In this post, I discussed this topic. It just so happens that Sean Carroll answered my question about it on his Midscape Podcast Oct 2022 AMA episode.
And coincidentally the same question was addressed by Time Maudlin on Curt Jaimangal's excellent Podcast Tim Maudlin on Quantum Realism, Bell's Theorem, Pilot Wave, and Interpretations of Quantum Mechanics
On this topic, I happen to agree with Tim Maudlin but it goes to show how two very smart people, Sean Carroll and Tim Maudlin can have opposite views on this. However, it may also point to some other angle to this i.e. it may depend on the precision of the language and what definition of the word time is being used.
It appears that Sean answered it in terms of time as a human (or more abstractly - a records and recall system) would perceive time. I call it a "useful" notion of time. Sure. But I was not talking in terms of such "useful" time. I am speaking in terms of time as simply the fact of change (ala Julien Barbour). Just to be clear I do not consider how humans perceive time to be part of physics as such. In other words, when, let's say the universe reaches equilibrium (thermal state), it will be true that, by definition, microstates from one moment to another moment will be indistinguishable from each other at the macro-level. But that does not mean the microstate at one moment (t1) will be the same as the microstate at the next moment (t1+epsilon) - which results from the current microstate and dynamical laws of physics that propel it to that next microstate naturally. I am talking about the time in the sense of the current moment (t1) and the next moment (t1+epsilon). Of course, such time passage will not be useful to any human entity per se, but it can still be thought of as the passage of time. As because the universe is in an equilibrium state and thus by definition the entropy is not changing, does not mean that the direction of flow of time from (t1) to (t1+epsilon) is meaningless and does not have a direction. That is what I mean that the fact of the increase of entropy from low to high is the cause of the direction of the flow of time is not true.
I think of the "forward" flow of time as not something that is one of the possible ways in which time can flow. To me the "forward" direction is the only choice time has to flow in...because of the very definition of "forward" (t1 -> t1+epsilon). It is similar to the existence of an object. We can have +3 count of apples. And just because -3 three as a concept exist that does not mean there can be -3 apples. Thus, even though the word "reverse" exists as a juxtaposition to "forward" it does not mean it can be meaningfully applied to the flow of time.
What do you think?
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