Undergrad Is the Hamilton-Jacobi Formalism a Classical Analogue to Quantum Wave Functions?

[vanhees71]

Wikipedia is amazingly good but not always reliable. For a good reason it's not accepted as a valid reference in scientific papers/discussions!

 

[fanieh]

Not exactly. One is the Schrodinger equation, the other is Eq. (15).Quantum potential belongs to quantum Hamilton-Jacobi equation, which is derived from Schrodinger equation.It depends on the context, but I usually use a single Schrodinger equation.

The S-function determine the trajectories of the BM particle.. and the trajectories can't affect the S-function.. is this the mathematical statement why you told name123 that the guiding wave of one particle couldn't affect the guiding wave of other particles?

About quantum potential. The S-function determine the quantum potential.. can't the quantum potential affect the S-function? and most importantly.. can't the quantum potential of one particle affect the quantum potential of other particles? Thanks.

 

[Demystifier]

The S-function determine the trajectories of the BM particle.. and the trajectories can't affect the S-function.. is this the mathematical statement why you told name123 that the guiding wave of one particle couldn't affect the guiding wave of other particles?

No.

About quantum potential. The S-function determine the quantum potential.. can't the quantum potential affect the S-function?

The S-function does not determine the quantum potential. But S-function affects quantum potential and is affected by it.

and most importantly.. can't the quantum potential of one particle affect the quantum potential of other particles?

When the particles are not entangled, no. When the particles are entangled, there are no separate quantum potentials for each particle.

 

[fanieh]

No.

In the context of the Hamilton-Jacobi equation.. what is the mathematical reason the guiding wave of one particle couldn't affect the guiding wave of other particles? I thought it was because the trajectories couldn't affect the S-function. Today I happen to be analyzing the work of a physicist with Ph.D. who is suggesting the pilot wave is connected to magnetic monopoles traveling faster than c in reciprocal space or Fourier transform of spacetime. Is there other official pilot wave researchers doing something akin to this. Anyway, your discussions with name123 is very relevant. Thanks.

The S-function does not determine the quantum potential. But S-function affects quantum potential and is affected by it.When the particles are not entangled, no. When the particles are entangled, there are no separate quantum potentials for each particle.

 

[vanhees71]

The entire thing is just splitting the Schrödinger equation in real and imaginary parts and making the ansatz
$$\psi=\rho \exp(\mathrm{i} S/\hbar),$$
leading naturally to a set of coupled partial differential equations for $\rho$ and $S$. This only makes the entire business of wavemechanics more complicated than necessary. As I said several times before, I don't see any merit in the dBB approach for the understanding of the philosophical meaning of quantum mechanics, and you should rather spend your time learning QT (which is impossible without the adequate mathematics) without such unnecessary philosophical detours.

 

[Demystifier]

what is the mathematical reason the guiding wave of one particle couldn't affect the guiding wave of other particles?

By mathematical reason, do you mean the actual equations? Or do you mean mathematical reason in plain English?

 

[fanieh]

By mathematical reason, do you mean the actual equations? Or do you mean mathematical reason in plain English?

Both in little ounces.. lol.. thanks..

 

[Demystifier]

Both in little ounces.. lol.. thanks..

I don't know how much math do you already know. For instance, have you ever solved a Schrodinger equation for a free particle? If yes, how about non-free?

 

[vanhees71]

There is no way to express mathematics in plain English. Mathematics the language to describe nature in the most precise and successful way. Attempts to translate it into plain English make it less understandable and almost always even wrong.

 

[fanieh]

I don't know how much math do you already know. For instance, have you ever solved a Schrodinger equation for a free particle? If yes, how about non-free?

I've read many textbook about it but forgot the exact details. You can just state it in English why the guiding waves or two particles can't communicate and only the particles.. i'll just look into it.. I don't know what equation you are referring to that proves it..

 

[Demystifier]

I've read many textbook about it but forgot the exact details. You can just state it in English why the guiding waves or two particles can't communicate and only the particles.. i'll just look into it.. I don't know what equation you are referring to that proves it..

Do you at least remember what is the role of the classical potential in Schrodinger equation?

 

[fanieh]

Do you at least remember what is the role of the classical potential in Schrodinger equation?

To solve the Hamiltonian.. anyway isn't the reason guiding waves (trajectories) of two particles can't affect each other is simply because trajectories can't affect the S-function? This seems to be the obvious reason and I'm just confirming it..

 

[Demystifier]

To solve the Hamiltonian..

No.

anyway isn't the reason guiding waves (trajectories) of two particles can't affect each other is simply because trajectories can't affect the S-function?

No.

I'm afraid it's not going to work this way. I cannot teach you mathematical details of Bohmian mechanics if you haven't already learned mathematics of standard QM, before which you need to learn mathematics of classical mechanics. Sorry!

 

[fanieh]

No.No.

I'm afraid it's not going to work this way. I cannot teach you mathematical details of Bohmian mechanics if you haven't already learned mathematics of standard QM, before which you need to learn mathematics of classical mechanics. Sorry!

Ok. I'm reading some BM papers lately.. but if you found out in future which paper states the reasons and the mathematical details.. please share the paper.. thanks a lot

 

[Demystifier]

but if you found out in future which paper states the reasons and the mathematical details.. please share it.. thanks a lot

There are plenty. For instance, the Appendix of my paper
https://arxiv.org/abs/1112.2034
presents a lot of mathematical details. But as you will see, it assumes a lot of background knowledge.

 

[vanhees71]

Sigh, if you insist to learn quantum mechanics in an even more complicated way than the standard treatment (which is complete and contains all physics there is in quantum mechanics), use a textbook about Bohmian mechanics. As far as I can judge, a didactically good book on the subject is

D. Duerr, S. Teufel, Bohmian Mechanics, Springer Verlag 2009

although I got even less convinced why one should learn the details of BM after flipping through the book, because it just claims to make QM "ontological" in the sense of a classical-particle picture without any other progress towards the understanding of QM. I'm not convinced that any physical theory is "ontological" in any way to begin with, and why this should be a goal for physics research.

 

[Demystifier]

I'm not convinced that any physical theory is "ontological" in any way to begin with

That's a very interesting statement. That explains why many of my arguments on quantum foundations did not have any effect on you. Perhaps you should say the above every time when someone tries to explain you advantages of other quantum interpretations.

 

[fanieh]

There are plenty. For instance, the Appendix of my paper
https://arxiv.org/abs/1112.2034
presents a lot of mathematical details. But as you will see, it assumes a lot of background knowledge.

One of the most brilliant physicists of our times, Lubos Motl, wrote the following in https://motls.blogspot.com/2016/04/bohmian-mechanics-is-incompatible-with.html

"Bohmian mechanics is in severe conflict with relativity because the guiding wave is a multi-local, i.e. non-local, object, and it has to be able to exert superluminal influences in order to emulate quantum mechanics."

You were saying the guiding wave didn't have superluminal influence. If true, and if Lubos misunderstood BM. Then it means even for such basic concept as guiding wave, we must give what is its counterpart in orthodox QM for other physicists to follow.

I understood your paper, even the math. The appendix is about partial trace and reduce density matrix which you need for subsystem in entangled systems. It's like saying when you get the reduced density matrix of a subsystem by tracing the rest, the improper mixed state is like proper mixed state, and there is no super luminal link to the other particles. But note density matrix is just a tool and doesn't specify the actual state of the system.

What is the counterpart of guiding wave in orthodox QM.. is it simply the wave function? If so, then it's simple to understand wave function of separated object not entangled don't have effect on each other.. and for entangled object, each subsystem doesn't have wave function.. it mean each substystem doesn't have guiding wave but only one wave for the entire system? If wrong. then you must at least share what is the counterpart of guiding wave in QM so Lubos Motl may also understand the basic idea of BM and not miscomprehension (due to lack of genuine Bohmians correcting him).

 

[Demystifier]

One of the most brilliant physicists of our times, Lubos Motl,

If true, and if Lubos misunderstood BM.

Which he did.

I understood your paper, even the math. The appendix is about partial trace and reduce density matrix which you need for subsystem in entangled systems. It's like saying when you get the reduced density matrix of a subsystem by tracing the rest, the improper mixed state is like proper mixed state, and there is no super luminal link to the other particles. But note density matrix is just a tool and doesn't specify the actual state of the system.

That's correct.

What is the counterpart of guiding wave in orthodox QM.. is it simply the wave function?

Yes.

If so, then it's simple to understand wave function of separated object not entangled don't have effect on each other.. and for entangled object, each subsystem doesn't have wave function.. it mean each substystem doesn't have guiding wave but only one wave for the entire system?

Exactly.

then you must at least share what is the counterpart of guiding wave in QM so Lubos Motl may also understand the basic idea of BM and not miscomprehension (due to lack of genuine Bohmians correcting him).

Lubos first needs to work on his personality, especially modesty and respect of people with different opinions.

 

[stevendaryl]

I agree with that.

 

[fanieh]

Which he did.That's correct.Yes.Exactly.

Demystifier. In Bohmian Mechanics. Do the polarization of photons or electrons have definite values before measurement in the double slit experiment. Any paper how to analyze how these interact with the double slits?

Second. What is the counterpart or analogy of the Hamilton-Jacobi equation in Quantum Field Theory? If trajectories and actual particles are in the beabble in Hamilton Jacobi equation in BM.. what are the beables in HJ version or counterpart of QFT? Quantum Mechanics is just very low energy and doesn't really model the real world as it's in Galilean space.. we need at least special relativity & QM as minimum even as effective field theory.. or even use the full load of general relativity and QFT as this is the world we live in.. Planck scale is part of our world. What's the best implementation of GR and BM right now or out there? Thanks.

 

[vanhees71]

I think, you cannot treat photons in BM, because they are relativistic for sure, and there is no working relativistic version of BM. On the other hand for massive particles non-relativistic QM works perfectly well in its realm of applicability, which is a great deal of atomic, molecular, and condensed-matter physics!

 

[Demystifier]

Demystifier. In Bohmian Mechanics. Do the polarization of photons or electrons have definite values before measurement in the double slit experiment.

No.

Any paper how to analyze how these interact with the double slits?

See e.g. https://arxiv.org/abs/1305.1280

Second. What is the counterpart or analogy of the Hamilton-Jacobi equation in Quantum Field Theory? If trajectories and actual particles are in the beabble in Hamilton Jacobi equation in BM.. what are the beables in HJ version or counterpart of QFT? Quantum Mechanics is just very low energy and doesn't really model the real world as it's in Galilean space.. we need at least special relativity & QM as minimum even as effective field theory.. or even use the full load of general relativity and QFT as this is the world we live in.. Planck scale is part of our world. What's the best implementation of GR and BM right now or out there? Thanks.

There are no unique answers to those questions, various different proposals exist.

 

[fanieh]

No.See e.g. https://arxiv.org/abs/1305.1280There are no unique answers to those questions, various different proposals exist.

Ok. Btw.. is there a QFT version of MWI?
BM is just a MWI with position preferred basis chosen.. if we remove the position preferred basis.. it's back MWI in essence.
In the pure unitary universe without preferred basis. Have you written a paper or are you sure 100% that the interaction Hamiltonian can't select the position preferred basis? And it needs additional assumption in the universal wave function?

 

[Demystifier]

Ok. Btw.. is there a QFT version of MWI?

Yes.

Have you written a paper or are you sure 100% that the interaction Hamiltonian can't select the position preferred basis?

To a certain extent it can, but not in the ontological sense.

And it needs additional assumption in the universal wave function?

Yes.

 

[fanieh]

Yes.

Any reference? You mean the orthodox QFT can be interpretated as MWI since the difference is only all branches exist?

To a certain extent it can, but not in the ontological sense

What do you mean in the "ontological sense"? In the nothing happens in many world papers you guys discussed years back. You didn't give details (confirm or deny) how the interaction Hamiltonian can create position basis in the universal wave function. Are you saying there is no way to be sure because we can't solve the Hamiltonian of interacting objects (environment, subsystems)? I just want to know now what is the case as I want to go back to studying MWI. I think the position basis in BM is only temporary or preferred because of something. Remove that something and it's back to a formless MWI. Can the following be true?

In the Beginning, there is no basis of any kind.. there is simply the universal wave function of MWI where nothing happens..
Then position preferred basis is chosen..
Then the laws of physics came to be..

Yes.

 

[Demystifier]

You mean the orthodox QFT can be interpretated as MWI since the difference is only all branches exist?

Yes.

What do you mean in the "ontological sense"? In the nothing happens in many world papers you guys discussed years back. You didn't give details (confirm or deny) how the interaction Hamiltonian can create position basis in the universal wave function. Are you saying there is no way to be sure because we can't solve the Hamiltonian of interacting objects (environment, subsystems)? I just want to know now what is the case as I want to go back to studying MWI. I think the position basis in BM is only temporary or preferred because of something. Remove that something and it's back to a formless MWI. Can the following be true?

If you want to study MWI and questions like this, I would suggest you to first study the theory of decoherence, preferably from the book by Schlosshauer.

 

[fanieh]

Yes.If you want to study MWI and questions like this, I would suggest you to first study the theory of decoherence, preferably from the book by Schlosshauer.

I have read the Schlosshauer book cover to cover. I wanted to ask you this so let me ask now.
Is it possible in the beginning. it's really MWI.. then a force of nature (5th force) chooses the position preferred basis and turn it into BM?? .

 

[Demystifier]

I have read the Schlosshauer book cover to cover. I wanted to ask you this so let me ask now.
Is it possible in the beginning. it's really MWI.. then a force of nature (5th force) chooses the position preferred basis and turn it into BM?? .

http://fqxi.org/data/essay-contest-files/Nikolic_ultimate.pdf

 

[Demystifier]

@fanieh you are so fast in making questions. Do you ever try to answer them by yourself?