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Thanks, Jerry: that’s interesting.
You say:
I am guessing that your answer is “no” and that the only allowed possibilities are that Alice sees “+1” both times and that Bob sees “-1” both times, or visa versa.
For the spacelike separated case you describe, “no” is indeed my answer.
You are right to distinguish superluminal influence from superluminal signalling, and to see that (for anyone who answered “yes”) there would be the possibility of superluminal influence without superluminal signalling in that case.The application of Asher Peres’s dictum “Unperformed measurements have no results” is a bit unclear here. If a measurement is performed but its result is then completely erased, does that count as a performed or an unperformed measurement? Asher was happy to be called a positivist, so maybe he would have said that counts as an unperformed measurement. I am not a positivist, and I don’t think it is meaningless to talk about results of measurements which have been reset. So I think his dictum doesn’t apply here. That’s why I think it matters to say “no” instead of “yes” in answer to your question.
Thanks, Jerry.
A little clarification:
You sayHealey and Gao agree Alice expects the result “+1” only 50% of the time
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In her situation prior to each of her individual measurements Alice expects each of its possible results to be equally likely. But in her situation prior to the whole sequence of her future measurements Alice expects either a sequence of all +1s or a sequence of all -1s, each with probability 1/2, and expects no other sequence (in particular, she assigns probability 0 to a sequence of an equal number of +1s and -1s).
All of these expectations are “consistent” with each other and with Bob’s expectations since a rational agent’s expectation varies as that agent’s situation changes so as to give the gent access to additional information.In my previous reply I said that when the Born Rule is applied from an agent situation indexed to a spacetime point p on Bob’s worldline that is timelike later than Bob’s outcome (such as point 3 in Figure 1) it yields chance 0 or 1 for each of Alice’s measurement outcomes in regions a – e. So from that agent situation, each of Alice’s outcomes is certain to be opposite to Bob’s. But from a point on Alice’s worldline at the same lab time t as point p, application of the Born Rule yields chance 1/2 for each of Alice’s possible measurement outcomes in regions a – e. If the Born Rule were to be (incorrectly) applied at lab time t it would yield incompatible values for “the” chance at that lab time of each of Alice’s possible measurement outcomes in regions a – e.
But there is no such thing as the chance at t of each of Alice’s outcomes. There are just the chances at each spacetime point of these events and these chances differ from one point to another on the spacelike hyperplane indexed by t.
Knowing his outcome, Bob can predict Alice’s outcomes with certainty. Since Alice cannot know Bob’s outcome before that event enters her back light cone, all she can predict with certainty at points on her worldline before making those measurements is that, whatever they are, they will be opposite to Bob’s. That is how correct applications of the Born Rule from different agent situations correctly predict the perfect anticorrelations between Bob’s and Alice’s measurement outcomes in the second scenario, in which Bob’s measurement precedes (in the lab frame) all of Alice’s measurements. (Relativistically, there is no relevant difference between the first and second scenarios.)
It is easy to fall into the trap of asking what “we” can predict using quantum theory, as if prediction is a concept that makes sense without regard to the spacetime location of the predictor. Taking the “God’s eye” perspective of one not situated in a spacetime such as that depicted in Figure 1 it may seem natural to think of prediction as just a logical or probabilistic relation between events at different lab times, each represented by a horizontal line in the diagram. But prediction is a concept that makes sense only from the perspective of a situated agent with access to certain information but prevented by that situation from accessing other information (s)he would like to have. In this situation prediction is just what is needed to form reliable beliefs about this inaccessible information.
PS In my previous post I meant to cite Bell’s 1964 paper “On the Einstein Podolsky Rosen Paradox”, not his later paper “La Nouvelle Cuisine”. He does not talk about ‘predetermination’ in the more recent paper, but he continues to assume that it is meaningful at a time to assign a unique chance to an event at a later time. But assignments of probability and chance cannot be made that way without assuming an absolute time or a preferred frame. In a relativistic spacetime with no preferred frame, each meaningful chance assignment must be made from a spacetime point, not at a time.
The Born Rule should always be applied not at a time (that would already introduce a preferred frame in relativity) but from what I have elsewhere called an agent situation—a physically specified situation that may or may not actually be occupied by an agent. In this Gedankenexperiment we may take an agent situation to be adequately specified by a spacetime point, which may be thought to mark the momentary location of an (actual or merely hypothetical) idealized agent applying the Rule.
In the second scenario there are several relevant agent situations–points on Alice’s world line immediately prior to her measurements a- e, and points just after point 3 on Bob’s worldline.
In the passage from my previous post quoted in Shan’s reply I was assuming that the Born Rule is being applied from points on Alice’s world line immediately prior to her measurements a – e. From those agent situations, the application correctly issues in the probability assignments I gave in that post: the chance of a +1 outcome of Alice’s measurement and the chance of a -1 outcome of Alice’s
measurement both equal 1/2, as I stated in the original post.I now add that the Born Rule may also be applied from points just after point 3 on Bob’s worldline (in the lab frame before any of Alice’s measurements). From those agent situations, the application correctly issues in a chance of either 1 or 0, depending on the outcome of Bob’s measurement. It is these chances that enable Bob (or anyone else who might have been located at such a point on Bob’s world line) to predict Alice’s outcomes with certainty, and afterwards to explain the perfect anti-correlation between the results of Alice’s and Bob’s spacelike separated measurements.
It is only if one illicitly smuggles in the nonrelativistic assumption that the chances of Alice’s outcomes change at an instant everywhere at once consequent upon Bob’s measurement having one definite outcome rather than the other that one can one take an application of the Born Rule from points just after point 3 on Bob’s worldline to give “the real” chances of Alice’s outcomes at that instant.
It is interesting that even Bell makes that illicit assumption when giving his version of the EPR argument in “La Nouvelle Cuisine” to conclude that after Bob’s measurement the outcomes of Alice’s (first) measurement “is predetermined”. It is certain relative to the contents of the back light cone of Bob’s outcome, but it is not certain relative to the contents of Alice’s back light cone at a point on her world line just before she makes her (first) measurement, even though her world line reaches that point after (in the lab frame) the outcome of Bob’s measurement. The whole notion of “predetermination” must be reinterpreted in relativity by identifying “the past” of an event with its back light cone—so events that occur at different places at the same time in the lab frame have different pasts.
If Shan is right that almost everyone agrees with his application of the Born Rule in his second scenario, then almost everyone is wrong!
Hi Mark,
No, I don’t agree. I regard retrocausation here as a desperate and unnecessary response to the situation you present. (Though I’m happy to entertain this as a conceptual possibility in other contexts and for other reasons.)
Equation (13) and its equivalents represent probabilistic correlations between the outcomes of possible measurements on X and Y, not between the values of magnitudes in/on X and Y (including whatever magnitudes record the outcomes of Xena’s and Yvonne’s measurements in their labs.) So it is only in thought that we can collect all of the same X and Y cases together for W and Z to measure: not even Xena and Yvonne can physically collect them together, since any attempt to do so by observing X and/or Y would disrupt the sensitive correlations coded in the superposed state (13). But we can still consider how to handle the cases you mention.
Once Zeus has measured z and obtained OK, Wigner is indeed sure to get + if he measures y (as long as Zeus’s measurement has not disturbed Y), and (provided he trusts Zeus’s measurement report—see Step 1 of my reconstruction of the argument) he may infer that Xena’s outcome was t.
Consider instead the case in which Wigner first measures w and obtains OK, and then Zeus measures x. This time it is not Wigner’s perspective but Zeus’s that we should take when insisting on unitary evolution of the total quantum state. From that perspective, Wigner’s measurement of w yields a state in which Zeus’s overall probability of getting an outcome of +1 in a measurement of x is 1/3 (without regard to Wigner’s outcome). At first sight it looks like Zeus is certain to get an outcome +1 conditional on Wigner’s getting an outcome OK, thereby certifying the prior outcomes of Xena’s and Yvonne’s measurements as h-. But this assumes both that Wigner’s intervening measurement on Y has not uncorrelated the outcome of Zeus’s subsequent measurement of x from Xena’s actual outcome when measuring f, and that Zeus can trust Wigner’s report of his own measurement outcome.
Both these assumptions are questionable. I think the first rests on what I called Intervention Insensitivity and argued against in my paper. The second may seem more plausible, and I made an analogous assumption in step 1 of Wigner’s reasoning in my paper. But notice that Zeus’s representation of Wigner’s state following Wigner’s prior measurement is entangled with that of Y (as well as X). So one could argue that whatever Wigner says about his outcome (more carefully, whatever Zeus measures Wigner’s outcome to be) is not a reliable guide to Wigner’s actual outcome. In particular, even if Zeus takes Wigner’s outcome to have been OK (because that’s what he observes it to be in a hypothetical future measurement on W) Wigner’s actual outcome might equally well have been FAIL. In that case, Zeus’s probability of getting h when measuring x would again be 1/3 (not 1) when conditionalized on the outcome of a measurement of Wigner’s outcome.
As you see, the assigned quantum states play a more important role in predicting measurement outcomes than the assumed unique outcomes of prior measurements. That’s why it’s not necessary to make a desperate appeal to retrocausation.PS I’m not confident that this is the clearest response to your interesting question, but I don’t have time to improve on it right now!
Dear Ruth,
Let me comment on something you said in your last post:
Richard noted earlier (if I understand correctly) his assumption that the existence of a measurement result in the world has no relation to whether anyone knows what it is, nor to any particular physical condition of the system under study. So it seems that when one party engages in what they consider a ‘measurement’, that doesn’t erase a measurement result that is simply out there in the world. That would be according to this ontology–which as I’ve noted seems ad hoc and lacks a physical account of ‘measurement.’
The understanding you express in the first sentence is almost right. The qualifications are that in many circumstances the existence of a measurement result in the world does have a relation to whether anyone knows what it is ((s)he’s the one who performed the measurement!), and in some circumstances this measurement result is represented by the physical condition of the system under study.
But I don’t see why your second sentence follows from this understanding. I think all measurement results are “out there in the world”, in that every measurement result is represented/determined by a true magnitude claim about some system. There is nothing ad hoc about this: if there were no true magnitude claims then an application of the Born rule would have nothing to which to assign probabilities! Only if one were to take a quantum state to correspond to “an element of physical reality” would it be reasonable to expect QM itself to yield a physical account of ‘measurement’. In my view quantum states are objective in just the same sense that Born probabilities are objective: but neither correspond to “elements of physical reality”.
(By the way, I don’t see why anyone would think that merely making a measurement would erase the result of a previous measurement.)Dear Shan,
I quote two sentences from your draft paper:
In Bob’s frame, since after the superobserver’s reset measurement the states of Alice and the particles are the same as their initial states, the result of Bob’s measurement has no correlation with the result of Alice’s measurement. Then we have E(a,b)=0 for any a, b.
I think these two sentences incorrectly derive a lack of correlation between Alice’s outcome and Bob’s in Bob’s frame.
The state Bob assigns after (in his frame) the superobserver has undone Alice’s measurement is irrelevant to Bob’s use of QM to calculate the correlation between Alice’s and Bob’s actual outcomes. That state would be relevant to the correlation of Bob’s outcome with a hypothetical $second$ measurement by Alice: it would predict $E(a,b)=-cos(a-b)$ for the correlation between Bob’s outcome and the outcome of Alice’s hypothetical second measurement.
To correctly calculate the correlation between his outcome and the outcome of Alice’s actual measurement, Bob must assign a state at a time (in his frame) before the superobserver’s intervention. He can assign the state (1) to the pair of spin 1/2 particles on a spacelike hypersurface prior to his own(Bob’s) measurement, and thereby correctly predict the same correlation $E(a,b)=-cos(a-b)$ as Alice. (For simplicity I assumed here that the spin state of the pair is invariant under Lorentz boosts. This may be false for the state (1), but if the relative velocities are small enough this won’t matter. If you replace the + with a – in the spin state (1) I think the assumption would be true. If the relative velocities were large enough to matter for the state (1), Bob would have to make sure to transform the directions a, b correctly, thereby reaching exactly the same predicted correlation as Alice.)
When Alice and Bob correctly apply QM to this scenario they make identical predictions for the correlation between the outcomes of their measurements. There is no contradiction between unitary QM and relativity.Mark,
Wbar measures an observable z on a quantum system composed of everything in Fbar’s lab (including the quantum coin, Fbar herself, her measurement apparatus and recording devices, …). z is a two-valued observable with orthonormal eigenstates okbar, failbar. No-one, including Frauchiger and Renner, has any idea of how to measure this observable. But under the assumptions of their argument, z uniquely corresponds to a self-adjoint operator on a Hilbert space that is the tensor product of a vast number of component Hilbert spaces in which are represented possible states of the coin, of Fbar, …. . The argument simply assumes that every self-adjoint operator corresponds to a measurable observable, including z. Given this assumption, it is not necessary further to specify any operational procedure for measuring z.
Shan,
Re 3. I think your derivation of $E(b,c)=4sin^2[(a-b)/2]cos^2[(a-b)/2]-1$ is incorrect. The derivation proceeds by separately considering two possible outcomes of Carol’s measurement and then summing over the associated probabilities, treated as exclusive and exhaustive. In effect, this is to treat Carol’s measurement as inducing a physical collapse in the state of 12D, in violation of the condition of unitary evolution of this state. But the calculation of $E(d, a) = −cos(d − a)$ (correctly) assumed there was no such collapse.
The reasoning of your derivation is analogous to the familiar fallacy of assuming passage of an x-spin up eigenstate through a z-oriented S-G magnet induces collapse into a z-spin eigenstate, implying that on subsequent passage of the “recombined beams” through a second x-oriented S-G magnet an atom would be equally likely to be recorded in the up and down emerging beams. In fact, of course, if the recombination has been performed properly, the atom will certainly be recorded as emerging from the x-oriented S-G magnet in the up beam.
In the third argument it is crucial that after Carol’s measurement Alice has completely erased its result—effectively “recombining the states” corresponding to the two possible outcomes of Carol’s measurement into a single superposed state. This is why it is wrong to analyse the $E(b,c)$ correlation as resulting from mutually exclusive possible processes, each corresponding to a distinct one of Carol’s possible measurement outcomes.
Re 2. You can easily derive $E(b,c)$ in Bob’s frame (after suitably representing the directions b,c in that frame) ) in the way I gave in my paper. If the relative velocities are small enough, the directions will be represented in essentially the same way in all the relevant frames, since Lorentz transformations reduce to Galilean transformations. So in the non-SR case Bob’s derivation will go through in his frame, just as Alice’s derivation of $E(a,d)$ goes through in her frame. But Alice will reject Bob’s derivation, and Bob will reject Alice’s derivation, since they will disagree about the objective time order of two pairs of events that are actually spacelike separated—a relativistic relation that makes no sense in Galilean spacetime.
Re 1. I don’t like to speak of influences on wave functions, because I don’t think wave functions are capable of bearing causal relations, even though they are objective. But certainly by performing a local measurement one may gain information that permits one to reassign the quantum state of a distant system (as happens in the EPR case). In my view this involves no “causal” influence or nonlocal processes.
Note that while (31) has the mathematical form of a Bell inequality, it is a simple consequence of Boolean algebra, given the assumption that it concerns objective events that can be described as definite outcomes of measurements: no Bell-type locality assumption is involved in deriving this inequality.Shan,
1. It is important to notice that a quantum state assignment on a fixed spacelike hyperplane (like the hyperplane t*^3) may itself be made with respect to different inertial frames (say, Alice’s and Bob’s). Quantum states on different spacelike hyperplanes (like t^3 and t*^3) are not related by a boost transformation. So a derivation of E(b,c)= -cos(b-c) in Alice’s frame would still proceed from an assignment of a quantum state on t*^3 even though that is not a simultaneity slice in Alice’s frame. To derive the relation E(b,c)= -cos(b-c) in Alice’s frame you would first have to transform both the state on t*^3 as well as the angles b,c from Bob’s frame (in which the derivation is easiest) to Alice’s frame. This cannot affect the result of the calculation, since E(b,c) is invariant under changes of frame. But the calculation would be unnecessarily complicated.
2. The boosts (and rotations) must be Lorentz transformations, not Galilean boosts here. This is important because the whole discussion must be set in Minkowski spacetime, not Galilean spacetime: if it were not, then there could be no switching of time order of spacelike separated events between frames. Such Lorentz transformations are standard in discussions like that of my reference (17).
3. I don’t understand how you have derived your alternative value for E(b,c) in the special case c=b, a=d. Can you explain?Ruth,
A modern version of the Stern-Gerlach experiment uses a hot-wire detector (see, for example, http://web.mit.edu/8.13/www/JLExperiments/JLExp18.pdf ).
In this case, potassium atoms pass through an S-G magnet, thereby entangling their spin and translational quantum states (not collapsing the spin state)! Interaction with the hot wire likely ionizes the atom, and the charged ion is then collected on a plate, thus producing a current in a circuit including the wire and plate. So what is directly measured is the current in the circuit, which varies as the wire is tracked across what one tends to think of as the beam of potassium atoms emerging from the S-G magnet. But the QM representation is not of two separate beams, but as an entangled superposition of spin+translational states of the emerging atoms. Ionization of an atom on the hot wire certainly involves interaction with its spin state and induces further entanglement, this time with the state of the wire constituents. So you might think of this as a measurement of the atom’s position, rather than of its spin-component. In my view, its is only when an interaction in this whole sequence corresponds to stable decoherence in the state of some system or other that one is entitled to make a meaningful claim about the value of a magnitude on that system. Like most actual quantum measurements, this is a very complicated situation, and it is pretty clearly false that the spin of the atom is itself decohered as a result of these interactions. So there is no reason to believe it is meaningful (let alone true) that the atom has a definite spin-component at any time after it emerges from the S-G magnet. But before passing through that magnet its quantum spin state was a superposition, so there is even less reason to assign it a definite spin-component prior to the measurement.Probabilities may be assigned to events (e.g. a coin landing heads) or to propositions asserting their occurrence. Born probabilities are assigned either to events of magnitudes taking on values, or to magnitude claims about what those values are. I use the language of claims rather than propositions, since claims are what people actually make, while propositions are rather dubious abstract objects. But I’m happy saying Born probabilities are assigned to events, if you prefer.
Ruth,
In my view quantum theory may be applied to predict probabilities for certain magnitude claims, each restricting a dynamical variable to a Borel subset of real numbers. When quantum theory is targeted on a quantum system, a quantum state is assigned to that system in order to apply the Born rule to yield these probabilities. The magnitude claims assigned probabilities may be about that system, or they may be about some other system with which it will interact. I give an example of the former kind of application in my paper “Quantum decoherence in a pragmatist view: Dispelling Feynman’s mystery”. Foundations of Physics 42 (2012), 1534–55. Applications of quantum field theory never yield probabilities for magnitude claims about the quantum fields on which they are targeted, and only sometimes about particles such as photons that are their associated quanta. Even applications of non-relativistic quantum mechanics typically issue in probabilities of magnitude claims about systems other than those assigned quantum states in the application. But the Born rule always explicitly yields probabilities for magnitude claims, whether or not these may be glossed as measurement outcomes. If they can, the measurement outcomes supervene on values of “observables” (i.e. dynamical variables)–but not necessarily observables of the system assigned a quantum state when applying the Born rule. Only significant magnitude claims may be assigned probabilities: which these are depends on what interactions are involved. Models of decoherence are a guide to the significance of a magnitude claim. In a spin-component measurement what get assigned probabilities will typically not be magnitude claims about that spin-component but about a magnitude on some other “detector” system with which the spinning system interacts. That is why the spin-component itself need not have a definite value before or after its measurement. My book The Quantum Revolution in Philosophy offers an introduction to this way of thinking about quantum theory. It is based on several other published papers.
I do assume an “eternalist” spacetime within which measurement events and (the histories of) all systems are represented (if not located—I don’t think I’m committed to spacetime substantivalism), though I dislike the “blockworld” metaphor.Shan,
You focus on an important part of the third argument.
In my paper I first considered the use of QM to predict the probabilistic correlation E(a,d) in equation (29), and then appealed to Lorentz symmetry to justify the analogous equation for E(b,c). So let’s consider the argument for equation (29).If Carol had performed no measurement (C and 1 had never interacted) then QM may be legitimately applied to calculate E(a,d) (equation (28). It is true that Alice and Dan perform their measurements in different inertial frames, but that does not invalidate this application of QM in Alice’s frame (or, if we so chose, in Dan’s frame). The two measurements are timelike separated, as in a standard timelike-separated Bell test. The relative motion of the two frames does not rule out application of QM here (see my reference (17) for details on how to handle such cases of relative motion of frames). But it does require careful analysis of what spin-components are actually measured, since Dan’s representation of the directions a and d will differ from Alice’s because of the Wigner rotation associated with their relative velocities. But once this has been taken care of, there is no problem applying QM to calculate E(a,d) as in equation (28).
In my paper I attributed the following reasoning to Alice to justify equation (29).
In the present case, C and 1 interacted twice between t^1 and t^4, but these interactions had no overall effect on the state of the joint system 12D at the time when Alice performed her measurement of a-spin: its state was the same at t^3 as it had been at t^1.
Do you think there is something wrong with Alice’s reasoning here? It seems valid to me, but I recognize that this is a crucial part of the argument. Alice and Dan may assign different (since Lorentz boosted) states to 12D, but they must still agree on the probabilistic correlations E(a,d) predicted by QM.
The third argument makes no assumption of hidden variables. In particular, it makes no assumption concerning the actual spin values of the measured particles, either before or after the spin measurements. It assumes only that each measurement has a definite physical outcome, which may correspond to a light flashing red rather than green (for example), considered as registering the actual outcome of the spin measurement. Of course, in the case of Carol’s and Dan’s measurements all evidence of that registration must be completely erased by Alice and Bob prior to their own spin measurements.
We don’t need to appeal to Fine’s result to prove inequality (31). This is a straightforward consequence of Boolean algebra, applied to the assumed physical outcomes of A,B,C,D’s measurements in multiple repetitions of the entire sequence of measurements. Just draw the 4-set Venn diagram and consider the relative frequency measures of the 16 elements of the partition.Shan says
In the thought experiment, the EPR pair of spin-1/2 particles is measured two times in the same state. It seems to me that this is equivalent to measuring two EPR pair of spin-1/2 particles in the same state.
In the thought experiment the EPR pair is effectively measured four times in the same state: by CD,AD,BC and AB. But there are only four actual outcomes, unlike in measuring four EPR pairs, for which there would be eight actual outcomes—two distinct outcomes for each measured spin-component, one in each of two separate experiments. That is why the set-ups are not equivalent, even though QM predicts the same probabilities in both set-ups.
Ruth wants to consider what she calls QTC. In my paper I considered only what she calls QTNCP. That is indeed how I think of quantum theory—as a theory that involves no physical collapse. Many believe there can be no definite physical outcomes of quantum measurements if there is no physical collapse. I think this belief is connected to the view that a state vector represents the physical condition of the system to which it is assigned, so that condition cannot be definite if the vector is an “uncollapsed” superposition. I maintain that the role of the quantum state is not to represent the condition of the system to which it is assigned, but to prescribe rational credences regarding the (
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assumed
) definite condition of that or some other system following a suitable interaction. QM cannot explain definite outcomes since it must take them for granted. That’s why it is so important that it can consistently do so!
As stated in the first sentence of the paragraph in which equation (31) appears, it is a central assumption of this third argument that every spin measurement performed by A,B,C and D has a definite, physical outcome. Consistent with that assumption, the measurements by A, B destroy all
- records
of C’s and D’s definite, physical outcomes. So none of A,B,C,D can
- know
what all these definite, physical outcomes were: they all objectively occur (at various spacetime locations), even though they are not all intersubjectively knowable by anyone. Objectivity should not to be equated with intersubjective knowability here—that would confuse metaphysics with epistemology.
As stated in the last sentence of the same paragraph, inequality (31) is not derived using any locality assumption. As Arthur Fine showed in the referenced publication, (31) is a consequence of the existence of a joint distribution of values of variables representing the (assumed) definite physical outcomes of the spin measurement performed by A,B,C and D. If all those values exist in each run of the experiment, then their statistical distribution in many runs of the experiment must conform to (31). This is true without assuming anything like Bell’s Local Causality, and independent of any causal hypotheses as to how these outcomes were produced.Shan,
You say
” it seems to me that Richard’s result about the Limits of Objectivity is not valid. This result is derived from the third argument in his paper. I think the argument is based on the implicit assumption of locality, like Bell’s theorem, and one should drop this locality assumption, not the objectivity of outcomes.”Where do you think this assumption is made in the third argument discussed in my paper? In formulating the argument I was concerned to make no such assumption.
Richard
I think we have arrived back at the starting point of my first post on Bohmian mechanics (under a different thread—the one I emailed to you originally). There I compared the Bohmian research program after quantum theory to a Lorentzian research program after special and general relativity.
Bohm and GRW are not quantum theories but non-quantum rivals (even if a Bohmian theory is empirically equivalent to a quantum theory). Similarly, a Lorentzian theory empirically equivalent to a relativistic theory is not a theory of relativity.
If we didn’t have the theory(ies) of relativity, we might well use a Lorentzian theory instead of STR while acknowledging its evidentiary infirmities and continue to play “catch up” by working toward Lorentzian theories empirically equivalent to GTR. But we don’t need to since we have relativity—with no such evidential infirmities.
Similarly, if we didn’t have quantum theory, we might well use Bohmian mechanics
while acknowledging its evidentiary infirmities and continue to play “catch up” by working toward Bohmian interacting field theories empirically equivalent to the Standard Model. But we don’t need to since we have quantum theory—with no such evidential infirmities.
You will doubtless reply that the analogy is bad because quantum theory (in all forms) has conceptual infirmities—that it is inherently inexact, vague, supported by terrible philosophy, riddled with talk of observers, etc.
I maintain that quantum theory may be precisely formulated with no talk of observers or measurements and can be shown to be free of conceptual problems (no measurement problem, no superluminal influences, no tension with relativity, no problematic quantum field-theoretic ontology, no Schrodinger cats or Wigner’s friends, etc.). Perhaps I shouldn’t be too provocative,but I can’t resist quoting Bob Dylan at this point:
“Don’t criticize what you can’t understand. Your sons and your daughters are beyond your command—the times they are a-changing.”
I agree that the discoverers of the theory gave many terribly confused accounts of what they had discovered and why one should accept it, relied on bad philosophy, and gave unsound arguments against (e.g. Bohmian) apostates. But creative physicists aren’t noted for the quality of their thinking outside of their specialty (Einstein and Bell being shining exceptions)!Everything is fair except the last sentence. The existence of atoms is strongly supported by the evidence. The existence of a Higgs boson is also supported by the evidence, though not nearly as strongly. By contrast, the existence of Bohmian trajectories, a preferred spacetime foliation, etc. is not.
I don’t want to permanently and irrevocably give up on the goal of describing the world as accurately and completely as possible. But I think that goal is at least (probably) humanly unachievable, and possibly even incoherent, since it presupposes that there is some set of concepts rich enough to permit such a complete description. Pragmatism is not incompatible with the realist program: but it is flexible enough to make room for alternative programs. Its central insight is that concepts are intellectual tools for coping with the world, and that we can create concepts and use them in a variety of ways in pursuit of our goals. One way of doing this is to create theories that posit beables: if the theory works, you can hope the beables exist. That, I take it, is the Bohmian program. But the problem with that program is that even if the theory is empirically adequate the existence of the beables remains a hope—it is not supported by the evidence. Quantum theory does not posit beables: instead, it offers advice on what descriptive claims to make about magnitudes and entities supplied by other theories. We have good reason to accept quantum theory because that advice proves to be good, empirically. If your goal is an accurate and complete description of the world, then quantum theory won’t meet it: if your goal is predictive and explanatory success, then quantum theory does meet it. I take science to have the latter goal. I don’t see the Bohmian program making progress toward either goal, since I don’t think the evidence supports Bohmian theories. But (speaking personally) I’d love to see some other theory that is supported by the evidence and that does provide a rich description or representation of the physical world. And I don’t rule out the possibility that further developments in the Bohmian program could lead to such a theory, though I wouldn’t put money on it!
I started to compose a short reply to your last post, Travis, but decided that your pointed questions required a more extended response. So instead I’ve attached a piece I wrote a few years ago on what quantum theory teaches us about the concept of physical reality.
In brief, like Einstein I think of the “real” in physics as a a type of program to which we are, however, not forced to cling a priori.
I approach quantum theory not as an instrumentalist or operationalist, but as a pragmatist. For a pragmatist, quantum theory contributes to the goals of physics (prediction and explanation of natural phenomena) by following a different type of program.Like you, I would be happy if physics some day were able to return to Einstein’s realist program in physics. But science doesn’t have to make one happy! Unlike you, I don’t see any sign that pursuing a Bohmian research program will help do this: as Einstein said, that way is too cheap. Meanwhile, I am astonished by the human creativity involved in coming up with a different program for doing excellent physics the quantum way—a way that is neither instrumentalist nor operationalist but pragmatist.
At the end of your first paragraph you ask “Am I at least close to right so far?”
No. In formulating or understanding quantum theory it is not necessary to appeal to a microscopic/macroscopic distinction. As a fundamental theory, quantum theory may be applied to systems of arbitrary size.
Quantum mechanics may be applied to systems of particles, so by applying it we are committed to the existence of particles, or at least to treating things as systems of particles (perhaps as a permissible idealization, even though we might not treat them that way if we were instead applying a relativistic quantum field theory to the same things). When we apply quantum mechanics to such systems, we assign them a wave-function (density operator, state vector, whatever). This does not represent a beable. It does not represent the particles’ physical properties or relations: its evolution does not represent their behavior. Its function is not descriptive but prescriptive: it tells the one who applies it what statements assigning values to magnitudes are significant enough to be assigned probabilities, and what those probabilities are. What statements are significant depend on what environment the system is in. The environment may include something we could use as a measurement apparatus, or it may not: either way, it is interactions with the environment that constrain to what statements we can legitimately apply the Born rule. These may be statements about the system, the environment, or both. We can use quantum models of environmental decoherence to help us determine what statements are significant enough to be assigned probabilities. Significance is not a “yes/no” matter, and there is no precise criterion that specifies when, and to what, the Born rule may be legitimately applied. Bell would not like this. But it’s important to stress that this is not a vagueness in the formulation of quantum mechanics, but calls for the same kind of decision that is required in any application of a physical theory, classical or quantum.
“Is there some clean, unambiguous way of saying exactly what, according to the theory, is real?”
The quantum state is not a beable: in that sense it is not real. But quantum states are objective: when assigning a quantum state to a system one can make an incorrect assignment. In that sense a quantum state is real. Are particles real? Yes, according to quantum mechanics, since every correct application of quantum mechanics involves claims about systems of particles. Sometimes, according to relativistic quantum field theory: some correct applications of relativistic quantum field theory involve claims about particles (but in other correct applications no such claim would be significant). I expect you and Bell would not like relativistic quantum field theory’s refusal to give a clear, unambiguous answer to the question “Are particles real, or are fields real, in relativistic quantum field theory?” But recent work by philosophers of physics has shown how hard it is to impose either a particle ontology or a field ontology on such a theory! The problem goes away if one rejects the presupposition that a fundamental theory must come equipped with an ontology.
“To me, as long as you can’t specify *sharply* what the theory says is real, I can’t really take it seriously as a candidate fundamental theory.”
OK, but here you are expressing what I have come to regard as a metaphysical prejudice analogous to the Cartesian prejudice against Newtonian forces. Both prejudices attempt to constrain the form of any fundamental physical theory. We are lucky that Newton broke free of the first prejudice and that Heisenberg, Schrodinger etc. broke free of the second.
I hope that helps some. I have published papers containing more details, and I’m presently finishing a book in which I try to lay out my view of quantum theory more carefully and patiently.“It would seem that the theory would then have to involve local beables, out of whose configurations facts about results of experiments would arise.”
Appearances can be deceptive!
Assume a fundamental physical theory should not involve talk of measurement or observation. (I don’t mention axioms, because I don’t think theories, fundamental or not, need be derived from axioms.)
Must a fundamental theory posit its own local beables? Must a fundamental theory posit any beables of its own? Of course one could take the attitude that nothing could count as a fundamental theory unless these questions received positive answers. But someone could then adopt a different, more relaxed, attitude toward fundamentality. Observer-free quantum theory is fundamental in two senses: We have been able successfully to use it successfully to predict and explain a host of phenomena that cannot otherwise be predicted or explained (e.g. by classical physical theories) without encountering any empirical problems traceable to its deficiencies; and, in some form, the theory may be applied to all known phenomena with the single exception of those thought (by many) to require a quantum theory of gravity.
But observer-free quantum theory does not posit its own ontology: it “borrows” an independently available ontology from the rest of physics. The wave function is not a beable at all (many experiments are hard to reconcile with the assumption that it is): “observables” are not beables—corresponding physical magnitudes are beables, but quantum theory should not be understood to introduce them as elements of its own ontology. Bell talks about beables recognized in ordinary quantum mechanics, including settings of switches and knobs, and currents. These are not novel quantum posits and don’t have to be built out of elements of quantum ontology; when we apply quantum mechanics we often help ourselves to them (though nothing prevents us from applying quantum mechanics to these things if we want to understand their behavior better). Any legitimate application of the Born rule in quantum theory concerns values of magnitudes not introduced as novel quantum posits but taken over from the rest of physics, new as well as old. Among these applications are many that successfully account for experimental phenomena.
The success of quantum theory should teach us that a fundamental theory need not be “self-standing”. It need not present us with a description or representation of reality solely in its own terms. We might experience metaphysical yearnings for a theory that did, but physics–even supremely successful physics–need not conform to our favorite metaphysics. We can understand quantum theory as currently our best fundamental theory in this less narrow-minded sense without talking about observation and measurement, and without becoming instrumentalists or operationalists. It is Bohmian mechanics, not quantum mechanics, that requires defense using philosophical ideas from outside of physics.I disagree that the condition that X has no influence on B can be expressed as Prob(B/X,Y)=Prob(B/Y): that condition merely expresses the inequality of two general probabilities, each of which may be used to infer a (different) chance of an outcome event being of type B (there is no unique chance of an event’s being of type B in this case—see my paper). To connect probabilities and chances to Bell’s intuitive statement of local causality one needs at least to show that the first of these chances could have resulted from a hypothetical intervention that brought about an X-type outcome (rather than a different X’-type outcome). But this is not true: if one accepts quantum theory one thereby accepts that an X-type(as opposed to an X’-type) outcome could not have been brought about as a result of a hypothetical intervention. In that sense, quantum theory implies both that Prob(B/X,Y)/=Prob(B/Y) and that an X-type outcome has no influence on whether the other outcome is or is not of type B.
Roderich, (in response to your 1898)
We can’t decide whether B is function of events on all or part of H without applying some theory. Simply observing relative frequencies of 1 in a sequence of supposedly similar sets of events can’t exclude failure of a corresponding functional relation in unobserved sets.
If we apply quantum theory, we see that Prob(B/S(H))=1 but Prob(B/S(HP(R_B)))=½. I’ll use the word ‘certain’ to refer to probability 1. Then B is certain conditional on S(H), but B is not certain conditional on S(HP(R_B)). Your formulation of locality implies that events outside P(R_B) cannot influence events in R_B: I take it that one thing this is intended to exclude is influencing whether or not events in R_B are certain. I claim there is no such influence here: specifying the outcome at R_A or the state on H outside (P(R_B) does not alter the fact that B is certain conditional on S(H), but B is not certain conditional on S(HP(R_B)). That Prob(B/S(H))=1 but Prob(B/S(HP(R_B)))=½ does not establish failure of locality, as you have defined it.Dear Roderich,
In section 7 of your paper you lay out an argument as to why (L) implies (R1). Here’s why that argument fails to establish its intended conclusion.
I quote the crucial steps from your paper:
“Assume locality. Alice’s experiment takes place in a space-time region A and Bob’s in B at spacelike separation. There is a Lorentz frame in which A is finished before B begins; thus, in this frame, there is a time at which Alice’s experiment already has a definite outcome. She can therefore predict Bob’s outcome with certainty, although she cannot transmit this information to Bob before Bob carries out his experiment. Anyway, Bob’s outcome was already fixed on some spacelike hypersurface before his experiment.”
What that last sentence means depends on the meaning of ‘fixed’. Two possible meanings are relevant:
1. An event e may be said to be fixed relative to events on a spacelike hypersurface whose future domain of dependence includes e.
2. An event e may be said to be fixed relative to events in the past light cone of e.
Since the argument assumed locality, only events in its past light cone can influence Bob’s outcome. So anyone who accepts (L) should adopt meaning 2 as the appropriate understanding of fixity. Based on that understanding, what can it mean to say e is (or is not) fixed relative to events on a spacelike hypersurface whose future domain of dependence includes e? I see two possible ways to understand this:
1a. e necessarily occurs if certain events occur somewhere on this spacelike hypersurface.
1b. e necessarily occurs if certain events occur on this spacelike hypersurface in e’s past light cone.
But (L) renders events outside Bob’s outcome’s past light cone unable to influence it. So 1b is the right way to understand 1. Since Alice’s outcome lies outside the past light cone of Bob’s, it follows that Bob’s outcome is not fixed relative to events on a spacelike hypersurface that includes B within its future domain of dependence. The state of affairs inside the past light cone of B, but before B itself, did not include a fact about the value Bz that Bob will obtain if he carries out a quantum measurement of I x sigma-z.
This objection to your version of the EPR argument generalizes, to become an objection to Bell’s derivation of his condition on probabilities from his statement of local causality (in La Nouvelle Cuisine, 2004 p. 243). I’ve explained this in greater detail in my paper “Local causality, probability and explanation” posted on the IJQF John Bell workshop 2014: see especially section 3.Best,
RichardDear Roderich,
In section 7 of your paper you lay out an argument as to why (L) implies (R1). Here’s why that argument fails to establish its intended conclusion.
I quote the crucial steps from your paper:
“Assume locality. Alice’s experiment takes place in a space-time region A and Bob’s in B at spacelike separation. There is a Lorentz frame in which A is finished before B begins; thus, in this frame, there is a time at which Alice’s experiment already has a definite outcome. She can therefore predict Bob’s outcome with certainty, although she cannot transmit this information to Bob before Bob carries out his experiment. Anyway, Bob’s outcome was already fixed on some spacelike hypersurface before his experiment.”
What that last sentence means depends on the meaning of ‘fixed’. Two possible meanings are relevant:
1. An event e may be said to be fixed relative to events on a spacelike hypersurface whose future domain of dependence includes e.
2. An event e may be said to be fixed relative to events in the past light cone of e.
Since the argument assumed locality, only events in its past light cone can influence Bob’s outcome. So anyone who accepts (L) should adopt meaning 2 as the appropriate understanding of fixity. Based on that understanding, what can it mean to say e is (or is not) fixed relative to events on a spacelike hypersurface whose future domain of dependence includes e? I see two possible ways to understand this:
1a. e necessarily occurs if certain events occur somewhere on this spacelike hypersurface.
1b. e necessarily occurs if certain events occur on this spacelike hypersurface in e’s past light cone.
But (L) renders events outside Bob’s outcome’s past light cone unable to influence it. So 1b is the right way to understand 1. Since Alice’s outcome lies outside the past light cone of Bob’s, it follows that Bob’s outcome is not fixed relative to events on a spacelike hypersurface that includes B within its future domain of dependence. The state of affairs inside the past light cone of B, but before B itself, did not include a fact about the value Bz that Bob will obtain if he carries out a quantum measurement of I x sigma-z.
This objection to your version of the EPR argument generalizes, to become an objection to Bell’s derivation of his condition on probabilities from his statement of local causality (in La Nouvelle Cuisine, 2004 p. 243). I’ve explained this in greater detail in my paper “Local causality, probability and explanation” posted on the IJQF John Bell workshop 2014: see especially section 3.Best,
RichardIndeed I do believe (not merely suspect) that statements about probability and fixity must be relativized in the way I suggested. I question your use of the word “pre-determines”. Certainly Alice’s outcome (ideally) lies on a spacelike hypersurface whose future domain of dependence includes Bob’s outcome. But points on that hypersurface outside Bob’s outcome’s backward light cone do not lie in its absolute past. The relevant notion of pre-determination (also fixity, also chance) is determination by the contents of Bob’s outcome’s backward light cone. Since Alice’s outcome lies outside Bob’s backward light cone it can play no role in pre-determining Alice’s outcome. This is not merely a semantic issue. Just as we ordinarily take the past to be fixed in a Newtonian spacetime because we assume that in principle it is accessible to our present observations, so also we should consider the absolute past of Bob’s outcome as fixed in a relativistic spacetime because it is in principle accessible from that event. Events like Alice’s outcome are just as inaccessible from the spacetime location of Bob’s outcome as events in its absolute future, so (by parity of reasoning with the Newtonian case) they are not fixed, relative to Bob’s outcome and so not candidates for “pre-determining” that outcome.
Of course, if we had some independent reason for thinking Alice’s outcome is in principle accessible from Bob’s outcome that would also be a reason to re-evaluate that reasoning. I believe quantum theory gives us no such reason.Roderich,
In response to your 1835 you ask (re my 2,3)
“I am happy to change my statement to “Bob’s outcome was already fixed on some spacelike hypersurface before his experiment.” Would that take care of your concern?”
No, this does not address my concern. In a relativistic spacetime fixity, like chance, should not be relativized to a spacelike hypersurface but to the backward light cone of a spacetime region (ideally, a point) representing the momentary location of a hypothetical optimally informed agent. Then whether Bob’s outcome was fixed depends on what that backward light cone is, in such a way that differently located Alice and Bob could both be right even when they disagree about whether Bob’s outcome was “already” fixed.
Let me make it clear that I see no philosophical problems with your favored program for going beyond quantum theory, and I encourage you to pursue it. I’d help you if I were a (better) physicist, and the payoff could be great if it proves successful! I do have an epistemic worry about the extra local beables required by the program: they remind me of Bohmian trajectories and the Everettian universal quantum state in their inherent experimental inaccessibility. But that worry should not derail pursuit of the program.
Meanwhile, what are we to make of quantum theory, the best physical theory we have and arguably the best physical theory we have ever had? My present interest as a philosopher is in showing why that theory is free of any conceptual problems and metaphysical extravagances like superluminal influences, “flashes”, many worlds or a physical role for consciousness; and seeing what philosophers and others can learn from its novel non-representational strategy for informing us about the world and how to understand it. I think too many “Interpretations” of quantum theory misunderstand quantum theory and so fail to learn the right lessons—about probability, causation, explanation, laws, and (most importantly) about different uses of physical models to achieve the goals of science—description, prediction and explanation of physical phenomena.
I understand quantum theory as a theory that enables us to explain experimental violations of Bell inequalities in a way that appeals to localized conditions whose obtaining causes the localized events recorded in those experiments. So I think it’s appropriate to say quantum theory helps us explain their violation causally. (See my paper posted in the previous IJQF forum on the meaning of the wave function).
But this explanation does not mention any beables (local or nonlocal) continuously connecting those events to their cause(s). Is that giving up on causal explanations, or giving a causal explanation of a kind some (e.g. Einstein) would not like?I understand quantum theory as a theory that enables us to explain experimental violations of Bell inequalities in a way that appeals to localized conditions whose obtaining causes the localized events recorded in those experiments. So I think it’s appropriate to say quantum theory helps us explain their violation causally. (See my paper posted in the previous IJQF forum on the meaning of the wave function).
But this explanation does not mention any beables (local or nonlocal) continuously connecting those events to their cause(s). Is that giving up on causal explanations, or giving a causal explanation of a kind some (e.g. Einstein) would not like?The nonfactorizablity I was talking about is a property of joint probability distributions (by contrast with the factorizability needed to derive CHSH inequalities in conjunction with the probabilistic independence of the “hidden states” from the choice of subsequent measurement settings—the assumption you reject). If (as I believe) the probabilities that figure in such distributions aren’t elements of the (physical) ontology—if they aren’t beables—then failure of factorizability does not entail a nonfactorizable ontology.
Thanks, that’s the clarification I was looking for.
Now I’ll have to think more about whether I agree with your answer!Here’s a more substantial issue.
In your introduction you lay out “the options on the table”, but don’t include the option of a past-common-cause explanation with no superluminal influences but with no beables continuously linking this non-factorizable common cause to its joint effects. I think this is the best take on how quantum theory explains violations of Bell inequalities—and therefore the best explanation we currently have.If that’s right, then the “options” you list are research programs in search of new theories seeking to go beyond quantum theory in search of a deeper, or more complete, explanation. Is that how you see them?
Suppose Alice does imagine it could have been different (as I think she should).
My thought was that in the case I described Bob has a case that Alice’s choice had no influence on the chance of his outcome, since (as it happened) he was the one who fixed the joint spin axis in this instance with the result that his outcome had a 50-50 chance of either result.Ken,
Thanks, this is very interesting.
Here is a small (corrected!) question. In part of your answer to your own question “Is this model local?” you say “Alice’s measurement settings are certainly a contributing causal factor to the probabilities at Bob’s apparatus”. Suppose in one instance Alice’s vector underwent an anomalous rotation but Bob’s didn’t. Would you still say that in this instance Alice’s measurement setting was a contributing factor to the chance of Bob’s getting one outcome rather than the other? Or do you take causal factors to be general conditions rather than particular events, so that even though the local beable influence chain here went from Bob to Alice and not vice versa, in other instances it went the other way around?
To Bob at 1775,
I gave the reason in section 3 of my paper and illustrated it in the space-time diagrams of figures 2 and 3. Please explain what you don’t understand so I can help you see the force of this reason.
To Bob at 1775,
I gave the reason in section 3 of my paper and illustrated it in the space-time diagrams of figures 2 and 3. Please explain what you don’t understand so I can help you see the force of this reason.
Bob,
I found out only today about your comments: for some reason I am receiving only selective notifications of comments’ postings.
Section 2 of my paper is indeed independent of quantum theory, as are the arguments of Bell it addresses.
But quantum theory plays a major role in sections 3-6. Section 5 outlines a view of quantum theory, while section 6 applies quantum theory, so viewed, to what Bell called the EPR-Bohm scenario to show how quantum theory explains violations of CHSH inequalities with no superluminal causal influences: this is something we cannot explain without using quantum theory, and there are those who maintain we cannot explain it even using quantum theory (even though everyone agrees we can use quantum theory to predict correlations in violation of CHSH inequalities).
Section 3 is mainly about the relation between general probabilities supplied by a theory and chances of particular events in a relativistic space-time, but it uses quantum theory as an important illustrative example in which general probabilities are supplied by applications of the Born rule. This example is important because of its bearing on the arguments of Bell analyzed in section 2.
Section 4 is mainly about the relation between chance and causation. But again this has an important payoff when it comes to assessing the claim that violation of CHSH inequalities entails violation of Bell’s Local Causality condition.
My paper argues for two main theses, one negative, the other positive:
1. Once one understands the relations between probability, chance and causation, one can see why violation of CHSH inequalities does not entail instantaneous action at a distance.
2. Once one understand quantum theory, one can see how we can use that theory to explain violation of CHSH inequalities while denying this violation involves any instantaneous action at a distance.As I make clear in the last paragraphs on page 13 and 16, neither chance nor quantum theory is about agents, and we can talk of chance and apply quantum theory to calculate chances of events that might occur in a world without agents. But if there were no physically situated agents in a world then no-one in that world would need to talk of chances or to apply quantum theory.
I can’t answer your question about a universe with classical stochastic dynamics without more details as to what I am supposed to be imagining. But I suspect that the scenario you have in mind would yield a unique chance of an event like Alice’s next polarization recording, in which case Bell’s Local Causality condition could be unambiguously applied to that chance. Quantum theory yields no such unique chance—see section 3 of my paper.
Shan,
I take myself to be clarifying standard quantum mechanics, not modifying it, so I don’t think there is any physical collapse on “measurement”—merely the periodic reassignment of wave function required as the physical situation of a hypothetical agent changes and so gives access to new information about “the result”.
Immediately in the past light cone of her measurement event Alice should assign an entangled wave function to the photon pair and the corresponding reduced density operator to her own photon. At the same time in the lab. frame (in which Bob’s measurement occurs first) Bob should assign a pure polarization state to Alice’s photon, reflecting the outcome of his measurement on his photon (which he takes to have been absorbed into his apparatus, and so no longer to be assigned a quantum state.)Shan,
I take myself to be clarifying standard quantum mechanics, not modifying it, so I don’t think there is any physical collapse on “measurement”—merely the periodic reassignment of wave function required as the physical situation of a hypothetical agent changes and so gives access to new information about “the result”.
Immediately in the past light cone of her measurement event Alice should assign an entangled wave function to the photon pair and the corresponding reduced density operator to her own photon. At the same time in the lab. frame (in which Alice’s measurement occurs first) Bob should assign a pure polarization state to Alice’s photon, reflecting the outcome of his measurement on his photon (which he takes to have been absorbed into his apparatus, and so no longer to be assigned a quantum state.)Roderick,
Thank you for clarifying a number of issues that are often confused.
I think further clarification is still needed on three points (see my contribution to this forum).
1. Your formulation of Locality appeals to a notion of influence you allow may be symmetric in a way that a causal relation cannot be. What could this amount to beyond mutual counterfactual dependence? Without further clarification I can’t see why failure of the principle as you formulate it should be thought to have anything to do with the intuitive idea of locality that Bell was trying to capture, as formulated in the initial intuitive statement of a principle of local causality in La Nouvelle Cuisine which he formulated in explicitly causal terminology.
2. In your rendering of the EPR argument (following Bell) you say this:
“Anyway, Bob’s outcome was already fixed before his experiment.” This would be a reasonable thing for Alice to say, and a reasonable thing for Bob to say in a Newtonian world. But it would not be a reasonable thing for Bob to say in a relativistic world, where fixity or certainty must be relativized to a space-time point (or region), since this is required to define the past as it backward light-cone.
3. Point 2 extends to “the” probability of Bob’s outcome: this must also be relativized to a space-time point or region. Alice and Bob correctly assign different probabilities to Bob’s outcome at the same time in (say) the lab. frame, after Alice’s measurement but before Bob’s (assumed space-like separated). Bell did not notice the need for this relativization, thus rendering his more formal probabilistic statement of Local Causality unclear. I agree that each probability is evidentially related to a relative frequency (cf. your response to Werner): but the relative frequencies also differ since they are defined over different reference classes.Shan,
Thank you for your comment. As you point out, on my understanding a wave function does not describe or represent the physical state of a system to which it is assigned. Moreover, a system may be assigned more than one wave function at once, since each assignment is relative to the physical situation of a hypothetical assigner. In the example you use in your own argument, the wave function to be assigned to the distant photon relative to the physical situation immediately in the future light cone of the nearby measurement of polarization with respect to a (or to a’) differs from the wave function to be assigned relative to the immediate past light cone of the measurement on the distant photon, even if these assignments are made at the same time in the lab. frame. So while the result of the polarization measurement with respect to a or to a’ requires reassignment of the distant photon’s wave function relative to the situation of the one making the nearby measurement, it does not require any change in that photon’s wave function relative to anyone about to make a measurement of its polarization. The polarization measurement with respect to a or to a’ induces no collapse in the other photon’s wave function for two reasons: first, there is no single wave function capable of collapsing (or not collapsing); and second, even if it does occur, reassignment of a wave function relative to the physical situation of a hypothetical agent (if required) does not represent any physical change in the system to which the wave function is being assigned—it couldn’t, because a wave function does not represent the physical state of that system.
Here I think I agree with Shelly’s objection to your argument.Ken,
I don’t want to throw stuff out: I just want to make sure there is a principled way of letting in enough stuff to answer Bob’s question as to what quantum probabilities are probabilities of: i.e. without using any of Bell’s proscribed words such as ‘measurement’. If there is a principled and consistent way of allowing more stuff in, I’d be very happy to do so. Indeed, I might be so happy that I would be prepared to swallow retrocausality (if clearly explained), which is one reason I encouraged you to keep trying!
To Bob at #1134,
I think my last remark about the position of a detected photon is a first step toward addressing your second aspect of the measurement problem. Some experimenters talk as if the results of their measurements simply reveal the value the measured magnitude already had (e.g. where it was). I think they can get away with this talk as long as they are careful in what inferences they draw from it, since on my pragmatist view the content of a claim is always a function of the role it plays in inferences. Perhaps you agree, since you want to confine reasoning to a frame (is that your word? I forget).
To Ken at #1133,
I agree: but I wouldn’t want to do that. I don’t want to restrict claims about positions and such to contexts that we ordinarily think of as measurements (like opening the box). Claims about positions are both significant and (sometimes) true whenever a system’s state is environmentally decohered in position basis. Of course it’s not a coincidence that that is true when we open the box. (Though measuring the position of a photon doesn’t decohere the quantized EM field in “position basis”, so there we have to think of decohering the “pointer” position instead, perhaps when a photo-electron has initiated an avalanche in a photodiode.)
To Ken at #1127,
I remain a retroskeptic, but keep trying!
The hand-waving response to the classically entangled gloves problem is to appeal to massive environmental decoherence of their state ensuring that each glove may be truly claimed to have its own classically developing trajectory since they were together. Then we get back a factorizable common cause explanation of the kind Bell wanted. Lack of such decoherence in the quantum entangled photons’ state rules out an explanation in terms of a factorizable common cause, but not a common cause that is not factorizable. (See my submission on the IJQF web site to the Bell at 50 volume).
To Robert at #1126,
Would you agree with me that the measurement problem is, fundamentally, giving a fully QUANTUM description of the measurement process?
Not quite. The measurement problem is a consistency problem: to reconcile a quantum model of a unitary interaction that entangles wave functions of system and apparatus with the interpretative assumption that a wave function completely describes the system to which it is assigned.
That problem is dissolved by noting that a wave function does not describe the system to which it is assigned—neither completely nor incompletely—but merely prescribes the correct degrees of belief one should hold in claims expressing alternative outcomes of the interaction, where the application of quantum theory presupposes that exactly one outcome will occur.
To Ken at #1123
For me, this just adds to the evidence that \psi is best viewed as a collection of classical probability distributions, most of which are wrong. The correct distribution one should use is conditional on the future measurement geometry (i.e. the choice of the next strong measurement.) So \psi is isomorphic to something like P(m(x,t)|G), where m(x,t) are some spacetime-localized microstates, and G is the future measurement geometry-choice. For any given G, P is just a classical probability distribution, but you can’t use it until you know G
I think is a good way to look at \psi. But why not take the t in m(x,t) to refer to the future measurement time? Then the theory is not committed to any PO of its own, but helps itself to an independently specified ontology only when it needs one (as a first approximation, the magnitudes of classical physics defining the pointer basis for the decoherence involved in the “measurement”)?
Before asking for the meaning of the wave function shouldn’t we ask which wave function we are talking about?
Too often talk of “the wave function” seems to arise from the perspective of a quantum model without regard to its applications (to an entire toy universe? to an actual system in the lab.?)
For dBB, Everett and REF there is one “special” wave function—that of the actual universe/multiverse. Effective wave functions or branch wave functions derived from this may have a lesser claim to beable status.
But for other views (QBist, Bohrian, Rovelli’s(?), my pragmatist) there are many wave functions with equal status (for QBists that status is subjective, or at least personal; for me, that status is objective but non-beable), and a single system may consistently be assigned more than one of these at once, relative to something else (an agent’s epistemic state for QBists; the physical situation of a hypothetical agent for my kind of pragmatist).
Presumably one can’t perform a protective measurement on the wave function of the universe.
Since there are views of the meaning of the wave function in which there is no measurement problem, it is clear that “the solution of this problem” has implications for (dis)solving the measurement problem.
The term ‘realist’ needs to be used with discretion here since it could mean so many different things. One who holds that the wave function of a system (relative to the physical situation of a hypothetical agent) is determined by the values of physical magnitudes (many on other systems) is to that extent a realist, even if (s)he denies that the wave function is a beable, or that it is ontic in the sense of specifying (directly or indirectly) properties of that system.Hi again, Max,
My position lies between the two options you lay out. The wave function is a source of probabilities only in the shallow sense that in the conventional formulation one applies quantum mechanics by calculating probabilities from the wave function by applying the Born rule. Neither the wave function nor the probabilities one calculates from it are physical objects, fields, beables, or anything like that.
But both wave function and probabilities are objective in ways subjective Bayesians deny.
To make one thing clear, both wave functions and probabilities are relational: a system does not have a wave function, and a wave function is not (in general) uniquely assigned. But what these are relative to is not the actual epistemic state of any agent, but to something physical, representing the situation of a hypothetical localized agent. An important aspect of this physical situation is the space-time location of such a hypothetical agent. That’s why Alice and Bob (whether or not they exist!) should assign different wave functions to Alice’s photon immediately after Bob’s measurement, and use the Born rule to assign different probabilities to Alice’s outcomes.
Given such a physical specification of a hypothetical agent’s situation, there is a right answer to what the wave function and probabilities are, no matter what any actual agent may think. That’s an important difference with subjective Bayesians’ view. What makes an answer right is again physical conditions in the world, which I take to be specifiable by true magnitude claims. Bob’s correct wave function assignment to Alice’s photon, for example, is what it is because of Bob’s outcome in his measurement. And what makes the entangled Bell state the correct state for any agent in Alice’s or Bob’s position to assign to the photon pair is the physical conditions involved in preparing that state.
So wave function assignments and Born probability assignments are objectively true (or false) depending on how the world is: but this does not make wave functions or probabilities “elements of physical reality”. It is also objectively true that we are are currently exchanging views about probability, but that is not a physical fact, even though it is physical facts that make it true.Ulrich,
I’m afraid your session is scheduled for a time that is too late for me to participate. I will certainly read the posts afterwards when I have time since I find your views interesting & would like to learn more.
Richard
Hi Ken,
I’m trying to understand your new point about the ontic to epistemic transition.
In the classical case, is W ontic because measuring a particle at xsub0, tsub0 uniquely specifies W at all x,t (making it look like a physical field)?
If so, how does it become epistemic? Is that because the initial velocity was not specified/measured, so at a later time tsub1, no xsub1 is singled out to give a unique time, position pair to take the place of xsub0, tsub0 in specifying the new W(x,t)?(Apologies for the early post: I mistook the start time!)
To Max at #946,
While I basically agree with you, I do think that protective measurement is helpful by forcing us to think about the significance of applying quantum mechanics to a single actual system, where one has no real statistics.
Here it is important to distinguish between probability and statistics. As we all (should!) know, probability cannot be non-circularly defined in terms of relative frequencies, either actual or “virtual”, even though statistics can provide the best evidence for probabilistic claims when they are available.
The kind of view of the wave-function you were suggesting (which I think is basically right) is better expressed by calling the wave-function a source of probabilities rather than as a description of the statistical properties of ensembles, whatever they are supposed to be (something I have never seen clearly explained). Probabilistic claims can be applied to any number of systems, and they function in the same way whatever that number—as guide to coherent degrees of belief.
We can go on to argue about what probabilities are, but I doubt that talk of statistics in ensembles will be helpful in this debate.
Max,
Thanks, that’s helpful. It seems that protective measurement avails itself of the usual “buck-passing” move of assuming that at some stage in the von Neumann chain one can either appeal to a collapse or read a superposition as a mixture FAPP.
I have a question about what can be inferred from the final system-apparatus state in Max’s equation (11) (which he takes to be just the zeroth order approximation). It seems that to infer from (11) that we have measured the expectation value of O we need to appeal to some general principle connecting state assignments to value assignments. One such principle is the eigenstate-eigenvalue link (in that direction). EPR explicitly used this as well as their reality criterion in arguing for the incompleteness of quantum mechanical description, though Einstein’s own later versions of the argument did not.
I think both the original EPR reality criterion and this eigenstate-eigenvalue link are controversial interpretative assumptions: moreover, I think they they are both false. What do you think?In answer to Matt Pusey at #890,
Yes, one can make magnitude claims about spin. These are all claims about angular momentum, called spin for purely historical reasons when its components take on values +/-1/2 in units of h-bar.
One can make magnitude claims about arbitrary components of spin, and also about total spin—though these are rather dull since the only true claim is that total spin has value (root-3)/2, whenever that claim is significant.
The claim that an electron (say) is a spin 1/2 particle, though true, is not itself a magnitude claim. Instead, it is a true claim about the mathematics of quantum models, true because if one wants to apply quantum theory to electrons (or to an electron field) one should build a model in a 2-dimensional complex Hilbert space (or other corresponding mathematical structure).
To #785,
“how are you going to address what I call the SECOND measurement problem: that the measurement actually measured some microscopic property? ”
I think this way of talking, though often permissible, should rarely be taken literally. Entangled photons have their linear polarization measured every day in quantum optics laboratories by passing them through a polarizer and absorbing them at a detector. I think at no point does one of these photons have a linear polarization.
There are occasions in which decoherence licenses magnitude claims about the position of a particle after detection by a detector, as when Markus Arndt’s group got their fullerenes to stick to a specially prepared silicon surface and then scanned them with an STM. Each fullerene had some pretty definite, stable, position on the silicon surface after detection, even though it had no well-defined position in the interferometer prior to detection.
So I guess I’m with the theoreticians on this issue, and merely tolerate experimentalists’ talk of muon trajectories, unless these muons’ states were stably decohered in position basis on their way to the detector. The discussion by Mott and Bell about the formation of alpha particle tracks in a cloud chamber is relevant here.
To Robert at #7
“I challenge you to say anything in the advanced QM course without using wave functions or operators or Hilbert space.”
Not accepted!
Of course one has to talk of such things when discussing the mathematics of quantum models. And in such a context one naturally mixes such talk with talk of how the models are going to be applied to physical systems, if only to motivate what might otherwise be regarded as rather dry mathematics.
But if one is seeking analytical clarity about how quantum models are applied it is very important to distinguish talk about the model from talk about the physical system(s) to which it may be applied.Unlike Max Tegmark (apparently) I don’t think the physical world is mathematical. In classical physics we use mathematics pretty straightforwardly to describe the physical world, when we say (for example) the mass of the sun is however many kilograms, or the current outside temperature is so many degrees Celsius. Actually, philosophers of science have worried about how mathematics can be used descriptively even in such simple cases. We don’t think the world contains coordinate systems, but we still use their mathematics in applying classical physics. But when it comes to quantum theory, the application of the mathematics of the models is at least more subtle. It becomes important to ask whether a particular element of a mathematical model is being used to describe or represent something in the physical world (directly or indirectly) or for some other purpose. We can associate dynamical properties of a physical system (such as z-spin up) with subspaces of Hilbert space, but can we say that a spin 1/2 system has such a property just in case its quantum state lies in that subspace? Different views of quantum theory will answer that question differently.
To Robert at #767,
You say
“There are aspects of your presentation which suggest that you entertain the
opinion widespread among the decoherence advocates that all one needs to do is
to consider an appropriate “big” wavefunction developing unitarily in a large
closed system, and then the physics will drop out of it by applying Born’s rule
here and there as needed. Actually, this will not work; the probabilities you
get in this way are what I call in Sec. 9.2 of my book “one time
probabilities”; what is lacking is the temporal correlations which are crucial
to the physics.”In appealing to models of environmental decoherence as a guide to the significance of magnitude claims, I think I am considering temporal correlations in this sense. The “pointer basis” in a model of environmental decoherence is typically selected very rapidly and persists robustly for a long time thereafter. In this way appeal to such a model to underwrite the significance of claims about magnitudes whose operators are very nearly diagonal in the pointer basis does rely on the temporal correlations of the model. It must, since at any instant the Schmidt decomposition will always pick out (elements of) a unique basis.
Richard
To Robert #772,
Man physicists use the word “describes” when they really mean “applies to”. In what sense does Hilbert space (or a vector or operator in Hilbert space) describe anything? How do we use it to describe anything?
After long rejecting Bohr’s infamous remark that there is no quantum world as rabid antirealism, I came to have some sympathy with the continuation “the point of physics is not to describe nature, but to determine what we can say about nature” (not an exact quote, sorry). I think to understand quantum theory we need both to ask what we can say about the physical world and also show why much of what we can say is true. But quantum theory itself does not say anything about the world we could not say without using waves functions, vectors, operators or Hilbert space.
Richard
To Matt at #771,
I do want quantum probabilities to be objective, and I’ve said a bit about what I think that involves in my BJPS paper in the references to my posted topic paper.
I can add this: To accept quantum theory is to grant expert status to its Born probabilities in assigning one’s degrees of belief—to treat these as authoritative. As for the wave-function that’s input to the Born rule, to treat that as objective is to undertake to be guided by relevant frequencies in outcomes of measurements. As to what counts as repeating the same measurement on the same kind of system to get those statistics, I take this to be an objective matter in that the community of physicists takes it to be a matter of fact to be resolved by argument and further experiment. Not much of this look like an extension of logic, as people like Keynes and maybe Carnap hoped!To Ken at #774,
Nice example! Non-optimally-informed agents can still use quantum theory as long as they recognize that they could have done better if they had made full use of all physically accessible information. I think this is what is going on with assignment of entangled states to systems that no longer exist in delayed choice entanglement-swapping experiments.
Richard
Matt,
I can make sense of talk of the wave function of the universe if this refers to a state assignment to some restricted set of degrees of freedom of the universe—say its large scale spatial structure. Such an assignment might be useful in guiding an agent situated within that universe (or even in another one!) in forming rational degrees of belief about that universe’s large scale structure, as expressed in significant magnitude claims—significant because of decoherence with other degrees of freedom in their environment.
I’ll have to think more about stuff going on in regions of the universe forever outside the observable universe of any hypothetical agent. As a first reaction, I see no problem, since one can certainly apply quantum theory to non-actual universes in which everything is unobservable. But this has a point only insofar as one can “project” oneself into that universe as a very hypothetical physically situated agent.
RichardTo Ken, again,
“if different agents can use different states, then the theory of QM that determines (objectively!) which state they should use *must* refer at some point to the knowledge that an agent has at her disposal…? Otherwise, how could two different agents end up with different states?”An objectively correct state assignment relative to an agent-situation will be backed by true magnitude claims concerning events in the back light cone of that situation. Since different agent-situations have different back light cones, the backing conditions of correct state assignments relative to those agent-situations will also generally differ. That’s why different assignments are correct relative to different agent-situations.
None of that referred to agents or their knowledge. Rather, it explained why if there are any agents in these situations they will be well-advised to assign different states as the best way they have of adjusting their beliefs on the basis of the knowledge available to them.
We have to keep straight the distinction between quantum models and how they work, and how they assist agents in arriving at well-advised epistemic states.
I don’t want to be disagreeing with straw QBists, so I accept their wish to consider only coherent belief states!
Richard
Richard
Hi Ken,
For a given agent-situation there is an objectively correct state assignment: what this is is in general different for different agent-situations. An agent-situation is not an agent: it is something physically characterized in terms of a space-time region (ideally a point) and perhaps also physical processes connecting that region to other regions relevant to the system whose state is to be assigned. So one can talk freely about (different) correct state assignments to a system in a world devoid of actual agents.
Does this help?
What’s confusing about the top of page 6? I don’t want to confuse people!
Ulrich Mohrhoff replied to one of your updates:
“Hi Richard,
You said it: “Quantum mechanics can’t explain why there is a unique outcome since its application presupposes that there is.” This cannot be over-emphasized.
Since your upcoming presentation begins at 1.30 am my time (Indian Standard Time), I don’t think I will be in a condition to participate in the text chat. Hence a few comments here, in advance.
You write: “Bell’s argument … assumes that an event has a unique chance. But the use of wave-functions in generating Born probabilities shows why both wave-functions and chances must be assigned relative to the space-time location of a hypothetical agent applying quantum mechanics.”
This sounds quite similar to what QBism is saying, a critical appraisal of which I uploaded last month: http://arxiv.org/abs/1409.3312. You are absolutely right in denying (as you seem) that a given event has a unique chance. Since quantum mechanics *correlates* events, the probability of a given event depends on the events on the basis of which it is assigned. But this is not quite the same as making probabilities dependent on the spacetime locations of the agents assigning them. More on this in Sect. 9 of the aforementioned preprint.
You continue: “When this is done, quantum mechanics can be used to explain violation of Bell inequalities with no superluminal influences.” Explain? Predict, yes, but that it does anyway. Rejecting an explanation (in this case, superluminal influences) doesn’t quite amount to explaining what is going on.
Best,
UlrichUlrich,
Thank you for your comments, and especially for referring me to your arxiv posting.
I have learned a lot from QBists, but I agree with you that one doesn’t need to be a subjective Bayesian to understand the significance of Born probabilities. A quantum state assignment is relative not to the epistemic state of an actual agent, but to the physical situation of a merely hypothetical agent including space-time location. This restricts such an agent’s access to information and so would make it necessary for him/her/it to aim for an ideal epistemic state that took account of all and only information about events in his/her/its backward light cone in forming beliefs about matters not so accessible. Quantum mechanics helps us actual agents to set degrees of belief using Born probabilities, among other things to derive objective chances (single case probabilities for individual events) relevant to our physical situations. But these objective chances are not physical propensities that (sometimes) make these events happen—they are not beables, and certainly not local beables.
Certainly rejecting one explanation does not amount to having another. But quantum mechanics can explain violations of Bell inequalities as the joint of effect of a nonfactorizable common cause (whatever event(s) in the overlap of the backward light cones of the detection events backed assignment of the relevant entangled state). See my paper posted on the IJQF web site, which you can find by clicking on my name under Blogs: Members.
Best,
RichardThanks, Matt, this was helpful.
1. Since I do not think the quantum state is an intrinsic property of an individual system my view of the wave function is not ontic in terms of your classification. But since I do think that many wave function assignments are objectively true because of how the physical world is (not because of what anyone believes about it) I am not happy having the view called epistemic.
2. Is my view realist? I do think quantum theory helps us make lots of true claims about unobserved features of microscopic physical things, and in this way furthers the realist goal of describing the fundamental features of the world, whether or not we are observing, or can observe them. In this sense it is a theory “without observers” in Goldstein’s sense. But I don’t think that the wave function or other elements newly introduced in quantum models themselves describe new kinds of physical features of the system to which they are assigned: quantum theory does not introduce any new beables. I would like to see a theory that gives a richer description of the physical world than quantum theory, but the desire for a more full-blooded realist theory should not influence one’s understanding of the quantum theory that we have.
3. I depart from QBism by taking quantum state assignments and Born probabilities to be objective rather than subjective: so I reject the global subjective Bayesianism of QBists, at least in the sense that I see this as just one philosophical option one doesn’t have to take to understand quantum theory. And I take quantum state assignments to be relative, not to an actual agent’s epistemic state, but to a merely hypothetical agent’s physical situation. There are other differences (e.g. with regard to the significance of models of decoherence) , but these are the main ones.
4. That last point is relevant to your second question: The correct quantum state assignment relative to the physical situation of one hypothetical agent may differ from the correct quantum state assignment relative to that of a different hypothetical agent. Bob and Alice can assign Alice’s photon different quantum states at the same lab. Time because Bob is in a position to know his outcome though spacelike separated Alice is not. (Bob should “collapse” his state, but Alice should not.)
5. In answer to your last question: Yes, that is the important disanalogy: I accept that we could get rid of wave functions and replace them with probability distributions.Shan,
Thank you for your post. It will take me some time to digest the different opinions I’ve seen expressed on the significance of protective measurement. I note that Max Schlosshauer disagrees with your own evaluation of its significance in his topic, and I hope to learn from this debate. I’ll let you know if and when I know what to think: at present I remain skeptical in the best Socratic tradition as one who knows that he does not know!
Richard
Does the wave-function describe a physical system or our knowledge of that system? No.
It describes neither. So what’s the use of wave-functions?
The primary use of a wave-function is to prescribe (not describe!) how firmly to believe claims about the values of physical magnitudes on a physical system.
Anyone who accepts quantum mechanics uses the wave-function to do this by plugging it into the Born rule and adjusting her degrees of belief to match the corresponding Born probabilities.Probabilities for what? The values of magnitudes (x-position, z-spin, energy,…). So the Born rule should be stated so as to assign probabilities to claims about the values of magnitudes, not claims about measurement outcomes.
But don’t we know that can’t work, because there is no consistent non-contextual simultaneous assignment of values to all “observables”?
There isn’t, but there doesn’t need to be. The Born rule can be legitimately applied only to significant magnitude claims!You mean claims about magnitudes in an experimental arrangement suitable for their measurement?
In general, “No”: plenty of magnitude claims about what happened long ago in a far-away uninhabited galaxy are perfectly significant. If you are concerned about which these might be, ask whether application of a model of decoherence would pick out a “pointer basis” close to diagonal in a basis of eigenfunctions of your favorite “observable” magnitude on your favorite quantum system. If yes, it’s O.K. to apply the Born rule: otherwise, not.
Why do this?
1. It is consistent: Kochen/Specker-type proofs don’t rule it out.
2. It works: beliefs formed in this way are reliably confirmed by experimental statistics: that’s why you should accept quantum mechanics and use it this way.What about the measurement problem? What about Bell?
The measurement problem arises only if one mistakenly takes the wave-function completely to describe a system to which it is assigned, including the entangled system+apparatus in a measurement. Since it doesn’t describe a system at all, no problem! (Quantum mechanics can’t explain why there is a unique outcome since its application presupposes that there is. Is that a problem? Only for those who put unreasonable demands on quantum mechanics—it’s still the best theory around!)
Bell showed that no theory of local beables satisfying a factorizability condition he took to follow from an explication of an intuitive local causality requirement is consistent with certain quantum predictions, now amply confirmed by experiment. Quantum mechanics doesn’t satisfy this factorizability condition, but Bell’s argument for that condition from the intuitive local causality requirement makes assumptions that fail in quantum mechanics. Specifically, it assumes that an event has a unique chance. But the use of wave-functions in generating Born probabilities shows why both wave-functions and chances must be assigned relative to the space-time location of a hypothetical agent applying quantum mechanics. When this is done, quantum mechanics can be used to explain violation of Bell inequalities with no superluminal influences.
