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

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• fanieh
In summary: QT can be understood in orthodox minimally interpreted QT. You don't need the de Broglie-Bohm pilot wave approach. There are (at least) to ways to see this relation. The conventional one is to take the Schrödinger equation of the problem at hand and solve it in singular perturbation theory, which is also known as (S)WKB method, standing for (Sommerfeld)-Wentzel-Kramers-Brillouin method. The idea is to make an ansatz$$\psi(t,q)=\exp \left (\frac{\mathrm{i}}{\hbar} S(t,q) \right)$$and
fanieh said:
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?

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

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

fanieh said:
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?

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.

Demystifier said:
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..

fanieh said:
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?

Demystifier said:
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..

fanieh said:
To solve the Hamiltonian..
No.

fanieh said:
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!

vanhees71
Demystifier said:
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

fanieh said:
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.

fanieh
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.

vanhees71 said:
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.

Demystifier said:
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).

fanieh said:
One of the most brilliant physicists of our times, Lubos Motl,

fanieh said:
If true, and if Lubos misunderstood BM.
Which he did.

fanieh said:
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.

fanieh said:
What is the counterpart of guiding wave in orthodox QM.. is it simply the wave function?
Yes.

fanieh said:
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.

fanieh said:
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.

akvadrako, vanhees71, fanieh and 1 other person
Demystifier said:

I agree with that.

martinbn, Demystifier and vanhees71
Demystifier said:
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.

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!

fanieh said:
Demystifier. In Bohmian Mechanics. Do the polarization of photons or electrons have definite values before measurement in the double slit experiment.
No.

fanieh said:
Any paper how to analyze how these interact with the double slits?
See e.g. https://arxiv.org/abs/1305.1280

fanieh said:
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.

Demystifier said:
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?

fanieh said:
Ok. Btw.. is there a QFT version of MWI?
Yes.

fanieh said:
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.

fanieh said:
And it needs additional assumption in the universal wave function?
Yes.

Demystifier said:
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.

fanieh said:
You mean the orthodox QFT can be interpretated as MWI since the difference is only all branches exist?
Yes.

fanieh said:
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.

Demystifier said:
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?? .

fanieh said:
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

vanhees71
@fanieh you are so fast in making questions. Do you ever try to answer them by yourself?

vanhees71
Demystifier said:
@fanieh you are so fast in making questions. Do you ever try to answer them by yourself?

Ive been thinking of this for months. Schlosshauer only mentioned about the theme about "nothing happens in many worlds" indirectly only in 2 pages.. in page 337 "Everett Branches and the Preferred-Basis Problem". The book doesn't mention at all how the initial environment and system got decomposed in MWI. It didn't mention about the Factorization problem. It is only in PF archives that I can read about it.

Anyway. You sure there is no fatal flaw in the concept that a 5th fundamental force created the position preferred basis in MWI to become BM. Well. I'd lecture this to thousand of students so hope it's not illogical or false.. lol.. thanks..

Last edited:
fanieh said:
Oh. I wrote the reply before I saw you asked it.. Again..

Schlosshauer only mentioned about the theme about "nothing happens in many worlds" indirectly only in 2 pages.. in page 337 "Everett Branches and the Preferred-Basis Problem". The book doesn't mention at all how the initial environment and system got decomposed in MWI. It didn't mention about the Factorization problem. It is only in PF archives that I can read about it.

Anyway. You sure there is no fatal flaw in the concept that a 5th fundamental force created the position preferred basis in MWI to become BM. Well. I'd lecture this to thousand of students so hope it's not illogical or false.. lol.. thanks..

fanieh said:
Ive been thinking of this for months. Schlosshauer only mentioned about the theme about "nothing happens in many worlds" indirectly only in 2 pages.. in page 337 "Everett Branches and the Preferred-Basis Problem". The book doesn't mention at all how the initial environment and system got decomposed in MWI. It didn't mention about the Factorization problem. It is only in PF archives that I can read about it.
You can read https://arxiv.org/abs/1703.08341 Sec. 3.3 Refs. [22,23,24].

fanieh

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