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The reason I’m late to the party is the oddity of my time zone (India), not that I want to have the last word!
To my mind, the wave function is a computing “machine” with inputs and outputs. (I’m happy to note that some of you would agree with this.) Pop in (a) the outcomes of the relevant measurements that were made, (b) the times when they were made, (c) a measurement to the possible outcomes of which we want to assign probabilities, and (d) the time of this measurement — and out pop the wanted probabilities.
The measurement problem has two major components:
(i) How to account for the collapse of the wave function, which supersedes or disrupts its unitary evolution at the time of (or during) a measurement. This is a pseudo-problem, for the time on which \psi functionally depends is the time of the measurement to the outcomes of which it serves to assign probabilities, not the continuously advancing time on which an evolving physical state depends.
(ii) How to account for the absence of interference between macroscopically distinct states. In other words: establish what von Weizsäcker has called the semantic consistency of the theory, i.e., find a way of thinking in which the quantum-mechanical correlation laws are consistent with the existence of their correlata (measurement outcomes). Unlike Shan (#1114), who believes that the reification of the wave function can help solve this problem, I think that the transmogrification of a calculational tool into an evolving ontic state is what makes it impossible to solve this problem. Another reason solving problem (i) won’t help solving problem (ii) is that the former only arises in the wave-function formulation of quantum mechanics whereas the latter is a problem concerning quantum mechanics regardless of how it is formulated.
I do not think (as Lee at #1118 appears to) that quantum mechanics requires completion. What is incomplete is not the formal apparatus of quantum mechanics but the physical world, inasmuch as the latter is not spatiotemporally differentiated “all the way down”, as I tried to explain in my contribution to this workshop (and in some of the references therein). That the spatiotemporal differentiation of the physical world is incomplete is the reason \psi cannot be an ontic state existing at every instant of time. It is also what makes it possible to establish the theory’s semantic consistency.
When asking ourselves what (if anything) in the micro-world corresponds to any of the mathematical ingredients of the theory’s formal apparatus — not just the wave function — we ought not lose sight of the fact that “to our present knowledge subatomic reality is not a micro-world on its own but a part of empirical reality that exists relative to the macroscopic world, in given experimental arrangements and well-defined physical contexts outside the laboratory”. This quote is from B. Falkenburg’s excellent book Particle Metaphysics. There (most probably) is a deeper level or reality, but (most probably) we won’t be able to discern it by reifying our calculational tools. For this we need both well-defined physical contexts in the macroworld and the quantum-mechanical correlation laws. I like to say this by paraphrasing Kant’s famous statement that “thoughts without content are empty, intuitions without concepts are blind”: without measurements the formal apparatus of quantum mechanics is empty, measurements without the formal apparatus of quantum mechanics are blind.
The deeper reality I (for one) discern is too complex and unfamiliar to most quantum philosophers to even try and outline it here (that I attempted in my contribution), but I want to conclude by saying that reifying our calculational tools is more like erecting an opaque wall between ourselves and that deeper reality. First we must make the correlation laws consistent with the existence of their correlata, and then we must look through the correlation laws and their correlata at what lies beyond them.
Thanks to all and especially Shan for having me as a participant at this great workshop.
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,
UlrichGood 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,
UlrichDear All,
My scheduled time is now up, but I will be happy to respond to any further questions or comments later.
Ulrich
Ken, here I respond to your note concerning the last footnote of my paper, which I reproduce here for the benefit of the others:
“Actually, the diachronic correlations between events in timelike relation are as spooky as the synchronic correlations between events in spacelike relation. While we know how to calculate either kind of correlation, and therefore know how to calculate the probabilities of possible events on the basis of actual events, we know as little of a physical process by which an event here and now contributes to determine the probability of a later event here as we know of a physical process by which an event here and now contributes to determine the probability of a distant event now.”
It’s true that many temporal correlations have the same mathematical form as Bell-inequality violating spatial correlations, but that doesn’t make them “spooky”; there are certainly many local-interacting models that can make sense of correlations between the past and future of a single particle. So I didn’t really understand that last sentence. All that such an explanation requires is that the intermediary beables are affected by at least one of the measurement settings. The reason that the exact same correlations seem “spooky” in the case of EPR-Bell geometries is that we instinctively don’t want to allow the (past) beables to be affected by the (future) measurement settings, not because we don’t know how to explain time-like correlations in the first place.
I used “spooky” rather loosely here and need to apologize for it. My presupposition is that all that quantum mechanics gives us is correlations between measurement outcomes, and that we don’t know of any physical mechanism or natural process by which the outcome of a measurement determines the probabilities of the possible outcomes of a subsequent measurement, any more than we know any physical mechanism or natural process by which Alice’s outcome determines the probabilities of the possible outcomes of Bob’s measurement (in Alice’s mind only, QBists would insist).
It’s my turn to admit that I’m not clear about the intent of your last sentence, but given what I believe is required of an explanation, I do not believe that we know how to explain time-like correlations.
Thanks again for your questions,
Best,
UlrichKen, on to your next bundle of questions.
The other concern I have has to do with your use of the word “atemporal” near the end. Whenever I see this word accompany terms that normally have temporal meaning, I wonder whether the author is (accidentally or purposefully) imagining a 5th time dimension in which things can “happen” in some order without any usual-4th-time-dimension time being involved. Would you say that this new type of causality is effectively happening in some new dimension of time?
While “causality” does normally have a temporal meaning, it doesn’t necessarily have such a meaning. There may be no superluminal causal connections, but the term “superluminal causal connection” is not self-contradictory. (This is just a counterexample.)
I certainly do not imagine another time dimension, though I’m familiar with the difficulty we have in imagining any dimension (including time) except in analogy with a spatial dimension. Whatever happens, happens in the usual time dimension. An atemporal dimension in which “things can ‘happen’ in some [temporal] order” is a contradiction in terms. So, no, this new causality is not effective across any temporal dimension. The different stages of the “transition” from undifferentiated unity to multiplicity coexist, but still there is some kind of causal arrow that makes it legitimate to speak of “stages”, in the sense that the multiplicity exists because of the spatial relations that Being entertains with itself; Being does not exist because of the multiplicity of the manifested world.
is there a block-universe account of these last paragraphs that might help me make sense of them in 4D?
I’m afraid there isn’t. The whole block universe concept strikes me as an illegitimate spatialization and reification of mathematical tools we use to calculate distances and durations.
Is it mere updating of possibilities upon learning new information, or something more than that?
It is more than that, but I’ll admit that it’s hard to get one’s mind around the idea, considering the years I have spend in disabusing myself of the habit of reifying our calculational tools, which makes it impossible to look beyond them.
Dear Ken,
Many thanks for your challenging questions. I’ll start with this one:
I’m reading from your approach that we can say nothing about what happens in between those ultimate measurements. So it’s not just interferometer arms in which nothing can be said to happen; it’s also all the space between us and a gravitationally-lensing supercluster. This seems a bit extreme, at least for those like me who want to understand what the path integral is telling us about what’s happening when we’re not looking. Can you offer me any hope in the case of the supercluster?
I’m afraid I can’t, for I wouldn’t know a sufficiently fundamental difference between the lab interferometer and the gravitationally-lensing supercluster. Do you? Besides, it’s not a question of looking. It’s a question of there being an objective fact of the matter about the path taken by the photon (or whatever).
I’ll need more time to contemplate your subsequent questions, so I’ll shoot this off right now.
Richard,
You are welcome to ask questions any time, even now, if it’s not too late for you. (I just finished my breakfast.)
Ulrich
Dear all,
Maybe my recent critical appraisal of QBism may be of interest to some.
UlrichSo why is there no answer to the question “Which outgoing particle is identical with which incoming one?”? Because the incoming particles (and therefore the outgoing ones as well) are one and the same entity. What’s more, there is no compelling reason to believe that this identity ceases when it ceases to have observable consequences owing to the presence of individuating properties. We are free to take the view that intrinsically each particle is numerically identical with every other particle; what presents itself here and now with these properties and what presents itself there and then with those properties is one and the same entity. For want of a better word I call it “Being” with a capital B.
As I see it, the main reason it is so hard to make sense of the quantum theory is that it answers a question we are not in the habit of asking. Instead of asking what the ultimate constituents of matter are and how they interact and combine, we should ask: how are forms manifested? This question, too, has a straightforward answer: The shapes of things are manifested with the help of reflexive spatial relations. By entering into reflexive spatial relations, Being gives rise to (i) what looks like a multiplicity of relata if the reflexive quality of the relations is ignored and (ii) what looks like a substantial expanse if the spatial quality of the relations is reified.
To my mind, the most fruitful way to understand the necessary distinction between the classical or macroscopic domain (which contains measurement-independent properties) and the non-classical or quantum domain (whose properties exist only if, when, and to the extent that they are measured) is that it is essentially a distinction between the manifested world and its manifestation.
Quantum mechanics thus presents us with a so far unrecognized kind of causality — unrecognized within the scientific literature albeit well-known to metaphysics. This causality is associated with the atemporal process of manifestation, which effects the transition from a condition of complete indefiniteness and indistinguishability to a condition of maximal definiteness and distinguishability. It must be distinguished from its familiar spatiotemporal cousin, which links states or events across time or spacetime. The latter causality plays no role in the manifestation, which is why it is inapplicable to the subject-matter of quantum mechanics — the correlation laws that are instrumental in the process of manifestation. The atemporal causality associated with the process of manifestation thus casts new light on quantum theory’s mysterious violation of outcome-independence. The reason why local explanations do not work is the same as the reason why the manifestation of the spatiotemporal world cannot be explained by processes that connect events within the spacetime arena.
The eigenvalue–eigenstate link is an interpretive principle that saves the appearances in the context of the wave-function formulation of quantum mechanics. To go beyond a metaphysically sterile instrumentalism, a different interpretive principle needs to be used, as well as as a different formulation of quantum mechanics: Feynman’s. Both the wave-function formulation and Feynman’s feature a pair of dynamical principles; in the former they are unitary evolution and collapse, in the latter they are summation over amplitudes and summation over probabilities. In the context of the wave-function formulation, unitary evolution seems “normal”; what calls for explanation is collapse. In the context of Feynman’s formulation, adding probabilities seems “normal”; what calls for explanation is why we have to add amplitudes. What is at issue, then, is not what causes the wave function to collapse but why we have to add amplitudes whenever quantum mechanics requires us to do so. To answer this question I have proposed the following interpretive principle:
(I) Whenever quantum mechanics requires us to add amplitudes, the distinctions we make between the alternatives correspond to nothing in the physical world. They cannot be objectified (represented as real).
Next, I apply this interpretive principle to two paradigmatic setups, one concerning distinctions between regions (of space or spacetime), the other concerning distinctions between things. Applied to a two-way interferometer experiment, (I) tells us that the distinction we make between “the particle went through the left arm” and “the particle went through the right arm” corresponds to nothing in the physical world, whence it follows that physical space cannot be an intrinsically differentiated expanse. Its so-called parts need to be physically realized by the sensitive regions of detectors (defined in terms of macroscopic positions), and the indeterminacy principle prevents them from being realized “all the way down”.
Applied to an elastic scattering event involving two particles of the same type (two incoming particles N and S, two outgoing particles E and W), the interpretive principle (I) tells us that the distinction we make between the alternative identifications (N=E, S=W) and (N=W, S=E) corresponds to nothing in the physical world. There is no answer to the question “Which outgoing particle is identical with which incoming one?” Now why would that be so? Watch this space.
I suggest all participants write a few posts under his or her topic, which gives a clear summary of his or her ideas, before the workshop starts. This will be helpful for discussions during the workshop.
OK, here goes. The question I am asking here is this: why focus on the wave function? After all, there are (by a recent count) at least nine different formulations of quantum theory. The wave-function formulation presents us with two mysteries: why is the unitary evolution disrupted by the occasional collapse, which results in the assignment of probability 1 to a particular outcome, and why is probability 1 sufficient for the factuality of that outcome? The only way the latter mystery can be solved is by adopting the so-called eigenvalue-eigenstate link, which postulates that probability 1 is sufficient for the factuality of that outcome. But doing so makes the quantum-mechanical correlation laws, which presuppose the existence of correlata (measurement outcomes), inconsistent with the existence of the correlata, which is absurd.
The consistency of the quantum-mechanical correlations with the existence of their correlata can be demonstrated if one gives up the eigenvalue-eigenstate link. The demonstration takes place in two steps. First I show (here in outline, in greater detail in some of the referenced papers) that the world is not spatially differentiated (or partitioned) “all the way down”: its spatial (and hence spatiotemporal) differentiation is incomplete. From this I deduce the existence of a non-empty class of objects whose positions are “smeared out” only relative to an imaginary spatiotemporal background that is more differentiated spacewise than the actual world. If anything truly deserves the label “macroscopic”, it is these objects. The testable correlations between the outcomes of measurements of their positions are consistent with both the classical and the quantum laws. This makes it possible to attribute to these positions the measurement-independent reality that is lost by giving up the eigenvalue-eigenstate link, and it enables them to define the obtainable values of observables and to indicate the outcomes of measurements.
Trigger phrases like “measurement” and “macroscopic object” are likely to elicit accusations of instrumentalism, Copenhagenism, or some such. Common or garden instrumentalism, however, leaves the meaning of “macroscopic” up for grabs. What is accomplished here is a consistent definition of “macroscopic” in the theory’s own terms. And that’s only the beginning. (To be continued.)
Richard, thank you for your response to my comments (both at #768).
I realize that our difference (if any) concerns the use we make of the wave function, and that there are different legitimate ways of using the wave function. One can even use the ABL rule (in lieu of the Born rule) to assign probabilities on the basis of both past and future outcomes, as I suggested in quant-ph/0006116 and quant-ph/0703035. I have come to realize, though, that it wasn’t consistent to consider these ABL probabilities objective, as I did at the time, for if I take all (relevant) past and future outcomes as given, then I should also take the target outcome as given, in which case the probability assigned to it is a (subjective) ignorance probability. (One could still argue that probabilities counterfactually assigned to the possible outcomes of an unperformed measurement are objective.)
On the other hand, assigning Born probabilities with input from all relevant outcomes is equivalent to using Born probabilities with input from all outcomes within the past light cone of a hypothetical agent in the infinite or sufficiently distant future, so your understanding of the wave function includes mine and is consistent with it. As to the subjective/objective nature of probabilities in general and quantum-mechanical probabilities in particular, this depends so much on what is meant by subjective/objective (and probability or chance) that today the issue seems to me rather pointless (see Sect. 16 of my QBism preprint).
As regards explaining violations of Bell inequalities, I gather from your paper “Local Causality, Probability and Explanation” that you require two things of an explanation: it must show that the phenomenon to be explained was to be expected, and it must say what the phenomenon depends on. The violations are to be expected because they are predicted, and they depend “counterfactually but not causally on the quantum state \Phi^+” as well as “counterfactually on that state’s backing conditions, as described by true magnitude claims”. But then counterfactual dependence doesn’t seem sufficient, for “the second requirement on explanation is met” because “the separate recording events, as well as the event of their joint occurrence, depend causally on the event o that serves to back assignment of state \Phi^+ to the photon pairs.” Not only does this seem to contradict your statement that “the theory has no resources to describe any causes mediating between o and these recording events” but the causality invoked also seems to be of a rather watered-down variety.
What I would require of an explanation of the quantum-mechanical correlations is some physical mechanism or natural process, which there isn’t. While of course there is no law against re-defining terms, the danger in doing so is that something important doesn’t get the attention it deserves, namely the fact that good old-fashioned causal explanations simply do not work in the quantum domain.
Two other minor quibbles. Firstly, you claim to meet Bell’s strictures against the presence of the term “measurement” in your formulation of quantum mechanics, but you seem to have added another term to the proscribed list and used it, namely magnitude claims. Secondly, you claim that an omniscient God (or creature) could describe and understand the physical world without a concept of chance. I’m not so sure. Such an entity would have complete knowledge of all events including their statistical correlations.
Best,
Ulrich
