B What is the comparison between the Born rule and thermodynamics?

[Blue Scallop]

Wrong. There is decoherence, but you just can't use pure MWI to explain it. What I'm saying is that pure MWI is an incomplete theory.

I think what you are saying is for example, you have a three-particle entangled system and you measure just two of them the outcomes may not show any sign of interference (in other words, suffer decoherence), you have to measure all three at once to find the correlations that demonstrate interference.

If this is true. Why can't she accept it it's natural and has to propose the particles have to become randomized before there is even a decoherence?

 

[Demystifier]

you have a three-particle entangled system and you measure just two

The "you" which performs the measurement must also be described as a subsystem of quantum particles.

 

[A. Neumaier]

Perhaps, but I am really curious to see how do you think on that.

Well, whatever she answers is correct, as it is a question about subjective probability. Subjects do not need to act rationally.

 

[Demystifier]

Well, whatever she answers is correct, as it is a question about subjective probability. Subjects do not need to act rationally.

Again, I disagree.

 

[A. Neumaier]

When it comes to statistics and probability, I disagree with you almost always.

Again, I disagree.

Disagreeing doesn't make you correct.

 

[Blue Scallop]

The "you" which performs the measurement must also be described as a subsystem of quantum particles.

I'm trying to make what you are saying relate to Kastner paper.
You seemed to be saying that decoherence can occur even without phase randomization inside a subsystem.
Reading Kastner paper again. She talked about "einselection of pointer observable".

In a natural close quantum system in unitary dynamics without phase randomization.. can einselection of pointer observable occur naturally? She seemed to be saying not. How about you?

 

[Demystifier]

Disagreeing doesn't make you correct.

Disagreeing on such basic things makes me unmotivated to discuss more complicated things on probability in physics with you.

 

[Demystifier]

You seemed to be saying that decoherence can occur even without phase randomization inside a subsystem.

Yes.

In a natural close quantum system in unitary dynamics without phase randomization.. can einselection of pointer observable occur naturally? She seemed to be saying not. How about you?

I say yes, provided that one uses a better interpretation of QM (e.g. Bohmian).

 

[Blue Scallop]

Yes.I say yes, provided that one uses a better interpretation of QM (e.g. Bohmian).

Of course Bohmian can solve it because the pointer observable is automatically position.
But let's discuss pure MWI which is more challenging.. according to Zurek Einselection rough guide paper:

"We believe that the point of view based on decoherence settles many of the questions which were left
open by MWI and CI. This includes the origin of probabilities as well as the emergence of “objective
existence”, although more needs to be done.
In particular, one issue which has been often taken for granted is looming big, as a foundation of the
whole decoherence program. It is the question of what are the “systems” which play such a crucial role in
all the discussions of the emergent classicality. This issue was raised earlier,2,28 but the progress to date has
been slow at best. Moreover, replacing “systems” with, say, “coarse grainings” does not seem to help all
— we have at least tangible evidence of the objectivity of the existence of systems, while coarse-grainings
are completely “in the eye of the observer.”Do you have any idea what he meant replacing systems with coarse grainings?

Generally. In pure MWI, it's true systems can't even be defined? really? just confirming so I'd know it's not just the thoughts of Kastner or Zurek. Thanks.

 

[Demystifier]

In pure MWI, it's true systems can't even be defined?

Yes, that's what I think.

 

[Blue Scallop]

Yes, that's what I think.

But you said in pure unitarity, decoherence is possible.. isn't it that having system is related to decoherence.. so in pure unitarity, where there is decoherence, system is automatically defined...

or maybe it's about the preferred basis, but pure unitarity has system and basis.. unless you mean there is no basis in pure unitarity? really?

 

[Demystifier]

But you said in pure unitarity, decoherence is possible.. isn't it that having system is related to decoherence.. so in pure unitarity, where there is decoherence, system is automatically defined...

or maybe it's about the preferred basis, but pure unitarity has system and basis.. unless you mean there is no basis in pure unitarity? really?

What do you mean by "pure unitarity"?

 

[Blue Scallop]

What do you mean by "pure unitarity"?

pure unitarity = closed system in unitary (or unitarity) evolution

so does pure unitarity automatically have system?

But why did Zurek ask "It is the question of what are the “systems” which play such a crucial role in all the discussions of the emergent classicality"

Was he asking about the preferred basis or the mere existence of systems? If not what was he talking about (since a close quantum system in unitarity dynamics has systems in the first place)?

 

[Demystifier]

pure unitarity = closed system in unitary (or unitarity) evolution

so does pure unitarity automatically have system?

But why did Zurek ask "It is the question of what are the “systems” which play such a crucial role in all the discussions of the emergent classicality"

Was he asking about the preferred basis or the mere existence of systems? If not what was he talking about (since a close quantum system in unitarity dynamics has systems in the first place)?

It looks as you fail to distinguish a system from a subsystem.

 

[Blue Scallop]

It looks as you fail to distinguish a system from a subsystem.

Ah, you meant the system he was describing was the subsystem of the internal "system+environment" which are subystems for the systems. I know. So rephrasing, it think what he was asking was "It is the question of what are the “SUBsystems” which play such a crucial role in all the discussions of the emergent classicality". But in a close system with unitarity dynamics.. there is automatically a subsystem, right? Or do you need a preferred basis to have a subsystem?

 

[Demystifier]

Or do you need a preferred basis to have a subsystem?

Yes.

 

[Blue Scallop]

Yes.

But in a closed system with unitarity dynamics.. you said decoherence can occur inside.. but how can it have a subsystem when there is no preferred basis at all?

 

[Demystifier]

But in a closed system with unitarity dynamics.. you said decoherence can occur inside.. but how can it have a subsystem when there is no preferred basis at all?

I didn't say that there is no preferred basis at all. There isn't in MWI, but there is in Bohmian interpretation.

 

[Blue Scallop]

I didn't say that there is no preferred basis at all. There isn't in MWI, but there is in Bohmian interpretation.

You mean if there is no preferred basis.. there is no subsystem? Like the two are linked together?

 

[Demystifier]

You mean if there is no preferred basis.. there is no subsystem? Like the two are linked together?

Yes.

 

[Blue Scallop]

I didn't say that there is no preferred basis at all. There isn't in MWI, but there is in Bohmian interpretation.

About Bohmian, I have difficulty integrating consciousness to Bohmian mechanics. Can you write a paper relating Consciousness to Bohmian Mechanics to explore its conceptual plausibility? Why didn't you write such paper..

Say. Do you have any access to say a Raman Spectroscope? Neumaier too?

Anywhere you are in the planet, I (and a lot many others) can influence any molecular system on Earth that one can test with instruments. Other people I know can do this and extensively tested by the Chinese Academy of Science. I have spent 10 years trying to understand the physics of it.

I'm still undecided whether it's Bohmian, a MWI thing or Copenhagen or even a new force of nature. It's such a weary search.

Such difficulty is natural for every new stuff, it is hard in the beginning really.

 

[Demystifier]

Can you write a paper relating Consciousness to Bohmian Mechanics to explore its conceptual plausibility?

I can't write such a paper, but I have written this:
https://arxiv.org/abs/1112.2034

Why didn't you write such paper..

Because it would contradict what I wrote here:
http://philsci-archive.pitt.edu/12325/

 

[Blue Scallop]

I can't write such a paper, but I have written this:
https://arxiv.org/abs/1112.2034Because it would contradict what I wrote here:
http://philsci-archive.pitt.edu/12325/

I just read this. All I can say is that there are more things in the world than are dreamt of by most physicists.. and I can't continue describing it because it's against forum rule here. But you can read it in quality journals. Thanks anyway for stuff you shared in this thread which make many concepts more clear.

 

[PeterDonis]

there are more things in the world than are dreamt of by most physicists.. and I can't continue describing it because it's against forum rule here

Exactly. So please don't post about it. If you do so again, you will receive a warning.

 

[atyy]

The Born rule is about the probability $p$, not the average value. So the general Born rule is actually
$$p = \mathrm{Tr} (\rho \pi),$$
where $\pi=\pi^2$ is a projector.

In physics, probabilities and averages give the same information, so I accept vanhees71's definition of the Born rule.

 

[stevendaryl]

In physics, probabilities and averages give the same information, so I accept vanhees71's definition of the Born rule.

I was about to say that, but I wasn't sure that it's true. From probabilities you can compute averages, but I'm not sure about the other way around. For example, suppose that I tell you that \langle S_z \rangle = 0. That doesn't give me much information about probabilities of various values of S_z.

But maybe if for some observable A, I know \langle A^n \rangle for every n, does that uniquely determine the probability?

 

[atyy]

But maybe if for some observable A, I know \langle A^n \rangle for every n, does that uniquely determine the probability?

Yes, it's like Taylor series. For example, the cumulant expansion specifies a generating function or characteristic function, which is equivalent to specifying the probability distribution. The generating or characteristic function is analogous to the partition function of statistical physics and QFT.

This can fail, but I think such cases are not physical.

 

[A. Neumaier]

But maybe if for some observable A, I know \langle A^n \rangle for every n, does that uniquely determine the probability?

This is called the moment problem. Although correct under suitable additional conditions on the probability measure, it has a negative answer in general, i.e., the expectations of all powers of $A$ do not determine its probability distribution. For counterexamples see, e.g.,

J. Stoyanov, Inverse Gaussian distribution and the moment problem, J. Appl. Statist. Science 9 (1999), 61-71.
https://www.researchgate.net/publication/246535073

These counterexamples are not exotic as they include, for example, certain inverse Gaussian distributions.

 

[Blue Scallop]

I didn't say that there is no preferred basis at all. There isn't in MWI, but there is in Bohmian interpretation.

Demystifier, please clarify something.

Zurek summarized it:

Let us summarize our results for the environment-induced selection of preferred states and discuss the implications for the general preferred-basis-problem outlined in Sect. 2.5.2 and for our observation of only particular phyiscal quantities in the world around us.

System-environment interaction Hamiltonians frequency described a scattering process of surrounding particles (photons, air molecules, etc.) interacting with the system under study. Since the force laws describing such processes typically depend on some power of distance (such as @ r ^-2 in Newton's or Coulomb's force law), the interaction Hamiltonian will usually commute with the position operator. According to the commutativity requirement (2.89), the pointer states will therefore be approximate eigenstates of position. The fact that position is typically the determinate property of our experience can thus be explained by referring to the dependency of most interactions on distance.

Bill Hobba kept mentioning the above. For example Bill stated that:

The basis is chosen in theory ie the position basis is implicit in the normal form of the Schrodinger equation. When expressed in that basis virtually all interactions turn out to be radial ie the V(x) in the Schrodinger equation. Its purely arbitrary what basis you chose to write your equations in - writing them in the position basis is what's usually done and you can easily see their radial nature.

Now let's take your nutshell about MWI:

"In a nutshell, the argument is this:
To define separate worlds of MWI, one needs a preferred basis, which is an old well-known problem of MWI. In modern literature, one often finds the claim that the basis problem is solved by decoherence. What J-M Schwindt points out is that decoherence is not enough. Namely, decoherence solves the basis problem only if it is already known how to split the system into subsystems (typically, the measured system and the environment). But if the state in the Hilbert space is all what exists, then such a split is not unique. Therefore, MWI claiming that state in the Hilbert space is all what exists cannot resolve the basis problem, and thus cannot define separate worlds. Period! One needs some additional structure not present in the states of the Hilbert space themselves.

As reasonable possibilities for the additional structure, he mentions observers of the Copenhagen interpretation, particles of the Bohmian interpretation, and the possibility that quantum mechanics is not fundamental at all. "

My question:

Does the above mean that without preferred basis or additional structure, Bill stuff about the radial nature of interactions choosing position as the basis won't even occur?

Or is this radial thing (or interaction Hamiltonian within the pure MWI without preferred basis) a separate thing from the concept of additional preferred basis put in by hand?

 

[Demystifier]

Does the above mean that without preferred basis or additional structure, Bill stuff about the radial nature of interactions choosing position as the basis won't even occur?

Yes.

 

[Blue Scallop]

Yes.

But then according to Peterdonis, he suggested the interaction Hamiltonian (which can be where the Hobba radial argument was based) was independent of the preferred basis as when he wrote "(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.)"

What is your say about this Hamiltonian itself able to create subsystems without additional structure (prepared basis) put in by hand? Any counterarguments for his statements?

 

[Demystifier]

In physics, probabilities and averages give the same information, so I accept vanhees71's definition of the Born rule.

Consider a physical system in which the average value of position is $<x>=0$. What is the probability that the position is $x=1$ nm?

 

[Demystifier]

What is your say about this Hamiltonian itself able to create subsystems without additional structure (prepared basis) put in by hand? Any counterarguments for his statements?

For the sake of conceptual simplicity, consider a classical system (e.g. a planet) with a measured trajectory $x(t)$. And suppose that this trajectory can be explained theoretically by two different Hamiltonians. Without considering any other experiments/measurements, is it possible to determine which Hamiltonian is the correct one? It seems obvious to me that the answer is - no. Therefore, the Hamiltonian itself is not a physical object. Therefore it cannot define physical objects, including physical subsystems.

 

[vanhees71]

To reconstruct the probability distribution, you need all moments of it, the average is not enough. This has nothing to do with the foundations of QT. So please for get this irrelevant discussion of standard theorems of probability theory and take Born's rule to mean the probabilities for the outcome of measurements given the operator algebra of observables and the state in terms of the statistical operator.

 

[Blue Scallop]

For the sake of conceptual simplicity, consider a classical system (e.g. a planet) with a measured trajectory $x(t)$. And suppose that this trajectory can be explained theoretically by two different Hamiltonians. Without considering any other experiments/measurements, is it possible to determine which Hamiltonian is the correct one? It seems obvious to me that the answer is - no. Therefore, the Hamiltonian itself is not a physical object. Therefore it cannot define physical objects, including physical subsystems.

Hope Peterdonis can address this as it's his belief the state vector may be sufficient in itself to create the subsystems.

Anyway. What would happen if you use the Schroedinger equations without any implicit basis in the pure MWI (without any basis). Can the Schroedinger Equation still produce output with all nonorthogonal results? And what good would be this output?

And can you propose experiments more complex than the Stern-Gerlach setup to tell whether the state vector in MWI can or really can't produce a basis without additional structure. What efforts are being done in this department?

 

[Demystifier]

Anyway. What would happen if you use the Schroedinger equations without any implicit basis in the pure MWI (without any basis). Can the Schroedinger Equation still produce output with all nonorthogonal results? And what good would be this output?

One could get the spectrum of Hamiltonian.

And can you propose experiments more complex than the Stern-Gerlach setup to tell whether the state vector in MWI can or really can't produce a basis without additional structure.

I cannot.

 

[Blue Scallop]

One could get the spectrum of Hamiltonian.I cannot.

Theoretically if say you suddenly removed the position basis of an object let's say a post office postcard.. what would happen to the atoms and molecules inside.. would they become damaged like being exposed to fire where all atoms/molecules are rearrange permanently or destroyed??

And can you think of a theoretical way to save the information of position somewhere so that you can dematerialize the post office postcard.. and rematerialize it later with all positions intact?

 

[Demystifier]

Theoretically if say you suddenly removed the position basis of an object let's say a post office postcard.. what would happen to the atoms and molecules inside.. would they become damaged like being exposed to fire where all atoms/molecules are rearrange permanently or destroyed??

The question does not make much sense to me. What does it mean to remove the position basis of an object?

 

[Blue Scallop]

The question does not make much sense to me. What does it mean to remove the position basis of an object?

Simple.. to remove the position basis so the object would no longer have position.. or in terms of Bohmian Mechanics.. to remove position as preferred.. so it's like transforming the object into pure MWI vector or Hilbert space. Now if this occurs.. are the information of the arrangements of the molecules of the object still intact? Only they become pure Hilbert space vectors? and if you enable the position basis again.. would the information return or would the object become unrecognizable and become a mere blob because the nonorthogonal conversion to orthogonal is random hence the position information can't be stored and reread?

 

[Demystifier]

Simple.. to remove the position basis so the object would no longer have position.. or in terms of Bohmian Mechanics.. to remove position as preferred.. so it's like transforming the object into pure MWI vector or Hilbert space. Now if this occurs.. are the information of the arrangements of the molecules of the object still intact? Only they become pure Hilbert space vectors? and if you enable the position basis again.. would the information return or would the object become unrecognizable and become a mere blob because the nonorthogonal conversion to orthogonal is random hence the position information can't be stored and reread?

I think such a question can be meaningfully asked only by using mathematical equations.

 

[stevendaryl]

Consider a physical system in which the average value of position is $<x>=0$. What is the probability that the position is $x=1$ nm?

But if you also know \langle x^2 \rangle, \langle x^3 \rangle, ...?

 

[Blue Scallop]

I think such a question can be meaningfully asked only by using mathematical equations.

Ok, mathematically.. if we remove the position basis.. then there would be no decoherence and no subsystems if there are no other basis to define it. And it's back to pure Hilbert space vectors with unit trace 1.

So the question is.. what kind of information can be stored in the Hilbert space nonorthogonal states? How complex the information it can hold? Can they store a Barbie doll information? or nothing? just want to have idea...

 

[PeterDonis]

suppose that this trajectory can be explained theoretically by two different Hamiltonians

Is this possible? Can you give an actual example?

 

[atyy]

Consider a physical system in which the average value of position is $<x>=0$. What is the probability that the position is $x=1$ nm?

To be more conventional, one can use the term "expectation" in place of "average". Conceptually, there is no difference. You can see A. Neumaier's post #78 for the mathematical fine print.

 

[Demystifier]

Ok, mathematically.. if we remove the position basis.. then there would be no decoherence and no subsystems if there are no other basis to define it. And it's back to pure Hilbert space vectors with unit trace 1.

Yes.

 

[Demystifier]

Is this possible?

Yes.

Can you give an actual example?

Solution $x(t)=0$.
$$H_1=\frac{p^2}{2m}$$
$$H_2=\frac{p^2}{2m}+\frac{k x^2}{2}$$