Insights The Fundamental Difference in Interpretations of Quantum Mechanics - Comments

[PeterDonis]

Greg Bernhardt submitted a new PF Insights post

The Fundamental Difference in [URL="https://www.physicsforums.com/insights/fundamental-difference-interpretations-quantum-mechanics/"]Interpretations of Quantum Mechanics[/url]

Continue reading the Original PF Insights Post.

 

[Buzz Bloom]

Hi Peter:

I very much like the clarity of the dichotomy you present.

Sometimes I find myself comfortably accepting either of the two points of view at different times. The particular choice I make depends on my recognizing that the context makes one choice more convenient than the other. When I think about my practice of doing this, I interpret this as actually accepting both points of view at the same time, and when I do that I just ignore the apparent contradictions. I summarize this practice with the maxim:

Reality is fundamentally paradoxical.​

Regards,
Buzz

 

[lightarrow]

Peter, when you write "physically real", do you refer to which definition of it?

--
lightarrow

 

[PeterDonis]

when you write "physically real", do you refer to which definition of it?

There is no precise definition of the term "physically real". That's part of what makes discussions of QM interpretations difficult: one is trying to go beyond the basic model of QM, which is expressed in math and has precise definitions, to interpretations that use ordinary language, where words do not have precise definitions.

 

[microsansfil]

Hi,

Nice article that shows a facet of epistemic (#1)/ontological (#2) duality. My understanding (and thus my point of view) is that the observer (humain being, measurements apparatus) interact with something that resist to us ("real in itself"), but can only capture the interaction effects and not the causes.

To buid a rational and complet interpretation, it seems to me that we need to dissect how we construct our knowledge from the effects we capture up to ours objectifications and taking in acount all the humain process from ours first-person experience. Moreover It could be relevant to be aware of our blind spot when we made ours objectivations/reifications.Patrick

 

[lightarrow]

There is no precise definition of the term "physically real". That's part of what makes discussions of QM interpretations difficult: one is trying to go beyond the basic model of QM, which is expressed in math and has precise definitions, to interpretations that use ordinary language, where words do not have precise definitions.

Ok, and do you think that term, "physically real" refers only to physical quantities as position, momentum, spin components, etc, or even to something else? For example could I pretend that "physically real" is the "setting of the experiment" if it's prepared in a specific and reproducible way?
To which of the 2 "paradigms" you describes belongs this vision?
Thanks.

--
lightarrow

 

[eltodesukane]

What are the Interpretations of Classical Mechanics ?

 

[A. Neumaier]

What are the Interpretations of Classical Mechanics ?

The book by Laurence Sklar, Physics and Chance, discusses the philosophy of classical mechanics. But the subject has fallen out of fashion since it is known that classical mechanics fails completely in the subatomic domain.

 

[PeterDonis]

do you think that term, "physically real" refers only to physical quantities as position, momentum, spin components, etc, or even to something else?

Please read what I said in the article: I said that viewpoint #2 says that the quantum state is "physically real". In other words, the wave function/state vector/whatever you want to call it, a particular well-defined thing in the math, represents something "physically real". The quantum state is not position, momentum, spin components, etc. It's the particular well-defined thing in the math.

 

[Ian J Miller]

In my opinion, part of the reason there is such scope for interpretations is that nobody actually KNOWS what Ψ means. Either there is an actual wave of there is not, and here we have the first room for debate. If there is, how come nobody can find it, and if there is not, how come a stream of particles reproduce a diffraction pattern in the two slit experiment? No matter which option you try, somewhere there is a dead rat to swallow. As it happens, I have my own interpretation which differs from others in two ways after you assume there is an actual wave. The first, the phase exp(2πiS/h) becomes real when S = h (or h/2) - from Euler. This is why electrons pair in an energy well, despite repelling each other. Since it becomes real at the antinode, I add the premise that the expectation values of variables can be obtained there. The second is that if there is a wave, the wave front has to arrive at the two slits about the same time as the particle. If so, the wave must transmit energy (which waves generally do, but the dead rat here is where is this extra energy? However, it is better than Bohm's quantum potential because it has a specific value.) The Uncertainty Principle and Exclusion Principle follow readily, as does why the electron does not radiate its way to the nucleus. The value in this, from my point of view, is it makes the calculation of things like the chemical bond so much easier - the hydrogen molecule becomes almost mental arithmetic, although things get more complicated as the number of electrons increase. Nevertheless, the equations for Sb2 gave an energy within about 2 kJ/mol, which is not bad.

 

[Stephen Tashi]

There is no precise definition of the term "physically real".

True, but your article inherits an imprecise meaning directly from imprecision of "physically real". It would be unreasonable to expect any commentary on interpretations of QM to be free of all ambiguity, but in order to get the "general drift" of what you are saying it would be helpful to have examples of how , in your opinion, different concepts of the reality of the wave function lead to well-known interpretations of QM.Even if we cannot precisely define "physically real" to the extent of proposing a physical test for it or a mathematical definition, it may be possible to agree on certain properties of "physically real" things. For example, thinking in terms of mathematics, if I grant that X and Y are physically real aspects of something then should I also say that any function f(X,Y) is also physically real? One would suspect the answer is "No". A tricky mathematician would have us consider the constant function f(X,Y) = 13. So perhaps the mathematical property of a physically real f(X,Y) should be that we can reconstruct the values of X and Y given the value of f(X,Y) or , more generally that we can reconstruct the values of X and Y from a given value f(X,Y) and values of some other functions of X and Y.

(Some people might want to add a third answer: the state describes an ensemble of a large number of similar systems, rather than a single system. For purposes of this discussion, I am considering this to be equivalent to answer #1, because the state does not describe the physically real state of a single system.)

I don't understand that passage. For example, is the fact that a person is a resident of the state of Texas a physically real property of that person? Isn't belonging to the ensemble of Texans a real property of that single person? Would we define a physically real property of a person to be sufficient information to distinguish a unique person?

 

[PeterDonis]

it would be helpful to have examples of how , in your opinion, different concepts of the reality of the wave function lead to well-known interpretations of QM.

I thought cases 1 and 2 in the article already described that, but I'll give it another shot.

Case 1 says the state is not real; it's just a description of our knowledge of the system, in the same sense that, for example, saying that a coin has a 50-50 chance of coming up heads or tails describes our knowledge of the system--the coin itself isn't a 50-50 mixture of anything, nor is what happens when we flip it, it's just that we don't know--we can't predict--how it is going to land, we can only describe probabilities.

Case 2 says the state is real, in the same sense that, for example, a 3-vector describing the position of an object in Newtonian physics is real: it describes the actual position of the actual object.

 

[Dr. Courtney]

I focus more on predictions than "interpretations."

One could have differing interpretations of Lagrangian, Hamiltonian, and Newtonian Mechanics (and I've met physicists who do argue one is right and the other two are "wrong"). However, all the predictions are the same.

The only interesting cases are where differing interpretations make different testable predictions. This is real science. Then we can perform an experiment to distinguish between them.

 

[Fra]

The only interesting cases are where differing interpretations make different testable predictions.

This is also my position, and in particular to understand how the choice of interpretation"implies" a certain research direction in the open questions, or even WHICH the open question are, such as unification of interactions. Then if a certain interpretations shows to provide a more fruitful "angle" to making progress, then that would be my "preferred" interpretation.

Lets note that this is a DIFFERENT selection strategy than those that think we need no modification to current theories, and that the preferred interpretation thus is some kind of "minimalist one". I fully agree that the minimalist selection principle makes sense if the interpretation served only the purposes of decreasing angst over understanding or not understanding the foundations..

/Fredrik

 

[Fra]

There is no precise definition of the term "physically real". That's part of what makes discussions of QM interpretations difficult: one is trying to go beyond the basic model of QM, which is expressed in math and has precise definitions, to interpretations that use ordinary language, where words do not have precise definitions.

I often feel that the descriptor "real", would be better replaced in these discussions with "objective", or observer invariant.

Thus real would mean, that different observers should arrive at a consistent descriptions of the same system. And then it begs the question of explaining how does one make this "consistency check"? This is a bit like trying to compare angles of vectors living at different tangent planes or so. You need some kind fo "parallell transport".

As I see it, the consistency check is that the two systems making the inferences must physically interact/communicate. If they can do this without distorting the opinion of the other party, then they are consistent, and they have reached a consensus. And in many cases where there is an "apparent" disagreement, this is often identifed as an interaction term or force between the observers! And accounting for this, one can add some new interactions and recover a new elevated level of objectivity. This is also typically the situation that works fine in classical mechanics. And while we have observers also in classical mechanics, the fact that they typically easily reach a consensus of observations, is why the observations rarely are emphasised as of fundamental importance.

So unless we can define the interaction that constitutes the consistency check, the notion of "real" is not only slightly ambigous, it seems too undefined to be recommended.

/Fredrik

 

[Stephen Tashi]

I thought cases 1 and 2 in the article already described that, but I'll give it another shot.

What I'm suggesting is that your give examples of the thesis of your article - that the two cases naturally divide the various interpretations- e.g. perhaps Case 2 leads to the Many Worlds or the Bohmian interpretation etc.

Case 1 says the state is not real; it's just a description of our knowledge of the system, in the same sense that, for example, saying that a coin has a 50-50 chance of coming up heads or tails describes our knowledge of the system--the coin itself isn't a 50-50 mixture of anything, nor is what happens when we flip it, it's just that we don't know--we can't predict--how it is going to land, we can only describe probabilities.

Parsing that definition seems to hinge on whether probabilities are "real". In your definition, must a physically real state be sufficient to produce a deterministic outcome ?

Case 2 says the state is real, in the same sense that, for example, a 3-vector describing the position of an object in Newtonian physics is real: it describes the actual position of the actual object.

What aspect of that example is significant?

One feature of that example is that if point particle_1 has the same 3-vector as point particle_2 then particle_1 and particle_2 are the same particle. By contrast, if we are only given that particle_1 and particle_2 are both in a laboratory in Texas then, from that description, the names might refer to different particles.

Another aspect of that example is that we can measure the 3-vector associated with a particle. However, we could also determine whether a particle is in a laboratory in Texas, so the ability to measure the 3-vector seems not to be the outstanding feature of the example.

 

[PeterDonis]

I often feel that the descriptor "real", would be better replaced in these discussions with "objective", or observer invariant.

Perhaps, but that would fail to acknowledge the fundamental difference in interpretations which was the main topic of the article. I think all interpretations agree that the quantum state/wave function is observer invariant; that's not where the difference lies.

 

[PeterDonis]

What I'm suggesting is that your give examples of the thesis of your article - that the two cases naturally divide the various interpretations- e.g. perhaps Case 2 leads to the Many Worlds or the Bohmian interpretation etc.

Ah, ok. If you want a quick categorization of some common interpretations, here it is:

Case 1: Copenhagen, ensemble

Case 2: Many worlds, Bohmian*

* - the Bohmian interpretation is kind of a special case, because it contains nonlocal hidden variables: the actual particle positions. The standard Bohmian interpretation considers these to be in principle unobservable, but it also considers the wave function--the "quantum potential"--to be real, which is why I put it in case 2.

But one could easily envision an extended Bohmian interpretation in which they were observable. This would amount to a new theory extending QM and making testable predictions that could distinguish it from standard QM, which would take it out of the topic area discussed in the article. Similar remarks apply to things like the GRW model, which adds an additional "objective collapse" process that makes different testable predictions from standard QM.

 

[PeterDonis]

Parsing that definition seems to hinge on whether probabilities are "real".

Sure, that's why I said we're dealing with vague ordinary language. I'm not trying to put a specific definition on the word "real". I'm just trying to say that, as far as I can tell, people who espouse Case 1 interpretations consider the quantum state to be like probabilities, and in common ordinary language usage probabilities do not describe the physically real state of anything; they just describe our knowledge (or the limitations thereof). If it helps, substitute "case 1 says the quantum state is like probabilities" for "case 1 says the quantum state is not real".

In your definition, must a physically real state be sufficient to produce a deterministic outcome ?

Case 2 interpretations of QM do not say a physically real state produces a deterministic outcome (that would contradict standard QM); they just say the quantum state is physically real. So I don't see how this helps to clarify anything relevant to this discussion.

What aspect of that example is significant?

Just what I said: case 2 interpretations treat the quantum state vector similarly to the way Newtonian physics treats the position 3-vector of a particle: it describes the physically real state of something.

I think you're making this more difficult that it needs to be. I'm not trying to be abstruse.

 

[Auto-Didact]

I am somewhat surprised this thread is allowed at all, since interpretations of QM is purely a philosophy of science/physics topic. This side discussion about the imprecision of language is a red herring, since there are already certain words in philosophy which have specified meanings to make clear distinctions, for example, physical is such a word. As was said before in post 5, the main distinction between interpretations of QM is precisely whether or not the state is itself ontic or epistemic; everything else (e.g. whether or not it is determistic or stochastic) is independent with regard to the ontic/epistemic distinction.

Moreover, some 'interpretations' of QM, in particular the collapse ones, are clearly not interpretations but incomplete extensions to or revisions of QM, i.e. alternative theories awaiting mathematical completion. It is here most clearly that philosophers of physics, i.e. physicists and other scientists focusing on these philosophical themes of their discipline by extending theories and placing extensions and alternative hypotheses in proper context, have contributed more to this aspect of physics than regular physicists have done so far.

This is an essential aspect of science which does not nearly get enough attention, mostly because in the practice of physics we don’t often explicitly run into such difficulties (implicitly is a whole different story) and therefore don't see the need for philosophical expertise. When we do however run into these difficulties, this kind of philosophical reevaluation of some theory is the correct method to take that actually can point the way forward. It is somewhat a matter of luck that in the early 20th, both Einstein and the founders of QM acknowledged this and so could end up discarding and reformulating core traditional principles of physics and so end up creating the correct mathematical formulations thereof, which we today refer to as relativity and QM.

Today we are somewhat priviliged that the philosophers of physics have already simplified and classified the different interpretations and also given instructions on how to proceed. It is tragic that not many physicists have been willing to listen. In any case, the only way physicists can do more in advancing our understanding of QM deeper than what the philosophers of physics have done so far, is by actually creating new mathematical theories based on or incorporating those ideas from first principle, with hopefully one of the resulting mathematical theories being self-consistent and simultaneously not being trivially equivalent to QM itself.

The collapse theories tend to be of this variety, but their dynamical formulations to this day remain mathematically incomplete. Somewhat unfortunate is that the domain of physics concerned with critical phenomenon, of which the mathematical theory is very much a theory of principle, has become somewhat directly associated with condensed matter physics, which is itself a collection of constructive theories. This is unfortunate because the mathematical methods required by the theoreticians to derive these theories from first principles are precisely the mathematical methods taught to condensed matter physicists except in a very different context and with a completely different purpose.

 

[meopemuk]

Peter,

thank you for condensing this debate to two simple alternatives. I think, following Einstein and Bohr, we can make this dilemma even simpler. The question is: "Does God really play dice?"

If your answer is "no", then you have to complain

... it implies that QM must be an incomplete theory; there ought to be some more complete description of the system that fills in the gaps and allows us to do better than merely probabilistic predictions.

But if you are OK with God playing dice, then there is nothing wrong with the probabilistic behavior of Nature. All these quantum events are simply unpredictable. So, existing quantum mechanics does a good job at describing this unpredictability. If somebody asks you why the electron hit this particular place on the screen, you can simply reply: "I don't know and don't care. It was just random."

I think, with this thought all of us should rejoice: we finally came to a satisfying end of the scientific quest (at least in this particular direction). We don't have to keep unraveling the never-ending chain of cause-and-effect relationships. Because we came to the class of quantum events, which don't have causes, since they are truly random. Congratulations everyone!

Eugene.

 

[bhobba]

In my opinion, part of the reason there is such scope for interpretations is that nobody actually KNOWS what Ψ means.

That's not quite true.

I would become acquainted with Gleasons Theorem:
https://en.wikipedia.org/wiki/Gleason's_theorem

At a rigorous mathematical level:
file:///D:/Users/Owner/Downloads/Gleasonexplained.pdf

Or the version I came up with (its the same as in the above but I worked hard to spell each step out - see post 137):
https://www.physicsforums.com/threads/the-born-rule-in-many-worlds.763139/page-7

I will post my view on the reason for different interpretations in a minute. Of course it in no way changes the excellent article Peter wrote - just a different view.

Thanks
Bill

 

[DennisN]

Nice article, Peter Donis!

I've recently developed a new interpretation, MII, the Many Interpretations Interpretation.
It's incredibly simple, only two postulates, and it is guaranteed to satisfy every physicist;

1. The system exists in a superposition of interpretations.
2. When the system is observed, it collapses into the interpretation most favored by the experimenter.

An added benefit is that this interpretation explains why there are so many different interpretations (due to different people), but it fails to explain why we get a particular interpretation for a particular person.

 

[bhobba]

Nice article Peter.

Ok - what do I think about interpretations?

Well first I think everyone should know a couple - they all shed light of the formalism.

But what do we have then - what exactly is the central mystery of QM. I don't think it's that it's probabilistic - Einstein for example despite his famous quote - didn't really have a problem with that - he just thought it evidence it was incomplete like statistical mechanics is incomplete without knowing its underlying basis - classical mechanics. He even came up with his own interpretation - the Ensemble - to make that idea clearer. The real issue boils down IMHO to two things.

1. Simply a carry over of the arguments some have about the meaning of probability:
http://math.ucr.edu/home/baez/bayes.html

Einstein hated subjectivity coming into physics and rebelled against Copenhagen because it took a more subjective view - that's another reason he came up came up with his Ensemble Interpretation:
https://en.wikipedia.org/wiki/Ensemble_interpretation

Here his issue with QM is clearly laid out - how is the observation selected from the ensemble - he deliberately chose that name because its widely used in statistical mechanics and wanted to pinpoint clearly the issue - we know why in statistical mechanics - we need to also know why in QM. Einstein had zero issue with as a practical matter it was probabilistic - after all he made fundamental contributions to statistical mechanics himself and had no issue with it there. He simply thought - there must be something behind why is it we can only use probabilities.

2. The issue is gone into quite deeply by Schlosshauer:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

Here he pinpoints what he thinks is the central issue - its how an improper mixed state becomes a proper one. It, at a more technical level is just a variation on how is the result selected from the ensemble.

There are all sorts of answers depending on the interpretation:

1. Many Worlds. Nothing is selected - they all happen - but in separate worlds.
2. Who cares - science always assumes things - this is just another assumption - you don't like that particular assumption ie it somehow becomes a proper mixed state then its simply your issue - nature is as nature is.
3. Bohmian Mechanics. The result exists before observation because everything is objectively real.
4, Decoherent Histories. Reformulate the problem in a different way as the stochastic theory of histories (a history is simply a sequence of projection operators) - its like Many Worlds without the Many Worlds.
5. Nelsons Stochastic's - at a level we can't experimentally reach yet - or maybe never will be able to - there are stochastic processes similar to statistical mechanics.

Tons of others.

I hold to 2 - but some are not satisfied with that. That's the key issue IMHO.

Thanks
Bill

 

[bhobba]

To buid a rational and complet interpretation, it seems to me that we need to dissect how we construct our knowledge from the effects we capture up to ours objectifications and taking in acount all the humain process from ours first-person experience. Moreover It could be relevant to be aware of our blind spot when we made ours objectivations/reifications.

I think we have many rational and compete interpretations - that's the issue. Which do you pick?

My view is it doesn't really matter - I have picked one - but really who cares. As a practical matter it's wise to know at least a couple - they all shed light on the formalism. For example, naively, and you will find it even in some textbooks, you may think QM has collapse - it doesn't - as many worlds proves. To understand it you have to go back to the actual axioms of QM as found in a good source like Ballentine - there you will see nothing at all about collapse - its simply part of some interpretations. That's the real value of this interpretation stuff IMHO.

Thanks
Bill

 

[bhobba]

I think, following Einstein and Bohr, we can make this dilemma even simpler. The question is: "Does God really play dice?"

I know where you are coming from - but I would express it slightly differently - but that difference IMHO is crucial.

That god played dice with the universe didn't really worry him - despite the famous quote. After all, as I mentioned previously he made foundational contributions to statistical mechanics. Einstein thought there was a reason why God payed dice - like there is in statistical mechanics. In his view this was evidence it was incomplete - which is what he thought to his dying day. And indeed it is incomplete eg we don't have a theory of Quantum Gravity below the Plank Scale. Einstein wanted to know what God thought when he made the world - he simply thought it went beyond just probabilities. It's just a conviction he had about the world. He may even be correct - who knows what we may uncover when a complete theory of Quantum Gravity is finally arrived at.

Thanks
Bill

 

[Auto-Didact]

Here he pinpoints what he thinks is the central issue - its how an improper mixed state becomes a proper one. It, at a more technical level is just a variation on how is the result selected from the ensemble.

Exactly. This stochastic selection of the state from the ensemble which occurs during a measurement is precisely what makes QM a mathematically inconsistent theory consisting of deterministic unitary evolution and a stochastic non-unitary reduction. The former is the orthodox viewpoint of QM theoreticians.
The latter is not used to mathematically derive the theory as the former is, but is instead empirically seen and thus tacked on next to the mathematical derivation as phenomenology.

To understand it you have to go back to the actual axioms of QM as found in a good source like Ballentine - there you will see nothing at all about collapse - its simply part of some interpretations. That's the real value of this interpretation stuff IMHO.

I agree with all of this except specifically that collapse is de facto not actually an interpretation of QM because orthodox QM has no collapse, orthodox QM being purely the Schrodinger equation and its mathematical properties. As I said above however QM as a whole is a mathematically inconsistent conjoining of the Schrodinger equation and the stochastic selection of the state from the ensemble which occurs empirically.

Collapse is therefore a prediction of a phenomenologic theory which directly competes with QM, but which has yet to be mathematically formulated. This theory should then contain QM as some particular low order limit, analogous to how Newtonian mechanics is a low order limit of SR.

The reason this theory has continued to defy mathematical formulation is because the two aspects of QM, i.e. unitary evolution and stochastic reduction, aren't easily mathematically unified due to all kinds of incompatible views and differing attitudes between their respective underlying mathematical bases. I believe higher category theory might be necessary to resolve this issue.

 

[lightarrow]

Please read what I said in the article: I said that viewpoint #2 says that the quantum state is "physically real". In other words, the wave function/state vector/whatever you want to call it, a particular well-defined thing in the math, represents something "physically real". The quantum state is not position, momentum, spin components, etc. It's the particular well-defined thing in the math.

Thanks.

--
lightarrow

 

[stevendaryl]

Very nice, and concise, summary of the key aspects of the disagreement over interpretations of QM, @PeterDonis.

The PBR theorem, which for a long time left me cold, because it didn't seem to prove anything new, seems to be a strong argument against the claim that \psi is epistemological.

Here's my nonmathematical of what I think their argument amounts to: If \psi is just epistemological, then there would be a possibility of two situations that differ only in our knowledge. For a classical example, with coin flips, we can have two situations:

1. I flip a coin and look at it and see that it's "heads". We describe this by "P(H) = 1, P(T) = 0". It has zero probability of being tails.
2. I flip a coin and don't look at it. We describe this by "P(H) = 1/2, P(T) = 1/2". It has equal probability of being tails.

If I prepare two coins, one via procedure 1, and one via procedure 2, there may be no difference in the coins in the two cases: It's possible that they're both "heads". So obviously, there is no empirical test that is guaranteed to distinguish, once and for all, which of those cases we're in.

In contrast, consider two spin-1/2 particles, one of which is prepared to have spin-up in the z-direction |psi_1\rangle = |U\rangle, and the other of which is in the superposition state:|\psi_2\rangle = \frac{1}{\sqrt{2}} (|U\rangle + \beta |D\rangle). PBR argues that if the quantum state is epistemological, just reflecting our knowledge, then there should be no way to empirically distinguish these two in a single test. If they can be distinguished in a single test, then that shows that there is something "real" about the difference. The PBR theorem shows that if two systems do not have identical wave functions, then it is possible (in principle) to distinguish them in a single experiment.

Okay, they don't actually show that. What they show is that if you have two different wave functions, you can use them to construct two different composite (entangled) states of two identical systems such that a single experiment suffices to distinguish the two states.

 

[bhobba]

This stochastic selection of the state from the ensemble which occurs during a measurement is precisely what makes QM a mathematically inconsistent theory consisting of deterministic unitary evolution and a stochastic non-unitary reduction. The former is the orthodox viewpoint of QM theoreticians.

No - its perfectly consistent.

If you don't think so you need to see a rigorous presentation and the exact axioms its based on:
https://www.amazon.com/dp/0387493859/?tag=pfamazon01-20

If you can find an inconsistency be my quest. Many very great mathematicians have studied it and found none. Of course I too have read it - it has none I can find. But be my quest - post the exact inconsistency. Schrodinger's equation is a deterministic equation about something (the wavefunction) that determines probabilities - there is no inconsistency in that. Imagine you have a coin that has a predictable mechanism inside it so its bias deterministically varies in time. You can write a deterministic equation giving the probabilities of getting heads or tales if flipped.

Thanks
Bill

 

[stevendaryl]

No - its perfectly consistent.

I think an actual inconsistency is impossible to prove because one half of the quantum formalism is informal: The notion of what it means to measure a quantity. Since measurement necessarily involves macroscopic systems with astronomical numbers of degrees of freedom, there is no feasible way to do an exact analysis of the measurement process. When you're talking about huge numbers, there is the possibility of what I would call a "soft contradiction", which is something that maybe false but you're not likely to ever face the consequences of its falseness. An example from classical thermodynamics might be "Entropy always increases". You're never going to see a macroscopic violation of that claim, but our understanding of statistical mechanics tells us that it can't be literally true; there is a nonzero probability of a macroscopic system making a transition to a lower-entropy state.

 

[bhobba]

I think an actual inconsistency is impossible to prove because one half of the quantum formalism is informal: The notion of what it means to measure a quantity.

Mathematical consistency is what I am talking about. Everything is defined rigorously in mathematical language in the reference I gave - includung to measure ie
page 12 'Suppose L is an abstract Boolean σ-algebra. We shall define a Y-valued observable associated with L to be any σ-homomorphism B(Y) into L. If Y is the real line we call these observables real valued and refer to them simply as observables.' Here B(Y) is the all the Borel subsets of Y into L.

Just another example of how a theory becomes unrecognizable once mathematicians get a hold of it.

What mathematical consistency independent physical consistency in a physics theory means I am not sure of.

Thanks
Bill

 

[A. Neumaier]

Mathematical consistency is what I am talking about. Everything is defined rigorously in mathematical language in the reference I gave - includung to measure ie
page 12 'Suppose L is an abstract Boolean σ-algebra. We shall define a Y-valued observable associated with L to be any σ-homomorphism B(Y) into L. If Y is the real line we call these observables real valued and refer to them simply as observables.' Here B(Y) is the all the Borel subsets of Y into L.

This is only a definition of what an observable is, not a definition of what it means to have measured something. (The link addresses only the classical situation, where this actually can be modeled, in principle.)

 

[bhobba]

This is only a definition of what an observable is, not a definition of what it means to have measured something. (The link addresses only the classical situation, where this actually can be modeled, in principle.)

Meaning - of course that's something different that the math bypasses. Of course - it's what an observable is - not the MEANING of to measure/observe. That however is a minefield if you want to pin it down exactly - but almost trivial in use.

Thanks
Bill

 

[stevendaryl]

Mathematical consistency is what I am talking about. Everything is defined rigorously in mathematical language in the reference I gave - includung to measure ie
page 12 'Suppose L is an abstract Boolean σ-algebra. We shall define a Y-valued observable associated with L to be any σ-homomorphism B(Y) into L. If Y is the real line we call these observables real valued and refer to them simply as observables.' Here B(Y) is the all the Borel subsets of Y into L.

Without getting into the mathematical details of how that works, I certainly believe that a formalization of measurement along mathematical lines such as those can be made consistent. My worries about inconsistency are not found there. What the authors are describing is an abstraction of the measurement process. However, an actual measurement in the real world is an interaction involving a macroscopic number of particles, each of which is presumably described by quantum mechanics. So the inconsistency that I worry about is not in the mathematical formalism, but in applying the mathematical formalism to a real measurement. Is the description of the measurement process as a complex quantum interaction among a macroscopic number of particles consistent with the abstraction described in that paper?

 

[bhobba]

So the inconsistency that I worry about is not in the mathematical formalism, but in applying the mathematical formalism to a real measurement. Is the description of the measurement process as a complex quantum interaction among a macroscopic number of particles consistent with the abstraction described in that paper?

Its a textbook by mathematicians for mathematicians.

Now in applying it you have to map the formalism to things you want to apply the theory to. In principle you should be able to do it, but using the methods in that book I haven't seen it, but using normal methods at least a partial solution is known in decoherence models. Its like Hilbert's Euclidean Geometry axioms and Euclid's. Everybody in practice uses Euclid - but in principle you could use Hilbert's.

Thanks
Bill

 

[stevendaryl]

Now in applying it you have to map the formalism to things you want to apply the theory to. In principle you should be able to do it, but using the methods in that book I haven't seen it, but using normal methods at least a partial solution is known in decoherence models.

I don't think that decoherence changes anything in principle. In practice, decoherence makes it impossible to see macroscopic superpositions. So we're free to assume that once decoherence has occurred, that the miracle of collapse has already happened. We're free to assume that in the practical sense that observations are not likely to prove us wrong.

 

[A. Neumaier]

the MEANING of to measure/observe. That however is a minefield if you want to pin it down exactly - but almost trivial in use.

This is the root of the problem in clarifying the precise meaning of quantum mechanics, and hence the source of the many interpretations.

 

[bhobba]

This is the root of the problem in clarifying the precise meaning of quantum mechanics, and hence the source of the many interpretations.

Yes .

But then again it likely applies to a number of areas in applied math if you think about it hard enough eg normal probability theory - John Baez certainly thinks so:
http://math.ucr.edu/home/baez/bayes.html

Thanks
Bill

 

[bhobba]

I don't think that decoherence changes anything in principle. In practice, decoherence makes it impossible to see macroscopic superpositions. So we're free to assume that once decoherence has occurred, that the miracle of collapse has already happened. We're free to assume that in the practical sense that observations are not likely to prove us wrong.

Correct - other assumptions are required without detailing them eg you assume an observation has occurred once decoherence happens.

Thanks
Bill

 

[Fra]

This is the root of the problem in clarifying the precise meaning of quantum mechanics, and hence the source of the many interpretations.

Another distinguishing factor that reflects the selection principle for our interpretations is wether it is rational to enter the minefield in order to progress fundamental physics or not?

This is another factor that divides us.

/Fredrik

 

[A. Neumaier]

Yes .

But then again it likely applies to a number of areas in applied math if you think about it hard enough eg normal probability theory - John Baez certainly thinks so:
http://math.ucr.edu/home/baez/bayes.html

Yes, see https://www.physicsforums.com/posts/5918976/ for a reference that discusses this in some depth.
But in classical mechanics this is no fundamental issue since probability enters only through the approximation process.

 

[A. Neumaier]

whether it is rational to enter the minefield in order to progress fundamental physics

This is not primarily a matter of ratio but of personal preferences and risk profiles.

I find it worth my time to ponder about the measurement problem at its root.

 

[Fra]

So the inconsistency that I worry about is not in the mathematical formalism, but in applying the mathematical formalism to a real measurement.

Indeed. And this is exactly where the physics part lies.

A mathematician can easily enter the mine field as he can walk without feet.

I think of the mathematical theory of QM as incoherent from the point of a general inference perspective. Sometimes i think of this as inconsistent reasoning. But this reasoning is not deductive in nature its more abductive but even such may have consistency requirements.

/Fredrik

 

[AlexCaledin]

... mathematical theory of QM as incoherent ...

But how it can be coherent? What happens in every local measurement is choice between variants of the whole universe, while QM is telling about a limited experimental system.

 

[bhobba]

I think of the mathematical theory of QM as incoherent from the point of a general inference perspective. Sometimes i think of this as inconsistent reasoning. But this reasoning is not deductive in nature its more abductive but even such may have consistency requirements.

Gee - I wonder why it has never been falsified.

The mathematics is not incoherent - what is incoherent is thinking the obvious mapping you use to apply is somehow at fault - it isn't. Its like saying the obvious mapping you use in applying Euclidean Geometry to points and lines is incoherent. Its a very difficult philosophical question when looked at deeply enough - but even 10 year olds have no trouble doing it. The same in QM - if you look at it very deeply its a morass (just one obvious thing - since observations occur here in the macro world how does a theory that assumes such in the first place explain it - a lot of progress has been made - I think the answers we now know are just fine - others disagree) - if not its rather obvious. Its a matter of taste if you think such questions are worthwhile. I happen to think going too deep into it isn't that worthwhile - but not everyone agrees.

Thanks
Bill

 

[bhobba]

But how it can be coherent?

The same way arithmetic is coherent.

Thanks
Bill

 

[Greg Bernhardt]

Great job Peter!

 

[Stephen Tashi]

Why is the concept of the collapse of a wave function any more (or any less) of a problem in logical consistency than other applications of probability theory where there are probabilities of various outcomes followed by only one of the outcomes happening?

Mathematical probability theory (based on measure theory) says nothing about events actually happening and has no axiom stating that it is possible to take take random samples. Taking random samples (i.e. "realizing" the outcome of a random variable) is a topic for applications of probability theory, so it involves an interpretation of probability theory not explicitly given in the mathematical axioms.

Sure, that's why I said we're dealing with vague ordinary language. I'm not trying to put a specific definition on the word "real". I'm just trying to say that, as far as I can tell, people who espouse Case 1 interpretations consider the quantum state to be like probabilities, and in common ordinary language usage probabilities do not describe the physically real state of anything; they just describe our knowledge (or the limitations thereof). If it helps, substitute "case 1 says the quantum state is like probabilities" for "case 1 says the quantum state is not real".

It's controversial whether probabilities (in physics) represent a state of knowledge or whether they are objective. However, your make it clear that your definition of "physically real" excludes a quantity that represents a probability.

Case 2 interpretations of QM do not say a physically real state produces a deterministic outcome (that would contradict stan; they just say the quantum state is physically real. So I don't see how this helps to clarify anything relevant to this discussion.

To make a classical analogy, suppose we take a coin with uniform mass density and bend it in the middle at angle theta. When used in a coin toss experiment, the angle theta may affect the probability that the coin lands heads. In your view, the angle theta is a "physically real" aspect of the coin and the probability of the coin landing heads is not.

Is that a good analogy, from your point of view?

 

[PeterDonis]

It's controversial whether probabilities (in physics) represent a state of knowledge or whether they are objective.

Yes, agreed; but as you note, for purposes of this discussion I am using the term in the former sense.

In your view, the angle theta is a "physically real" aspect of the coin and the probability of the coin landing heads is not.

Yes.