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

[martinbn]

If I understood you correctly, you simultaneously hold the following 4 beliefs:
1. Probability has no meaning for a single event.
2. Wave function has a meaning for a single event.
3. The only meaning of wave function is to determine the probability.
4. The 3 statements above are mutually consistent.
Do I miss something?

2. Is unclear to me. What does it mean?

 

[Demystifier]

2. Is unclear to me. What does it mean?

I don't know, ask @vanhees71!

 

[Lord Jestocost]

I always thought an ontic interpretation assumes more than the existence of observations...

Indeed. Ontic interpretations have to fulfill a twofold task:

1) A claim concerning the existence of the “stuff” which physics is about
2) A claim concerning the character of its existence.

Statements that some “stuff” exists are meaningless phrases when not complemented with a statement how that “stuff“ exists. Orthodox quantum mechanics is silent about point 2, thus not belonging to what is denoted ontic interpretations. Orthodox quantum mechanics has never denied that something “exists” or – so to speak – that there is an “out there”. That was and is a fairy tale still spooking around in the realm of folk science.

 

[vanhees71]

probability for a single event is total nonsense... if one were talking about Kolmogorov probabilites. Quantum probability gives up that idea by breaking the very thing in classical probability theory that prevents that to happen. If you allow the information contained in a probability distribution to effectively couple to physical interaction and have a uniquely distinguishible effect on outcomes... that's what you get. That's really the difference. When you want to use the word "probability" in QT, you have to let go of your Kolmogorovian interpretation of it. I still don't see it as a reasonable choice and would have preferred to formulate it within classical probability theory framework to prevent such weirdness in terminology and confusion but whatever.

I have no clue what you are talking about. Take the most simple example. Say we have a neutron's spin prepared in the $\sigma_z=+1/2$ eigenstate, $\hat{\rho}=|1/2 \rangle \langle 1/2|$. Now use a Stern-Gerlach apparatus to measure $\sigma_x$. All I know from knowing that the neutron is prepared in the state $\hat{\rho}$ are the probabilities for the two possible outcomes of my measurment, $\sigma_x=+1/2$ or $\sigma_x=-1/2$ being $P_{\sigma_x=1/2}=P_{\sigma_x=-1/2}=1/2$. For such a physically meaningful experiment the quantum probabilities can be interpreted in the Kolmogorovian sense, but it doesn't so much matter which axiomatic system for probability theory you use. It's rather a question what it means for physics to say the probability for getting the one or the other result is 1/2. For me it doesn't tell you anything for just a single measurement. To experimentally test whether the prediction for the $\sigma_x$-measurement is correct, I simply have to prepare many neutrons in the state $\hat{\rho}$, measure $\sigma_x$ and count how many times I get either result using the usual statistical analysis methods to provide a significance for the validity or invalidity of the predicted probabilities. I never understood, what the Qbists (or even classical Bayesianists) mean when they say probabilities would have some meaning for a single event.

 

[vanhees71]

2. Is unclear to me. What does it mean?

I've explained how I understand this statement above: States (statistical operators; wave functions are only special cases representing pure states in the usual sense as they define the corresponding statistical operator or equivalently a ray in Hilbert space) are, on the one hand, associated with an equivalence class of preparation procedures and as such refer to a single system. On the other hand the preparation in a state only implies probabilistic properties for the system, i.e., it provides the probabilities for the outcome of the measurement of any observable of the system. In my opintion, this can be tested only on an ensemble of equally prepared systems. I could never make sense of Bayesianistic claims that a probability has any meaning for a single event.

 

[Demystifier]

Orthodox quantum mechanics is silent about point 2, thus not belonging to what is denoted ontic interpretations. Orthodox quantum mechanics has never denied that something “exists” or – so to speak – that there is an “out there”. That was and is a fairy tale still spooking around in the realm of folk science.

The problem with orthodox way of thinking is that it changes its statements depending on the context. If you ask them whether something exists out there without observation, they say that it does. But when you point out that the mere existence implies nonlocality via the Bell theorem, they say that the notion of existence without observation is meaningless philosophy.

 

[physika]

they say that the notion of existence without observation is meaningless philosophy.

But what/who observes that observer/agent (whatever is called)...

 

[martinbn]

I've explained how I understand this statement above: States (statistical operators; wave functions are only special cases representing pure states in the usual sense as they define the corresponding statistical operator or equivalently a ray in Hilbert space) are, on the one hand, associated with an equivalence class of preparation procedures and as such refer to a single system. On the other hand the preparation in a state only implies probabilistic properties for the system, i.e., it provides the probabilities for the outcome of the measurement of any observable of the system. In my opintion, this can be tested only on an ensemble of equally prepared systems. I could never make sense of Bayesianistic claims that a probability has any meaning for a single event.

But the statement says that the wave function applies to a single event. I understand what is meant by "the wave function applies to a single system", but event?

 

[martinbn]

The problem with orthodox way of thinking is that it changes its statements depending on the context. If you ask them whether something exists out there without observation, they say that it does. But when you point out that the mere existence implies nonlocality via the Bell theorem, they say that the notion of existence without observation is meaningless philosophy.

No, they don't. The say that the system at hand exists out there. But the values of the observables don't exist prior the measurement. For example an atom exists, but the value of the spin of the atom along the z-axis does not until you make a measurement.

 

[physika]

Now things come into existence physically by interaction.

X interacts with Z, Y interacts with W, Z interacts with S...
And so on..
Endless chain.
Which is the first interactor ??

 

[vanhees71]

No, they don't. The say that the system at had exists out their. But the values of the observables don't exist prior the measurement. For example an atom exists, but the value of the spin of the atom along the z-axis does not until you make a measurement.

I find it important to say "an atom exists, but the value of the spin of the atom along the z-axis does not until you prepare it as such." Merely measuring something on a system doesn't necessarily prepare it in a corresponding state.

 

[Demystifier]

No, they don't. The say that the system at hand exists out there. But the values of the observables don't exist prior the measurement. For example an atom exists, but the value of the spin of the atom along the z-axis does not until you make a measurement.

If so, then there is something about system that is not described by values of the observables. What is that? QM doesn't say, implying that QM is incomplete. And yet, orthodox guys insist that it is complete. Another inconsistency typical for orthodox guys.

 

[Demystifier]

But what/who observes that observer/agent (whatever is called)...

They self-observe themselves, of course.

 

[physika]

They self-observe themselves, of course.

then, they are autonomous.
and existing.

 

[martinbn]

If so, then there is something about system that is not described by values of the observables. What is that? QM doesn't say, implying that QM is incomplete. And yet, orthodox guys insist that it is complete. Another inconsistency typical for orthodox guys.

It does say. It is called the state of the system. In classical physics the state consists of values of observables. In QM it does not.

 

[Demystifier]

It does say. It is called the state of the system. In classical physics the state consists of values of observables. In QM it does not.

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?

 

[Killtech]

I have no clue what you are talking about. Take the most simple example. Say we have a neutron's spin prepared in the $\sigma_z=+1/2$ eigenstate, $\hat{\rho}=|1/2 \rangle \langle 1/2|$. Now use a Stern-Gerlach apparatus to measure $\sigma_x$. All I know from knowing that the neutron is prepared in the state $\hat{\rho}$ are the probabilities for the two possible outcomes of my measurment, $\sigma_x=+1/2$ or $\sigma_x=-1/2$ being $P_{\sigma_x=1/2}=P_{\sigma_x=-1/2}=1/2$. For such a physically meaningful experiment the quantum probabilities can be interpreted in the Kolmogorovian sense, but it doesn't so much matter which axiomatic system for probability theory you use. It's rather a question what it means for physics to say the probability for getting the one or the other result is 1/2. For me it doesn't tell you anything for just a single measurement. To experimentally test whether the prediction for the $\sigma_x$-measurement is correct, I simply have to prepare many neutrons in the state $\hat{\rho}$, measure $\sigma_x$ and count how many times I get either result using the usual statistical analysis methods to provide a significance for the validity or invalidity of the predicted probabilities. I never understood, what the Qbists (or even classical Bayesianists) mean when they say probabilities would have some meaning for a single event.

Except that in Stern Gernlach the choice of the axis $x$ along which $\sigma_x$ is measured can be determined after the $\hat{\rho}$ state is prepared.

So let's do a bold assumption here that the preparation of the initial state $\hat{\rho}$ is to be independent of the experiment it is let loose on. In Stern Gerlach case, it means that the initial state remains the same regardless the choice of axis $x$. Now let's build a minimal Kolmogorov probability space that can still properly describe the probability distributions along any axis. This produces a rather complex highly dimensional joint probability distribution (instead of just projection along one axis you think about) which we need to reproduce. The problem is that measurements along different axis have a fairly untypical correlation that doesn't allow to decompose it into a small independent basis. It's up to us to come up with a state space that can actually produce that distribution.

I'll cut to the point: the quantum Hilbert space is almost the minimal possible state space that has that ability so we build our probability space on it. But if we effectively have to put $\hat{\rho}$ into our physical state space and it already can be projected along any axis and has a distribution along that, then it practically means that the probability distribution that we have for measurement is merely directly proportional to some underlying unknown entity from the physical state space. So if someone talks about "probability for a single event" i understand it on the basis of that underlying proportionality.

Look, Kolmogorov defined probability based on a measure over a real state space - attributing probabilities only to sets of the power set (or rather Borel set) over the actual state space. This ensures an independence of the physical information from our knowledge about the system (encoded in the probabilities). Quantum probabilities give up this separation so we can never be sure if the probability distributions we obtain from the theory purely represent our knowledge of the system or are actually a mixtures of physical and knowledge information.

So Stern Gerlach from a radical Kolmogorovian perspective is that the actual relevant physical information (in terms of all possible observables) contained in the initial physical state is an angular distribution of complex numbers describing an amplitude and phase information along every angle. This information cannot be reduced in any way if the separation of physical and knowledge information is to be uphold. It's just that we have only a single attempt to obtain an observation from it which is entirely inadequate to describe the actual state the system was in before we destroyed it by "measurement" - whereas "measurement" actually means forcing the state into a one of a few possible different states which we are however at least able to detect/distinquish.

 

[CelHolo]

I find it important to say "an atom exists, but the value of the spin of the atom along the z-axis does not until you prepare it as such." Merely measuring something on a system doesn't necessarily prepare it in a corresponding state.

I think you have to be careful even with this language as it can seem to imply nonlocality in entangled states after measuring one system.
So if in a Bell state say (ignoring normalisation and using the z-spin basis) :
$\ket{\uparrow\uparrow} + \ket{\downarrow\downarrow}$
measuring the first system to be spin-up then prepares the second system in the state $\ket{\uparrow}$, seemingly "creating" the spin value of the distant system.
This is why the eigenstate-eigenvalue link is avoided in some texts. It's pedantic as such for a single system of course.

 

[Killtech]

X interacts with Z, Y interacts with W, Z interacts with S...
And so on..
Endless chain.
Which is the first interactor ??

so it would seem that X, Z, Y, W and S influence cannot be neglected for correct prediction of observations. So the information they contain has to be in some way there.

But what do you mean by first? Like is $E$ or $B$ first in Maxwell equations? PDEs don't really define any kind of order of interaction. I mean the word interaction implies it going both ways making everyone the first? Hmm, I just wildly guessing here, because I honestly do not understand you question at all.

 

[PeroK]

The problem with orthodox way of thinking is that it changes its statements depending on the context. If you ask them whether something exists out there without observation, they say that it does. But when you point out that the mere existence implies nonlocality via the Bell theorem, they say that the notion of existence without observation is meaningless philosophy.

If so, then there is something about system that is not described by values of the observables. What is that? QM doesn't say, implying that QM is incomplete. And yet, orthodox guys insist that it is complete. Another inconsistency typical for orthodox guys.

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.

There might be a parallel with the history of numbers. The Greeks were happy with rational numbers, but when $\sqrt 2$ was shown to be irrational, they were not prepared to accept the existence of an irrational number. And, similarly, complex numbers were given the description "imaginary" - not in any mathematically objective sense, but because of an a priori prejudice about the nature of numbers.

When it comes to "existence" of an electron there seems to be an ongoing prejudice towards classical notions of how a particle must behave in order to "exist". If the electron were to behave classically, then there would be no question of its existence; but, if it behaves quantum mechanically, then its existence is in doubt. In particular, if the position of an electron is described by a single point, then the electron exists; but, if the position of an electron is described by a spatial function, then it doesn't exist to the same extent and the theory of the electron is incomplete.

I'm not convinced by any of that. Neither definite position nor position defined by a spatial wavefunction can be ruled out by appeals to logical completeness or consistency.

 

[CelHolo]

if the position of an electron is described by a spatial function, then it doesn't exist to the same extent and the theory of the electron is incomplete

I think the issue is that this function is a probability distribution for position measurements, if it was a spatial function that simply described some sort of classical extended object or charge distribution it would be easily accepted.
Not that the former is actually a problem but that's where the issue originates I think.

 

[Killtech]

I think the issue is that this function is a probability distribution for position measurements, if it was a spatial function that simply described some sort of classical extended object or charge distribution it would be easily accepted.
Not that the former is actually a problem but that's where the issue originates I think.

Well, this is in part the case. A pure probability distribution wouldn't be much of an issue here either if it could be always interpreted within classical probability theory, but we instead introduce quantum probabilities for that. The deviation from Kolmogorovs probabilities leaves us entirely blank of a solid interpretation - because we now cannot attribute those probability distribution to purely represent our lack of knowledge about the system as we would have classically. Instead it leaves the gate wide open for a huge variety of vastly different interpretation that just don't seem to be consistent with each other. That big confusion is kind of what makes up the core of the problem.

 

[PeroK]

I think the issue is that this function is a probability distribution for position measurements, if it was a spatial function that simply described some sort of classical extended object or charge distribution it would be easily accepted.
Not that the former is actually a problem but that's where the issue originates I think.

That's a good point. The difference in QM is quite deep.

 

[PeroK]

Instead it leaves the gate wide open for a huge variety of vastly different interpretation that just don't seem to be consistent with each other. That big confusion is kind of what makes up the core of the problem.

The inability of human intelligence to agree on an interpretation of QM does not, by itself, invalidate the theory. No more than the debate over the existence of complex numbers undermines the pure mathematics.

 

[Killtech]

The inability of human intelligence to agree on an interpretation of QM does not, by itself, invalidate the theory. No more than the debate over the existence of complex numbers undermines the pure mathematics.

I don't think there is a problem with the validity of the theory at all. It is just it's messy formulation which sparks the issue which we cannot make sense of. What's worse is that all that complain about it are unable to write it down formally what they are actually requesting / how a theory needs to be formulated to be easily make sense of.

... ah god, like just work out the damn actual and correct Kolmogorov probability space for QT / QFT and we are done with this nonsense.

 

[CelHolo]

I don't think there is a problem with the validity of the theory at all. It is just it's messy formulation which sparks the issue which we cannot make sense of. What's worse is that all that complain about it are unable to write it down formally what they are actually requesting / how a theory needs to be formulated to be easily make sense of.

... ah god, like just work out the damn actual and correct Kolmogorov probability space for QT / QFT and we are done with this nonsense.

There just isn't such a probability space, one way of characterising the difference in quantum probability is the absence of such a space. So demanding it be formulated seems fruitless.

 

[PeroK]

... ah god, like just work out the damn actual and correct Kolmogorov probability space for QT / QFT and we are done with this nonsense.

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

 

[CelHolo]

In most reconstructions of quantum theory the complex numbers are imposed by the condition of local tomography, if anybody finds that interesting.

 

[Killtech]

There just isn't such a probability space, one way of characterising the difference in quantum probability is the absence of such a space. So demanding it be formulated seems fruitless.

The very issue with this statement is that Kolmologovs theory is in no way restricting. My biggest issue with understanding the need for quantum probabilities was that Kolmogorovs theory is actually able to produce any kind of distributions and correlations (well fine, there is a restriction to Borel sets for it cannot handle Banach-Tarski stuff, but QFT is harmless and has no such thing). In its raw form probability theory doesn't even have a concept of locality so Bell-stuff isn't in any way special for PT.

The only issue is that you should not do it like the old physicst did: Take Kolmorogorvs theory and overburden it with their classical particle understanding - which by the way is all by itself deeply self-contradictory - and then expect that some magic to happen and a working theory appears. Because guess what? it doesn't! And now you can sell that proof by example as invalidation of Kologorov...

Like just scratch all your assumptions about the quantum world, most of all your crude idea of the singularity bombs (i.e. point like charged particles) and take only the math of QT that works and combine it into a consistent theory together with Kolmogorov core axiom of measurability. If you do that, Kolmogorov will dictate how you have to setup the physical state space to make it produce the needed joint distributions we seen during measurements. Let the math tell you what you are dealing with rather then starting with your own assumptions that you cannot let go of.

But if you deviate from that path you risk ending up building a duct tape attempt like the Kopenhangen quantum probability theory that is setup in a way that implicitly breaks the separation of physical and knowledge information. Sure, as a publicity stunt to make the most wonderous interpretation of a theory it's a cool trick, but do we really need that? But also kudos for showing that it is possible to make a deeply flawed assumption (point particles) work by modifying other more reasonable axioms/definition. It shows how unbelievably flexible math actually is.

 

[CelHolo]

The very issue with this statement is that Kolmologovs theory is in no way restricting. My biggest issue with understanding the need for quantum probabilities was that Kolmogorovs theory is actually able to produce any kind of distributions and correlations (well fine, there is a restriction to Borel sets for it cannot handle Banach-Tarski stuff, but QFT is harmless and has no such thing). In its raw form probability theory doesn't even have a concept of locality so Bell-stuff isn't in any way special for PT.

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.