I Classicality and the Correspondence Principle

[PeterDonis]

Is the above statement colored by intepretation?

No.

He thought of classical physics as an approximation derived from quantum physics.

That's how it is viewed now that we know about quantum physics, yes.

This means if for sake of discussion an object had no position basis

A basis is not a property of an object. It's a choice humans make in the math for convenience. It makes no sense to say an object has or doesn't have a position basis or any other basis.

In your case, he thought you answered differently because you thnk of classical physics as independent of quantum physics, is this right?

No.

So for those who think the wave function or state vectors are the objects themselves such as Many worlders, quantum physics is both map and territory?

No. Saying "the wave function is real" does not mean that the mathematical expression you write down on a piece of paper to describe a quantum system (the map) is the same as the system itself (the territory). Quantum objects don't know or care what math you use.

So when you believe positon basis has nothing to do with classical positions of objects. You were thinking in terms of the latter or Copenhagen context.

No. As I said above, what I said is independent of any particular interpretation.

While the Ph.D. expert was thinking of the former where the state vectors are the objects themselves hence the classical positions are the actual position basis themselves?

I don't know what your Ph. D. expert was thinking.

However, perhaps I can help by expanding a bit on what I said about classical positions. Consider a macroscopic object like a baseball. What is its "classical position"? Mathematically, it is the expectation value of the center of mass position of the baseball. In other words, there is a "center of mass position" operator $\hat{P}_{\text{CM}}$ which, given the quantum state $| \psi \rangle$ of the ball, has an expectation value. $\langle \psi | \hat{P}_{\text{CM}} | \psi \rangle$. The Ehrenfest theorem, which @Mentz114 mentioned, shows that this expectation value obeys the classical equations of motion for the center of mass of the ball; that's what justifies interpreting it as the "classical position" of the ball.

Now, what does this operator have to do with the "position basis" at the quantum level? Nothing. Saying that the center of mass of the ball is at some particular position tells you nothing at all about the position of any of the individual atoms in the ball. (More precisely, nothing at all beyond that it's within some spatial region around the center of mass.) It doesn't even tell you that any of the atoms in the ball even has a particular position. All of them can be fluctuating at the quantum level and never be in a position eigenstate at all. In fact, all of the atoms in the ball are entangled with each other, so none of them even has a well-defined wave function by itself, much less a wave function that is in a position eigenstate. (Strictly speaking, exact position eigenstates can't exist physically, but we can read "wave function with a sufficiently narrow spread in position" for "position eigenstate" above and it won't change any of what I said.) And, as I said before, the wave function of the ball as a whole, i.e., the $| \psi \rangle$ that appears in the expectation value above, is a function on a space with $3 \times 10^{25}$ dimensions or so (even more if we include spin degrees of freedom), not a function on ordinary 3-dimensional space.

 

[jlcd]

A basis is not a property of an object. It's a choice humans make in the math for convenience. It makes no sense to say an object has or doesn't have a position basis or any other basis.

I have given this a lot of thought.

If treating macroscopic objects as having classical positions and behaving classically to a good approximation has nothing to do with the "position basis" at the quantum level. How come there is a version of MWI where people debate how the preferred basis or factorization occured. You yourself mentioned this:

"If all you have is the pure state vector of the entire universe, how do you pick out the "cat" subspace? If your answer is, "well, I pick some particular basis...", then what justifies picking out that particular basis? If your answer to that is "well, that's the basis in which we have cats that are either dead or alive, instead of a superposition of dead and alive", then you're arguing in a circle."

Reference https://www.physicsforums.com/threads/why-does-nothing-happen-in-mwi.822848/page-2

From numerous threads and discussions and papers. Without a preferred basis in Many worlds, there is not even a position basis. Meaning all classical objects won't have positions. And classical objects were the same macroscopic objects which you somehow said has nothing to do with position basis. This is very puzzling and seem contradictory.

Unless you mean MWI is just a toy model.. tongue in cheek thing where one could say without preferred basis, objects couldn't exist. Yet when they go back to real world. They would state the opposite that objects have no relation to the position basis in the quantum?

But then decoherence is already proven to be true. And decoherence needs preferred basis.

Or maybe your arguments have the assumption decoherence already occurred and preferred basis was already chosen. And classical objects don't need to be related to the initial preferred basis? What would happen if the universe wouldn't have any position basis at all. Then there would be no decoherence in the position basis. If so then objects as we know it wouldn't even exist or wouldn't have shapes and invisible, and the Ph.D expert argument that without position basis, objects won't even exist hold?

Also if objects were not really state vectors or ray in hilbert spaces. Then you mean our QM and QFT is just model that only capture a small bit of reality. And we are still missing a lot about nature which future models can describe better and more completely?

 

[PeterDonis]

How come there is a version of MWI where people debate how the preferred basis or factorization occured.

Precisely because the basis is a human choice made for convenience, not anything built into the physics.

Without a preferred basis in Many worlds, there is not even a position basis.

Wrong. Saying that there is no preferred basis is not at all the same as saying there is no position basis.

decoherence is already proven to be true. And decoherence needs preferred basis.

No, it doesn't. Decoherence is an entanglement interaction between the measuring apparatus and the environment. Entanglement is basis independent.

maybe your arguments have the assumption decoherence already occurred and preferred basis was already chosen.

No.

What would happen if the universe wouldn't have any position basis at all.

Why do you keep talking as if a basis were a real thing, in the universe, when I've already said many times now that a basis is a human choice, made for convenience, not anything built into the physics? It's as if you kept saying that latitude and longitude lines were somehow already there on the Earth before humans established them by convention.

if objects were not really state vectors or ray in hilbert spaces.

We already know they aren't. That's confusing the map with the territory again.

we are still missing a lot about nature which future models can describe better and more completely?

I think this is true. But it's not anything specific to QM or QFT. All of our models of nature are missing a lot, which I expect that future models will describe better.

 

[jlcd]

Precisely because the basis is a human choice made for convenience, not anything built into the physics.
Wrong. Saying that there is no preferred basis is not at all the same as saying there is no position basis.
No, it doesn't. Decoherence is an entanglement interaction between the measuring apparatus and the environment. Entanglement is basis independent.
No.
Why do you keep talking as if a basis were a real thing, in the universe, when I've already said many times now that a basis is a human choice, made for convenience, not anything built into the physics? It's as if you kept saying that latitude and longitude lines were somehow already there on the Earth before humans established them by convention.
We already know they aren't. That's confusing the map with the territory again.
I think this is true. But it's not anything specific to QM or QFT. All of our models of nature are missing a lot, which I expect that future models will describe better.

About missing a lot. You are right. And all your explanations and arguments are consistent with the fact our present physics are missing a lot.

In the famous Letter to Virginia...

"You may break apart the atoms and molecules and see what created the fields inside, but there is a veil covering the unseen world which not the brightest physicist, nor even the united strength of all the brightest physicists that ever lived, could tear apart. Only us seers, sensitives, etc. can push aside that curtain and view and picture the supernal beauty and glory beyond. And guide physics to the next step. Is it all real? Ah, Virginia, in all this world there is nothing else real and abiding."

Thanks for all the help and assistances, Peterdonis. I'd try to digest all your thoughts for the next few weeks and read and study peer reviewed books, papers, articles, etc.