Hamiltonian in QM for QFT forces/fields effects

[jlcd]

In QM. Can you use the Hamiltonian (or kinetic plus potential energy) to describe the forces of nature that should supposedly use QFT or Lagrangian? I mean the fields have kinetic and potential energy components and what are the limitations in description and others if you only use them to describe the forces of nature?

This is for situation in which you just to know the Hamiltonian contributions from the forces of nature in the particles in QM.

 

[jlcd]

Or to rephrase it (or add to it). All the forces of nature, including those not yet discovered, can influence the Hamiltonian in quantum mechanics? So if you can keep track of the Hamiltonian in QM (at least in principle). You can account for all the complete forces of nature?

 

[PeterDonis]

@jlcd your questions seem confused. What specific, concrete problem are you trying to solve?

If there is no specific, concrete problem you're trying to solve, if you're just trying to learn about quantum mechanics in general, asking random questions about random things that come to your attention is not a good way to do it. You need to take the time to work through an actual textbook, read what it says, work the problems, and ask specific questions about specific things you have trouble with.

 

[jlcd]

Here's the problem I'm trying to address.

In pure unitary dynamics where there are only state vectors. The additional structure that cause the split betwen system and environment in decoherence could be a new dynamics or forces of nature as Kastner tried to describe or other decoherence physicists tried to propose.

So i'd like to know if any forces of nature could affect the Hamiltonian if we will only use QM to describe it or need to use very advance relativistic quantum field theory or relativistic quantum gravity.

In conveying to the public and physicists at large. I'd like to know if simply saying "a new Hamiltonian dynamics cause the split of system and environment in decoherence" is enough just to describe it or a way to talk to them or introduce these in articles to laymen, etc. so tell me at least if any forces of nature can affect the Hamiltonian in QM and the limitations so I'd have compass to study it.

 

[PeterDonis]

Here's the problem I'm trying to address.

What do you mean by "trying to address" the problem? What are you trying to accomplish?

 

[jlcd]

Simply a language to talk to laymen and experts.

In case there is a new force of nature that splits system and environment. Can one just use non-relativistic QM to talk about it? In electromagnetisms, electroweak and even gravity. It can affect the Hamiltonian of particles.. the kinetic and potential energy contribution of their behavior, affirmative? So for any forces of nature, it can affect the Hamiltonian of particles? This is a very reasonable QM forum question especially when it has element of mathematics and I am asking this so i can read the textbooks with better sense of it.

 

[PeterDonis]

Simply a language to talk to laymen and experts.

Why? For what purpose?

im asking this so i can read the textbooks with better sense of it

What textbooks have you already read? You are asking about an "A" level issue; the sort of issue that tenured professors and Nobel Prize winners are struggling with. Have you mastered the undergraduate, "I" level basics of QM? If you haven't, why would you expect to be able to understand an issue that the people at the top of the field are struggling with?

 

[PeterDonis]

In case there is a new force of nature that splits system and environment

Asking about this in the abstract is useless. You need to find a specific model, in a specific peer-reviewed paper, and ask about that. But if you don't have a mastery of the basics of QM, any paper that proposes such a specific model will be over your head.

 

[jlcd]

I have already understood for example quantum Darwinism. And my questions came from this paragraphs I'm reading:

https://arxiv.org/pdf/quant-ph/0105127.pdf
"Decoherence and einselection are no exception. They have been investigated for about two decades. They are the only explanation of classicality that does not require modifications of quantum theory, as do the alternatives (Bohm, 1952; Leggett, 1980, 1988, 2002; Penrose, 1986, 1989; Holland, 1993; Goldstein, 1998; Pearle, 1976; 1993; Ghirardi, Rimini, and Weber, 1986; 1987, Gisin and Percival, 1992; 1993a-c). Ideas based on the immersion of the system in the environment have recently gained enough support to be described (by sceptics!) as “the new orthodoxy” (Bub, 1997). This is a dangerous characterization, as it suggests that the interpretation based on the recognition of the role of the environment is both complete and widely accepted. Neither is certainly the case.

Many conceptual and technical issues (such as what constitutes ‘a system’) are still open. As for the breadth of acceptance, “the new orthodoxy” seems to be an optimistic (mis-)characterization of decoherence and einselection, especially since this explanation of the transition from quantum to classical has (with very few exceptions) not made it to the textbooks. This is intriguing, and may be as much a comment on the way in which quantum physics has been taught, especially on the undergraduate level, as on the status of the theory we have reviewed and its level of acceptance among the physicists."

I know this is very advance subject. But I have understood the essence. Now can't you at least tell how how the forces of nature can affect the Hamiltonian in QM? Because if it can't. Then I need to explore quantum field theory version of quantum darwinism. So it would only give me the drive to study it if the Hamiltonian is not enough for any new forces of nature. The latter is more in the form of fields which require Lagrangian formulations? I was supposed to ask this in the thread about "What is the relationship between QM and QFT". There you answered most questions. So I just want to add what is the minimum dynamics the Hamiltonian formulation in QM where it can still describe forces of nature in QFT. It can't? But particles still move under the influence of electromagnetism, and it is Hamiltonian in action. In strong force, the particles can be affected too so Hamiltonian can still be used. If there are new forces that can affect the particles kinetic and potential energies. I guess Hamiltonian can still describe it? What kinds of forces of nature where there is no Hamiltonian? Is this even possible?

Look. You want me to take physics undergraduate course to get answer to it. But I can't go back to school anymore. So I'm asking the reasonable questions so I'd know what kind of books to read in my limited time (we need to prioritize.. just like you don't get to read all books of cooking when you just want to have basic idea of how ice cream is made).

 

[A. Neumaier]

The additional structure that cause the split betwen system and environment in decoherence could be a new dynamics

No, it is an effective dynamics, based on the standard interactions.

 

[jlcd]

No, it is an effective dynamics, based on the standard interactions.

Are you basing it in the Thermal Interpration? Zurek Quantum Darwinism is a favor of MWI. In it, states are the primitive. In your case, the classical world is the primitive (fundamental)?

Kastner used the transactional formalism to create collapse.

I just wonder what else can create "collapse" and whether it can be tied up to the quantum nature of spacetime. You mentioned before how you believed the right understanding of quantum mechanics was related to quantum gravity. I read it in n archive browse a few days ago. Do you still believe?

 

[A. Neumaier]

Are you basing it in the Thermal Interpration?

My statement is independent of the interpretation. Just look at how decoherence is derived, and you'll find that it is an effective theory derived from the standard theory by suitable approximations.

In your case, the classical world is the primitive (fundamental)?

No. The q-expectations of Heisenberg fields and their products are fundamental.

You mentioned before how you believed the right understanding of quantum mechanics was related to quantum gravity.

I think that that solving the problems of quantum gravity probably need the right understanding
of quantum mechanics. But the latter does not depend on quantum gravity.

Do you still believe?

Of course. I don't change my convictions easily.

 

[jlcd]

My statement is independent of the interpretation. Just look at how decoherence is derived, and you'll find that it is an effective theory derived from the standard theory by suitable approximations.

No. The q-expectations of Heisenberg fields and their products are fundamental.

I think that that solving the problems of quantum gravity probably need the right understanding
of quantum mechanics. But the latter does not depend on quantum gravity.

Of course. I don't change my convictions easily.

If you simply use the Hamiltonian in standard non-relativistic QM to describe the forces of nature. What dynamics can you only model (I know one can miss many)? At least you can still use time variable to describe how the forces can affect the potential or kinetic energy?

To rephrase it. If you would only use the tool of ordinary QM in describing the forces in QFT. What is the best one can describe. This is when one simply want to use QM descriptions in describing or introducing to laymen the effects of say new forces of nature in the atomic physics of molecules, etc.

 

[A. Neumaier]

when one simply want to use QM descriptions in describing or introducing to laymen the effects of say new forces of nature

To do so, one must introduce laymen to a diluted version of quantum field theory - standard quantum mechanics is not suitable for this task.

 

[jlcd]

To do so, one must introduce laymen to a diluted version of quantum field theory - standard quantum mechanics is not suitable for this task.

But still the kinetic and potential energies (Hamiltonian) of particles can be affected by any new forces of nature. For example electromagnetism can repel two like charges and attract opposite ones. Why not? This is not how the Hamiltonian is used?

Also if you can can couple the kinetic and potential energies of molecules to a hidden degrees of freedom in the vacuum. Then the thermodynamics can be affected. Perhaps this is the only means where QM can still be useful descriptions?

 

[A. Neumaier]

kinetic and potential energies (Hamiltonian) of particles

This is a very simplified description where scalar quantum fields are replaced by external classical fields. It cannot even describe the motion of a single particle in an external classical electromagnetic field.

 

[jlcd]

This is a very simplified description where scalar quantum fields are replaced by external classical fields. It cannot even describe the motion of a single particle in an external classical electromagnetic field.

Ok. So QM stand powerless.

My point is. What if how classicality is derived from the quantum substrate has origin all the way to quantum spacetime. Even relativistic quantum field theory would be powerless. This is possible. Is it not? It's more logical.

And do you have any materials for this "diluted version of quantum field theory" just to see how the limitations of QM can be addressed by this diluted version of QFT or areas where they match

 

[A. Neumaier]

QM stand powerless.

Mainly, because you insist on Hamiltonians consisting of kinetic and potential energy terms. Real Hamiltonians may be very complicated compared to this.

do you have any materials for this "diluted version of quantum field theory"

See my article on the vacuum fluctuation myth. But to really understand, you need to take the troubles learning the real thing!

 

[jlcd]

Mainly, because you insist on Hamiltonians consisting of kinetic and potential energy terms. Real Hamiltonians may be very complicated compared to this.

See my article on the vacuum fluctuation myth. But to really understand, you need to take the troubles learning the real thing!

Of course I was not talking of the classical Hamiltonian but the one used in quantum mechanics. I'm familiar with it in quantum mechanics. Quoting Wikipedia: "a Hamiltonian is an operator corresponding to the sum of the kinetic energies plus the potential energies for all the particles in the system (this addition is the total energy of the system in most of the cases under analysis). Its spectrum is the set of possible outcomes when one measures the total energy of a system. Because of its close relation to the time-evolution of a system, it is of fundamental importance in most formulations of quantum theory. "

I was asking what would happen if we were describing forces of nature that can affect the dynamics of molecules.. Then we can at least use the Hamiltonian operator in quantum mechanics? We can at least describe how it would influence the total energy of the system, affirmative? The strong force can affect the dynamics or positions of particles. Only the weak force can't (not the positions).

This is all I want to know for now. Because it looks like how system and environment got split from the unitary only dynamics or actual state vector is related all the way to quantum spacetime. And because the math for QFT and quantum spacetime is dense. I just want to focus on their effects on the Hamiltonian or total energy of QM.

 

[A. Neumaier]

Of course I was not talking of the classical Hamiltonian but the one used in quantum mechanics.

So was I.

Quoting Wikipedia: "a Hamiltonian is an operator corresponding to the sum of the kinetic energies plus the potential energies for all the particles in the system

This is the simplest textbook case only. Don't trust each statement in Wikipedia to be the full truth in everything.

It does not cover electromagnetic interactions, only static Coulombic ones. For a charged particle in an electromagnetic field, the Hamiltonian looks already quite different. For realistic effective Hamiltonians coming from quantum field theory the Hamiltonian is exceedingly messy (explicit expressions may run over pages), with most terms not easily interpretable.

 

[jlcd]

So was I.

This is the simplest textbook case only. Don't trust each statement in Wikipedia to be the full truth in everything.

It does not cover electromagnetic interactions, only static Coulombic ones. For a charged particle in an electromagnetic field, the Hamiltonian looks already quite different. For realistic effective Hamiltonians coming from quantum field theory the Hamiltonian is exceedingly messy (explicit expressions may run over pages), with most terms not easily interpretable.

Ok. So QM with special relativity or QFT can describe matter at more details. Or better yet. QM with special relativity united with no prior geometry. I think this is the only mathematic tool powerful enough to describe the universe.

What is the best tool so far for QFT with no prior geometry have you encountered? Maybe it needs new mathematical formalism that can describe both QFT and General relativity where they are just emergence of something else (any ideas along this line?)?

 

[jlcd]

My statement is independent of the interpretation. Just look at how decoherence is derived, and you'll find that it is an effective theory derived from the standard theory by suitable approximations.

No. The q-expectations of Heisenberg fields and their products are fundamental.

I think that that solving the problems of quantum gravity probably need the right understanding
of quantum mechanics. But the latter does not depend on quantum gravity.

Of course. I don't change my convictions easily.

Here is something more sensible than asking about the math of background independent QFT (with no prior geometry) .

You said that that solving the problems of quantum gravity probably need the right understanding of quantum mechanics. But the latter does not depend on quantum gravity.

Well. Attempt at quantum gravity is more than quantizing general relativity. It is understanding the nature of quantum spacetime itself. What if quantum spacetime was emergent. Remember non-local correlations. So the measurement problem in QM could really be related to quantum gravity (or full formalism of quantum spacetime or beyond). At least this is possible, right?

 

[PeterDonis]

I know this is very advance subject. But I have understood the essence.

I'm not sure you do. See below.

Now can't you at least tell how how the forces of nature can affect the Hamiltonian in QM?

The specific reference you gave says nothing about a "new force of nature". If you want to ask about a model that actually has a "new force of nature" in it, then you need to give a specific reference that has such a model in it. Otherwise your question is not well-defined and is not answerable. As I've already said.

I'm asking the reasonable questions so I'd know what kind of books to read in my limited time

There isn't any book that is going to answer your question about a "new force of nature", because there is no such model in any textbooks, since no such model has ever had any experimental confirmation. There might be some peer-reviewed papers that talk about such a model, but you're the one that's asking about such a model so you must have some idea where you've seen one. You mentioned Kastner; is there a particular paper by Kastner that contains the kind of model you're asking about?

 

[PeterDonis]

Quoting Wikipedia

Wikipedia is not a good source. It's even less of a good source for an "A" level topic like this.

 

[PeterDonis]

The strong force can affect the dynamics or positions of particles. Only the weak force can't (not the positions).

What makes you think this?

 

[jlcd]

What makes you think this?

This thread is actually clarifications from a post you were discussing with Demystifier and someone called Electric to be (in two threads):

Post 1: "(One point that I have not raised is that the wave function is not the only "structure" present in QM; there is also the Hamiltonian, or Lagrangian if you are doing QFT. So one possibility that we have not discussed is that the "additional structure" is in the Hamiltonian, not the wave function; that the Hamiltonian of the cat, or the cat/environment system, is what picks out the alive/dead basis as the one that gets decohered.)"

Reference https://www.physicsforums.com/threads/irreversibility-vs-reversibility.909761/page-2#post-5734686

Post 2: "In QM the quantized Hamiltonian is still used to find the total energy in these situations It's the operator corresponding to the "energy" observable, yes. But this observable only measures the energy in the "system", i.e., the part that we are modeling using QM. It can't tell you anything about the part that we are not modeling using QM, i.e., the field. So if you consider the field as part of "the total system", then you would have to say that "the total system" is not completely modeled by QM in this case, so the "energy" you get from the QM operator is not the "total energy"."

Reference https://www.physicsforums.com/threads/hamiltonian-in-quantum-vs-classical.919627/page-2

In the second post, you stated how the "field" was not part of the QM hamiltonian. So if the additional structure is in the "field". Then it is not part of the Hamiltonian you were describing in post 1? If it's the field that is the source of the additional structure, then the right language is to say the Lagrangian of QFT couldbe the source of the additional structure that gives the preferred basis of unitary only dynamics?

 

[PeterDonis]

This thread is actually clarifications from a post you were discussing with Demystifier and someone called Electric to be (in two threads)

Ok. It would have been really, really helpful if you had said this and given the links in the first post in this thread. See below.

In the second post, you stated how the "field" was not part of the QM hamiltonian.

No, that's not what I said. I said that (in the particular model under discussion, which was non-relativistic QM using the Schrodinger Equation) the field was not part of the "system" whose energy is described by the Hamiltonian operator--i.e., the wave function. The field in that case is certainly part of the Hamiltonian, since it contributes to the potential energy that appears in that Hamiltonian. But that potential energy is the potential energy of the particle whose wave function the equation gives the dynamics for; it's not the potential energy of the field.

In other words, we have been going around in circles in this thread because your original motivation for starting it was that you had a simple misunderstanding of something I said in a post in a previous thread. That's why it would have been really helpful if you had linked to that post when you started this thread, so we could have figured all that out sooner.

Thread closed.