In Hilbert space, all things are quantumly possible

However, my post sucked and I didn't get around to emphasizing that. In quantum mechanics, it's possible for some state to have zero probability, and it's those probabilities that we're talking about everything being possible.

There's also the epistemic side where we know that there's a chance our theories are wrong in any given way. Those can't go to zero based on our model since the whole point is we're not restricting to a model. BTW, I really like your example as a good, clean limiting case.

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I'm sure people have come up with theories that violate conservation of charge, but they'd have to break U(1). I don't know what conservation CPT would break, if any; Noether's theorem shouldn't apply to it as a discrete symmetry.

The C in CPT is not only a change f charge but also a change of electron <---> positron, and quark <---> antiquark, and ...

The conservation or charge comes from the U(1) gauge symmetry. That is almost obvious if you ignore the mixing with the weak interaction, but after the mix you still have a U(1) gauge symmetry anyway.

Now, on logistical level, the mapping procedure is not free, it does have a physical/energetic/mental cost to handle it, and a more trivial representation of integer has a lower cost on this regard.

But the simpler integer representation can represent less many situations. If all one need to deal with in a certain frame is covered by a simpler shipper representation, from an economical perspective it can be argued it worth the risk of hitting a point where the representation will be insufficient as the situation evolved with cases it can't handle.

My impression is that your underlying premises are conflating all of this distinguishable aspects. But of course my impression is limited by my own narrow representation of the world, no matter how open and curious I can be about learning from experiences it makes me go through.

What leads you to claim that you can't encode infinite information given an infinite set to work with?

Ignoring that you have to give up a sense of personal identity at this point, there is nothing in the laws of physics that says the matter that makes up what we're presently calling me can't morph into a talking cucumber with a brain with my memories in it. It's just absurd number of extremely specific things that have to happen out of an ever more absurd number of possible things to happen.

For example, in the Unruh effect an inertial observer sees the vacuum in their Hilbert space as having no particles. However, a uniformly accelerating observer sees that same vacuum as containing particles.

This state of affairs is addressed via algebraic quantum field theory (AQFT), which doesn't take a Hilbert space as the primary thing one starts with, but views Hilbert spaces as derived concepts.

But I think if you ask experts (philosophers of nature, people into foundational quantum mechanics) most of them would be many worlds proponents.

I finished my masters in a quantum computing lab. The reality is that most physicists just don't care about foundational QM, and stick to the Copenhagen interpretation. To me the Copenhagen Interpretation does not even count as a complete theory. It just stays very fuzzy on when wave function collapse happens, which makes it impossible to falsify.

>Questions: 'Which of the following, in your opinion, provides the best interpretation of quantum phenomena and interactions?'

in what do they mean by 'best'. For calculating and doing practical physics then sure Copenhagen Interpretation. But for what is the underlying reality of the universe you might get a different answer.

Copenhagen has an observer - your particle goes all ways through both slits deterministically following Schrodinger type stuff until 'the observation' when a dice is effectively rolled to choose one. But how do the laws of physics know the bunch of atoms far away is in the form of an observing physicist having a look? It would be cleaner laws of physics wise for them to ignore that, resulting in multiple observers seeing different outcomes. But for calculating, rolling a dice is easier.

That said probably Hilbert spaces are tools.