Second law of thermodynamics and the arrow of time: why isn't time considered fundamental? 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.
 A: 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.
A: 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.
A: 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.
A: 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.
A: 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.
A: Time itself manifests itself as being an irresistible flow of a fluid like (non existent: but helps in imagination) substance, that is dynamic (relativity and time dilation). It comes into being and assumes it's identity of being an inevitable flow towards tomorrow and escape from the past only because we live inside Spacetime, already written out in it's full-at least that is what Eternalism says in physics, with the view of a block universe.
It says that all 4D spacetime is like a CD-information already recorded, but since we are inside the spacetime block, (the 4D thing) we perceive it as constantly unfolding itself according to the consequences of our actions, while the reality might be extremely different, with by necessity, free will infringed (so that in a particular universe, only a set of events seem to unfold which have already been recorded on the CD).
Maybe our free will is infringed wholly or to an extent, and may be, as a compensation from the un-intelligent (non conscious like us humans) universe, there are out there infinite block universes that have data in them that would unfold as a result of the infinite combinations of human action.
Now, for presentism, which IMO, says that the present is constantly evolving into the future as we would know it moments later, and it ceases to have a separate existence of it's own out there (+can only be accessed by beings far enough where the light of our present hasn't yet reached).
The future arises from expectations and evolving present-the table you see in the present will be the same one 10 second later, just that if you shift it, then nowhere in the universe would the table still be having separate physical existence forever at the original location-even the alien will eventually see the future of the table- and also from changing present situations. The past exists in memories, accessible to aliens only for seeing, not for changing it.
