Alhassanain(p) Network for Heritage and Islamic Thought

5. The objectivity of physical description in quantum theory

  If quantum state ascriptions and the consequent Born probabilities are relative to agent situations, then is there any non-relational physical description on which agents in all situations can agree?  The analogous question in the context of relativity theory receives a straightforward answer: frame-dependent descriptions including those of length and time-intervals may be thought to derive from frame-independent invariants such as the space-time interval. The question must be answered positively in the context of quantum theory in order to facilitate descriptive claims about the physical world any agent can endorse whatever that agent’s physical situation, so that these claims can contribute to the predictive and explanatory goals of physics.

       Section 3 explained why no claim expressed by a sentence of the formS : ‘The value of A ons lies in Δ’  (no NQMC) is implied by any quantum state ascription (QSA) or Born probability statement (BPS) - even in a case in whichS is correctly assigned Born probability 1 (relative to some agent situation)). NQMC’s were frequently and correctly made before the development of quantum theory and continue to be made after its widespread acceptance, which is why I call them non-quantum. While quantum theory adds no new ways of describing the physical world, it does offer authoritative advice to a situated agent, both on the content of NQMC’s relevant to its situation, and on the degree of belief appropriate to such claims. The appropriate degree of belief generally depends on the agent situation, so differently situated agents are frequently advised to hold different epistemic attitudes toward NQMC’s. But the content of a NQMC about a systems does not depend on agent situation. That is why any NQMC can be taken to offer a physical description that is objective, in the sense that the content of the claim is strongly agent-independent: it is independent of the physical as well as the epistemic state of any agent (human, conscious, or neither) that may make or evaluate it. But acceptance of quantum theory so drastically limits the content ofsome NQMC’s that they can no longer contribute to the explanatory or predictive goals of physics and so are best left unsaid.

5.1 Why violations of Bell Inequalities involve no physical non-locality

The distinctions just drawn between quantum state ascriptions, Born probability statements and non-quantum magnitude claims are important in explaining why quantum violation of Bell inequalities involves no physically problematic non-locality. Recall the discussion of non-local correlations in section 4. Remember that the eventM B when Bob measures the polarization of photonR along theb -axis occurs earlier in the laboratory frame than the eventM A when Alice measures the polarization of photonL along thea -axis. How should the relevant systems be described by NQMC’s? Consider the following claims:

D 1: Photon-detectorL records polarizationa or polarizationa ⊥ .

D 2: Photon-detectorL records polarizationa.

P 1: PhotonL has polarizationb or polarizationb ⊥ .

P 2: PhotonL has polarizationb .

Assume (all experts including Alice and Bob agree that) a photon pair is emitted in polarization state |Φ+,and detection is perfectly efficient.D 1 can be taken to express an NQMC that is licensed by quantum theory (because of the decohering polarization-correlation interaction betweenL and its detector+environment) and warranted for any agent at any time, simply because Alice’s photon detector is in good working order.D 2 can similarly be taken to express an NQMC that is licensed by quantum theory, but whereasD 2 is warranted for Alice as soon as she records theL polarization, Bob is justified in making claimD 2 only when Alice communicates to him the record of theL polarization later - unlessb=a , in which case Bob will be justified in claimingD 2 as soon as his detector records polarizationa on photonR . (Ifb≠a thenD 2 will be at most partially warranted for Bob before receipt of Alice’s message.)

       Now consider claimsP 1 andP 2. One might suppose that Bob is justified in claimP 2 after consulting his photon detectorR and finding that it has recorded polarizationb , and that his entitlement extends to claimP 1 by simple logic. But this is incorrect. Even ifM B occurs invariantly earlier thanM A , quantum theory grants an agent (like Bob) only an extremely limited license to claimsP 1 andP 2: the content of these claims is severely weakened by the severe restrictions on what material inferences they support. This is because in the interval betweenM B andM A photonL undergoes no interaction with its environment capable of delocalizing its quantum polarization state in a preferredb -b ⊥ basis. After his detector records polarizationb forR , Bob’s situation does warrant him in ascribing polarization state |b,to photonL : this becomes his new quantum polarization state for that photon. But no QSA implies any NQMC: the eigenstate-to-eigenvalue link fails.P 2 does support some material inferences to behavior characteristic of classically polarized light, importantly including that photon-detectorL would record polarizationb , and indeed will do so ifb=a . But Bob is already warranted in believing these conclusions by his assignment of quantum state |b ,to photonL , and so is any agent (including Alice) who knows the result of Bob’s measurement. Any agent can reach these conclusions by assigning |Φ+,to the photon pair and conditionalizing on Bob’s recordedR polarizationb . So this part of the content of claimP 2 can be secured without it. Moreover,P 2 will not support additional material inferences just becauseL undergoes no decoherence interaction robustly correlating itsb -polarization state to an environment. These considerations also undercut claimP 1. So Bob has no warrant for claimingP 2 if the content of this claim is taken to extend beyond that of the claim that his quantum polarization state forL is |b ,, and no warrant for claimingP 1 if the content of that claim is taken to extend beyond that of the claim that his quantum polarization state forL is either |b ,or |b ⊥ ,. These claims have no place in a careful agent-independent physical description capable of explaining the non-local correlations. Nor do analogous claims about the polarization ofR .

       Notice that we have now provided a reason why quantum theoretical analysis of these non-local correlations does not involve attributing to the polarizations of theL ,R photons in a pair

  ‘…any mutually independent existence (state of reality) [when] viewed separately, not even if [they] are spatially separated from one another at the particular time under consideration.’[22]

At most, quantum theory licenses a claim about the polarization prior to detection of theL -photon only with respect to theb -axis, and a claim about the polarization prior to detection of theR -photon only with respect to thea -axis: and the license it extends tothese claims is so severely restricted that neither amounts to a report on an independently existing state of reality. This is fortunate, since a well-trodden path takes one from the independent existence of pre-existing polarization states of both photons along every axis that their respective detectors simply reveal to Bell inequalities, whose experimentally-confirmed violation confirms quantum theoretical predictions derived from the Born rule as applied to state |Φ+,. If each arbitrarily-oriented photon-detector faithfully revealed a pre-existing polarization of the detected photon, and these polarizations were distributed among many pairs in state |Φ+,in a way that was independent of the detector settingsa ,b , then the only way to restore consistency with the Born rule predictions would be to allow that the polarization state of a photon could be non-locally altered before reaching the detector. That would constitute a blatant violation of a physical locality condition Einstein ([1948], p.322) stated as follows

aussere Beeinflussung von A hat keinenunmittelbaren Einfluss auf B; dies ist als << Prinzip der Nahewirkung >> bekannt  (‘an external influence on A has no immediate effect on B; this is known as the ‘principle of local action’ ‘)

The present pragmatist approach to quantum theory acquits it of any such violation of local action.

       Bell inequalities may be derived in a bipartite system like the photon pairLR without assuming anything corresponding to independently existing polarizations for each subsystem. The key assumptions here are of conditional probabilistic independence such as the following (Gisin [2009]) where I suppose that α, β are variables ranging over the possible values of polarization recorded byL, R detectors respectively along thea ,b axes, and λ (which may include the quantum state, here |Φ+,) specifies the situation of everything in the past irrelevant to the choice ofa ,b axes:

prob(α|a ,b , λ) = prob(α|a , λ) :  prob(β|a ,b , α, λ) = prob(β|b , λ)  (6)

Which together imply

prob(α, β|a ,b , λ) = prob(α|a , λ) × prob(β|b , λ)                               (7)

Gisin glosses these conditions as follows

...for any give “state of affairs” λ, what happens on Alice’s side does not depend on what happens on Bob’s side, and vice versa.

But if λ is just whatever earlier physical conditions warrant ascription of quantum state |Φ+〉 to the pair, and the probabilities appearing in (6) are taken to be consequences of the Born rule as applied to |Φ+〉 , then neither (6) nor (7) says anything about what happens in this situation. As in the BPS’s from which they follow, (6) and (7) describe nothing in the physical world: their role is simply to offer authoritative advice to an agent such as Alice or Bob on what to expect in the situation described. As section 2 explained, a Born probability statement does not purport to describe physical reality. Its role within the theory is to offer objective advice to a physically situated agent on how to apportion beliefs concerning matters of which it is ignorant. So understood, conditions like (6) and (7) do not express physical locality conditions. The fact that Born probabilities violate the second part of (6) does not make the quantum world physically non-local. But it is interesting to note that if Born probabilities had violated just thefirst part of (6), by choosing one axis of his detector rather than another during repeated runs of the experiment, Bob would have been able to guide Alice’s expectations and thereby manipulate her behavior in a way thatwould have violated Einstein’s principle of local action! So the no-signaling theorems remain critical to this acquittal of quantum theory from the charge of violating a physically motivated locality condition.

5.2 Objectivity, Inter-subjectivity and Wigner’s friend

       The content of a NQMC expressed byD 1 orD 2 is in no way relative to the situation of any actual or possible agent, even though an agent’s situation may well affect its warrant for making that claim. Moreover, because of the nature of the decohering polarization-correlation interaction betweenL and its detector+environment, the inferential power of one of these claims extends very far - far enough for such claims to be considered simply objective descriptions of the physical world for all practical and impractical purposes of any agent. An agent making such a claim may therefore be understood to be offering an objective description of the physical event normally taken to constitute the outcome of a measurement of linear polarization ofL along thea axis. It is by licensing, though not implying, such claims that quantum theory authorizes objective physical description of the world.

       As we have seen, the status of NQMC’sP 1 andP 2 is different. Even though their content need not be regarded as relative to the situation of any agent making them, quantum theory severely limits their inferential power. This so restricts their content that it is no longer appropriate to think of these claims as simply offering an objective description of the physical properties of photonL , or of any other physical state of affairs. This does not mean that such claims have no use. Bob may utterP 2 intending thereby merely to ascribe quantum state |b ,to photonL , and such a usage may acquire common currency within a community of quantum physicists. Indeed, physicists do often ascribe linear polarization states to photons. But this does not show that by saying something likeP 2 these physicists are offering objective physical descriptions. By familiarizing themselves with quantum theory they have internalized the limited inferential power attached to such a claim and they use it with that common understanding.

       The “paradox” of Wigner’s friend presents a challenge to the objectivity of physical description within quantum theory. To set up the “paradox”, imagine Schrödinger’s cat (and associated ‘diabolical device’) replaced by a human experimenter (Wigner’s friend) who records in a deviceD the result of a quantum measurement he has performed on a systems inside his isolated laboratory.[23]For example, suppose thats is the photonL just considered,D L detects its polarization along thea axis, and the friend is Bob. Meanwhile, another agentW remains outside the laboratory. After consulting the record ofD R, Bob ascribes quantum polarization state |b ,toL and applies the Born rule to calculate the probability, (|+a |b ,|2), ofD 2. He performs the measurement, consultsD L, and records the outcome by writingD 2 in his notebook.W , on the other hand, ascribes a quantum state |ΨW,to the enormously complex system composed ofL ,R, Bob,D L,D R, the notebook and everything else in the laboratory, and uses this to calculate the Born probability ofD 2. Even though this will not equal |+a |b ,|2, no inconsistency arises, since all BPS’s are relative to the physical situation of an agent making them, andW and Bob are in relevantly different physical situations: at this stage Bob has interacted, first withD R, and then withD L, butW has interacted with neither.

       An inconsistency would arise if one took a quantum state completely to describe a system in accordance with the eigenstate-eigenvalue link and assumed measurement collapses this state onto an eigenstate corresponding to the corresponding eigenvalue of the measured observable. Bob would then take his measurement ofL -photon polarization to collapse the state ofL -photon+D L onto an eigenstate of which a “pointer reading” onD L was an eigenvalue. But, treating Bob merely as part of the physical contents of the laboratory,W woulddeny that the state |ΨW,collapsed onto such an eigenstate untilhe ,W , made a measurement by entering the laboratory to see what polarizationD L had recorded. There is no threat of such inconsistent descriptions of the contents of the laboratory prior toW ’s entry on the present pragmatist approach, which denies any descriptive role to quantum states. But if quantum theory deniesW the license to use his quantum state |ΨW,to describe what is happening in the laboratory before he enters, while licensing Bob to make descriptive claims such asD 2, then how can a claim likeD 2  be taken to offer an objective physical description ?

       A default assumption underlying the objectivity of physical description dictates thatW accept Bob’s sincere reportD 2 when backed up byW ’s own independent investigations. This assumption is so deeply embedded in scientific methodology that it is hard to imagine how any kind of scientific activity could survive its wholesale rejection.W ’s quantum analysis of his situation may seem to challenge this assumption. Since he knows that Bob was to prepare his photon pair in polarization state |Φ+,, W’s initial quantum state |ΨW,t1 will include a representation of the polarization state of theL -photon that is a superposition of |a ,and |a ⊥ ,with appropriate non-zero coefficients. Subsequent interactions withD L, further recording equipment, Bob and Bob’s notebook will entangle this superposition with their quantum states. Nothing about this quantum state will even suggest what result (if any) Bob got in his measurement of the polarization of theL -photon.  But W’s quantum state will advise him to expect that, whatever that result may be, the laboratory will contain multiple mutually supporting records of it. So that while his quantum analysis alone providesW no warrant for believingD 2, it does warrantW in believing that his observation ofD L, consultation with Bob, reading Bob’s notebook, and any other examination of what is ordinarily taken to be evidence thatD 2 was true even before he entered the laboratory, will all be mutually consistent with each other, and consistent also -either withD 2or else withD 2⊥ : Photon-detectorD L records polarizationa ⊥ . It remains perfectly consistent withW ’s quantum analysis of the situation for him to suppose that it isD 2⊥ , notD 2, that correctly described the physical situation prior to his entering the laboratory, despite Bob’s sincere statement that he remembers recordingD 2 , backed up by allW ’s own observations on entering the laboratory.

       There is nothing strictly paradoxical about this situation. But it does prompt the skeptical concern that an agent who accepts quantum theory no longer has any reason to expect apparently sincere reports of fellow agents concerning readily observable properties of macroscopic objects to be reliable, not even if these are backed up by its own independent observations of these properties, together with what are ordinarily considered traces of them. Quantum theory does not validate the default assumption underlying the objectivity of physical description.

       I think the right way for a scientist to respond to this concern is simply to refuse to take this skeptical possibility seriously. A scientist begins by trusting his or her own observations as well as those of others and questions these only when further observations provide positive reasons for doing so. Nothing we learn from quantum theory or anything else in science providesW with any reason for questioning his own or his friend’s sincere observation reports concerning the outcomes of quantum measurements or the gross properties of macroscopic objects. Science concerns itself precisely with those physical descriptions that can be taken to be objective in the sense that they are open to support from multiple independent observations whose evidential import can be collectively undercut only by this kind of radical philosophical skepticism, yielding to which would render scientific investigation of any kind impossible. The extremely hypothetical scenario of Wigner’s friend fails to lift the burden of proof from one who would seek to deny the objectivity of physical descriptions such as that offered by the claimD 2.

       A further twist on the Wigner’s friend scenario will help to bring out a quantum limitation on the content of all NQMC’s (including not onlyD 2 but also claims such asS x from section 3), and indeed on all physical descriptions. ConsiderW ’s quantum state |ΨW,. Since the entire laboratory and its contents constitutes an isolated system,W will take |ΨW,to have evolved unitarily from its state |ΨW,t1 prior to his friend’s measurement of the polarization ofL to its state |ΨW,t2 just as he enters the laboratory to ask his friend about its result.

  |ΨW ,t2   =U 12 |ΨW ,t1             (8)

W should ascribe to the contents of the laboratory att 1 a quantum state that reflects his belief that his friend has not yet performed the planned measurement onL . SoW will be warranted in ascribing to these contents a state |ΨW,t1 that assigns Born probability 1 to NQMC’s onD L, Bob and his notebook that suffices to substantiate that belief. Mathematically, there will exist a Hamiltonian that would induce the time-reversed evolution of |ΨW,so that at a later timet 3 (wheret 3− t 2=   t 2 −t 1) it is restored to its value before the friend measured the polarization ofL

  |ΨW ,t3   =U †23 |ΨW ,t2   = |ΨW ,t1      (9)

IfW had the powers of a quantum demon, he could instantaneously replace the original Hamiltonian by this time-reversing Hamiltonian att 2, thereby restoring |ΨW,att 3 to its original value att 1.[24]Suppose that he does so, and postpones his entry into the laboratory untilt 3. Since the quantum state of the entire laboratory is identical to what it was before his friend had made any measurement of the polarization ofL ,W must fully expect that if he then asks his friend about the result of his measurement, the friend will say he has not yet performed any measurement. He must further fully expect that his own examination at, and at any time after,t 3 ofD L, Bob’s notebook, and anything else inside the laboratory will reveal no record of any such measurement ever having been made.W ’s action att 2 has, byt 3, erased all traces of Bob’s measurement of the polarization ofL and its result: Indeed,W has succeeded in erasing all traces of everything that happened inside the laboratory betweent 1 andt 3. 

       It is deeply embedded in the way we ordinarily think about the past that everything that happens leaves some trace of its occurrence, however epistemically inaccessible this may be to us. Dummett ([1969]) even took rejection of this assumption to be a significant motive for antirealism about the past - the view that statements about the past on which no present or future evidence bears have no determinate truth-value. Consideration of the extended Wigner’s friend scenario shows that one who wholly accepts quantum theory must limit the content of NQMC’s and indeed all other physical descriptions so that such a claim does not thereby exclude the physical possibility that the claimed state of affairs leave no trace whatever. But while allowing for this possibility does marginally weaken every physical description I do not see that quantum theory thereby makes physical description any the less objective.

6. Conclusion

I promised a diagnosis of the curious situation that while there are no serious and lasting disagreements among physicists on the use of quantum theory, disputes about its meaning began with its inception and continue unchecked. I suggest that what is largely responsible for this situation is the assumption (tacit or explicit) that the meaning of quantum theory must be given by saying what the physical world is like, according to that theory. That the meaning ofany theory is to be given by spelling out its truth-conditions is an assumption no pragmatist will leave uncontested. Rejecting this blinkered perspective on interpretation makes it possible to see that the real significance of quantum theory for the philosophy of science is how it advances the goals of physicswithout presenting us with novel ways of representing the world. In this paper I have indicated how this new perspective permits progress on long-standing problems such as the measurement problem and quantum non-locality: many details remain to be filled in subsequently.

One goal of physics emphasized by realists is explanation of natural phenomena. I anticipate the objection that quantum theory is only able to achieve its great explanatory success through its deployment of novel theoretical representations of the world. Since this pragmatist interpretation cannot account for quantum theory’s explanatory successes (the objection continues), it is merely a new name for a bad old way of thinking–instrumentalism! To confine the present paper within reasonable bounds, a second paper will be devoted to a detailed refutation of this objection.[25]

Funding

National Science Foundation (SES0848022).

Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant No. SES-0848022. I thank my Arizona colleagues Jenann Ismael and Terry Horgan for their helpful comments and suggestions on this work. Special thanks go to my hosts in Vienna, Prof. A. Zeilinger and Prof. M. Aspelmeyer, who made it possible for me to visit the Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences during summer 2009 under the Templeton Research Fellows Program “Philosophers-Physicists Cooperation Project on the Nature of Quantum Reality”, and additionally to Xiaosong Ma and the other scientists in the Institute for many enlightening discussions and for permission to reproduce Figure 2. I also wish to acknowledge the support of the Perimeter Institute for Theoretical Physics under their sabbatical program, and to thank its members and visitors for the intellectual stimulation they provided during my visit in Fall 2009: research at the Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. Finally I wish to thank the University of Sydney, and Huw Price, Director of the Centre for the Study of Time, for inviting me to give a series of lectures early in 2010 in conjunction with the award of an International Visiting Research Fellowship, thereby providing the stimulus and opportunity to share these ideas at a formative stage.