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I've come across this explanation that the "arrow of time" is a consequence of the second law of thermodynamics, which says that the entropy of an isolated system is always increasing. The argument is that the past looks different from the future because of this increase in entropy. However, this still doesn't make time vanish, since a hypothetical clock could still be ticking in a completely uniform universe, but only this time there is no change in entropy because it is already at a maximum. In this maximum entropy universe, the past would look just like the future, but that need not mean that time isn't still flowing. It is just that we $\it{associate}$ the flow of time with a change that is recognizable.

But after having watched a few episodes of Professor Brian Cox's Wonders of the Universe, I want to know the deeper reason behind why people make the entropy argument. I've heard Sean Carroll make a similar argument to a group of physicists, so I get the idea it is not just a sloppy popularization.

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The laws of physics are time reversible, so a clock could tick backwards as well as forwards. However in our current low entropy universe it is vastly more probable that the clock ticks forwards. In a maximum entropy universe the probablility of a backwards tick would be identical to a forwards tick, so on average the clock time wouldn't change.

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While this is correct in most cases, BarBar has just announced an observation of explicit T violation in the B meson system. Preprint. And such violation was implicit in the measurements of CP violation unless you are willing to give up CPT invariance. – dmckee Jul 28 '12 at 19:03
Ah yes, I must admit I had forgotten about CP violation ... – John Rennie Jul 28 '12 at 19:10
I don't understand what the last sentence is based on, what is the clock object here and what does reading off the time mean? Does the clock consist of micro or macroscopic variables. In the first case, I don't see how it moves in any direction, in the second, I don't see how the current entropy value affects it's behaviour. If it's a clock, in what way does it tell "different times" apart? – NikolajK Jul 28 '12 at 19:41
If you run a clock in what appears to you to be a thermal equilibrium universe using the T-breaking in B-mesons (or in K-mesons), all you are doing is producing antimatter, so using the available entropy sink of no antimatter around. When the antimatter equilibrates with the matter, you have CPT preventing any forward vs. backward motion, so John's answer is fine (and mine too). – Ron Maimon Jul 28 '12 at 21:03
@John, the reply is quite brief. Is it possible to write a more elaborate one? Or suggest a few good references? – Amey Joshi May 6 '15 at 13:27

The clock cannot move it's hands forward rather than backward in a maximum entropy universe--- the two processes would be symmetric. This is a simple point--- any computational process requires increasing entropy as a side effect, so if you have an internal conceptual notion of time defined by the relation of physical systems, there must be a background of low entropy you are increasing to make this happen.

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It is more probable that the clock simply would not run. Why do you think it will go forward and backward? – Anixx Jul 28 '12 at 14:06
@Anixx; It depends on the size of the clock. My statement is correct even for Brownian clocks. – Ron Maimon Jul 28 '12 at 20:13

I would like to add my two cents here to the title question:

Why isn't time considered fundamental?

Space is not fundamental either. For space to exist one needs an f(x,y,z). If d(f)/dx, d(f)/dy,d(f)/dz are all 0, then there is no way to define anything in space. It is the contours that allow for space to exist. It is similar for f(x,y,z,t) and in that sense time is as fundamental or as an epiphenomenon as space.

It is our experiential data that told us that there is an arrow of time. Nobody has observed anything going backward in time in the everyday world. The second law of Thermodynamics justified this experience mathematically and defines the arrow of time. Had we been able to time travel, or had we seen time travel in biological organisms, we would have had a different physics theory , that would include the observations, as then the second law of thermodynamics would be invalidated.

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In quantum mechanics the collapse of the wave function is not time-reversible. It can be shown that the second law of thermodynamics can be derived from this fact.

So fundamentally it is collapse of the wavefunction that does not allow time reversal.

You also can trace the casualty principle to the wavefunction collapse (you cannot transfer information without a measurement). So even the speed of light limit on information transfer is based on the wavefunction collapse irreversibility.

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Could you open a new discussion on this topic ? Schrodinger's equation is reversible but the collapse of the wave function is not ? – Shaktyai Jul 28 '12 at 16:49
Can you be more specific? "it can be shown" is way too weak a statement to support such claims. – drxzcl Jul 28 '12 at 18:03
@Shaktyai you are correct. – Anixx Jul 28 '12 at 23:02
@drxzcl entriopy does not rise in unitary evolution. – Anixx Oct 27 '13 at 6:18
If you look at thw Copenhagen interpretation for the collapse of the wave function, time is asymmetric. Can you uncollapse a wave function? How do you go from an eigenfunction to a superposition of eigenfunctions? – Peter R Feb 3 at 17:13

Space and Time is fundamental. We still don't know if spacetime is a part of some deeper entity. Einstein's equation do tell us that space exists, but what it is, no body knows. What is space made of or is time a single entity, this has been a subject of discussion.

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