Hilbert Dynamics in choosing position in BM/MWI

[Demystifier]

For those who don't have that book, can you summarize what, exactly, is the nature of the preference for position?

The way I understand decoherence mathematically is this:

• You start with some complex system with many components (I guess infinitely many in QFT).
• You form the density matrix for the composite system.
• You trace out the unobservable "environmental" degrees of freedom (typically, the electromagnetic field).
• What's left is a density matrix for the system(s) of interest, and voila, you have a mixed state.

You only described kinematics. Decoherence involves also the dynamics i.e. depends on the Hamiltonian.

So is the claim that this process naturally results in a mixed state in which massive objects have more-or-less well-defined positions?

Yes, but that's related to the fact that Hamiltonian is local in the position basis.

 

[martinbn]

.. is it possible MWI uses Spacetime itself as the Preferred Basis?

It's possible.

And what does this even mean!? To use spacetime as a basis!

 

[Demystifier]

And what does this even mean!? To use spacetime as a basis!

See
https://arxiv.org/abs/0904.2287
Sec. 3.2.

 

[martinbn]

See
https://arxiv.org/abs/0904.2287
Sec. 3.2.

Not sure how this clarifies the problem. The statement was that the space-time is used as a basis. That's complete nonsense. The statement wasn't to use the space-time, or some property of it, to produce in some canonical way a basis of the Hilbert space. It was that space-time can be a basis!

 

[Demystifier]

Not sure how this clarifies the problem. The statement was that the space-time is used as a basis. That's complete nonsense. The statement wasn't to use the space-time, or some property of it, to produce in some canonical way a basis of the Hilbert space. It was that space-time can be a basis!

Precise statements are always welcome, but in their absence it is equally welcome to distinguish what one said from what one meant.

 

[martinbn]

Precise statements are always welcome, but in their absence it is equally welcome to distinguish what one said from what one meant.

How can you possibly know what one meant if what one said was meaningless. In cases like that I believe that he should clarify his statements first. Otherwise you are discussing what you think the right statement/question is, which is not always what the person was trying to say. Anyway you give them/him too much credit.

Off topic: There are a number of users which post in very similar way and topics. Are they different or the same person using different accounts? What is the PF policy on that? I find it very hard to believe that there is more than one person who is interested in the same topics and is confused in exactly the same way and has the exact same way of writing.

 

[Demystifier]

How can you possibly know what one meant if what one said was meaningless.

In this case, by recalling what he said in the first post of the thread.

 

[PeterDonis]

by recalling what he said in the first post of the thread

In the OP he asked how the position basis is picked out as a preferred basis. How does "spacetime" do that? I don't see an answer to that question in the paper you linked to.

 

[Demystifier]

In the OP he asked how the position basis is picked out as a preferred basis. How does "spacetime" do that? I don't see an answer to that question in the paper you linked to.

Again, what one said in not necessarily what one meant. Of course, it is certainly possible that I misinterpreted his thoughts, but my experience with layman is that I usually understand them correctly. Anyway, let us leave him to say by himself whether my answer answers his question.

 

[PeterDonis]

what one said in not necessarily what one meant

If he didn't mean what he said, then I have no idea what he meant, or why you think your paper addresses what he meant. Can you specify?

 

[cube137]

I know a basis is a set of vectors, and spacetime is a manifold. I was asking about what set the factorization of the environment that uses position as preferred. And asking whether the mere existence of Spacetime can set the position basis as preferred basis in the factorization. I think what Demystifier was saying was that Spacetime chose the position basis in Bohmian Mechanics as preferred basis (hence creating the trajectories). So if let's say there was no Spacetime, it's back to unitary evolution in MWI. So MWI + Spacetime = BM for Demystifier. But I was asking initially if somehow MWI + Spacetime = classical world (with environment position factorization chosen).. without necessarily the Bohmian connection.

 

[PeterDonis]

I think what Demystifier was saying was that Spacetime chose the position basis in Bohmian Mechanics as preferred basis

And if that is what he was saying, I don't understand how that works, and I don't see it explained in the paper he linked to.

 

[cube137]

And if that is what he was saying, I don't understand how that works, and I don't see it explained in the paper he linked to.

There may be 2 separate concepts that we may be mixing... in Bohmians, particles have positions or localized.. while Preferred basis means the system chose position as preferred observable. Preferred basis occurs without Bohmian, I think what Demystifier was saying was that particles had position or localized because spacetime biased it that way. Which in latter discussion is no longer the preferred basis but why objects are localized in Bohmian. I'm reading threads made long ago called "nothing happens in many worlds" which I haven't participated so just clarifying some questions as I can't open the old thread and it's called Necro-posting too. Maybe Demystifer can clarify what his section 3.2 was saying when he wakes up from his sleeping tomorrow.

 

[PeterDonis]

I think what Demystifier was saying was that particles had position or localized because spacetime biased it that way

I don't understand how that would work either, nor do I see that explained in the paper he linked to. So I think we need some clarification, yes.

 

[Demystifier]

So MWI + Spacetime = BM for Demystifier.

Not exactly. MWI + particles in spacetime = BM.

But even if we ignore BM completely, the factorization problem of MWI can be avoided by postulating that position basis is a preferred basis. The mentioned section of my paper explains how position basis can be generalized to a spacetime basis. That section does not depend on BM.

 

[cube137]

Not exactly. MWI + particles in spacetime = BM.

But even if we ignore BM completely, the factorization problem of MWI can be avoided by postulating that position basis is a preferred basis. The mentioned section of my paper explains how position basis can be generalized to a spacetime basis. That section does not depend on BM.

What is another word for Spacetime basis? is it not position basis is in Hilbert space. How does it transform to Spacetime basis? What topics does it fall under in standard QFT? Ty

 

[Demystifier]

What is another word for Spacetime basis?

The expression "spacetime basis" is not used at all.

is it not position basis is in Hilbert space.

The "position" in position basis usually refers to space position, not spacetime position. There are attempts (including my own) to generalize it to spacetime position basis, but this is a very non-standard subject.

 

[cube137]

The expression "spacetime basis" is not used at all.
The "position" in position basis usually refers to space position, not spacetime position. There are attempts (including my own) to generalize it to spacetime position basis, but this is a very non-standard subject.

space position = located in 3D space.. like x, y, and z depths
spacetime position = I'm wondering what is meaning of a spacetime position or maybe do you mean the worldlines or geodesics of test particles of the minkowski spacetime?

 

[Demystifier]

I'm wondering what is meaning of a spacetime position

x y z t

 

[cube137]

x y z t

Ok. People are familiar with the concept that quantum particles don't have any worldlines because SR/GR are classical. Consider the double-slit experiment, for example. A worldline would go through only one slit, the quantum particle goes through both. I think what you are trying to do is to make the quantum particles as become like classical particles and taking a path so in essence your (quantum) particle has a worldline in the double slit, right?

I just want to have general idea how people can manipulate all equations to make anything possible. Also to understand the essence of it all better. Thank you!

 

[Demystifier]

I think what you are trying to do is to make the quantum particles as become like classical particles and taking a path so in essence your (quantum) particle has a worldline in the double slit, right?

In BM, yes. In MWI, no.