> No. The evolution of quantum systems is unitary and conserves energy.

I'm guessing that all the tiny parts of the wave function basically can't interact and collapse so just continue on forever. I don't see a conflict with unitary or conservation of energy. But these tiny pieces of wave function should continue to play their role in general relativity, gravitation, etc. That's my wild guess.

To pursue wild guesses, my guess is need a solid foundation in the physics. So, I tried again with quantum mechanics. I got a famous text. It claimed that the wave functions form a Hilbert space. Tilt! No way! They can be points in a Hilbert space, but a Hilbert space is complete which from some simple examples of convergence mean that the space has to have a lot of points (wave functions) that are not differentiable and not even continuous!

Then in QM I got to where they differentiate a Fourier transform. Okay. They are doing a differentiation under the integral sign. But, can't always do that. So, I get out a book with details, right, W. Rudin, Real and Complex Analysis, that is darned, fully, careful about such things. He has a nice chapter on the Fourier transform and does differentiate it. But he also justifies the differentiation by using the dominated convergence theorem which he also proves with great care in his early chapters on measure theory. Okay, that case of differentiation under the integral sign does work. So, then, back to the physics. But the physics lectures (an MIT thing) were never clear at all about such differentiation, were not even clear about their use of the Fourier transform, and never mentioned the dominated convergence theorem. Bummer. Further, soon it became clear that physics guy was going to be sloppy: He said that a wave function is differentiable. Okay. Then, seemingly amazingly, he went on to add that it is also continuous. Of course it's continuous: Every differentiable function is continuous.

So, for the unitary stuff, okay, I studied unitary top to bottom, side to side, from Halmos, in group representation theory, for the polar decomposition, etc. I'm eager to see the role in quantum mechanics. But I suspect again I'll have to get the math from math books, not the physics books!

I want to be careful about unitary, and the claim that no information is destroyed, etc. Careful. Really careful. Much more careful than that.

Heavily physics checks itself with experiments and, then, feels free to be sloppy with the math. But for considering wild stuff such as for goofy situations for wave functions, two particles entangled, the Einstein-Podolsky-Rosen (EPR) "spooky action at a distance", symmetry giving a conservation law, across billions of years and light years, I want the math correct right down to Bourbaki and axiomatic set theory -- no more of this sloppy stuff!

The sloppy math is why I left physics and continued with math. Now I'm ready, with enough solid math, to return to parts of physics, but just out of curiosity! I'll continue with the MIT QM lectures to get out of them what is there I don't know, but often I will have to be holding my nose over how he does the math. It's old for me: My ugrad physics prof kept telling me "Let's don't get hung up on the math". Well, I did and would say "Let's get the math straight. If we are going to differentiate under the integral sign, then let's hear about the dominated convergence theorem. And, by the way, for this stuff about integrating over unbounded sets, for that mostly we have to junk the Riemann integral and use the Lebesgue integral, so, let's do that. Let's start with sigma algebras, etc., something I never heard about in physics class!"

So, I can't push my wild guesses without more physics, and there I want to be careful about the math!