# Smolin: Realistic and anti-realistic interpretations of QM

Can you point to a theorem proving a recurrence theorem in the quantum case?

Poincaré recurrence is for finite-dimensional bounded dynamical systems only. Already a single hydrogen atom violates both assumptions, let alone the universe.
I was just assuming it holds for the sake of @Auto-Didact's argument, and trying to argue that it's irrelevant as a way to rule out unitary QM holding exactly.

A. Neumaier
2019 Award
I was just assuming it holds for the sake of @Auto-Didact's argument, and trying to argue that it's irrelevant as a way to rule out unitary QM holding exactly.
The real problem with decoherence alone is that the standard axioms of QM provide no relationship at all between the state vector of the universe and the state vector of a subsystem. But experimental predictions are always made with fairly small subsystems of the universe

Why do you define the "measurement problem" this way?
The measurement problem is essentially why the Born rule (describing irreversible measurements) exists in addition to unitary evolution (describing reversible non-measurements).
I think most people consider it to be something different; it just needs to describe our universe. What unitary QM predicts, at least considering the other assumptions of Poincaré recurrence (maybe finite dimensionality) is that eventually recoherance will happen. You seem to be a priori ruling that out.
Not me, but orthodox QM. The theory of QM = unitary evolution AND the Born Rule; the fact that they BOTH lay claim to describing Nature is the entire problem with QM, because they are mathematically deeply inconsistent with each other. This just means that we cannot find (or it is impossible to find) a single particular theory from pure mathematics which can simultaneously naturally describe both concepts.

If QM was just unitary evolution, no one would even give QM foundations a second thought and vanhees would be completely correct in his criticism about discussing QM foundations.
Can you point to a theorem proving a recurrence theorem in the quantum case?
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.18.2379The proof is a single page.

A. Neumaier
2019 Award
The theory of QM = unitary evolution AND the Born Rule; the fact that they BOTH lay claim to describing Nature is the entire problem with QM, because they are mathematically deeply inconsistent with each other.
I don't see any direct inconsistency. unitary evolution is claimed for an isolated system only, and the Born rule for a measurement only (during which the system measured is surely not isolated).
Can you point to a theorem proving a recurrence theorem in the quantum case?

Poincaré recurrence is for finite-dimensional bounded dynamical systems only. Already a single hydrogen atom violates both assumptions, let alone the universe.
This proof assumes a Hamiltonian with discrete spectrum, which is a very special situation.
No molecules, no quantum fields - not a good model for the universe....

Even for a Hamiltonian with discrete spectrum, recurrence in the 2-norm (which is proved in the paper quoted) says very little - e.g., it says nothing about how close the mean position of a particle comes to the initial mean position.

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vanhees71
I don't see any direct inconsistency. unitary evolution is claimed for an isolated system only, and the Born rule for a measurement only (during which the system measured is surely not isolated).
The reason you aren't seeing an inconsistency is because you are carefully seperating out two aspects as two idealizeable systems; isn't the universe as a whole is an isolated system?

From the perspective of a mathematical physics basing itself upon the theory of complex analysis, QM - i.e. unitary evolution and the Born rule - as a mathematical model is as inconsistent as it gets; this is because unitary evolution is a completely holomorphic notion, while the Born rule involves complex conjugation, i.e. is distinctly non-holomorphic.
This proof assumes a Hamiltonian with discrete spectrum, which is a very special situation.
Smolin (or more accurately his book) is my source for the argument of quantum Poincaré recurrence. I can argue for or against discrete spectra or whether or not he was referring to the universe as a quantum system peri-Big Bang, but I suggest you take it up with him.

A. Neumaier
2019 Award
you are carefully seperating out two aspects as two idealizeable systems
But it is well-known that these are two idealizations; general (possibly dissipative) quantum mechanics is governed by other equations, those of Lindblad type!
isn't the universe as a whole is an isolated system?
Yes; strictly speaking, it is the only isolated system containing us!
QM - i.e. unitary evolution and the Born rule - as a mathematical model is as inconsistent as it gets
Not more than conservative and dissipative differential equations. But there is no inconsistency since they model different aspects of a dynamical system.
Smolin (or more accurately his book) is my source for the argument of quantum Poincaré recurrence.
No matter whose argument it is, it is meaningless for the real universe. Anything displaying macroscopic motion, be it an electric current in a wire, the Moon orbiting the Earth, light coming from a distant star, or the universe as a whole, requires a Hamiltonian with a partly continuous spectrum.

vanhees71
bhobba
Mentor
This is anti-realist in the sense above because your interpretation does not treat the observer as a physical system subject to the same mathematical treatment/physical theory as the world he observes, eg your observer is not a factor of a tensor product Hilbert space.
That issue is gradually being resolved:
You will also find people, some that post here, (I or Vanhees are not amongst them) that think QM may not even involve the common-sense concept of 'reality'. It is actually a difficult thing to pin down.

Thanks
Bill

vanhees71
But it is well-known that these are two idealizations; general (possibly dissipative) quantum mechanics is governed by other equations, those of Lindblad type!
That's not the point in speaking about idealization; instead the point is whether the seperate solutions for these idealizations carry over into the practical unideal case where they are not treated seperately.
Not more than conservative and dissipative differential equations. But there is no inconsistency since they model different aspects of a dynamical system.
Not so much different aspects of different systems, but different 'phases' of the same system, namely the 'being measured'-phase and the 'not being measured'-phase.

A. Neumaier
2019 Award
into the practical unideal case where they are not treated separately.
In practical cases they are always treated separately; people in their right mind never apply both. They know when to apply which idealization and when neither works. Confounding the two cases is a sure sign of insufficient understanding.

The measurement problem is not about the conflict of the two idealizations but about how to derive the rule for handling a subsystem measured inside an isolated system. If everything is known about the isolated system, everything about the subsystem should follow. (This is one of the key points in my critique of the wave function as basic object in QM, given in my recent paper Part I.) Hence such a derivation should exist. In the thermal interpretation it does.

In practical cases they are always treated separately; people in their right mind never apply both. They know when to apply which idealization and when neither works. Confounding the two cases is a sure sign of insufficient understanding.
You misunderstand; the point is not to apply both simultaneously, but to give a single mathematical expression which can describe both sequentially, using a single mathematical concept i.e. a single branch from pure mathematics. Everything else - especially seperating and treating each using idealizations i.e. approximative schemes - is just fluff.

A. Neumaier
2019 Award
You misunderstand; the point is not to apply both simultaneously, but to give a single mathematical expression which can describe both sequentially,
Why should that be needed? No subsystem of the universe is isolated, hence the latter need not be described by precisely the same mathematical concept as the former.
using a single mathematical concept i.e. a single branch from pure mathematics.
The piecewise deterministic processes (PDP) of Breuer and Petruccione discussed in Subsection 5.1 of Part III of my series of papers do precisely that.

Auto-Didact
Why should that be needed?
Because all of physics and all of applied mathematics have ultimately been capable of giving such descriptions, QM being the sole exception so far; to give up on this is to give up on the original goal of mathematical physics.

As I posted before in #89, during much of the 18th and 19th century mathematicians and physicists struggled with a similar problem in fluid mechanics, which was ultimately resolved when boundary layers were discovered; dynamical collapse models are the analogue of this for QM.
The piecewise deterministic processes (PDP) of Breuer and Petruccione discussed in Subsection 5.1 of Part III of my series of papers do precisely that.
I'm looking forward to that part. But first things first: Game of Thrones!

samalkhaiat
Again, just because you don't find fundamental physics important,
How very charming of you! Fundamental physics is not important to me?? Mister, it is very important to me because I make my living doing fundamental physics. Fundamental physics (as opposed to philosophical gibberish) is a mathematical structure with testable predictions. If you can’t translate your sentences to meaning-full mathematical statements (which I’m sure you can’t), then what you say is just philosophical gibberish having nothing to do with fundamental physics (my job).

vanhees71 and weirdoguy
samalkhaiat
Well, I think you are right. I shouldn't waste my time anymore to discuss philosophical issues in this forum. It's kind of fighting against religious beliefs rather than having a constructive scientific discussion.
It is even worst. When there is only one philosopher, he throws at you terms such as Platonist and Realist. If you bring in another one, you have it: modern realist; post-modern realist; neo realist; “far-right” realist; etc. And with few more philosophers, the realist spectrum may become the entire real line $\mathbb{R}$. As long as they keep their “classification” for themselves, I am not bothered because what they say about “reality” is not physics.

I (as a physicist) don’t require that a theory correspond to “reality” because I don’t know what reality is. Stephen Hawking once said: “Reality is not a quality you can test with litmus paper”. A physical theory is nothing but a mathematical structure with predictive power. So, it is meaningless to ask whether it corresponds to “reality”. All that we can ask is that its predictions should be in agreement with the experimental results. QM does this extremely good.

“Roger is worried about Schrodinger’s poor cat. Such a thought experiment would not be politically correct nowadays. Roger is concerned because a density matrix that has $| \mbox{cat alive}\rangle$ and $|\mbox{cat dead} \rangle$ with equal probabilities also has $|\mbox{cat alive} \rangle + |\mbox{cat dead}\rangle$ and $|\mbox{cat alive}\rangle – |\mbox{cat dead}\rangle$ with equal probabilities. So why do we observe either $\mbox{cat alive}$ or $\mbox{cat dead}$? Why don’t we observe either $\mbox{cat alive} + \mbox{cat dead}$ or $\mbox{cat alive} - \mbox{cat dead}$? What is it that picks the alive and dead axes for our observations rather than alive + dead and alive - dead. The first point I would make is that one gets this ambiguity in the eigenstates of the density matrix only when the eigenvalues are exactly equal. If the probabilities of being alive or dead were slightly different, there would be no ambiguity in the eigenstates. One basis would be distinguished by being eigenvectors of the density matrix. So why does nature choose to make the density matrix diagonal in the alive/dead basis rather than in the alive + dead / alive – dead basis? The answer is that the $|\mbox{cat alive}\rangle$ and $|\mbox{cat dead}\rangle$ states differ on a macroscopic level by things like the position of the bullet or the wound on the cat. When you trace out over the things you don’t observe, like the disturbance in the air molecules, the matrix element of any observable between $|\mbox{cat alive}\rangle$ and $|\mbox{cat dead}\rangle$ states average out to zero. This is why one observes the cat either dead or alive and not a linear combination of the two. This is just ordinary quantum mechanics. One doesn’t need a new theory of measurement, and one certainly doesn’t need quantum gravity”
S. Hawking in “The Nature of Space and Time”.

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bhobba, vanhees71, Mentz114 and 2 others
stevendaryl
Staff Emeritus