I What Makes Ontology Easy for Kids but Challenging for Quantum Physicists?

[Killtech]

Given that complex probability amplitudes are at the root of the non-classical aspects of QM, then this debate echoes the original debate about complex numbers. Scott Aaronson has a neat anecdote about this when he was troubled by why nature chose the complex numbers and got talking to some maths grads. They just laughed and said "because the complex numbers are algebraically closed, of course".

https://www.scottaaronson.com/democritus/lec9.html

"the central conceptual point: that nature is described not by probabilities (which are always nonnegative), but by numbers called amplitudes"

Ugh... that quote is taken from your link. Like, no. What we measure is real because our measurement devices measure in real numbers. Well actually in finite numbers and Incidence counters even in integers. That's what spans the space of predictions we need to correctly describe. How we do it is up to us but of course we always take the best tools for a job. Probability amplitudes however are intrinsics of a theory, which is neither directly nature, nor directly our observation of it. All it is, is being useful... and we found that out long ago that combining the phase and amplitude of fields makes the calculus very convenient regardless weather we deal with classical fields or wave functions. It's just deeply inherent to everything related to sine/exp functions (and therefore naturally PDEs related to them). Sorry, there is just nothing special about complex numbers other then how they relate to other mathematical constructs from which they derive their situational convenience.

Oh, and in case you were wondering, there is no kind of restrictions that would prevent you to use a complex space as a underlying state space of a probability space. Kolmogorov doesn't bother at all how you calculate your probabilities as long as they are measurable functions (i.e. those cannot do Banach Tarski stuff) - this is what you call a random variable. In fact Kolmogorov actually allows you to make your state space not even of anything related to numbers at all if you fancy it. It just has to be well defined enough to produce a set in terms of Zermelo-Fraenkel. So if you think complex numbers are in any way restricting you from using classical PT, well then you are mistaken.

 

[CelHolo]

But the non-commutative complex algebra of quantum observables does prevent you from using classical probability theory since it prevents realising the observables as random variables on a common probability space.

 

[Killtech]

The rest of your response was hard for me to understand but it's easy to show that the CHSH inequality follows from assuming that the four observables being measured are random variables on a single sample space as Kolmogorov probability would. This was shown in the 80s by Tsirelson and is covered in textbooks on quantum probability and information. It's nothing really to do with "burdening" Kolmogorov probability with "classical particle understanding". Thus QM violating these constraints indicates it's not a Kolmogorov theory.

Just like Special and General Relativity teach one that geometry must be generalised, so as well quantum theory teaches one that probability theory must be generalised. I don't see the demand for QM to have a Kolmogorov formulation as sensible, any more than GR should have a Euclidean formulation.

You should maybe look at CHSH a little deeper. It's achieving it's purpose very well, but what it is going beyond a pure Kolmogorov assumptions and introduces a concept of hidden variables and specifically the property of them being local. It's core is coming up with a workable definition of locality that allows handling in a very general context to provide a framework for experiments to check the assumption of locality. And it perfectly achieves that goal.

Kolmogorov doesn't makes any such assumptions. Why do i need to tell you that? Have you actually ever read what the axioms of Kolmogorov even are? What does non locality even have to do with non measurability in the mathematical/Lebeque meaning??

 

[PeroK]

"the central conceptual point: that nature is described not by probabilities (which are always nonnegative), but by numbers called amplitudes"

Ugh... that quote is taken from your link. Like, no. What we measure is real because our measurement devices measure in real numbers. Well actually in finite numbers and Incidence counters even in integers. That's what spans the space of predictions we need to correctly describe. How we do it is up to us but of course we always take the best tools for a job. Probability amplitudes however are intrinsics of a theory, which is neither directly nature, nor directly our observation of it. All it is, is being useful... and we found that out long ago that combining the phase and amplitude of fields makes the calculus very convenient regardless weather we deal with classical fields or wave functions. It's just deeply inherent to everything related to sine/exp functions (and therefore naturally PDEs related to them). Sorry, there is just nothing special about complex numbers other then how they relate to other mathematical constructs from which they derive their situational convenience.

Oh, and in case you were wondering, there is no kind of restrictions that would prevent you to use a complex space as a underlying state space of a probability space. Kolmogorov doesn't bother at all how you calculate your probabilities as long as they are measurable functions (i.e. those cannot do Banach Tarski stuff) - this is what you call a random variable. In fact Kolmogorov actually allows you to make your state space not even of anything related to numbers at all if you fancy it. It just has to be well defined enough to produce a set in terms of Zermelo-Fraenkel. So if you think complex numbers are in any way restricting you from using classical PT, well then you are mistaken.

All of your posts seemed to be based on something other than an understanding of QM. Ultimately, the reason QM was adopted in the first place and the reason it's still the only game in town 100 years later is that it explains the body of 20th century experimental physics.

You can chew the philosophical fat as much as you want, but until you have a working theory that explains all of 20th century experimental physics without QM, then you have nothing. Just a weak assertion that you could do it otherwise.

 

[PeterDonis]

You should maybe look at CHSH a little deeper. It's achieving it's purpose very well

Um, you do know that the CHSH inequalities are violated in actual experiments (which confirm the predictions of QM), right?

 

[Killtech]

But the non-commutative complex algebra of quantum observables does prevent you from using classical probability theory since it prevents realising the observables as random variables on a common probability space.

Really? Put the Hilbert space of QT states as your state space of your probability space. Then using linear operators together with Borns rule gives you a measurable function i.e. a valid definition of random variable.

To realize non-commuting observables you have to use stochastic processes. Every time a measurement takes place i.e. you measure a random variable, the stochastic progresses stochastically, otherwise it progresses deterministically. The Markov kernel (time evolution) is given by a combination of the Hamilton operator with a non unitary measurement operator representing the measurements.

 

[Killtech]

Um, you do know that the CHSH inequalities are violated in actual experiments (which confirm the predictions of QM), right?

Yeah of course! I do know that physics exhibits a non local properties.
But now do you know that Kolmogorovs theory is not local??

 

[CelHolo]

Have you actually ever read what the axioms of Kolmogorov even are?

Yes.

what it is going beyond a pure Kolmogorov assumptions and introduces a concept of hidden variables and specifically the property of them being local

Tsirelson proved you can derive the CHSH inequalities just from the assumption of a common probability space in the 80s. I think you're charging ahead in "dismantling" QM without having a decent command of the material.

 

[Killtech]

Tsirelson proved you can derive the CHSH inequalities just from the assumption of a common probability space in the 80s. I think you're charging ahead in "dismantling" QM without having a decent command of the material.

Kolmogorov has not the slights concept of locality. The question of locality cannot be decided within that framework alone. You have to define it somehow, which adds additional assumptions.

I ask you a stupid question: is there a version CHSH inequality that holds specifically for objects measured at the very same location and that aren't isolated in any way, can freely interact with each other before and during their measurement? As in can you show that the very core of CHSH inequality isn't the issue of locality but rather indeed the definition of probability? Kolmogorov does not distinguish between those to cases btw...

CHSH and Tsirelson deal with the concept of locality. You cannot take that part away from those and expect them to hold anyway. Or do you actually claim that those have nothing to do with locality?

And this isn't about dismantling QM in anyway. Just straighten out some nomenclature. It does not affect either the math and calculus of QM nor does it affect any of its the predictions. It just says that if you have probabilities in any theory you can just reverse engineer the underlying probability space.

 

[PeterDonis]

now do you know that Kolmogorovs theory is not local??

I said nothing whatever about the Kolmogorov axioms. I was responding to your claim about the CHSH inequality. It seems odd to say that that inequality is "achieving its purpose very well" when it makes predictions that are falsified by experiments.

 

[Killtech]

I said nothing whatever about the Kolmogorov axioms. I was responding to your claim about the CHSH inequality. It seems odd to say that that inequality is "achieving its purpose very well" when it makes predictions that are falsified by experiments.

Oh, sorry. I though the idea of the inequality was to provide a tool to decide the question that Einstein has put up via an experiment. It's achieving its goal by deciding/settling the problem, no?

Of course not everyone may like the outcome but that's an entierly different matter.

 

[CelHolo]

CHSH and Tsirelson deal with the concept of locality. You cannot take that part away from those and expect them to hold anyway. Or do you actually claim that those have nothing to do with locality?

Yes. They're simply constraints on any four binary random variables sharing a common probability space.

 

[PeterDonis]

I though the idea of the inequality was to provide a tool to decide the question that Einstein has put up via an experiment. It's achieving its goal by deciding/settling the problem, no?

If you mean that experimentally showing that the CHSH inequality is violated rules out certain types of models, sure, that goal has been achieved. But the claims you are making don't appear to be about ruling out certain types of models. You appear to have some specific type of model in mind that is not ruled out and that somehow "explains" QM without all the problems that other people see. If you do, you should give a specific reference that tells us what that model is, so we have a basis for discussion. For example, if you think some version of "Kolmogorov theory" does the job, give us a reference that explains what that theory is and what predictions it makes.

 

[Killtech]

Yes. They're simply constraints on any four binary random variables sharing a common probability space.

Oh boy. The whole point of the exercise is the assumption that the quantum systems in Alice and Bobs lab cannot communicate. But if that isolation restriction (which is trying to represent the core property of distance) is lifted, then there is just nothing preventing the violating the inequality by as much as possible, even beyond Tsirelson's bound. If the system in Alice's lab can tell Bob's what it settled for during its measurement and before Bob's system was measured, then of course it can conveniently change itself to whatever it needs to to produce any desired distribution.

If you allow Einsteins "spooky action at range" to be involved in the experiment, then of course you can violate any such inequality.

Why do you think we even put so much effort into these kind of experiments to make them at a distance, specifically deciding the orientation of the measured axis only after the two photons were emitted, if distance doesn't even have a role to play?? Are you suggesting physicists just waste a lot of tax payer money for nothing?

 

[CelHolo]

I think you just don't know the mathematics, it's quite easy to derive the CHSH inequalities from the assumption of a common probability space. See Streater's Lost Causes in theoretical physics for a full explanation.

 

[Killtech]

I think you just don't know the mathematics, it's quite easy to derive the CHSH inequalities from the assumption of a common probability space. See Streater's Lost Causes in theoretical physics for a full explanation.

Break that common probability space into that of a two step stochastic process - i.e. deviate from the assumptions made for CHSH but which is still perfectly fine within Kolmogorovs framework.

Now you have 4 random variables $A_t$ and $B_t$ with $t \epsilon \{0,1\}$ for measurement instead of the two you had before. The first two represent the measurement which comes first - technically either Alice or Bob could be first. You can however only execute one measurement at a time and have to progress and update the system afterwards. So we have to decide for either measure $A_0$ or $B_0$ and lose the ability to measure the other permanently. In order to make the next measure we need to progress by applying a transition matrix representing our interaction with the complete system (our first measurement). Then we have to pick the random variable $B_1$ or $A_1$ whichever is complimentary to the one we picked first and measure it.

Since the transition matrix can reorder probabilities in any possible way and also has the information about our interaction we can easily pick it to update the probability space to whatever it needs to be. It is the one that gives us a massive degree of freedom which we don't have if we put both measurements into the same $t$ level of the process.

I case this sounded somehow familiar, this is just the very same old process you have for a collapse interpretation, except that you restate it in terms of a Markov transition matrix. So it's a terribly old idea that we know works fine enough. So pure classical QT framework, just a marginally different terminology.

 

[PeterDonis]

Break that common probability space into that of a two step stochastic process - i.e. deviate from the assumptions made for CHSH but which is still perfectly fine within Kolmogorovs framework.

As I have already asked you once, please give a reference for the specific model that you have in mind. You can't just wave your hands. Either there is a valid reference describing a specific model with the properties you keep claiming, or there isn't.

 

[meekerdb]

Well, if ontology is about what Kant called "Ding an sich" (I don't know, how to translate Kant into English), then it's something not subject to the natural sciences, because the natural sciences are about nature as can be objectively observed. Objectively means the observations must be reproducible and independent from the individual making the expression.

Take, e.g., classical electrodynamics and the electromagnetic field. Is the classical electromagnetic field ontic, providing an "ontology of light"? I don't know, because if one thinks about it, it's just a mathematical framework describing the phenomena of emission of "light" (e.g., the Sun as a thermal light source) and its registration at some distant place. We never directly observe the field but just its action on some matter. Usually it's the photoelectric effect which provides a signal in a detector (photoplate, CCD cam, the retina of our eyes etc). So "is light really" the electromagnetic field or is it the photo electron ejected from matter which then leads to a "signal" we can preceive?

I think an answer to this question is pretty irrelevant from the point of view of the natural sciences. It's simply easier to talk about the electromagnetic field about some "thing" with a kinematics and dynamics in its own right as if it were something like a substance though for a substance it doesn't have a typical "substance-like" (charge-like) conserved quantity. It basically has been introduced by Faraday (based on his experience with experiments and observations) and then brought in a mathematical form by Maxwell to have a concise way to talk about these electromagnetic phenomena.

Pushed to it's limit, neither the light nor the electron is ontic. They are all "things" we merely theorize from our perceptions. At one time there were different theories explaining those same perceptions, e.g. when the Greeks thought of vision as rays that reached out from one's eye. This seems to point to Quine's concept of ontologies as whatever entities are assumed in one's theory of the world.

 

[Ian J Miller]

From an ontological point of view, either there is a physical wave of there is not. If you wish to assert there is not and ψ is just a mathematical convenience, then how do you account for the following paper: Lundeen, J. S., Sutherland, B., Patel, A., Stewart, C., Bamber, C. 2011. Direct measurement of the quantum wavefunction. Nature 474: 188 – 191.

 

[meekerdb]

If it's real how do you explain that the same result can be obtained by Feynmann's path integral method?

 

[*now*]

I think RQM’s ‘anti-realist’ reference is itself also arguably axiomatically ontic.

 

[Ian J Miller]

If it's real how do you explain that the same result can be obtained by Feynmann's path integral method?

First, for me the observation overrides any theoretical concern. If it is not there, how can you measure a phase shift? Second, does not the path integral method effectively give the least action result? If so, the same action determines the phase shift of the wave, does it not?

 

[Demystifier]

This leaves us with two possibilities:

1) QM is manifestly incomplete - and anyone who believes in orthodox QM must lack something in terms of the intellectual capability to think logically. I.e. they embrace an obvious contradiction.

2) You place excessive demands on a fundamental theorem of nature that, from a matter purely of logical consistency, are not required. I.e. there is no inconsistency, only your perception that this particular fundamental theory of nature is deficient.

When orthodox QM is presented in instrumental form, just as a set of practical rules for computing probabilities of measurement outcomes, it's perfectly consistent. But I see inconsistencies when the orthodox guys start to make a philosophy out of it, i.e. when they try to explain what those rules mean at a deeper level. (The very first inconsistency that many of them commit is that they use philosophy to argue that one should not do philosophy.) Anyway, if some of my demands are too excessive, I would like to know what those demands are.

 

[PeroK]

Anyway, if some of my demands are too excessive, I would like to know what those demands are.

My understanding of this thread in broad terms is that orthodox QM does not demand that all measurables have well-defined values at all times and that you believe that this makes QM incomplete and inevitably leads to philosophical inconsistencies.

But I see inconsistencies when the orthodox guys start to make a philosophy out of it, i.e. when they try to explain what those rules mean at a deeper level. (The very first inconsistency that many of them commit is that they use philosophy to argue that one should not do philosophy.)

I can well understand that. It's impossible to be totally aphilosophical (since, as you point out, even arguing to keep philosophy out of physics is a philosophy in itself). From my point of view, the whole debate about ontology is a quagmire from which it may be impossible to emerge. I would say - and this is more than "shut up and calculate" - that even if the philosophical questions that QM raises are unanswerable, then this could equally be seen as a warning against expecting too much from a philosophical analysis of natural science.

 

[CelHolo]

then how do you account for the following paper: Lundeen, J. S., Sutherland, B., Patel, A., Stewart, C., Bamber, C. 2011. Direct measurement of the quantum wavefunction

This was dealt with long ago by Bill Unruh and others. It's impossible to directly measure the quantum state, just as it is impossible to directly measure any set of probability distributions, what they actually do is measure a POVM with postselection.

Today papers about weak measurements aren't formulated in terms of measuring the state.

 

[vanhees71]

So you are saying that the state always exists, while values of the observables exist only when they are measured, is that right? But it creates a lot of additional questions:

One must be more careful to formulate things right. It is an indication that we don't do this properly, because we always start from scratch. I come more and more to the conclusion that there's no way to make progress, but here's one more try:

A quantum system is described by states, represented by a statistical operator in Hilbert space. A state is operationally defined by an equivalence class of preparation procedures.

Observables are operationally defined by an equivalence class measurement procedures. The preparation in a state at some initial time $t_0$ implies the propabilities (and only the probabilities) for the outcome of measurements of any observable you decide to measure. An observable has a determined value, if with 100% probability a measurement of this observable results in this value. Otherwise the observable does not have a determined value.

A measurement a priori does not prepare the system. It depends on the measurement device, whether you are able to perform a von Neuman filter procedure (confusingly often called a filter measurement in the literature) or not.

1. Why do values not exist before measurement?

The quantum formalism is the result of many observations and experimental facts. There is no sensible way to answer such "why questions" in the natural sciences, which figure out as precisely as possible how Nature behaves but never can answer why she behaves the way she does. Discussions concerning this quesions touch the realm of religion and are not subject of the natural sciences.

2. How the values know that there is a measurement out there?

Measurements are interactions between the measurement device and the measured object. The dynamics is described by quantum (statistical) theory.

3. What's the precise definition of measurement?

It's given by a concrete measurment apparatus.

4. Can measurement be derived from something more fundamental, or is measurement a primitive concept?

The construction of measurment devices is based on the known natural laws as any technical development. The "primitive concepts" behind this constructions thus are the corresponding theories describing them.

5. Does a value (randomly created in a measurement) have influence on the state?

Of course the state of the measured system changes due to the interaction with the measurement device. Whether or not the system persists to exist, i.e., can be in a meaningful way separated from the measurement device an/or "the environment" depends on the specifics of the measurement device. Thus this is a question to be answered theoretically using the theory but it cannot be answered by inventing some new fundamental postulate of the theory.

6. If the answer to 5. is "yes", does this influence violate unitarity, linearity, locality and/or the Schrodinger equation?

A closed system's dynamics is described by unitary time evolution. Attempts to extend QT beyond this standard formulation so far failed (or there are even counterarguments, e.g., by Susskind et al concerning the use of Lindblad equations generalizing the unitary time evolution of the standard theory).

Since measurement devices are at some point necessarily macroscopic devices it is impossible to describe this unitary time evolution completely and one has to use the methods of quantum statistical physics to find an effective description of the macroscopically relevant degrees of freedom, involving coarse-graining, dissipation, and entropy production, i.e., in terms of a description of the relevant degrees of freedom in the sense of an open quantum system. This is unavoidable to get a well-established "stored" measurement result, i.e., there is necessarily some irreversibility involved in establishing a measurement result.

All this has been formulated already in the very early days of QT by Bohr, but today are almost 100 years further and have a plethora of methods to treat open quantum systems mathematically in a clear way.

 

[physika]

So you are saying that the state always exists, while values of the observables exist only when they are measured, is that right? But it creates a lot of additional questions:
1. Why do values not exist before measurement?
2. How the values know that there is a measurement out there?
3. What's the precise definition of measurement?
4. Can measurement be derived from something more fundamental, or is measurement a primitive concept?
5. Does a value (randomly created in a measurement) have influence on the state?
6. If the answer to 5. is "yes", does this influence violate unitarity, linearity, locality and/or the Schrodinger equation

likewise, why don't they take, any possible value, for example up and up.
the entangled pair.

 

[physika]

But I see inconsistencies when the orthodox guys start to make a philosophy out of it, i.e. when they try to explain what those rules mean at a deeper level. (The very first inconsistency that many of them commit is that they use philosophy to argue that one should not do philosophy.)

Excellent.

 

[CelHolo]

The quantum formalism is the result of many observations and experimental facts. There is no sensible way to answer such "why questions" in the natural sciences, which figure out as precisely as possible how Nature behaves but never can answer why she behaves the way she does

Yeah I find this an odd question. To make scientific progress we had to realize that often most/all observables do not have a well-defined value. To me it would be like having a problem with GR because nobody has told you "why" spacetime is curved. Isn't QM a success because it correctly captures these new fascinating aspects of nature?

 

[vanhees71]

Exactly!