Nobody understands quantum physics?

[Morbert]

You represent outcomes with projectors. For example, in the case of particle position, the projector would be something like $|x\rangle\langle x|$. That's enough for computing the probability of position $x$. However, the formalism you outlined talks about probabilities of position, not about position itself. A formalism that talks about position itself should have a real-valued variable $x$, and the formalism you outlined does not have such a variable. (The operator $\hat{x}$ would not count because it's a hermitian operator, not a real-valued variable.)

Compare this formalism with classical stochastic mechanics. There one has a function $x(t)$, which is a stochastic (not deterministic) function of $t$. Such a quantity is missing in the quantum formalism.

Where we disagree is I don't think such a variable is needed "to explain why a single outcome (rather than all outcomes at once) realizes at all". We can show that, when presented with a sample space of experimental outcomes, QM rules out the possibility that all outcomes (or even more than one) will occur at once, since the probability is 0, as shown in my last post. Similarly, we can show that "no outcome occurs" also has a probability $p(\varnothing) = \mathrm{tr}_{sD}([I_{sD}-\sum_i\Pi_i(t)] \rho_s\otimes\rho_D) = 0$.

I.e. We can interpret QM as returning probabilities for possible outcomes, without a variable corresponding to the "true outcome", and this interpretation won't suffer from problems like implying all outcomes might occur at once.

 

[Demystifier]

Where we disagree is I don't think such a variable is needed "to explain why a single outcome (rather than all outcomes at once) realizes at all".

A 5 year child asks: Mommy and daddy, why there is no Sun during the night?
Daddy: Because during the night the probability of seeing Sun is zero.
Mommy: Because Earth is round and during the night the Sun is on the other side.

Both explanations are true, but which is better?

 

[martinbn]

A 5 year child asks: Mommy and daddy, why there is no Sun during the night?
Daddy: Because during the night the probability of seeing Sun is zero.
Mommy: Because Earth is round and during the night the Sun is on the other side.

Both explanations are true, but which is better?

This is misleading. How about a 5 year old wants to have a sibling. The parents say sure. The child ask: where is it now? Parent one: it doesn't exist yet. Parent two: there are exact values of the position variables, we just don't know them.

 

[Fra]

Parent two: there are exact values of the position variables, we just don't know them.

The point would i think be that its not just we that doesnt know, Noone or no thing, has been able to learn them, which is why we do not obet bell inequality. It might well be "lost in chaos" and thus it decouples from any inference.

I think the difference betwteen a subatomic variable and the sun, is that it would take nothing less than a black hole to scramble the information of where the sun went for all the environment. Putting a blindfold on daddy at night also gives zero probability of seeing rhe sun but that isnt the mechanism.

/Fredrik

 

[Morbert]

A 5 year child asks: Mommy and daddy, why there is no Sun during the night?
Daddy: Because during the night the probability of seeing Sun is zero.
Mommy: Because Earth is round and during the night the Sun is on the other side.

Both explanations are true, but which is better?

I think this is where the subjectivity comes into play. Everyone would agree that for macroscopic matters like the the solar system, explanations like the 2nd are better. When it comes to microscopic matters, many people are happy to frame QM as characterising microscopic systems in terms of macroscopic tests and responses, without grounding it in some primitive ontology.

At the same time, this doesn't mean the notion of explanation is entirely surrendered. E.g. The Dad might instead explain why there is no sun at night by talking about the way in which the solar system is "prepared" and the dynamics it obeys.

 

[Fra]

At the same time, this doesn't mean the notion of explanation is entirely surrendered. E.g. The Dad might instead explain why there is no sun at night by talking about the way in which the solar system is "prepared" and the dynamics it obeys.

Except dad cant "control" or prepare a source of suns. The sun (or rather the earth) goes where it wants. Its exactly here we need a bridge in the two views.

/Fredrik

 

[Demystifier]

When it comes to microscopic matters, many people are happy to frame QM as characterising microscopic systems in terms of macroscopic tests and responses, without grounding it in some primitive ontology.

Well summarized!

 

[Demystifier]

This is misleading. How about a 5 year old wants to have a sibling. The parents say sure. The child ask: where is it now? Parent one: it doesn't exist yet. Parent two: there are exact values of the position variables, we just don't know them.

Parent 3 (it's a modern family involving more than two parents): It doesn't exist yet, it will be made out of food that mommy eats, very much like you make a tower out of sand.

 

[A. Neumaier]

Given a sample space of possible outcomes $\{o_i\}$ of an experiment involving measured system $s$ and detector array $D$, the probability of an outcome occurring in a given run is $$p(o_i) = \mathrm{tr}_{sD}(\Pi_i(t)\rho_s\otimes\rho_D)$$The probability of an event like $o_i\lor o_j$ occurring is $$p(o_i\lor o_j)=\mathrm{tr}_{sD}([\Pi_i(t)+\Pi_j(t)]\rho_s\otimes\rho_D)$$The probability of all outcomes occurring at once in a given run is $$p(o_1\land o_2\land\dots\land o_N) = \mathrm{tr}_{sD}(\Pi_1(t)\Pi_2(t)...\Pi_N(t)\rho_s\otimes\rho_D) = 0$$Where am I going wrong?

This is fine. But

• it does not conform to the definitions in Wikipedia that you cited (which is quite sloppy, so this is the minor problem).
• Your events are still classical, i.e., outside the framework of quantum mechanics. They are added to the quantum formalism in an ad hoc manner, without any rules for identifying their meaning.

What does it mean in quantum terms for a detector to produce an event? To give your POVM a meaning you need to refer to the classical description of the experiment done to identify the projectors with real events. This is what I mean with classical.

 

[martinbn]

Parent 3 (it's a modern family involving more than two parents): It doesn't exist yet, it will be made out of food that mommy eats, very much like you make a tower out of sand.

But your need for hidden variables is like parent 2.

 

[A. Neumaier]

The magnetic moment of the electron is proportional to its spin and as such of course an observable as any other and thus behaves probabilistic.

No. Only the sign behaves probabilistic, but $g-2$ is a universal constant, a coefficient in the Hamiltonian.

 

[vanhees71]

Yes, but to measure $(g-2)$ you must somehow measure the gyration frequency, and this can be done only by measuring a component of the magnetic moment.

 

[Demystifier]

But your need for hidden variables is like parent 2.

No, it's like parent 3. Hidden variables in this case are positions of atoms (of which the food and sibling are made), not position of the sibling. Only fundamental stuff needs to always exist, emergent stuff may be created.

 

[martinbn]

No, it's like parent 3. Hidden variables in this case are positions of atoms (of which the food and sibling are made), not position of the sibling. Only fundamental stuff needs to always exist, emergent stuff may be created.

Why are positions of particles fundamental?

 

[A. Neumaier]

Yes, but to measure $(g-2)$ you must somehow measure the gyration frequency,

This doesn't alter the fact that a constant is measured, not a spin observable.

All high precision measurements in quantum physics measure constants, not state-dependent observables.

Only measurements of state-dependent observables are subject to Born's rule, and these are quite inaccurate.

and this can be done only by measuring a component of the magnetic moment.

This is quite wrong.

The ultrahigh precision measurements of $g-2$ are not measurements of a spin component, but measurements of two frequencies whose ratio is then taken. See Section 9.4 of my paper Quantum tomography explains quantum mechanics (Version v4).

 

[gentzen]

The problem with Bohr is that he is so unclear in his writing that it invites such "philosophing" about "what might the author have wanted to say", and that's why QT till today is often displayed as something mystic. I find Bohr' and Heisenberg's writings did a bad job in "interpreting QT", because they were too philosophical rather than to wrap off all the dust of the unclear quarter of a century of "old quantum theory", where you had no clear picture of how to describe "quantum phenomena", leading to indeed vague and inconsistent pictures like "wave-particle duality", which was substituted by Bohr just by the even more obscure "complemantarity principle". I think with modern QT there's no need for such philosophical distortions of a very elegant and clear mathematical formulation which just does what all deep physical theories do, i.e., summarizing many empirical facts into a scheme of a few generally valid basic principles, with which all these and (hopefully) many to be discovered phenomena in the future can be described.

I was "surprised" how my conversation with WernerQH went. I remembered him as someone with whom I had constructive and interesting exchanges in the past. So I went back and read some of his early posts and our exchanges. Conclusion: He has not changed, what is different is the current context. That context is set by DrChinese rejecting Bohr's analysis and understanding of quantum phenomena, and then vanhees71 accidentally joining him by disqualifying Bohr's explanations as mere philosophy.

Well, the quest for unification is not my quest. I guess my quest is just to be able to communicate (about physics), without too much appeal to authority.

The current state of quantum phyics is such that some appeal to authority is still needed. And you cannot just replace Bohr by Ballentine (or Peres) as "your authority," because (1) they are not accepted by sufficiently many people as authority and (2) they never accepted their status as authority, and hence did not act and write in a way that would make them suitable authorities.

It is wrong to see the debate between Einstein and Bohr as a quibble about philosophy. Maybe Bohr's complementarity was a philosophical concept brought forward in the hope that "mathematical" scientific success could be transfered to "non-mathematical" disciplines like Biology. That hope partially became true because of people like Max Dellbrück encouraged by Bohr, but complementarity itself was a failure in that respect.

But Einstein did not attack complementarity. He fought for physical concepts and physical intuition, and Bohr did exactly the same. Bohr's physical intuition is not philosophy, even if he was bad at explaining it. And he sure wrote problematic philosophical texts, like:

A new epoch in physical science was inaugurated, however, by Planck's discovery of the elementary quantum of action, which revealed a feature of wholeness inherent in atomic processes, going far beyond the ancient idea of the limited divisibility of matter.

There is wholeness in Biology, and maybe this explains why it was a "non-mathematical" discipline, because how can you analyse something which cannot be decomposed? What we have in physics is actually contextuality (not wholeness), which yields to mathematical analysis without much resistance.

Just because Bohr's writting was sometimes hard to understand doesn't mean that it was philosophy. Same for Einstein's hole argument in general relativity. Just because it is hard to understand doesn't mean that it would be philosophy instead of physics.

 

[gentzen]

As long as you don't explicitly measure, the probability that the neutron has turned into a proton indeed gradually increases.

Yes, that's the theorist's picture. The experimentalist knows that the neutron decays even when he's not "measuring", and on a time scale shorter than microseconds.

I guess you are misinterpreting my intentions (see my reply to the old post by vanhees71 above). I just try to explain the standard picture, not defend my own interpretation(s) or Neumaier's thermal interpretation. Of course there will be a time where I will again defend "them," but not in the current context where serious physical mistakes are commited (not by you) from my point of view.

 

[vanhees71]

This doesn't alter the fact that a constant is measured, not a spin observable.

All high precision measurements in quantum physics measure constants, not state-dependent observables.

Only measurements of state-dependent observables are subject to Born's rule, and these are quite inaccurate.

This is quite wrong.

The ultrahigh precision measurements of $g-2$ are not measurements of a spin component, but measurements of two frequencies whose ratio is then taken. See Section 9.4 of my paper Quantum tomography explains quantum mechanics (Version v4).

The frequencies are precisely about spin precession, and that's of course an observable in the usual sense of the word. For details see (open access), e.g.,

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.141801

 

[A. Neumaier]

Yes, but to measure $(g-2)$ you must somehow measure the gyration frequency, and this can be done only by measuring a component of the magnetic moment.

The frequencies are precisely about spin precession, and that's of course an observable in the usual sense of the word. For details see (open access), e.g.,

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.141801

Spin precession frequencies are not the same as components of the magnetic moment.

Frequencies are measured by (here NMR) spectroscopy, not by quantum measurements according to Born's rule.

And these frequencies are constants, too, and not observables with random outcomes.

 

[WernerQH]

I just try to explain the standard picture, not defend my own interpretation(s) or Neumaier's thermal interpretation.

Thank you for clarifying, and for your thoughtful comments in general. Actually I've been exposed to the "standard picture" ad nauseam. (I learnt quantum mechanics fifty years ago.)

 

[WernerQH]

Frequencies are measured by (here NMR) spectroscopy, not by quantum measurements according to Born's rule.

I can't make sense of this at all. In NMR the spins interact with a field varying at radio frequencies, but the interaction term still depends on the angle between the spin and the varying field. Perhaps you think of a spin as precessing at an exactly defined frequency, but it could also be an average frequency. Random deviations from the momentary direction cannot be resolved experimentally.

 

[A. Neumaier]

I can't make sense of this at all. In NMR the spins interact with a field varying at radio frequencies, but the interaction term still depends on the angle between the spin and the varying field.

Yes, the interaction can only be defined in terms of the spin vector.

But the measurement of the constant $g-2$ is unrelated to measuring components of the spin vector (which are observables whose results are state-dependent).

Measuring a constant has nothing at all to do with Born's rule.

 

[Demystifier]

Why are positions of particles fundamental?

Because here (a story told to a child) we are using a classical model, where particles are small objects with well defined positions by definition.

 

[vanhees71]

In NMR you measure

Yes, the interaction can only be defined in terms of the spin vector.

But the measurement of the constant $g-2$ is unrelated to measuring components of the spin vector (which are observables whose results are state-dependent).

Measuring a constant has nothing at all to do with Born's rule.

What's measured are in fact decay electrons as a function of time, showing oscillations with the frequency $\omega_a$. That's of course related to the precession of the muon spin. If it were not, how do you think would this measurment have anything to do $(g-2)$ in the first place. NMR is used to accurately measure the magnetic field, which is the other ingredient needed to get $(g-2)$ from the measured $\omega_a$. It's all in the quoted paper, and in more detail in Ref. [56] in there:

https://doi.org/10.1103/PhysRevD.73.072003
https://arxiv.org/abs/hep-ex/0602035v1

 

[martinbn]

Because here (a story told to a child) we are using a classical model, where particles are small objects with well defined positions by definition.

Wait, are we not giving analogies, while we have QM in mind?

 

[WernerQH]

But the measurement of the constant g-2 is unrelated to measuring components of the spin vector (which are observables whose results are state-dependent).

How can you count rotations without ever measuring an angle?

 

[Demystifier]

Wait, are we not giving analogies, while we have QM in mind?

In QM, I don't know what is fundamental. But in non-relativistic QM position could be fundamental. Momentum, on the other hand, could not, because Bohmian mechanics with momentum ontology cannot reproduce predictions of standard QM.

 

[vanhees71]

It's a very theoretical concept telling the one or the other observable fundamental. For me, fundamental since the beginning of the 20th century are symmetries, first of the spacetime models and then other more abstract symmetries (both local gauge symmetries, which however are not true symmetries but just redundancies in the description, and global (accidental) symmetries like flavor/isospin/chiral symmetry in the light-quark sector of QCD, etc.).

From this point of view position is a derived not a fundamental quantity. It can be defined for all kinds of massive particles in both non-relativistic QM and relativistic QFT as well as for massless spin-0 and spin-1/2 quanta in relativistic QFT.

Although you keep claiming otherwise, Bohmian mechanics can only be formulated in some sense for non-relativistic QM. I've no clue, whether or not it provides an "ontology", but the Bohmian trajectories seem not to be observable in any sense at all.

 

[martinbn]

In QM, I don't know what is fundamental. But in non-relativistic QM position could be fundamental. Momentum, on the other hand, could not, because Bohmian mechanics with momentum ontology cannot reproduce predictions of standard QM.

Then you are in the position of parent two.

 

[Fra]

In qbism (or variants of it), the central perspective is that of the agent. So I take the agents/observers empirical first hand observations are primary. But these are subjective and generally do not qualify as "observables" in the sense of QM. These "variables" are not available for eavesdropping in the environment, they are exclusive and hidden, but I think it makes sense to think they of them as real.

It seems to me that maybe these primary variables at least bear a similarity of bohmian solipsistic variables? These are protected from obeying bells inequality because they are truly hidden, so all, except the agent itself. Unlike an ignorance, which IS in principle available, it's just the physicists who are unaware of it.

I think the notion of "observables" of QM is too narrow, meaning that just because something is not an "observable" in the technical sense, really doesnt mean it can't be observed by any observer.

/Fredrik