And it's not like nonrelativistic quantum mechanics and Newtonian mechanics have that different a conception of time. Both describe the evolution of a system using differential equations in time, both treat the world as having a single shared time (like "frames in a movie"), etc. I think the main differences are what evolves in time, and also quantum mechanics possibly needing different rules for what happens to the system when a "measurement" happens.
Also, the idea that "none of the areas of physics make time pass [except thermodynamics], because to them time is symmetric", isn't true, because e.g. the standard model doesn't have time symmetry.
Also also, I don't think it's a helpful simplification to say that relativity simply allows for "distortion of spacetime". SR says that the symmetries we expect of spacetime are wrong, and that a very different group of symmetries applies.
> Both describe the evolution of a system using differential equations in time
All areas of physics use differential equations, and so does relativity which you are contrasting these two against next.
> both treat the world as having a single shared time (like "frames in a movie"),
I think you misunderstand what the "frames in a movie" meant. It was about the distinction of time being modeled as discrete or continuous.
What you are talking about ("single shared time") is indeed a shared property of all other areas, which are not relativity, by the virtue of not being relativity (which introduces the distortions that make a single shared time impossible). But that is a tautology.
> I think the main differences are what evolves in time
All four areas are somehow describing the evolution of matter and energy. Again, not a difference.
> and also quantum mechanics possibly needing different rules for what happens to the system when a "measurement" happens.
Measurement, collapse and conscious observers are unnecessary additions which are not needed for a complete description of quantum mechanics. I would instead argue that the main difference to classical mechanics and relativity is the superposition principle (which has nothing to do with measurement): The idea that the properties of things are not in one state at a time but in a combination of states simultaneously. And that in turn means you can not model time as a simple 1D axis anymore.
> because e.g. the standard model doesn't have time symmetry.
My point was about flipping the direction of the flow or the role of past and future. The standard model has time reversal symmetry if you also flip matter and anti-matter, which for the sake of the argument makes no difference because you can't tell which one you are made of. From the POV of anti-matter people we are the ones made from anti-matter or matter which moves backward in time. Which strengthens the point that only thermodynamics assigns a clear direction to the flow of time.
> SR says that the symmetries we expect of spacetime are wrong, and that a very different group of symmetries applies.
Can you elaborate on that? Are you referring to the free fall equivalence principle?
> All areas of physics use differential equations, and so does relativity which you are contrasting these two against next.
Yes, but the way in which Newtonian mechanics and quantum mechanics use DEs is similar was the point, and the way GR uses them is very different.
> Measurement, collapse and conscious observers are unnecessary additions
Maybe, I don't know. I meant to say "possibly", not "probably", sorry.
> All four areas are somehow describing the evolution of matter and energy... I would instead argue that the main difference to classical mechanics and relativity is the superposition principle
I think we're sort of in agreement? Quantum mechanics describes how superpositions evolve over time. The "what", for example, might go from particles to wavefunctions.
> My point was about flipping the direction of the flow or the role of past and future.
Also, the idea that "none of the areas of physics make time pass [except thermodynamics], because to them time is symmetric", isn't true, because e.g. the standard model doesn't have time symmetry.
Also also, I don't think it's a helpful simplification to say that relativity simply allows for "distortion of spacetime". SR says that the symmetries we expect of spacetime are wrong, and that a very different group of symmetries applies.