Is General Relativity Merely a Classical Framework for Calculations?

[bhobba]

Back to GR. If next year we had experimental signature that can distinguish whether Bohmian Mechanics is correct or MWI or objective collapse.. would it change how GR would be united with QM? Like could GR be classical limit of QM.. or QM could be classical limit of GR.. etc. and the need or not need to quantize GR?

That would depend, obviously, on what way it is different. Since BM, MW etc has deliberately been cooked up to be indistinguishable from standard QM that is highly unlikely, but one never knows.

Just as an example of a conjecture that would see Primary State Diffusion:
http://arxiv.org/pdf/quant-ph/9508021.pdf

BTW GR is already united with QM up to about the plank scale:
https://arxiv.org/abs/1209.3511

Statements that QM and GR are in conflict misunderstand the problem as explained in the link above.

Thanks
Bill

 

[bluecap]

That would depend, obviously, on what way it is different. Since BM, MW etc has deliberately been cooked up to be indistinguishable from standard QM that is highly unlikely, but one never knows.

Just as an example of a conjecture that would see Primary State Diffusion:
http://arxiv.org/pdf/quant-ph/9508021.pdf

BTW GR is already united with QM up to about the plank scale:
https://arxiv.org/abs/1209.3511

Statements that QM and GR are in conflict misunderstand the problem as explained in the link above.

Thanks
Bill

Do you have a paper where a certain field (like higgs field or even neither scalar field nor vectorial field (like EM)) can give rise to both quantum and geometry unifying QFT and GR? Because there may be a third missing ingredient that can unite them, and does it mean it should be neither field or geometry at all because these two are emergence?

 

[bhobba]

Do you have a paper where a certain field (like higgs field or even neither scalar field nor vectorial field (like EM)) can give rise to both quantum and geometry unifying QFT and GR? Because there may be a third missing ingredient that can unite them, and does it mean it should be neither field or geometry at all because these two are emergence?

Sorry - don't know any like that.

Thanks
Bill

 

[jambaugh]

Hmmmm. I think I understand what you mean, but can you elaborate in light of Gleason which would seem to suggest you can, and in a unique way.

Gleason's theorem refers to the probability as a measure on the lattice structure of the subspaces of a Hilbert space. But that lattice is not a classical set lattice and this is at the heart of the issue.
[... pause while I do some network searches...]
It has been a while since I walked through the details and I found a preprint by Knuth: https://arxiv.org/pdf/0909.3684v1.pdf that seems to contradict my statement as well so let me read up and get back to you.

(The resolution is, I believe, the fact that the quantum probabilities are squares of a lattice valuation, I'm also going to read his reference in the above: https://arxiv.org/pdf/0907.0909v3.pdf )

 

[bluecap]

On a Monday.. I want to imagine the local particles guide by Bohmian wave function.. on Tuesday.. Many worlds as my cat duplicates 9 times.. but then I realized that in most actual scenario.. you have quantum fields theory.. like when photons interacting with atoms and becoming two photons, etc.

In quantum field theory.. "a point in space does not take on a specific physical quantity, merely a spectrum of possible quantities. The value that is actually chosen depends on a separate mathematical construct known as the state vector, which is not assigned to any specific location; it spends all of space".

So without using complex mathematics.. jus share how do you imagine bohmian fields on the Monday? what happened to the initial position or the pilot wave guiding it? Please describe using English roughly...

 

[stevendaryl]

There is a perfectly valid classical analogue to that as well. The value of your lottery ticket, and simultaneously the value of all other lottery tickets distributed throughout the country, will (within your mind) suddenly collapse from their expectation value to their prize value once you learn the results of the drawing. Or more "physical" if you observe that perfume molecule at some point in the room you will update (collapse) your probability density function to one centered at the observed location and starting with 0 deviation (delta function).

Everyone keeps explaining collapse in terms of that analogy, even though Bell's theorem can be interpreted as saying that that analogy is false. It doesn't have to be interpreted that way, but it is hard to see how that analogy can really work in light of Bell's theorem.

 

[Zafa Pi]

I'm mastering this paper shared by Bhobba over a hundred times. http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

This is from the 1st paragraph of chapter 1:
"According to the Superposition Principle, any two state vectors in a Hilbert space of a quantum mechanical system, can be linearly added together to form another valid state of the system: for |ψ⟩ , |φ⟩ ∈ H

|Ψ⟩ = a |ψ⟩ + b |φ⟩ ∈ H (1.1)

where a, b ∈ C . This causes the occurrence of many purely quantum mechanical effects, such as interference in the double slit experiment"

This gave me quite a chuckle. It's like saying Newtonian Mechanics is what makes things move. Prior to The Principia there was a profound silence and the world was still.

 

[bluecap]

I want to learn to see things in quantum way. For example when a baseball is flying through the air.. I want to see it as quantum baseball.. should I use quantum mechanics or quantum field theory in imagining it's internal state? How do you tell whether to use QM or QFT on everyday objects you see? And to shift from qm to qft back to qm visually quickly.. is it like replacing the positions by operators so the positions of the baseball needs to replaced by operators (in QFT)? So when the baseball flying, should I think of it in terms of operators and state vector (QFT) or position and state vector (QM)

 

[bhobba]

I want to learn to see things in quantum way

It written in the language of math. That's the language you need to use and study.

Generally speaking you use QM and only go to QFT if it fails eg you can't account for spontaneous emission in QM - so you go to QFT and it works.

For the baseball its classical so you look at it that way.

Why is the baseball is classical and how does Newtonian physics follow on from QM? The simplest way is to derive the Principle Of least Action from QM and use that to develop Newtonian Mechanics. That is done by Landau in his book I have already mentioned.

Thanks
Bill

 

[bluecap]

I've been thinking a lot before I ask anything so it won't sound silly.

About the Bohmian pilot wave that is supposed to be deterministic and set the initial conditions. But isn't it possible a randomizer field is piggy back to the pilot wave that makes it random and the randomizer is the source of the born rule in BM? any papers?

 

[bhobba]

It's like saying Newtonian Mechanics is what makes things move.

It's actually key to many quantum effects rather than the somewhat misleading wave-particle duality. For example it is one of the keys to the double slit which depends in the uncertainty and superposition principle rather than the wave-particle duality as is told in popularization's and beginner texts:
:https://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

But yes since it basically expresses the vector space structure of quantum states it does look a bit like - well so? The key is seeing how you apply it like in the double slit.

Thanks
Bill

 

[PeterDonis]

Can you take the analogy to General Relativity? Can we say that in GR, the world is still classical and the Einstein Equations are just for calculation purposes?

"Classical" in this context just means "not quantum". So GR is a classical theory.

This thread is wandering over a very wide field because the original question was vague (and based on a misconception--see above). I suggest that you take some time to learn more about QM and GR so you can formulate more specific questions. Thread closed.