system
Given the following post, respond as if you're commenting on Reddit:
human
What leads us to believe that time is moving in only one direction?

It's occurred to me that all our perspective on the passage of time is based on our memories. That is to say there has been a change between something we had known in the past and the present we now inhabit.The problem with this is all of it is biochemically based. If time were really running in reverse (from the end of time all the way back to the big bang), and you could stop at any point and ask a human if it was going in reverse, they would most likely say "no, because things I remember in the past are different than they are today." Even something more absolute such as the expansion of the universe, increase in entropy or movement of light is still based on our perception of the passage of time. So in summary is there anything, equation, theoretical or otherwise that leads us to believe that time really is moving forward rather than that our perception of time is progressing.

Note: I am already conceding to the more equation minded among us that I have no reason to think time is moving any direction other than forward, just as I have no reason to think that there is intelligent life in another galaxy or a planet with my name on it.  Evidentially unsubstantiated and all that.
gpt
Time is not symmetric in our universe. The relationship between the dimensions of space is purely symmetric; you can move either from left to right and from right to left. Both "forwards" and "backwards" are equally meaningful in all three spatial dimensions.

But time is not symmetric that way. Worldlines — trajectories through space and time, basically — must always be *timeline* and *future-directed* in our universe. "Timelike" is a technical (and potentially confusing) word that simply means it's not possible for anything in the universe to move through about three hundred million meters of space in less than one second of time in any frame of reference — and in fact, for technical reasons it's not possible for any *matter* to move even that fast. "Future-directed" means just what it sounds like: There's no way to "turn around" in time such that you're "pointed" toward the past, because of the inherent asymmetry.

Now, you may hear tell that almost everything we know of is *time-reversible.* That's another potentially deceptive technical term. It means that for almost any phenomenon you can observe in nature, it's possible to *imagine* that phenomenon happening backwards without violating any of the laws of physics. When you throw a ball straight into the air, it takes exactly as long to go up as it does to come back down. But that doesn't mean that it's possible to *reverse time* in any meaningful sense of the phrase. It just means that, for nearly any phenomenon in the universe, *if it happened backwards,* no laws of physics would be violated. That doesn't mean that if you were God and reversed the "direction" of time, that things would necessarily happen backwards, like a movie being run through the projector in reverse.

In your thought experiment, you imagined running time backwards from the end of all things, stopping along the way to interrogate a person to see if she remembers the past or the future. This is not actually a valid thought experiment. What you're doing is postulating that *if time were reversed,* everything would happen just as it would've if time ran normally, only backwards. But that isn't true. There's inherent randomness in the universe, and that means that if you go from one state of a complex system to another, then reverse the flow of time, you're not guaranteed to get the initial state back again.

This is the essence of the famous second law of thermodynamics. Put qualitatively, systems tend to evolve *away from* being ordered and *toward* being disordered. This has nothing to do with whether time is "running futureward or pastward." It has to do with the ratio of the number of disordered states to the number of ordered states. A system with a lot of entropy has a great many more possible disordered states than possible ordered states, so just by pure random chance, it's far more likely that the system will evolve from an ordered state into a more disordered state. A bowl of cold soup will not magically suck heat from the air and become hot again, regardless of which "direction" time is "running."

If you took the universe at some late state, when the scale factor was very large and everything was cold and dark, and reversed the "direction" of time, the universe would begin to contract. Everything would get more dense, and consequently hotter, but you would not see complex structures form spontaneously. Instead, you'd just end up with a nearly perfectly homogenous soup of matter. No galaxies, no stars, certainly no hedgehogs. Just an evenly distributed gas of dust and individual molecules slowly rising in temperature until it reached, at about ten billion years from the Big Bang in your backwards universe, an average temperature of about three degrees absolute. No us, no people to interrogate, just a cold gas of nothing interesting.