Meaning of the Wave Function

[Christopher A. Fuchs]

QBismOnlineForum201410

Slides by Ruediger Schack on “QBism and the character of the world”

[Ulrich Mohrhoff]

I can’t seem to find these slides.

[Christopher A. Fuchs]

The slides are there now.

[Robert Griffiths]

Dear Ruediger,

I looked at the slides and I have some questions not necessarily directly related to them, but related to QBism. Here are the first two:

1. How does QBism treat the two measurement problems: (i) the
Schrodinger cat problem and (ii) how the pointer is related to properties of
the microscopic system before the measurement took place. And what use is made
of the quantum wavefunction in discussing these.

2. Would the approach involving subjectivist Bayesian probabilities be
needed if (counterfactually) classical mechanics reigned supreme? Or it the
world were classical, but with a stochastic dynamics replacing Hamiltonian
dynamics (“classical GRW”)? Alternatively, how is the QBist approach motivated
by specific quantum mechanical phenomena, and how does it help to think about
them?

[Ulrich Mohrhoff]

Dear all,
Maybe my recent critical appraisal of QBism may be of interest to some.
Ulrich

[Ruediger Schack]

Dear Bob,

1. How does QBism treat the two measurement problems: (i) the
Schrodinger cat problem and (ii) how the pointer is related to properties of the microscopic system before the measurement took place. And what use is made of the quantum wavefunction in discussing these.

Thanks for your questions. To answer 1 (i), say I assign a superposition state to a cat in a box. This quantum state is my state of belief and refers to my expectations regarding the outcomes of any measurement I choose to perform on the cat. There is no measurement problem here. Regarding 1 (ii), QBism does not talk about properties of microscopic systems because, again, the quantum wavefunction expresses an agent’s beliefs about the consequences of his actions, nothing more or less.

[Ruediger Schack]

Dear Bob,

You ask: “Alternatively, how is the QBist approach motivated
by specific quantum mechanical phenomena, and how does it help to think about them?”

Take, for example, the no-cloning theorem. It has a trivial explanation if one thinks of the wave function as epistemic. Take the Kochen-Specker theorem. It implies that measurements do not have pre-existing outcomes. Take Bell’s theorem. It suggests strongly that there are no hidden variables. QBism is motivated by these and other consequences of the quantum formalism.

[Quantum Speculations]

Hi Ruediger and Chris,

I would like to know whether QBism has some unsolved problems in its current stage. I do think some of Bohr’s views on QM are deep, and searching for the ultimate reality may be “risky game”. But I also think that the beautiful mathematical formalism of QM, which was discovered by our intuition and lucky guess, already implies the existence of the underlying physical reality, and we do have abilities (though not logical) to discover some aspects of reality,

Shan

[Ruediger Schack]

Dear Shan,
This a very nice question, thank you. Let me answer the second part first. I agree entirely that quantum mechanics helps us to learn about reality. I was trying to express this in the title of my talk: QBism and the character of the world. QBism is sometimes (wrongly) labeled as anti-realist. This label is misleading because QBism does not reject reality but the particular assumptions about reality, made, e.g., by hidden-variable theories and ontological models. By taking the quantum formalism seriously and striving for total consistency, QBism arrives at a view where reality does not take the form of a static block universe, but is agent-dependent and malleable.

Maybe the biggest open question for QBism is how to derive quantum mechanics from a simple physical principle. Our programme to rederive quantum mechanics in the SIC formalism is an attempt to do just that. Here the physical principle is the idea that measurement outcomes do not exist prior to a measurement. This idea is expressed in the simple form the Born rule assumes in the SIC formalism. We have made a lot of progress, but there remain big conceptual and technical questions.

[Robert Griffiths]

Dear Ruediger,

Let me pose some additional questions now that the technical difficlties besetting yesterday’s exchange seem to have been settled.

3. Regarding your answer (in 897) to my question about how the pointer
position in a measurement is related to properties of the microscopic system
before the measurement took place, you replied that “QBism does not talk about
properties of microscopic systems because, again, the quantum wavefunction
expresses an agent’s beliefs about the consequences of his actions, nothing
more or less.”
What worries me about your answer is that you seem to be abandoning a
lot of the most significant advances of physics in the 20th century, namely the
explanation of properties of matter in terms of properties of its microscopic
constituents. Thus just yesterday when because of technical difficulties I was
unable to participate in the discussion I went to our physics colloquium where
the speaker discussed all sorts of results coming from measurements of
colliding beams at the LHC where the Higgs particle was (they claim)
discovered. His talk was filled with references to particle tracks, especially
muons and electrons, as recorded in an enormous detector, and then on the
inferences made from this, that the Higgs decayed into this and that. Is the
aim of QBism to render all such talk obsolete, and if so what can be put in the
place of it.

4. The issue of locality. Your Am. J. Phys. (AJP) paper claims that the
(non)locality problem is solved because Alice is always at a single spacetime
location. I do not at all understand this. It seems to be easy to imagine
experiments in which Alice sends automatic devices off to Mars arranged to
carry out certain measurements at some time when she is doing other
measurements in her lab on Earth at spacelike separation. She will or will not
see superluminal influences. I do not see how this is addressed in AJP.
To take another example, a few years ago neutrinos seemed to be violating the
speed limit. This was settled by somebody finding a faulty cable, not by a
declaration that this is obviously unthinkable.

5. Why should we put our bets on QBism rather than GRW or Bohm or
consistent histories or some other alternative on the market?

[Ruediger Schack]

Dear Bob,

Thanks again for your questions. Yesterday, my answers were shorter than your questions, and I fear that this pattern will be repeated today. Please don’t interpret this as a lack of interest on my part. It is not.

Concerning your question 3, maybe QBism does not want to make claims about particle tracks, or talk about the Higgs decaying into this and that, obsolete. But QBism tries to remind physicists that this is indeed just talk. This talk is extremely useful when we try to make sense of data and plan experiments, but ultimately only a consistent application of the quantum formalism guarantees consistent predictions. How is talk about particle tracks fundamentally different from talk about which path a particle took in a double slit experiment?

Your question 4 about locality makes a good point. Our AJP paper does indeed not address the issue of whether quantum mechanics allows signaling or not. Our paper assumes both special relativity and the quantum formalism and therefore rules out superluminal signaling from the outset. Apparently we failed to make this sufficiently clear in the paper. On the other hand, doesn’t almost all the literature on nonlocality in quantum mechanics assume no-signaling?

Finally, why QBism and not some other interpretation? QBism tries to change the way we think about quantum mechanics. You want to put your money on an interpretation which gives rise to new questions and new developments. Betting on QBism is a risky investment with a potentially large payoff.

[Ruediger Schack]

I am aware that, because of yesterday’s technical problems, the discussion of my talk has been rescheduled for later today. Unfortunately, it is already late evening in Egham, which means I won’t be able to participate.

[Quantum Speculations]

Hi Ruediger,

Thanks a lot for your answers to my questions!

I am sorry for the wrong schedule. May you be available this evening in Egham? I can set a new time slot suitable for you.

Best,
Shan

[Ulrich Mohrhoff]

Good morning, Ruediger.

I’m glad to have this opportunity to pick your brains about QBism.

I begin with a question that is rhetorical since I answer it myself. Shouldn’t QBists make a distinction between a direct experience and an indirect experience such as the indirect experience of a spin component (via the direct experience of an apparatus pointer)? To some extent this is a rephrasing of Robert’s question about “how the pointer position in a measurement is related to properties of the microscopic system before the measurement took place”. Since I agree with you that no property is a possessed property unless it is a measured property, I wouldn’t refer to properties that a microscopic system has before a measurement, but I would make a distinction between the experience/measurement of a pointer position and the experience/measurement of a spin component.

Your responses to Robert are a bit indecisive. After replying that “QBism does not talk about properties of microscopic systems” you retract a bit, saying that “maybe QBism does not want to make claims about particle tracks … obsolete”, but you also throw down the gauntlet by asking: “How is talk about particle tracks fundamentally different from talk about which path a particle took in a double slit experiment?”

If you refuse to distinguish between direct and indirect experiences, as you must since you claim that QBism has no measurement problem, then you have to treat particle tracks the same way you treat the path of a particle in a double slit experiment. Your discussion of Wigner’s friend makes it clear that this is indeed what you do: there is a particle track only if it is experienced, and only for those agents who have experienced it or have received a trustworthy report from someone who has experienced it, as when Wigner’s friend reveals her outcome to Wigner. My first non-rhetorical question is: What would be a QBist’s answer to the question why different agents experience the same particle track? I know that quantum mechanics predicts that the experiences of different agents will be strictly correlated with the real particle track out there, but how would a QBist, who does not believe in real particle tracks out there, answer this question — say, in terms of agents’ betting behavior?

Now I too have to retract somewhat. I agree with you that no property of a microscopic system is a possessed property unless it is a measured property. What you are saying is that no property of any kind is a possessed property unless it is experienced. The question then is, how do you define properties? For me, as a disciple of Bohr, a spin component is defined by the direction of the gradient of a magnetic field, which is defined by a macroscopic apparatus. How do you define a spin component without the benefit of the distinction between microscopic system and macroscopic apparatus?

Coming to my next question, a QBist’s favorite Bohr quote refers to “relations between the manifold aspects of our experience”, where I emphasize the first person plural because of its importance to Bohr. In your paper with Chris and David (arXiv:1311.5253v1) you quote the same phrase with two significant alterations: “[cor]relations between the manifold aspects of [her] experience” (your square brackets, my emphasis of the first person singular). Say, Chris and David each experience a bottle of wine. The importance of Bohr’s first person plural is that it turns the respective experiences of Chris and David into a single, objective bottle of wine. What makes it possible to speak of a shared objective world is the possibility of communicating in an unambiguous language, and this possibility exists because our experiences allow themselves to be thought of as experiences of interacting objects (bundles of properties) and causally related events, from which the experiencing subjects can abstract themselves. How do QBists communicate without the benefit of an objective world?

The QBist answers I have seen to this question are very confusing. On the one hand, Chris (the real one) writes: “The world is filled with all the same things it was before quantum theory came along, like each of our experiences, that rock and that tree, and all the other things under the sun” (arXiv:1003.5209v1). On the other hand, what could be objective if the traffic signal is in a superposition of red and green unless it is experienced by a driver or he gets a trustworthy report from his front-seat passenger? Could you say something that will help dispel my confusion?

Your answers, however brief, will be greatly appreciated.

Best,
Ulrich

[Ruediger Schack]

Dear Shan,

Thanks for the offer of a new time slot, but I am not free today. I’ll try my best, however, to answer Ulrich’s latest set of questions.

All the best,

Ruediger

[Ruediger Schack]

Dear Ulrich,

Many thanks for your questions. Let me try to answer them one by one.

You ask:

What would be a QBist’s answer to the question why different agents experience the same particle track? I know that quantum mechanics predicts that the experiences of different agents will be strictly correlated with the real particle track out there, but how would a QBist, who does not believe in real particle tracks out there, answer this question — say, in terms of agents’ betting behavior?

My answer:

“Real particle tracks” do not feature in quantum mechanics. Therefore quantum mechanics cannot predict that “the experiences of different agents will be strictly correlated with the real particle tracks out there.” But quantum mechanics allows one agent (Alice) to make predictions about — to gamble on — the content of another agent’s (Bob’s) report about his experiences. A consistent application of quantum mechanics requires Alice to treat Bob as a physical system. This gives Alice a tool to make bets on what Bob will tell her about the particle tracks he saw.

You ask:

Now I too have to retract somewhat. I agree with you that no property of a microscopic system is a possessed property unless it is a measured property. What you are saying is that no property of any kind is a possessed property unless it is experienced. The question then is, how do you define properties?

My answer:

Since QBism does not make use of the concept of properties, I don’t see why a QBist should be required to define properties.

You ask:

For me, as a disciple of Bohr, a spin component is defined by the direction of the gradient of a magnetic field, which is defined by a macroscopic apparatus. How do you define a spin component without the benefit of the distinction between microscopic system and macroscopic apparatus?

My answer:

QBist quantum mechanics is about action. According to QBism, the purpose of quantum mechanics is to enable an agent to gamble consistently on the consequences of his actions on the world. Actions can take many forms, from kicking a pebble to probing a sample by applying a magnetic field and radio frequency signals.

You ask:

Coming to my next question, a QBist’s favorite Bohr quote refers to “relations between the manifold aspects of our experience”, where I emphasize the first person plural because of its importance to Bohr. In your paper with Chris and David (arXiv:1311.5253v1) you quote the same phrase with two significant alterations: “[cor]relations between the manifold aspects of [her] experience” (your square brackets, my emphasis of the first person singular). Say, Chris and David each experience a bottle of wine. The importance of Bohr’s first person plural is that it turns the respective experiences of Chris and David into a single, objective bottle of wine. What makes it possible to speak of a shared objective world is the possibility of communicating in an unambiguous language, and this possibility exists because our experiences allow themselves to be thought of as experiences of interacting objects (bundles of properties) and causally related events, from which the experiencing subjects can
abstract themselves. How do QBists communicate without the benefit of an objective world?

My answer:

Well, you know that QBism takes a different tack. No two agents ever experience the same thing. For a QBist, Chris’s and David’s experiences are not derived from the objective properties of the bottle of wine. Rather, their respective, highly individual, experiences add to the reality of the bottle. Chris and David communicate in the many diverse ways that people, and especially old friends sharing a bottle of wine, have at their disposal. Like any language, the language they use is far from unambiguous; all they can hope to do is strive for as much clarity as possible. But they have no need for a pre-existing objective world to have a conversation that enriches the experience of each of them. In the language of quantum mechanics, communication is taking measurement actions to elicit responses.

You ask:

The QBist answers I have seen to this question are very confusing. On the one hand, Chris (the real one) writes: “The world is filled with all the same things it was before quantum theory came along, like each of our experiences, that rock and that tree, and all the other things under the sun” (arXiv:1003.5209v1). On the other hand, what could be objective if the traffic signal is in a superposition of red and green unless it is experienced by a driver or he gets a trustworthy report from his front-seat passenger? Could you say something that will help dispel my confusion?

My answer:

No QBist would ever say that a “traffic signal is in a superposition of red and green unless it is experienced by a driver”. To repeat what I wrote earlier in this forum: when an agent writes down a superposition state, he does not mean that the traffic signal has a property “is in a superposition of red and green”. He simply expresses his beliefs about what he will experience when he chooses to look at the signal. Now, for the purpose of traffic safety, it is irrelevant whether the traffic signal has an objective colour before I experience it. What matters is that I take the correct action based on what colour I see.

All the best,

Ruediger

[Ulrich Mohrhoff]

Dear Ruediger,

Many thanks for your detailed answers to my questions. I have a few comments, numbered 1 to 5 corresponding to your five answers.

1. Actually there are ways to assign probabilities to particle tracks (suitably defined), and your answer seems to accept that, having Alice making bets on Bob’s report about the tracks he saw.

2. QBists claim not to be solipsists. This means they are able to communicate and to understand, even trust, each other. How do they communicate without using words that refer to properties of things?

3. Actions need to be formulated. How do QBists talk about their actions (e.g., kicking a pebble) without using what Bohr called “classical language” — a language in which spin-1/2 particles in an inhomogeneous magnetic field are deflected either up or down and actions have consequences to which probabilities can be assigned?

4. Apologies for not having made myself sufficiently clear. I agree with you that no two people ever experience exactly the same thing (in both senses of numerically identical and exactly alike), and that experiences are not derived from the objective properties of the wine bottle. I would even be willing to say that our respective experiences of the bottle constitute the objective bottle, not just add to its reality, although this goes a little too far: what actually constitutes the objective reality of the bottle is a shared language, which enables us to think and talk about the bottle as if it were part of a world that exists in itself, independently of our experiences. But I agree with you that C and D have no need for a pre-existing objective world to have a conversation that enriches the experience of each of them, and that our language is far from unambiguous.

Where I disagree with you is that there is no unambiguous language whatsoever. There is an unambiguous core, a minimal language (which Bohr called “classical language”) without which communication would simply be impossible. (When Bohr insists that quantum mechanics presupposes this language he is usually understood as saying that it presupposes classical physics, which is the kind of nonsense he never said but keeps being accused of.) And because of this there is an objective world that conforms to this language, a world in which (successful) measurements have definite outcomes. This means not only that only definite outcomes are experienced but also that it is perfectly consistent to assume that outcomes that are not experienced are definite as well. Wigner never expects his friend to report a superposition of the possible outcomes of her intended measurement. (This is not the same as reporting a possible outcome of a different measurement, incompatible with the intended one, in case she changed her mind.) Such a report is never experienced. So maybe our views would converge if we spoke of reports rather than of experiences.

In any case, I agree with Bohr that the possibility of unambiguous communication is a sine qua non in all of science. We are on the same page where \psi-ontology is concerned. To construct an objective world on reified probability algorithms is to construct castles on quicksand. But to deny the possibility of unambiguous communication is to construct no castles at all, and that is not science.

5. I used the customary language to which we both object, hoping that it will be understood with that objection in mind. To be sure, “being in a quantum state” means being associated with an algorithm for assigning probabilities to the possible outcomes of any possible measurement. So, indeed, Wigner’s friend is not “in” a superposition in which she has “propensities” for giving different reports. Yet in your paper with Chris and David you write:

“Acting as an agent, Alice can use the formalism of quantum mechanics to model any physical system external to herself. QBism directs her to treat all such external systems on the same footing, whether they be atoms, enormous molecules, macroscopic crystals, beam splitters, Stern-Gerlach magnets, or even agents other than Alice.”

I take this to mean that I could perform a measurement on the traffic signal that is incompatible with a measurement that determines its color (red or green). The question is not whether the signal has an objective color before I experience it. The question is whether I can experience it not having a definite color. If I can’t, then it is perfectly consistent to assume that it has a definite color whether or not I experience which one it is, unlike a spin component, which doesn’t have a definite value unless someone (no matter who or where) measures it. If you say that I can, you’ve lost me again.

All the best to you,
Ulrich

[Ruediger Schack]

Dear Ulrich,

It is tempting to again answer your points one by one. But I fear that this might not lead to more clarity in the end. So what I will do instead is focus on the issue of properties. I also intend this to be my last contribution to the online workshop.

According to QBism, measurements on nuclear spin components and measurements on traffic signals have this in common: their outcomes do not reveal pre-existing properties. Despite your objections, it seems to me that treating all physical systems on the same footing is the only consistent approach. But if properties are not responsible for measurement outcomes, in what way does it make sense for a QBist to speak of “properties” at all? Here is how. According to QBism, the quantum formalism allows an agent (an agent does not have to be human: a robot could use the quantum formalism to inform its actions) to gamble consistently on the outcomes of his quantum measurement actions. Quantum mechanics provides a consistency criterion in the form of the Born rule, which depends on the dimension of Hilbert space. (This can be seen particularly clearly in the SIC representation of the Born rule.) So Hilbert-space dimension is a system property in this particular sense: it does not determine any outcomes, it does not even determine any outcome probabilities, but it shapes the way that an agent’s probability assignments should be interconnected.

All the best,

Ruediger

[Ulrich Mohrhoff]

Dear Ruediger,

Thank you for your patience and helpful answers!

Best,
Ulrich

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