A Synopsis of the Minimal Modal Interpretation of Quantum Theory

Jacob A. Barandes1, ∗ and David Kagan2, † 1Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138 2Department of Physics, University of Massachusetts Dartmouth, North Dartmouth, MA 02747 (Dated: June 6, 2014) We summarize a new realist interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory’s basic dynamical content essentially intact. Much as classical systems have specific states that evolve along definite trajectories through configuration spaces, the traditional formulation of quantum theory asserts that closed quantum systems have specific states that evolve unitarily along definite trajectories through Hilbert spaces, and our interpretation extends this intuitive picture of states and Hilbert-space trajectories to the case of open quantum systems as well. Our interpretation—which we claim is ultimately compatible with Lorentz invariance—reformulates wave-function collapse in terms of an underlying interpolating dynamics, makes it possible to derive the Born rule from deeper principles, and resolves several open questions regarding ontological stability and dynamics.

contrast to the smooth time evolution that governs dynamically closed systems. The Copenhagen interpretation is also unclear as to I. INTRODUCTION the ultimate meaning of the state vector of a system: Does a system’s state vector merely represent the experi- In this letter and in a more comprehensive companion menter’s knowledge, is it some sort of objective probabil- paper [1], we present a realist interpretation of quantum ity distribution,1 or is it an irreducible ingredient of real- theory that hews closely to the basic structure of the the- ity like the state of a classical system? For that matter, ory in its widely accepted current form. Our primary goal what constitutes an observer, and can we meaningfully is to move beyond instrumentalism and describe an ac- talk about the state of an observer within the formalism tual reality that lies behind the mathematical formalism of quantum theory? Given that no realistic system is of quantum theory. We also intend to provide new hope ever perfectly free of quantum entanglements with other to those who find themselves disappointed with the pace systems, and thus no realistic system can ever truly be of progress on making sense of the theory’s foundations assigned a specific state vector in the first place, what [2,3]. becomes of the popular depiction of quantum theory in which every particle is supposedly described by a specific wave function propagating in three-dimensional space? A. Why Do We Need a New Interpretation? The Copenhagen interpretation leads to additional trou- ble when trying to make sense of thought experiments The Copenhagen interpretation is still, at least accord- like Schrödinger’scat, Wigner’s friend, and the quantum ing to some surveys [4,5], the most popular interpreta- Zeno paradox.2 tion of quantum theory today, but it also suffers from a A more satisfactory interpretation would eliminate the number of serious drawbacks. Most significantly, the defi- need for an ad hoc Heisenberg cut, thereby demoting nition of a measurement according to the Copenhagen in- measurements to an ordinary kind of interaction and terpretation relies on a questionable demarcation, known allowing quantum theory to be a complete theory that as the Heisenberg cut (Heisenbergscher Schnitt)[6,7], be- arXiv:1405.6754v3 [quant-ph] 5 Jun 2014 seamlessly encompasses all systems in Nature, includ- tween the large classical systems that carry out measure- ing observers as physical systems with quantum states of ments and the small quantum systems that they measure; their own. Moreover, such an interpretation should fun- this ill-defined Heisenberg cut has never been identified damentally (even if not always superficially) be consis- in any experiment to date and must be put into the inter- tent with all experimental data and other reliably known pretation by hand. (See Figure1.) An associated issue features of Nature, including relativity, and should be is the interpretation’s assumption of wave-function col- general enough to accommodate the large variety of both lapse, by which we refer to the supposed instantaneous, discontinuous change in a quantum system immediately following a measurement by a classical system, in stark 1 Recent work [8–10] casts considerable doubt on assertions that state vectors are nothing more than probability distributions over more fundamental ingredients of reality. ∗ [email protected] 2 We discuss all of these thought experiments in our companion † [email protected] paper [1]. 2

describes constant probabilities p1 and p2 for the system to be in macroscopically distinct ontic states q1 or q2, there would be nothing preventing the system’s ontic state from hopping discontinuously between q1 and q2 with respective frequency ratios p1 and p2 over ar- bitrarily short time intervals. Essentially, by imposing a dynamical rule on the system’s underlying ontic state, ? ? ? ? Heisenberg Cut ? ? ? ? we can provide a “smoothness condition” for the system’s Ψ physical conﬁguration over time and thus eliminate these Ψ kinds of instabilities.

Ψ In quantum theory, a system that is exactly closed and that is exactly in a pure state (both conditions that are unphysical idealizations) evolves along a well-defined trajectory through the system’s Hilbert space according to Figure 1. The Heisenberg cut. a well-known dynamical rule, namely, the Schrödinger equation. However, in traditional formulations of quantum theory, an open quantum system that must be de- presently known and hypothetical physical systems. Such scribed by a density matrix due to entanglements with an interpretation should also address the key no-go the- other systems—a so-called improper mixture—does not orems developed over the years by researchers working have a specific underlying ontic state vector, let alone on the foundations of quantum theory, should not de- a Hilbert-space trajectory or a dynamical rule govern- pend on concepts or quantities whose definitions require ing the time evolution of such an underlying ontic state a physically unrealistic measure-zero level of sharpness, vector and consistent with the overall evolution of the and should be insensitive to potentially unknowable fea- system’s density matrix. It is a chief goal of our inter- tures of reality, such as whether we can sensibly define pretation of quantum theory to provide these missing in- “the universe as a whole” as being a closed or open sys- gredients. tem.

II. THE MINIMAL MODAL INTERPRETATION B. Motivation from Classical Physics A. Conceptual Summary Our interpretation is fully quantum in nature. How- ever, for purposes of motivation, consider the basic the- For a quantum system in an improper mixture, our new oretical structure of classical physics: A classical system interpretation identifies the eigenstates of the system’s has a specific state—which we call its “ontic state”—that density matrix with the possible states of the system in evolves in time through the system’s configuration space reality and identifies the eigenvalues of that density ma- according to some dynamical rule that may or may not be trix with the probabilities that one of those possible states stochastic, and this dynamical rule exists whether or not is actually occupied, and introduces just enough minimal the system’s state lies beneath a nontrivial evolving prob- structure beyond this simple picture to provide a dynam- ability distribution—called an “epistemic state”—on the ical rule for underlying state vectors as they evolve along system’s configuration space; moreover, the dynamical Hilbert-space trajectories and to evade criticisms made rule for the system’s underlying ontic state is consistent in the past regarding similar interpretations. This min- with the overall evolution of the system’s epistemic state, imal additional structure consists of a single additional in the sense that if we consider a probabilistic ensemble class of conditional probabilities amounting essentially to over the system’s initial ontic state and apply the dy- a series of smoothness conditions that kinematically re- namical rule to each ontic state in the ensemble, then late the states of parent systems to the states of their we correctly obtain the overall evolution of the system’s subsystems, as well as dynamically relate the states of a epistemic state as a whole. single system to each other over time. In particular, note the insufficiency of specifying a dynamical rule solely for the evolution of the system’s overall probability distribution—that is, for its epistemic B. Technical Summary state alone—but not for the system’s underlying ontic state itself, because then the system’s underlying ontic Our new interpretation, which we call the minimal state would be free to fluctuate wildly and discontin- modal interpretation of quantum theory and which we uously between macroscopically distinct configurations. motivate and detail more extensively in our companion For example, even if a classical system’s epistemic state paper [1], consists of several parsimonious ingredients: 3

1. We define ontic states Ψi, meaning the states of the relating the possible ontic states of any parti- given system as it could actually exist in reality, in tioning collection of mutually disjoint subsystems terms of arbitrary (unit-norm) state vectors |Ψii in Q1,...,Qn to the possible ontic states of a corre- the system’s Hilbert space H, sponding parent system W = Q1 + ··· + Qn whose own dynamics is governed by a linear completely- Ψ ↔ |Ψ i ∈ H (up to overall phase) , (1) i i positive-trace-preserving (“CPT”) dynamical t0←t 0 and we define epistemic states {(pi, Ψi)}i as proba- mapping EW [·] over the given time interval t −t. bility distributions over sets of possible ontic states, Here PˆW (w; t) denotes the projection operator onto the eigenstate |ΨW (w; t)i of the density {(pi, Ψi)}i , pi ∈ [0, 1] , matrixρ ˆW (t) of the parent system W at the where these definitions parallel the corresponding ˆ 0 initial time t, and, similarly, PQα (i; t ) denotes the notions from classical physics. We translate logi- 0 projection operator onto the eigenstate |ΨQα (i; t )i cal mutual exclusivity of ontic states Ψi as mutual 0 of the density matrixρ ˆQα (t ) of the subsystem Qα orthogonality of state vectors |Ψii, and we make at the final time t0 for α = 1, . . . , n. In a rough a distinction between subjective epistemic states t0←t sense, the dynamical mapping EW [·] acts as a (proper mixtures) and objective epistemic states parallel-transport superoperator that moves the (improper mixtures): The former arise from classi- parent-system projection operator PˆW (w; t) from cal ignorance and are uncontroversial, whereas the t to t0 before we compare it with the subsystem latter arise from quantum entanglements to other ˆ 0 projection operators PQα (i; t ). systems and do not have a widely accepted a priori meaning outside of our interpretation of quantum In generalizing unitary dynamics to linear theory. Indeed, the problem of interpreting objec- CPT dynamics in this manner, as is necessary in tive epistemic states may well be unavoidable: Es- order to account for the crucial and non-reductive sentially all realistic systems are entangled to other quantum relationships between parent systems systems to a nonzero degree and thus cannot be and their subsystems, note that we are not described exactly by pure states or by purely sub- proposing any fundamental modification to the jective epistemic states.3 dynamics of quantum theory, such as in GRW- 2. We posit a correspondence between objective epis- type spontaneous-localization models [11], but are simply accommodating the fact that generic temic states {(pi, Ψi)} and density matricesρ ˆ: i mesoscopic and macroscopic quantum systems X {(pi, Ψi)}i ↔ ρˆ = pi |Ψii hΨi| . (2) are typically open to their environments to some i nonzero degree. Indeed, linear CPT dynamical (See Figure2.) The relationship between subjec- mappings are widely used in quantum chemistry tive epistemic states and density matrices is not as as well as in quantum information science, in strict, as we explain in our companion paper [1]. which they are known as quantum operations; when specifically regarded as carriers of quantum 3. We invoke the partial-trace operationρ ˆQ ≡ information, they are usually called quantum Tr E [ˆρQ+E], motivated and defined in our compan- channels.4 A well-known, concrete example is the ion paper [1] without appeals to the Born rule or Lindblad equation [20]. Born-rule-based averages, to relate the density matrix (and thus the epistemic state) of any subsystem As special cases, these quantum conditional Q to that of any parent system W = Q + E. probabilities provide a kinematical smoothing 4. We introduce a general class of quantum conditional probabilities, 0 pQ1,...,Qn|W (i1, . . . , in; t |w; t) h 0 0 t0←t h ii ≡ Tr W PˆQ (i1; t ) ⊗ · · · ⊗ PˆQ (in; t ) E PˆW (w; t) 1 n W 4 See [12–14] for early work in this direction, and see [15] for a mod- h ˆ 0 ˆ 0 h ˆ ii ern pedagogical review. Starting from a simple measure of dis- ∼ Tr Pi1 (t ) ··· Pin (t ) E Pw (t) , tinguishability between density matrices that is non-increasing (3) under linear CPT dynamics [16], one can argue [17, 18] that linear CPT dynamics implies the nonexistence of the backward flow of information into the system from its environment. [19] strengthens this reasoning by proving that exact linear CPT dy- 3 As we explain in SectionIIE, there are reasons to be skeptical namics exists for a given quantum system if and only if the sys- of the common assumption that one can always assign an exact tem’s initial correlations with its environment satisfy a quantum pure state or purely subjective epistemic state to “the universe data-processing inequality that prevents backward information as a whole.” flow. 4

relationship p1, Ψ1 p (i , . . . , i |w) actual Q1,...,Qn|W 1 n p2, Ψ2 ontic state h ˆ ˆ ˆ i ≡ Tr W PQ1 (i1) ⊗ · · · ⊗ PQn (in) PW (w) (4) ρˆ p3, Ψ3

= hΨW,w| (|ΨQ1,i1 i hΨQ1,i1 | ⊗ · · · . . ⊗ |ΨQn,in i hΨQn,in |) |ΨW,wi

between the possible ontic states of any parti- epistemic possible tioning collection of mutually disjoint subsystems probabilities ontic states (eigenstates) Q1,...,Qn and the possible ontic states of the cor- (eigenvalues) responding parent system W = Q1 +···+Qn at any single moment in time, and, taking Q ≡ Q1 = W , also provide a dynamical smoothing relationship Figure 2. A schematic depiction of our postulated relationship between a system’s density matrixρ ˆ and its associated epis- 0 h 0 t0←t h ii temic state {(p1, Ψ1) , (p2, Ψ2) , (p3, Ψ3) ,... }, the latter con- pQ (j; t |i; t) ≡ Tr Q PˆQ (j; t ) E PˆQ (i; t) Q sisting of epistemic probabilities p1, p2, p3,... (the eigenvalues (5) of the density matrix) and possible ontic states Ψ , Ψ , Ψ ,... h ˆ 0 h ˆ ii 1 2 3 ∼ Tr Pj (t ) E Pi (t) (represented by the eigenstates of the density matrix), where one of those possible ontic states (in this example, Ψ2) is the between the possible ontic states of a system Q system’s actual ontic state. over time and also between the objective epistemic states of a system Q over time. developed by van Fraassen (whose early formulations in- Essentially, 1 establishes a linkage between ontic states volved the fusion of modal logic with quantum logic), and epistemic states, 2 establishes a linkage between (ob- Dieks, Vermaas, and others [25–29]. jective) epistemic states and density matrices, 3 estab- The modal interpretations are now understood to en- lishes a linkage between parent-system density matrices compass a very large set of interpretations of quantum and subsystem density matrices, and 4 establishes a link- theory, including most interpretations that fall between age between parent-system ontic states and subsystem the “many worlds” of the Everett-DeWitt approach and ontic states, either at the same time or at different times. the “no worlds” of the instrumentalist approaches. Gen- After verifying in our companion paper [1] that our erally speaking, in a modal interpretation, one singles out quantum conditional probabilities satisfy a number of some preferred basis for each system’s Hilbert space and consistency requirements, we show that they allow us to then regards the elements of that basis as the system’s avoid ontological instabilities that have presented prob- possible ontic states—one of which is the system’s actual lems for other modal interpretations, analyze the mea- ontic state—much in keeping with how we think concep- surement process, study various familiar “paradoxes” and tually about classical probability distributions. For ex- thought experiments, and examine the status of Lorentz ample, as emphasized in [29], the de Broglie-Bohm pilot- invariance and locality in our interpretation of quantum wave interpretation [30–32] can be regarded as a special theory. In particular, our interpretation accommodates kind of modal interpretation in which the preferred basis the nonlocality implied by the EPR-Bohm and GHZ- is permanently fixed for all systems at a universal choice. Mermin thought experiments without leading to superlu- Other modal interpretations, such as our own, instead al- minal signaling, and evades claims by Myrvold [21] pur- low the preferred basis for a given system to change—in porting to show that interpretations like our own lead to our case by choosing the preferred basis to be the evolv- unacceptable contradictions with Lorentz invariance. As ing eigenbasis of that system’s density matrix. However, a consequence of its compatibility with Lorentz invari- we claim that no existing modal interpretation captures ance, we claim that our interpretation is capable of en- the one that we summarize in this letter and describe compassing all the familiar quantum models of physical more fully in our companion paper [1]. systems widely in use today, from nonrelativistic point particles to quantum field theories and even string theory. D. Hidden Variables and the Irreducibility of Ontic States C. Modal Interpretations To the extent that our interpretation of quantum the- Our interpretation of quantum theory belongs to the ory involves hidden variables, the actual ontic states un- general class of modal interpretations originally intro- derlying the epistemic states of systems play that role. duced by Krips in 1969 [22–24] and then independently However, one could also argue that calling them hidden 5 variables is just an issue of semantics because they are time, we argue in our companion paper [1] that our in- on the same metaphysical footing as both the traditional terpretation is ultimately compatible with Lorentz invari- notion of quantum states as well as the actual ontic states ance and is nonlocal only in the mild sense familiar from of classical systems. the framework of classical gauge theories. In any event, it is important to note that our inter- Furthermore, we make no assumptions about as-yet- pretation includes no other hidden variables: Just as in unknown aspects of reality, such as the fundamental dis- the classical case, we regard ontic states as being irre- creteness or continuity of time or the dimensionality of ducible objects, and, in keeping with this interpretation, the ultimate Hilbert space of Nature. Nor does our in- we do not regard a system’s ontic state itself as being terpretation rely in any crucial way upon the existence of an epistemic probability distribution—much less a “pi- a well-defined maximal parent system that encompasses lot wave”—over a set of more basic hidden variables. In all other systems and is dynamically closed in the sense a rough sense, our interpretation unifies the de Broglie- of having a so-called cosmic pure state or universal wave Bohm interpretation’s pilot wave and hidden variables function that precisely obeys the Schrödingerequation; into a single ontological entity that we call an ontic state. by contrast, this sort of cosmic assumption is a neces- In particular, we do not attach an epistemic probability sarily exact ingredient in the traditional formulations of interpretation to the components of a vector represent- the de Broglie-Bohm pilot-wave interpretation and the ing a system’s ontic state, nor do we assume a priori the Everett-DeWitt many-worlds interpretation. Born rule, which we ultimately derive in our compan- Indeed, by considering merely the possibility that our ion paper [1] as a means of computing empirical outcome observable universe is but a small region of an eternally probabilities. Otherwise, we would need to introduce an inflating cosmos of indeterminate spatial size and age unnecessary additional level of probabilities into our in- [62–64], it becomes clear that the idea of a biggest closed terpretation and thereby reduce its axiomatic parsimony system (“the universe as a whole”) may not generally be and explanatory power. a sensible or empirically verifiable concept to begin with, Via the phenomenon of environmental decoherence, let alone an axiom on which a robust interpretation of our interpretation ensures that the evolving ontic state quantum theory can safely rely. Our interpretation cer- of a sufficiently macroscopic system—with significant en- tainly allows for the existence of a biggest closed system, ergy and in contact with a larger environment—is highly but is also fully able to accommodate the alternative cir- likely to be represented by a temporal sequence of state cumstance that if we were to imagine gradually enlarging vectors whose labels evolve in time according to recogniz- our scope to parent systems of increasing physical size, able semi-classical equations of motion. For microscopic, then we might well find that the hierarchical sequence isolated systems, by contrast, we simply accept that the never terminates at any maximal, dynamically closed sys- ontic state vector may not always have an intuitively fa- tem, but may instead lead to an unending “Russian-doll” miliar classical description. succession of ever-more-open parent systems.6

E. Comparison with Other Interpretations of Quantum Theory tainty [40]; coarse-grained histories or decoherence functionals [41, 42]; decision theory [43, 44]; Dutch-book coherence, SIC- POVMs, or urgleichungs [45]; circular frequentist arguments in- Our interpretation, which builds on the work of many volving unphysical “limits” of infinitely many copies of measure- others, is general, model-independent, and encompasses ment devices [40, 46, 47]; infinite imaginary ensembles [48]; quan- relativistic systems, but is also conservative and unex- tum reference systems or perspectivalism [49, 50]; relational or non-global quantum states [51–54]; many-minds states [55]; mir- travagant: It includes only metaphysical objects that are ror states [53, 54]; faux-Boolean algebras [29, 56]; “atomic” sub- either already a standard part of quantum theory or that systems [57]; algebraic quantum field theory [58]; secret classical have counterparts in classical physics. We do not posit superdeterminism or fundamental information loss [59]; cellular the existence of exotic “many worlds” [33–36], physical automata [60]; classical matrix degrees of freedom or trace dynamics [61]; or discrete Hilbert spaces or appeals to unknown “pilot waves” [30–32], or any fundamental GRW-type Planck-scale physics [47]. dynamical-collapse or spontaneous-localization modifica- 6 One might try to argue that one can always formally define tions to quantum theory [11, 37–39]. Indeed, our inter- a closed maximal parent system just to be “the system con- taining all systems.” Whatever logicians might say about such pretation leaves the widely accepted mathematical struc- a construction, we run into the more prosaic issue that if we 5 ture of quantum theory essentially intact. At the same cannot construct this closed maximal parent system via a well- defined succession of parent systems of incrementally increasing size, then it becomes unclear mathematically how we can generally define any human-scale system as a subsystem of the maximal parent system and thereby define the partial-trace op- 5 Moreover, our interpretation does not introduce any new viola- eration. Furthermore, if our observable cosmic region is indeed tions of time-reversal symmetry, and gives no fundamental role an open system, then its own time evolution may not be exactly to relative states [33]; a cosmic multiverse or self-locating uncer- linear, in which case it is far from obvious that we can safely 6

III. MEASUREMENTS AND LORENTZ admit certain joint epistemic probabilities that are con- INVARIANCE ditioned on multiple disjoint systems at an initial time, and such probabilities are not a part of our interpreta- A. Von Neumann Measurements and the Born tion of quantum theory, as we explain in our companion Rule paper [1].8 Similarly, one of Myrvold’s arguments hinges on the assumed existence of joint epistemic probabilities For the purposes of establishing how our minimal for two disjoint systems at two separate times, and again modal interpretation makes sense of measurements, such probabilities are not present in our interpretation. how decoherence turns the environment into a “many- As Dickson and Clifton point out in Appendix B of their dimensional chisel” that rapidly sculpts the ontic states paper, Hardy’s argument also relies on several faulty as- of systems into its precise shape,7 and how the Born rule sumptions about ontic property assignments in modal naturally emerges to an excellent approximation, we con- interpretations. sider in our companion paper [1] the idealized example A final argument of Myrvold—and repeated by of a so-called Von Neumann measurement. Along the Berkovitz and Hemmo [52]—is based on inadmissible as- way, we also address the status of both the measurement sumptions about the proper way to implement Lorentz problem generally and the notion of wave-function col- transformations in quantum theory and the relationship lapse specifically in the context of our interpretation of between density matrices and ontic states in our mini- quantum theory. Ultimately, we find that our interpre- mal modal interpretation. Myrvold’s mistake is subtle, tation solves the measurement problem by replacing in- so we go through his argument in detail in our companion stantaneous axiomatic wave-function collapse with an in- paper [1]. terpolating ontic-level dynamics, and thereby eliminates any need for a Heisenberg cut. C. Quantum Theory and Classical Gauge Theories

B. The Myrvold No-Go Theorem Suppose that we were to imagine reifying all of the possible ontic states defined by each system’s density matrix Building on a paper by Dickson and Clifton [65] and as simultaneous actual ontic states in the sense of the 9 employing arguments similar to Hardy [66], Myrvold [21] many-worlds interpretation. Then because every den- argued that modal interpretations are fundamentally in- sity matrix as a whole evolves locally, no nonlocal dy- consistent with Lorentz invariance at a deeper level than namics between the actual ontic states is necessary and mere unobservable nonlocality, leading to much addi- our interpretation of quantum theory becomes manifestly tional work [52, 58, 67] in subsequent years to determine dynamically local: For example, each spin detector in the the implications of his result. Specifically, Myrvold ar- EPR-Bohm or GHZ-Mermin thought experiments pos- gued that one could not safely assume that a quantum sesses all its possible results in actuality, and the larger system, regardless of its size or complexity, always pos- measurement apparatus locally “splits” into all the var- sesses a specific actual ontic state beneath its epistemic ious possibilities when it visits each spin detector and state, because any such actual ontic state could seem- looks at the detector’s final reading. ingly change under Lorentz transformations more radi- In our companion paper [1], we argue that we can make cally than, say, a four-vector does—for example, binary sense of this step of adding unphysical actual ontic states digits 1 and 0 could switch, words written on a paper into our interpretation of quantum theory by appealing could change, and true could become false. The only way to an analogy with classical gauge theories, and specifi- to avoid this conclusion would then be to break Lorentz cally the example of the Maxwell theory of electromag- symmetry in a fundamental way by asserting the exis- netism. Just as different choices of gauge for a given clas- tence of a “preferred” Lorentz frame in which all ontic- sical gauge theory make different calculations or proper- state assignments must be made. ties of the theory more or less manifest—each choice of Myrvold’s claims, and those of Dickson and Clifton as gauge inevitably involves trade-offs—we see that switch- well as Hardy, rest on several invalid assumptions. Dick- ing from the “unitary gauge” corresponding to our in- son and Clifton [65] assume that the hidden ontic states

8 The same implicit assumption occurs in Section 9.2 of [29]. 9 Observe that the eigenbasis of each system’s density matrix and rigorously embed that open-system time evolution into the therefore defines a preferred basis for that system alone. We do hypothetical unitary dynamics of any conceivable closed parent not assume the sort of universe-spanning preferred basis shared system. by all systems that is featured in the traditional many-worlds 7 The way that decoherence sculpts ontic states into shape is rem- interpretation; such a universe-spanning preferred basis would iniscent of the way that the external pressure of air molecules lead to new forms of nonlocality, as we describe in our compan- above a basin of water maintain the water in its liquid phase. ion paper [1]. 7 terpretation of quantum theory to the “Lorenz gauge” in [70–74] and thereby push proponents to argue that in- which it looks more like a density-matrix-centered version creasingly realistic measurement set-ups involving non- of the many-worlds interpretation makes the locality and negligible environmental interactions resolve the claimed Lorentz covariance of the interpretation more manifest inconsistencies [29, 53, 75, 76]. at the cost of obscuring the interpretation’s underlying ontology and the meaning of probability. Seen from this perspective, we can also better under- ACKNOWLEDGMENTS stand why it is so challenging [68] to make sense of a many-worlds-type interpretation as an ontologically and J. A. B. has benefited tremendously from personal com- epistemologically reasonable interpretation of quantum munications with Matthew Leifer, Timothy Hollowood, theory: Attempting to do so leads to as much meta- and Francesco Buscemi. D. K. thanks Gaurav Khanna, physical difficulty as trying to make sense of the Lorenz Pontus Ahlqvist, Adam Brown, Darya Krym, and Paul gauge of Maxwell electromagnetism as an “ontologically Cadden-Zimansky for many useful discussions on related 10 correct interpretation” of the Maxwell theory. Hence, topics, and is supported in part by FQXi minigrant taking a lesson from classical gauge theories, we pro- #FQXi-MGB-1322. Both authors have greatly appre- pose instead regarding many-worlds-type interpretations ciated their interactions with the Harvard Philosophy of as merely a convenient mathematical tool—a particu- Science group and its organizers Andrew Friedman and lar “gauge choice”—for establishing definitively that a Elizabeth Petrik, as well as with Scott Aaronson and Ned given “unitary-gauge” interpretation of quantum theory Hall. Both authors are indebted to Steven Weinberg, who like our own is ultimately consistent with locality and has generously exchanged relevant ideas and whose own Lorentz invariance. recent paper [77] also explores the idea of reformulating quantum theory in terms of density matrices. The work of Pieter Vermaas has also been a continuing source of IV. CONCLUSION inspiration for both authors, as have many conversations with Allan Blaer. In this letter and in a more extensive companion paper [1], we have introduced a new, conservative interpretation of quantum theory that threads a number of key requirements that we feel are insufficiently addressed by other interpretations. In particular, our interpretation [1] J. A. Barandes and D. Kagan, (2014), to be published, identifies a definite ontology for every quantum system, arXiv:1405.6755 [quant-ph]. [2] S. Weinberg and J. N. A. i. Matthews, Physics Today as well as dynamics for that ontology based on the overall (2013), 10.1063/PT.4.2502, in particular, “... Some very time evolution of the system’s density matrix, and sews good theorists seem to be happy with an interpretation together ontologies for parent systems and their subsys- of quantum mechanics in which the wavefunction only tems in a natural way. serves to allow us to calculate the results of measurements. But the measuring apparatus and the physicist are presumably also governed by quantum mechanics, so ultimately we need interpretive postulates that do not Falsifiability and the Role of Decoherence distinguish apparatus or physicists from the rest of the world, and from which the usual postulates like the Born As some other interpretations do, our own interpreta- rule can be deduced. This effort seems to lead to some- tion puts decoherence in the central role of transforming thing like a ‘many worlds’ interpretation, which I find the Born rule from an axiomatic postulate into a derived repellent. Alternatively, one can try to modify quantum consequence and thereby solving the measurement prob- mechanics so that the wavefunction does describe reality, and collapses stochastically and nonlinearly, but this lem of quantum theory. We regard it as a positive feature seems to open up the possibility of instantaneous com- of our interpretation of quantum theory that falsification munication”. of the capacity for decoherence to manage this responsi- [3] S. Weinberg, Lectures on Quantum Mechanics, 1st ed. bility would mean falsification of our interpretation. We (Cambridge University Press, 2012) p. 95, in particular, therefore also take great interest in the ongoing arms race the end of Section 3.7 (“The Interpretations of Quantum between proponents and critics of decoherence, in which Mechanics”): “... [I]t would be disappointing if we had critics offer up examples of decoherence coming up short to give up the ‘realist’ goal of finding complete descrip- tions of physical systems, and of using this description to derive the Born rule, rather than just assuming it. We can live with the idea that the state of a physical system is described by a vector in Hilbert space rather than by 10 Indeed, in large part for this reason, some textbooks [69] develop numerical values of the positions and momenta of all the quantum electrodynamics fundamentally from the perspective of particles in the system, but it is hard to live with no de- 0 ~ ~ Weyl-Coulomb gauge A = ∇ · A = 0. scription of physical states at all, only an algorithm for 8

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