative? The time derivative of time is tautologically $1$, so...what's the question? $\endgroup$ – ACuriousMind Dec 19 '15 at 1:53
  • $\begingroup$ You can move next to a black hole and your flow of time will change relative to ours, but I am not sure if in the precise sense you are asking. $\endgroup$ – user83548 Dec 19 '15 at 2:24
  • $\begingroup$ @skill patrol: could you please elaborate? I am not asking why a second is a second. I am saying that irreversibility of a process (which is supposed to explain arrow of time) does not imply constant speed of the same process. However, we observe constant speed. $\endgroup$ – Alex Dec 19 '15 at 2:25
  • $\begingroup$ @all: I'll try to clarify. The concept of arrow of time attempts to explain the fact that time has direction through irreversibility and entropy. However, we can not simply assume a linear relationship Δt=k*ΔS, where ΔS is entropy change. Because in this case, time would be local for each point in space, depending on how much entropy changed at that point. Time isn't local (for simplicity, we can look within same frame of reference). Why? $\endgroup$ – Alex Dec 19 '15 at 2:40