I experience reality in such a way that certain processes are irreversible. Eggs do not uncook, they only cook, that sort of thing. That's my arrow of time.
Conventional physics calls it "the" arrow of time. Much like how we used to call Earth "the" center of the universe. It feels like the kind of thing that we've gotten wrong before. Like maybe it says more about us than it says about eggs.
Could there be a process that is heading the opposite direction? A perspective for which eggs uncooking is the normal state of affairs? Who am I to shut the door on a possibility like that?
It's the kind of thought experiment that leads to theory creation: What if all events, and not just the small ones of particle physics, are symmetry-preserving? What might we have to change about our concept of energy to make that fit?
Edit: remember, we don't live in "The Clockwork Rocket", our GR uses the Lorentzian manifold, not a Riemannian manifold.
I tried that many years ago, it didn't work out. But that's ok, it was more about the journey anyhow.
My point is just that I had to get sufficiently "out there" in order to have panpsychism show up organically, but now that I have, it's a pretty comfortable perspective.
I thought I'd share because most people seem a bit repulsed by it, which is a shame because it's fun.
We don't really need time-orientability in relativity; it is perfectly reasonable to have solutions to the field equations which are static or stable periodic (and thus there is no clear past/future). Conversely, more generally we can get time-orientability in a wide variety of dimensions other than 3+1.
Relativity just tells us that where there is some global time-orientable feature, every observer will agree what's the past and what's the future of that feature. However, complex observers may have some internal degrees of freedom providing a local notion of time-orientability which could be unaligned with the global feature (and other observers' local features).
I don't see how any of this can relate to "consciousness" though. Also, our universe really doesn't admit backwards time travellers as far as we can tell, so whether and how the wider universe "corrects" observers who have different past/future orientations is really really really academic from a physics perspective. Sean Carroll's blog had a lot about that a decade or more ago, which you can probably dig out of preposterousuniverse.com or wherever.