My thoughts on - Sean Carroll - The Physics of Eternity

As always an excellent discussion between Robert K and Sean C.

One thing I disagree with Sean is his statement that the low entropy at the big bang is the cause of the (implied forward) direction of arrow of time. IMO the use of the word "forward" for time flow is the cause of the confusion which also leads us to entertain the (silly) idea of "reverse" flow of time. IMO time only flows in the order of before events to after events i.e. in only one direction. Think of it this way - positive three apples makes sense, but negative three apples is meaningless concept. So we could drop the qualifier "positive" and simply say three apples. Along the same lines we should drop the use of "forward" in "forward flow of time". We can simply say time flows and has order - before event to after event. That is all.

It is true that we observe that the entropy of our universe was low at the big bang and is always increasing in the direction of flow of time. But it is not the cause of the direction of flow of time. But the converse is true i.e. the flow of time causes the apparent increase in entropy by virtue of the fact that the point in phase space of the universe moves from moment to moment. The reason is simple and statistical. The point in phase space of universe is surrounded by more points where the entropy is larger. Therefore any movement of that point in phase space of the universe, ends up with universe with higher entropy over extended period of time. However, for epsilon durations the entropy is jittering i.e. going down and up again and again by small amounts with up trend over longer durations overall. But when it goes down, even for an epsilon duration the time is still marching in same order.

Time, unlike space, has a intrinsic direction or even better word is order. This idea is put forward by Tim Maudlin. And I agree with Tim. It was ok to call time as a dimension in the sense of an independent variable. But it was mistake to think of it as a space like dimension. In physics the word dimension is used to simply mean an independent variable. E.g. in dimension analysis any unit can be a dimension but that does not mean it is a spacelike dimension. In thermodynamics Pressure and Temperature and density (mass/volume) are dimensions in some sense, but we do not take them to be space-like dimensions. For that reason it is less correct to say that spacetime of SR is a 4d object. Instead the more correct way to say it is spacetime is a 3 space-like dimensions and 1 time-like dimension i.e 3+1D object. Spacetime is not a Euclidean space it is a Minkowski space with light cone structure are every point.

Similarly, when the universe will reach an equilibrium i.e. the entropy will stop changing (increasing) as long as there is a change in the state, time will be marching, once again in one direction - before events to after events. Time is simply a measure of change. If there is change, there is time. This is the idea put forward by Julian Barbour.

DISCLAIMER: Sean is billion times smarter than I am. I may be wrong about this.