> 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.
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.
Original statement was still inaccurate...
> Can you elaborate on that?
Galilean group -> Poincare group?