I am willing to grant that time is indeed an illusion b/c we do not have perfect perception of reality but it seems like all these new developments are squirreling time away into another part of the theory by calling it something else like "dynamics", "rule application", "evolution", etc. The physically relevant relations happen one way or another & whatever they're calling the deltas between the new primitive states & their evolution is still referring to some coordinate (whether implicit or not) that is essentially the same thing as time.

Moreover, it's pretty obvious that when they're describing the theory they can not avoid evoking temporal language & metaphors so it's difficult to take them seriously when even they can't avoid describing what's going on w/o referring to time.

My naive way to think about a reality without time is that all the possibile states of reality are already there, all together. The rules are about how to move from one state to another one, like water flowing on the side of a mountain.

Those rules might be be deterministic or there may be a roll of a dice. Then what we perceive as time is the sequence of states, the memory of previous states. No ticks are needed: there might be no central clock like in CPUs, each part of reality might apply those rules continously and move the global state from one state to another one.

But this is not physics as we are doing it now, it's presocratic philosophy. They got the idea of atoms right among a number of ones that turned on wrong.

There's no motion in what you've described. You're describing a crystal or maybe a hologram. David Bohm is the main physicist I know about who has written on this topic but I'm sure there are a few others by now as well who are taking holographic principles seriously.

Not a physicist but this echoes my feelings when people talk about time as an emergent phenomenon.

I'm not a physicist either but this stuff isn't magic. Most of the mathematics used by physicists isn't complicated if you've managed to get past calculus.

At this point, numerous exotic mathematical tools from Langlands program, Lie algebras, algebraic geometry and topology have been used in physics.

I do agree that you can go quite far with calculus, linear algebra, and probability. But I do think that you overstate the case.

Algebraic geometry isn't any more complicated than multi-variable calculus. It's certainly more abstract but you get used to it after a while. Schemes¹ are not difficult to learn if you know basic commutative algebra & topology. If you don't know basic commutative algebra then you'll have a tougher time but it's again something that can be learned w/ enough practice & patience.

¹https://webhomes.maths.ed.ac.uk/~v1ranick/papers/eisenbudhar...

Very off-topic but use of "b/c" and "w/o" in all your posts makes you stand out quite a bit. And the particular use of "&", as well.

If you read a lot of analytical philosophy & meta-mathematics literature you'll notice it's not unique at all. That's where I learned the short-hand conventions.

at a macroscopic level obviously what they describe must look like "time" to match what we see

but time ticking because of some dynamic interaction mechanism between some things (like a mechanical clock) is very different than some fundamental/abstract/irreducible "time" which just is (like in einstein)