A Criteria for a good quantum interpretation

[Fra]

does this imply that QT can only be formulated using classical concepts?

Depends on if you talk about QM as it stands, then i would say yes. The way QM is constructed and empirically supported, it requires a classical context, and the quantum systems is a small subsystem "within it".

I agree this is a problem and not satisfactory and it begs the question. But I am trying to separate characterising and understanding the corroborated quantum theory, from trying to improve it (ie in the context of unification). The latter by definition shouldn't be discussed here unless its one of the mainstream ideas. Interpretations will not solve unification or unify it with GR. But interpretations may make certain unification hypothesis more or less natural and easy. But unfortunately I have never seem what the mwi, bohminan mechanics or other things has to offer for the unification, this is why i am not overly interested in them. But I am interested in how apparently different ideas sometimes find common junctions.

/Fredrik

 

[Demystifier]

Since in classical mechanics the system's phase-space variables always have a determined value, no matter whether you know them or not, upon measuring the before unknown value nothing happens to the system in an ideal measurement which is performed such that you can neglect the change of state of the system upon measurement. Of course, if you didn't know $(x,p)$ before the measurement and measure it, you just adapt your knowledge on the system making $\rho(x,p)=\delta(x-x_{\text{measured}}) \delta(p-p_{\text{measured}})$. This is simply an update adapting the probability distribution of deterministic observable to your knowledge after the measurement.

Fine, but if one assumes the statistical interpretation of QM, isn't it natural to interpret the word "statistical" analogously to the same word in classical statistical physics? In other words, if collapse is OK in classical statistical physics because it's just an update, then why an analogous interpretation of collapse is not OK in statistical interpretation of quantum physics?

I can understand that some interpretations of QM interpret collapse as update and some don't. But isn't it an irony that the statistical interpretation does not interpret collapse as update? At the very least, shouldn't this interpretation change its name?

 

[vanhees71]

The very distinction between classical and quantum physics we discuss all the time is that "statistical" means different things in classical and quantum physics. That's all what the entire EPR/Bell issue is about!

 

[Demystifier]

The very distinction between classical and quantum physics we discuss all the time is that "statistical" means different things in classical and quantum physics. That's all what the entire EPR/Bell issue is about!

OK, but what about mixed states? Does the word "statistical" in the context of mixed states in quantum statistical physics has the same meaning as "statistical" in classical physics? In other words, can we say that the true state of the system is always a pure state, while the mixed state just reflects our incomplete knowledge?

 

[vanhees71]

What should be with mixed states? If you have incomplete knowledge about a system you introduce statistics as in classical mechanics. It's statistics for quantum states. Of course they imply both "types" of probabilities.

A paradigmatic example is the preparation of a mixture in the gedanken experiment that you prepare a system in pure states $|\psi_k \rangle \langle \psi_k|$ randomly with probabilities $P_k$. Such a system is then described by the (proper) mixed state
$$\hat{\rho}=\sum_k P_k |\psi_k \rangle \langle \psi_k|.$$
The $P_k$ are of the type of classical probabilities, i.e., you know that the system is in one of the pure states $|\psi_k \rangle \langle \psi_k|$ but only probabilities for which one it is.

 

[Demystifier]

(proper) mixed state
$$\hat{\rho}=\sum_k P_k |\psi_k \rangle \langle \psi_k|.$$
The $P_k$ are of the type of classical probabilities, i.e., you know that the system is in one of the pure states $|\psi_k \rangle \langle \psi_k|$ but only probabilities for which one it is.

And how to interpret $P_k$ for the improper mixed state?

 

[vanhees71]

In imporper mixed state is a pure state. So I don't understand the question.

 

[Fra]

And how to interpret $P_k$ for the improper mixed state?

Can we label it an improper Heisenberg cut? And hence an improper observer.

Isn't this effectively the issues about open vs closed systems. A closed system, where you simlpy have a regular ignorance of the state, should always be a proper mixiture.

Improper mixture are associated to subsystems, which they of course are not closed. Improper mixturs in the subensemble also don't genereally evolve unitarily anyway, right?

But one can argue if there are ANY closed systems in nature? but this is a issue of the theory I think, not something solved by interpretations?

/Fredrik

 

[Demystifier]

In imporper mixed state is a pure state. So I don't understand the question.

Improper mixed state is not a pure state, but it is derived from a pure state. See e.g. page 22 of http://thphys.irb.hr/wiki/main/images/5/50/QFound3.pdf.

 

[Demystifier]

But one can argue if there are ANY closed systems in nature?

The whole universe?

More pragmatically, whenever the experiments on a subsystem are in agreement with a pure state description, we can say that approximately it is in the pure state.

 

[vanhees71]

Improper mixed state is not a pure state, but it is derived from a pure state. See e.g. page 22 of http://thphys.irb.hr/wiki/main/images/5/50/QFound3.pdf.

So you mean partial traces. Sure, if you deliberately coarse grain your description you usually end up in a mixed state, which is not surprising, because not completely determined states are described by mixed states. So even if the complete system is prepared in a complete way, i.e., in a pure state, the statistical properties of parts of it can be described by mixed states. That's particularly the case for entangled states.

Perhaps I should have simply said a non-pure state, i.e., a statistical operator such that $\hat{\rho}^2 \neq \hat{\rho}$.

 

[Fra]

The whole universe?

Yes, but then the problem is that the premise of QM is turn around. Instead of the "system" under inquiry is a small isolated subsystem in a classical environment where the observer capacity is dominant, the observer is a proper inside observer living inside the system its supposed to study. We effectively have quantum cosmology, and QM is not empirically validated for this. The procedure of a small inside observer, producing the ensembles of interactions required to establish a quantum state, seems to hit problems. Where the observer are forced to make lossy retention decisions. This is not something that is handled by QM.

This is incoherent IMO, and the reason why there is something wrong with QM. (Then I mean the theory, not the interpretation.

/Fredrik

 

[Demystifier]

Yes, but then the problem is that the premise of QM is turn around. Instead of the "system" under inquiry is a small isolated subsystem in a classical environment where the observer capacity is dominant, the observer is a proper inside observer living inside the system its supposed to study. We effectively have quantum cosmology, and QM is not empirically validated for this. The procedure of a small inside observer, producing the ensembles of interactions required to establish a quantum state, seems to hit problems. Where the observer are forced to make lossy retention decisions. This is not something that is handled by QM.

This is incoherent IMO, and the reason why there is something wrong with QM. (Then I mean the theory, not the interpretation.

/Fredrik

I'm not sure what do you mean by "theory, not the interpretation". If you mean a set of practical rules for making measurable predictions, then QM theory can deal with quantum cosmology. That's because, in practice, when you do cosmological observations you don't observe all microscopic details. E.g. you observe a galaxy (or a cluster of galaxies) but you don't observe every planet and every conscious observer on each planet.

 

[Fra]

To make a remote observation of a local quantum phenomoenon, such as nuclear reactions in a remote star, form Earth can be handle in a FAPP manner. As one can make classical remote indirect observations of temperature, glowing as or spectral lines. This is fine with me at least in the FAPP sense.

But with quantum cosmology I mean notion such as the wave function for the whole system (universe), how do you envision this ensemble? My point is not only practical problems, it seems its not even possible in principle for a small inside observer to colled and handle that amount of data. And if the argumentation of the soundness of reduced state and subsystems, where you toss the unitary evolution but think that the "TOTAL" system is still unitary, is not consistent logic in my mind.

So what I am trying to say is that, if we constrain our self to subatomic systems, in the way Vanhes seems to think? and do experiments and preparations, where the ensemble is defined, and you have one posterior state, where the prediction ends. In this view the "collapse" is terminal/final. The theory in its clean form, should not make statements about the state after that, unless its clarified. I find this part suspicious and the arguments for it, does involve considering effectively the whole quantum state of the universe. And IMO QM is not corroborated at this level. It is a pure mathematical extrapolation, and to me it is not conceptually sound.

/Fredrik

 

[Lord Jestocost]

Bohr has added an air of transcendence to quantum physics.

On the contrary! He explicitly warned against endless quibbling about ontological questions. As Bohr remarked:

“Physics is to be regarded not so much as the study of something a priori given, but rather as the development of methods of ordering and surveying human experience.” [bold by LJ]

 

[vanhees71]

Yes, but Bohr was the one making quantum theory pretty esoteric. He is topped by this only by Heisenberg and von Neumann ;-)). I never understood, why Bohr has been so dominant in establishing the interpretation instead of Born and particularly Dirac, where the foundations are presented much clearer. As Einstein adviced concerning theoretical physicists: "Don't listen to their words; look at their deeds."

 

[stevendaryl]

My opinion about interpretations of QM is that there are no good ones. I would distinguish between two different ways that an interpretation can be flawed:

1. Wrong.
2. Nonsensical.

I consider all collapse interpretations to be wrong, while I consider all non-collapse interpretations nonsensical.

(Actually, Bohmian mechanics is sort of an oddball here. It bears some similarity with non-collapse interpretations, but I consider it wrong, rather than nonsensical.)

 

[Lord Jestocost]

Yes, but Bohr was the one making quantum theory pretty esoteric.

With all due respect! In case you have nothing to comment on Bohr’s statement about physics, what the heck is the purpose of your comment?

 

[vanhees71]

Come on, show me one of Bohr's writings on the interpretational issues of quantum theory that's really understandable and to the point!

 

[stevendaryl]

Let me expand on why I think that interpretations of QM are either nonsensical or wrong.

Suppose I prepare an electron to be spin-up in the z-direction, and thereafter, nothing interacts with the electron. What is the probability that at a later time, the election has spin-up in the x-direction? It's a nonsensical question, because if nothing interacts with the electron, it will never be spin-up in the x-direction. It will continue to be spin-up in the z-direction forever.

So we change the question to: What is the probability that at a later time, I measure the electron to have spin-up in the x-direction? Then supposedly, that modified question is sensible, and has a simple answer: 50%. However, to say that "I measure the electron's spin in the x-direction" is to say that I set up some kind of apparatus that interacts with the electron such that if the electron had spin-up in the x-direction, the result would be that the apparatus would wind up in one state, the state of "having measured spin-up", and if the electron had spin-down in the x-direction, the apparatus would wind up in a different state, the state of "having measured spin-down". Furthermore, these two states have to be macroscopically distinguishable, so that I, the experimenter, can just read off which of the two states the apparatus is in.

But here's where the nonsensical or wrong conclusion comes in. Why does it make sense to ascribe probabilities to macroscopic results (whether the apparatus is in this or that macroscopically distinguishable state), but not to microscopic results (whether the electron is spin-up or spin-down in the x-direction, having been prepared to be spin-up in the z-direction)? It seems to me that either there is something fundamentally different about the macroscopic case (because of spontaneous collapse, or because consciousness is involved, or something), which I think is wrong, but not nonsensical, or they are not different in principle, just the macroscopic case is more complicated. If they are not different in principle, then it seems that either probabilities should apply in both cases, or they should apply in neither case.

The no-nonsense, pragmatic interpretation that I think most physicists ascribe to is actually nonsensical, in my opinion. They hold that probabilities do apply in the one case (macroscopic measurements) but not in the other (microscopic properties), but they also hold that there is no fundamental difference between the macroscopic and microscopic cases. That just seems nonsensical to me. If there is no fundamental difference, then why do probabilities apply in the one case and not the other?

Note: There is a similar conundrum in classical statistical mechanics. Concepts such as entropy don't make sense for a single particle, or even a collection of 3, 4, 5, or 20 different particles, but it makes sense for a macroscopic number of particles. It's possible that some explanation along those lines can also resolve the conundrum in quantum mechanics. But in classical statistical mechanics, the use of statistics is forced on us because in practice, we can't know the exact states of $10^{22}$ particles.

 

[PeterDonis]

Why does it make sense to ascribe probabilities to macroscopic results (whether the apparatus is in this or that macroscopically distinguishable state), but not to microscopic results (whether the electron is spin-up or spin-down in the x-direction, having been prepared to be spin-up in the z-direction)?

Because the process that produced the macroscopic result is irreversible, but a "microscopic result" (which basically means we just leave the system alone and work with whatever quantum state it was last prepared in) is not.

 

[stevendaryl]

Because the process that produced the macroscopic result is irreversible, but a "microscopic result" (which basically means we just leave the system alone and work with whatever quantum state it was last prepared in) is not.

But reversibility is a subjective thing. A collision involving 3 particles is reversible. A collision involving 100 particles is in principle reversible, but in practice, we treat it as irreversible.

I don't think it makes sense to make reversible/irreversible into a fundamental aspect of the theory when the microscopic interactions are all reversible.

 

[PeterDonis]

I don't think it makes sense to make reversible/irreversible into a fundamental aspect of the theory when the microscopic interactions are all reversible.

Perhaps not. But I don't think it's nonsensical to at least consider the possibility.

 

[Lord Jestocost]

... or they are not different in principle, just the macroscopic case is more complicated. If they are not different in principle, then it seems that either probabilities should apply in both cases, or they should apply in neither case.

The math shows that they are not different in principle. There is nothing more than a purely "quantum mechanical" von Neumann measurement chain.

 

[Lord Jestocost]

Come on, show me one of Bohr's writings on the interpretational issues of quantum theory that's really understandable and to the point!

I recommend to read Jan Faye's article "Copenhagen Interpretation of Quantum Mechanics" on the "Stanford Encyclopedia of Philosophy”. https://plato.stanford.edu/entries/qm-copenhagen/

In “‘B’ is for Bohr”, Ulrich Mohrhoff explains reasons why Bohr seems obscure to some – as I call it – matter-of-fact physicists:

„The second [reason] is that Bohr’s readers will usually not find in his writings what they expected to find, while they will find a number of things that they did not expect. What they expect is a take on the measurement problem, the so-called Heisenberg cut, the quantum-to-classical transition, locality, etc. What they find instead is discussions of philosophical issues such as the meaning of “objectivity,” of “reality,” of “truth,” the role of language etc. Bohr’s thinking is situated in a complex and diverse epistemological context that developed in Germany starting with Immanuel Kant. In this context, the fundamental problem was: how are phenomena given to us in intuition, and how do we build objects starting from what is given to us?”

 

[stevendaryl]

The math shows that they are not different in principle. There is nothing more than a purely "quantum mechanical" von Neumann measurement chain.

If there is no in-principle difference, then I don't see how we get from: "The electron is in a superposition of spin-up in the x-direction and spin-down in the x-direction" to "The measurement device is either in the state 'measured spin-up' or 'measured spin-down' with 50/50 probability of each."

Von Neumann explicitly put in a non-deterministic "collapse" that did not follow from Schrodinger's equation.

 

[stevendaryl]

Perhaps not. But I don't think it's nonsensical to at least consider the possibility.

I don't think it's nonsensical to believe that there is some difference in the macroscopic and microscopic situations, some effect (such as spontaneous collapse) that is negligible in the microscopic case. But I do think it's nonsensical to say that both that there are no in principle differences, and also that superpositions exist in the one case but not the other.

 

[vanhees71]

Let me expand on why I think that interpretations of QM are either nonsensical or wrong.

Suppose I prepare an electron to be spin-up in the z-direction, and thereafter, nothing interacts with the electron. What is the probability that at a later time, the election has spin-up in the x-direction? It's a nonsensical question, because if nothing interacts with the electron, it will never be spin-up in the x-direction. It will continue to be spin-up in the z-direction forever.

Let's just look at this statement. It's not what QT (the formalism) says. If you have prepared the electron to be in the state
$$\hat{\rho}=|\sigma_z=1/2 \rangle \langle \sigma_z=1/2|,$$
this tells you everything also about measurements on all other spin components. Particularly it tells you that the spin-x component is indetermined and what the probability is to find the one or the other possible outcome. It's of course
$$P(\sigma_x)=\langle \sigma_x|\hat{\rho}|\sigma_x \rangle=\frac{1}{2}, \quad \sigma_x \in \{1/2,-1/2\}.$$
There's no other meaning in the states than the probabilities for the outcomes of all possible measurements on that system (in this sense reduced to just the spin observables of an electron).

 

[vanhees71]

I don't think it's nonsensical to believe that there is some difference in the macroscopic and microscopic situations, some effect (such as spontaneous collapse) that is negligible in the microscopic case. But I do think it's nonsensical to say that both that there are no in principle differences, and also that superpositions exist in the one case but not the other.

Of course, but there's not the slightest hint to some "cut", i.e., that there are differences between "macro physical" and "micro physical" principle laws. To the contrary, the better the technical possibilities get the more the experimentalists can demonstrate "quantum properties" on macroscopic objects, e.g., the kg heavy mirrors of the gravitational LIGO/VIRGO detectors.

 

[Demystifier]

My opinion about interpretations of QM is that there are no good ones. I would distinguish between two different ways that an interpretation can be flawed:

1. Wrong.
2. Nonsensical.

I consider all collapse interpretations to be wrong, while I consider all non-collapse interpretations nonsensical.

(Actually, Bohmian mechanics is sort of an oddball here. It bears some similarity with non-collapse interpretations, but I consider it wrong, rather than nonsensical.)

Would you agree with the following? All realist interpretations are wrong, all non-realist interpretations are nonsensical. The realist interpretations (Bohm, GRW, many worlds, ...) are wrong because we don't know what is real and chances that our guesses are right are too slim. The non-realist interpretations (Copenhagen, QBism, statistical ensemble, relational, ...) are nonsensical because it does not make sense to think about things without imagining that they are real.