There was an excellent discussion on nature of time in the following video:
Here are my thoughts on the topic. I wish they had Tim Maudlin on the panel.
As I have said in some of previous blog posts, IMO, microphysics is not time reversible. It is velocity reversible which is a vector which has direction - forward and reverse. And the reversibility of microphysics is about reversing the direction of velocity vectors. Not reversing the time.
David said geometry is isotropic. However, even though Euclidean geometry is isotropic, Minkowski Spacetime geometry is not. It has a Light cone structure which partitions the spacetime into 5 zones. This also means that time has a intrinsic notion of order i.e. before to after. That is why there is a negative sign in the spacetime distance pythagorus theorem equivalent in Minkowski spacetime.
Spacetime is not a 4 dimensional object as in space-like dimensions. It is a 3 space-like + 1 time-like dimension object. The time dimension is a dimension in the sense of being a required independent or orthogonal variable. Its units are different units i.e. seconds a unit of duration vs meters a unit of distance. The time coordinate constantly changes and has a direction from before to after. We, by convention, happen to call this forward direction of time (IMO a mistake) which in turn leads us to think of reverse direction of time (silly), which in my opinion is a mistake. Just because reverse is opposite of forward does not mean that, the notion of reverse time is meaningful. I seriously think that calling before to after order as the forward direction leads to this confusion. It is somewhat like - it makes sense to talk about 3 apples. And -3 is opposite of +3. However there is no physical meaning to -3 apples. IMO the whole trouble started when time was spatialized. IMO physicists and philosophers should stop talking about time dimension as qualitatively same as other 3 space dimensions. In physics the word dimension is used to mean independent variable. For example, pressure or temperature or density could be considered dimensions with their own units to describe the state of a box of gas. But we do not confuse pressure dimension as space like dimension right? Another example is, we talk about Hilbert space of many dimensions, but clearly we do not mean space dimensions. In other words, lay people think of dimension to mean space like dimensions - hence the 3D movies and so on. But physicists and philosophers are expected to be more rigorous, or at leat that is the hope. So in that sense I thought the above discussion was sloppy.
Controversial comment
Einstein thought that quantum mechanics is incomplete and there may be hidden variables. It is true that Bell's theorem may have precluded that possibility to some extent. However we can apply the same skepticism to GR which does not seem to have a notion of present moment in it. Is it possible that instead of saying there is a block universe, can we say that aside from universe having a block like structure the notion of "present" is the missing ingredient? Even if the universe turns out to have a block like structure, is it possible that the past part of the block gets frozen up to the point of ever changing present moment, but the future is a potential extension of that block which is not frozen but is jittery because of the probabilistic nature of quantum mechanics? Somewhat like a partially open zipper where by the zipped up part is fixed but the part beyond the zip is freely movable?
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Past _______/ Open future
===========O-_____
\________
Sure when the zipper will close we know how it will look like i.e. ==================== . In that sense eventually future will look like a block when present moment zips it up but not until that happens.
Block universe is like a DVD. But without the DVD player play-head the picture is not complete.If there is no play-head in the universe does it mean that there is a ground hog day happening at every point at every moment?
Thus not having the notion of present reflected in the GR may be its short coming?
IMO attributing low entropy at the big bang or so called past hypothesis to the direction of time or arrow of time is a non-sequitur. The opposite is true. Time goes from before to after. The phase space of the universe is such that the current state of the universe, i.e. the phase space point is likely to move to regions we call higher entropy. Thus it is a statistical outcome of change of location in phase space. IMO time is simply a measure of change (ala Julian Barbour). When there is change there is time. Even when the universe eventually reaches a maximum entropy state, as long as there is change in the micro state of the universe, in some sense there is time.
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