Quantum-Bayesian and Pragmatist Views of Quantum Theory

First published Thu Dec 8, 2016; substantive revision Tue Feb 22, 2022

Quantum theory is fundamental to contemporary physics.^[1] It is natural to view a fundamental physical theory as describing orrepresenting the physical world. But many physicists and somephilosophers have questioned or rejected this view of quantum theory.They have viewed the theory as concerned with our observation anddescription of, knowledge or beliefs about, or interactions with theworld. Views of this kind have been expressed since the 1920s whenquantum theory emerged in close to its present form. This entry isconcerned with more recent developments of this tradition byphysicists and philosophers, much of it described as quantum-Bayesianor pragmatist. This entry discusses the form of quantum-Bayesianismknown as QBism in section 1, addressing common objections in section2. After section 3 briefly notes pragmatist influences on QBismsection 4 sketches a variety of self-described pragmatist approachesto quantum theory, while section 5 mentions some related views.

1. QBism

Because the term ‘Bayesianism’ may be understood in manydifferent ways, a variety of views of quantum theory could beconsidered Quantum-Bayesian. QBism is a form of Quantum Bayesianismthat may be traced back to a point of view on states and probabilitiesin quantum theory adopted by C.M. Caves, C.A. Fuchs, and R. Schack(2002). In its more recent incarnation (Fuchs, Mermin, & Schack2014) its proponents have adopted the name QBism for reasons discussedin§1.1. In deference to its contemporary proponents, this shorter name isused. Fuchs, Mermin, and Schack 2014, and DeBrota and Stacey (2019, Other Internet Resources) provide elementary introductions to QBism; Fuchs and Schack 2015, andFuchs and Stacey 2019 give more detailed summaries of the view; vonBaeyer 2016 is a popular book-length introduction

QBists maintain that rather than (either directly or indirectly)representing a physical system, a quantum state represents theepistemic state of the one who assigns it concerning thatagent’s possible future experiences. It does this by specifyingthe agent’s coherent degree of belief (credence) in each of avariety of alternative experiences that may result from a specific actthe agent may perform. To get an idea of the kinds of experience andact the QBist has in mind it is helpful to think of the possibleoutcomes of a quantum measurement on a physical system. But QBistshave proposed the extension of the view to encompasseveryexperience that may result fromany action (Fuchs, Mermin,and Schack 2014; Mermin 2017).

As quantum theory is usually presented, the Born Rule provides analgorithm for generating probabilities for alternative outcomes of ameasurement of one or more observables on a quantum system. Theseprobabilities have traditionally been regarded as objective, in linewith the idea that the theory is irreducibly indeterministic.

By contrast, QBists hold a subjective Bayesian or personalist view ofquantum probabilities (see entry oninterpretations of probability). Taking a quantum state merely to provide input to the Born Rulespecifying these probabilities, they regard quantum state assignmentsas equally subjective. The quantum state assigned by an agent thenprovides a convenient representation of an important part of his orher own overall state of belief. So quantum theory as a whole is“a users’ manual that any agent can pick up and use tohelp make wiser decisions in this world of inherent uncertainty”(Fuchs 2010, 8,Other Internet Resources).

QBists argue that from this point of view quantum theory faces noconceptual problems associated with measurement or non-locality. WhileQBism has implications for the nature of physical science, from thispoint of view quantum theory has few if anydirectimplications for the nature of physical reality.

1.1 History

Contemporary QBists (Mermin 2014: 422; Fuchs 2011) have soughtprecedents among such authorities as Erwin Schrödinger, NielsBohr, Wolfgang Pauli, J.A. Wheeler, and William James. But what cameto be known as quantum-Bayesianism and later QBism began as acollaboration between Caves, Fuchs, and Schack at the turn of the21^st century (Caves, Fuchs, and Schack 2002a,b), althoughCaves no longer considers himself a QBist. N. David Mermin (2014,2019) became a convert more recently and has proposed extending theQBist vision of science to resolve at least one long-standingconceptual issue raised by classical physics. Stacey (2019,Other Internet Resources) tracks changes from the Quantum-Bayesianism of 2002 to the QBism of2019.

In conformity with standard terminology, on which the word“Bayesian” does not carry a commitment to denyingobjective probability, proponents of QBism no longer take the“B” to refer simply to Bayesianism. Insisting thatprobability has no physical existence even in a quantum world, theyfollow Bruno de Finetti in identifying probability with coherentdegree of belief or credence. But according to Fuchs (2016,Other Internet Resources) “B” should not be taken to abbreviate“Brunism” since de Finetti would not have accepted all ofQBism’s metaphysics: so “QBism” is now bestunderstood simply as a stand-alone proper name for the view of quantumtheory described in what follows.

1.2 Probability

Applied to radioactive decay, the Born Rule of quantum theory is takensuccessfully to predict such things as the half-life of the firstexcited state of the hydrogen atom—that the probability that anatom of hydrogen in this state will be found to have decayed to theground state after \(1.1 \times 10^{-9}\) seconds (i.e., just over abillionth of a second) is ½. This prediction has beenexperimentally confirmed by measuring how the frequency with whichphotons are emitted by a large number of hydrogen atoms in the decayof this excited state decreases over time. Most physicists regard thisand other probabilities predicted by quantum theory as objectivephysical features of the world, typically identifying the probabilityof decay with the relative frequency of decay as measured in such anexperiment.

But there are strong reasons not to equate probability with any actualrelative frequency (see entryinterpretations of probability, §3.4). Many philosophers, including Karl Popper (1967) and DavidLewis (1986), have taken Born probabilities instead to exemplify adistinctive kind of objective property (propensity or chance,respectively) that may be ascribed to actual or possible individualevents. Lewis took quantum indeterminism to be the last hold-out ofobjective chance.

By contrast, QBists adopt a subjectivist or personalist interpretationof probability, in quantum theory as elsewhere (see entry oninterpretations of probability, §3.3). This makes the Born Rule of quantum theory not a law ofnature but an empirically motivated norm of rationality a wise agentshould follow in addition to those whose violation would render theagent’s degrees of belief incoherent. As usually formulated, theBorn Rule specifies probabilities for various possible measurementoutcomes given a quantum state: But QBists also adopt a subjectivistor personalist interpretation of quantum states.

The Schrödinger equation specifying the time development of asystem’s quantum state \(\psi\)

\[\tag{1}\label{ex1} H\psi = i\hslash \,{\partial \psi /\partial t} \]

is often thought of as the basic dynamical law of quantum mechanics,where \(H\) (called the Hamiltonian operator) is said to represent thesystem’s energy. Instead QBists take this equation as providinga synchronic constraint on an agent’s credences concerning theagent‘s experiences at different times, and not a diachronicconstraint on the system’s properties at those times. QBistsalso consider the Hamiltonian (along with all other observables)within the purview of each individual agent rather than objectivelydetermined by the system’s properties. It follows that equallyrational agents who assign the same quantum state to a system at atime \(t_1\) may consistently assign it different states at a time\(t_2\) because they apply the constraint supplied by theSchrödinger equation in different ways.

In its usual formulation the Born Rule does not look like a normativeconstraint on credences. QBists prefer to reformulate it purely as arelation among (subjective) probabilities without reference to aquantum state. In the form of Equation \((\ref{ex2})\) it relatesprobabilities \(q\) of actual measurement outcomes \(j\) toprobabilities of outcomes of a hypotheticalfiducialmeasurement of a special kind called a SIC.^[2]

\[\tag{2}\label{ex2} q(j) = \sum_{i=1}^{d^2} [(d+1) p(i) -1/d].r(j\mathbin{|}i) \]

This equation is not just a revision of the law of total probabilityit resembles, i.e.,

\[\tag{3}\label{ex3} q(j) =\sum_{i=1}^{d^2} p (i).r(j \mathbin{|} i) \]

because \(p(i)\), \(r(j\mathbin{|}i)\) in \((\ref{ex2})\) refer to ahypothetical measurement, not the actual measurement.

In more detail, suppose an agent has degrees of belief \(p(i)\) thatthe outcome of a SIC on a system would be the \(i\)^th, anddegree of belief \(r(j\mathbin{|}i)\) in the \(j\)^thoutcome of an actual measurement \(M\) conditional on the\(i\)^th outcome for the hypothetical SIC on that system.Then QBists take Equation \((\ref{ex2})\), stating a condition on theagent’s degree of belief \(q(j)\) that the outcome of \(M\) willbe the \(j\)^th, as their preferred formulation of the BornRule. In this expression \(d\) stands for the dimension of thesystem’s Hilbert space (assumed to be a positive integer).

Their idea is that when the fiducial measurement is a SIC,\(r(j\mathbin{|}i)\)) encodes the agent’s belief about the typeof measurement \(M\), while \(p(i)\) encodes his or her quantum statefor the system on which this measurement is performed. They maintainthat the Born Rule in this form is an empirically motivated additionto probability theory—a normative requirement of quantumBayesian coherence (Fuchs and Schack 2013; DeBrota, Fuchs, Pienaar,and Stacey, 2021) that supplements the usual coherence conditions ondegrees of belief required to avoid a Dutch book (a set of bets anagent is guaranteed to lose, come what may).

It is common (at least in physical applications) to identifyprobability 1 with objective certainty, at least for finiteprobability spaces. Einstein, Podolsky, and Rosen (1935, EPR) madethis identification in the following sufficient condition for realitywith which they premised their famous argument for the incompletenessof quantum mechanical description of physical reality:

If, without in any way disturbing a system, we can predict withcertainty (i.e., with probability equal to unity) the value of aphysical quantity, then there exists an element of physical realitycorresponding to this physical quantity. (EPR: 777)

QBists (Caves, Fuchs, and Schack 2007) reject this identification andrefute EPR’s argument that quantum description is incomplete bydenying this premise. Eschewing all objective physical probabilities,they rather identify probability 1 with an agent’s subjectivecertainty—full belief in a statement or event that an equallywell informed rational agent may believe to a lesser degree, or not atall.

1.3 Measurement

Those who believe that a quantum state completely describes the systemto which it is assigned and that this state always evolves linearly(e.g., according to the Schrödinger equation) face the notoriousquantum measurement problem: Application of quantum theory to theinteraction between a quantum system and a quantum measuring devicewould almost always leave these in a state that describes themeasurement as having no outcome, contrary to the direct experience ofcountless experimentalists (see entry onphilosophical issues in quantum theory, §4).

Some have followed Dirac (1930) and von Neumann (1932) in assumingthat a measurement is a physical process in which a quantum statealmost never evolves linearly but rather changes discontinuously andstochastically into one of a variety of possible states, each of whichmay describe its outcome. But attempts to state precisely when such aprocess occurs and to verify its occurrence experimentally have beenunsuccessful, and many understand quantum theory as excluding itsoccurrence.

QBists avoid this problem by denying that a quantum state (evenincompletely) describes the system to which it assigned. Any user ofquantum theory assigns his or her personal quantum state on the basisof available information, subject only to the normative constraints ofquantum-Bayesian coherence. This state assignment need conform neitherto “the way that system really is”, nor to the stateassignments of other users. Quantum mechanics is a single user theory,and any coincidence among states assigned by different users is justthat—coincidence. An agent may reassign a state on the basis ofnewly acquired information, perhaps described as observation of theoutcome of a measurement. When this happens, the new state is oftennot continuous with the old state. This represents no physicaldiscontinuity associated with measurement, but merely reflects theagent’s updated epistemic state in the light of experience.

Nevertheless, in certain circumstances different users may be expectedto come to assign similar or even identical quantum states by updatingtheir prior credences to take account of common (though neveridentical) experiences, some of which each may describe as experiencesof the outcomes of quantum measurements on systems. Because QBiststake the quantum state to have the role of representing anagent’s epistemic state they may avail themselves of personalistBayesian arguments purporting to show the convergence of priors onupdating in the light of common information. Also, just as de Finettishowed that a subjectivist agent’s credences may evolve as ifrefining estimates of an unknown objective probability, QBists (Caves,Fuchs, and Schack 2002b) have shown that the credences of a user ofquantum theory may evolve as if refining his or her assignment of anunknown objective quantum state.

J.S. Bell (2004) argued forcefully that the word“measurement” has no place in a formulation of quantummechanics with any pretension to physical precision. QBists frequentlyuse this word in formulating their view, but unlike Bohr and hisCopenhagen followers they do not think of a measurement as a purelyphysical process, but as describing an agent’s action on theworld that results in a specific experience of it. They view quantumtheory not as offering descriptions of the world involving theimprecise physical term “measurement”, but as anintellectual tool for helping its users interact with the world topredict, control, and understand their experiences of it. Fuchs (2010,Other Internet Resources) and Mermin (2017) are quite explicit and unapologetic that athoroughgoing QBist presentation of quantum theory would speak ofagents, their actions and their experiences—all primitive termsthey take neither to require nor to admit of precise physicalspecification.

1.4 Nonlocality

Bell’s arguments (2004) have convinced some physicists and manyphilosophers that certain patterns of correlation among spatiallyseparated events correctly predicted by quantum theory manifestnon-local influences between some of these events (see entry onaction at a distance in quantum mechanics). QBists use their view of measurement-as-experience to reject any suchnon-local influences.

For a QBist, what science rests on are not objective reports oflocalized physical events but the individual agent’sexperiences. Being present at a single location, at no time does anindividual agent experience spatially separated events.^[3] Correlations taken to manifest non-local influences supposedlyconcern events in different places—say where Alice is and whereBob is. But Alice can only experience events where she is, not atBob’s distant location. When she hears Bob’s report ofwhat he experienced at a distant location, this is an experience shehas whereshe is, not where Bob reports having had hisexperience. So quantum theory is answerable to patterns of correlationnot among spatially separated physical events, but among Alice’s(as also among Bob’s) spatially coincident experiences. QBistsargue that Alice, Bob, and any other agent can use quantum theorysuccessfully to account for her or his experiences with no appeal toany physical states (hidden or otherwise) or non-local physicalinfluences.

1.5 Decoherence

Classical mechanics is generally taken to be reducible to quantummechanics, at least approximately in some appropriate limit. Forexample, Newton’s second law of motion is sometimes said to bederivable from the Schrödinger equation in the limit of largemass. But to retrieve classical dynamics it is generally thoughtnecessary to supplement any such derivation with an account of whyordinary macroscopic objects do not exhibit the interference behaviorcharacteristic of quantum superpositions.

Quantum models of environmental decoherence are commonly thought toprovide such an account (see entry onthe role of decoherence in quantum mechanics). These typically involve the Schrödinger equation, this timeapplied to a system in interaction with its quantum environment. Theapplication can show how interactions entangle the quantum states ofsystem and environment in a way that selects a “pointerbasis” in which the system’s reduced (mixed) state remainsvery nearly diagonal indefinitely. Somehow a particular element ofthis basis is supposed to be identifiable as the system’sphysical state, evolving in a way that approximates classicaldynamics.

If the Schrödinger equation were a dynamical law governing theevolution of a physical quantum state this would provide a physicalfoundation on which to base a reduction of classical dynamics toquantum dynamics that appealed to quantum decoherence. But QBistsdeny that the Schrödinger equation is a dynamical lawgoverning the evolution of an objective quantum state. For them itmerely provides a constraint on an agent’s current epistemicstate. Fuchs (2010,Other Internet Resources) concluded that decoherence has no role to play in the misguidedprogram attempting to reduce classical to quantum dynamics.

Instead, QBists Fuchs and Schack (2012) have viewed decoherence as acondition on an agent’s present assignment of a quantum state toa system following one contemplated measurement, when making decisionsregarding the possible outcomes of a second measurement. As such, itfunctions as a normative synchronic coherence condition that may beseen as a consequence of van Fraassen’s (1984) ReflectionPrinciple. Instead of taking decoherence to select possible outcomesof a physical measurement process, QBists take these to be justwhatever experiences may follow the agent’s action on theworld.

1.6 Generalizations of QBism

Mermin (2014, 2019) has proposed extending QBism’s view of therole experience in science to what he calls CBism (Classical Bohrism).According to Carnap, Einstein was seriously worried about the problemof the Now:

that the experience of the Now means something special for man,something essentially different from the past and the future, but thatthis important difference does not and cannot occur within physics.(Carnap 1963: 37–38)

According to Mermin, Einstein had nothing to worry about because there\(is\) a place in physics for the present moment. He takes the presentmoment as something that is immediately experienced by each of us, andso (from a CBist perspective) just the sort of thing that physics isultimately about. By contrast, he says

space-time is an abstraction that I construct to organize suchexperiences. (Mermin 2014: 422–3)

According to Mermin, a common Now is an inference for each person fromhis or her immediate experience: But that it is as fundamental afeature of two perceiving subjects that when two people are togetherat an event, if the event is Now for one of them, then it is Now forboth.

Unlike QBism, CBism is not a subjective or personalist view of statesand probabilities in physics. But both QBism and CBism depend on ageneral view of science as an individual quest to organize one’spast experiences and to anticipate one’s future experiences.This is a view that has antecedents even in views expressed byphysicists generally thought of as realists, such as Einstein (1949:673–4) and Bell, whom Mermin (2019: 8) quotes as follows:

I think we invent concepts, like “particle” or“Professor Peierls”, to make the immediate sense of datamore intelligible. (J.S. Bell, letter to R.E. Peierls,24-February-1983)

2. Objections and Replies

2.1 Solipsist?

A common reaction among those first hearing about QBism is to dismissit as a form of solipsism. Mermin (2017) replies as follows:

Facile charges of solipsism miss the point. My experience of you leadsme to hypothesize that you are a being very much like myself, withyour own private experience. This is as firm a belief as any I have. Icould not function without it. If asked to assign this hypothesis aprobability I would choose1.0.Although I have no direct personal access to your own experience, animportant component of my private experience is the impact on me ofyour efforts to communicate, in speech or writing, your verbalrepresentations of your own experience. Science is a collaborativehuman effort to find, through our individual actions on the world andour verbal communications with each other, a model for what is commonto all of our privately constructed external worlds. Conversations,conferences, research papers, and books are an essential part of thescientific process. (84–85)

In his critical assessment of quantum Bayesianism, Timpson (2008)offers a more detailed defense against the charge of solipsism.

But even if one accepts the existence of other people and theirexperiences, adopting QBism does seem severely to restrict one’sapplication of quantum theory to anticipations of one’s ownexperiences, with no implications for those of anyone else.

2.2 Instrumentalist?

By portraying it as a tool for helping a user get by in an uncertainworld, QBism has been characterized as merely a form ofinstrumentalism about quantum theory. But this is no reason to rejectthe view absent arguments against such instrumentalism.

Instrumentalism is usually contrasted with realism as a view ofscience (see entry onscientific realism). The contrast is often taken to depend on opposing views of thecontent, aims, and epistemic reach of scientific theories. Crudely,the realist takes theoretical statements to be either true or false ofthe world, science to aim at theories that truly describe the world,and theories of mature science to have given us increasingly reliableand accurate knowledge even of things we can’t observe: Whilethe instrumentalist takes theoretical statements to be neither truenor false of the world, science to aim only at theories thataccommodate and predict our observations, and theories even in maturescience to have given us increasingly reliable and accuratepredictions only of things we can observe.

QBism offers a more nuanced view, both of quantum theory as a theoryand of science in general. Fuchs (2017a) adopted the slogan“participatory realism” for the view of science he takesto emerge from QBism (if not also a variety of more or less relatedviews of quantum theory). For QBism a quantum state assignment is trueor false relative to the epistemic state of the agent assigning it,insofar as it corresponds to that agent’s partial beliefsconcerning his or her future experiences (beliefs the agent shouldhave adopted in accordance with the Born Rule). But what makes thisquantum state assignment true or false is not the physical worldindependent of the agent.

The QBist does not take quantum theory truly to describe the world:but (s)hedoes take that to be the aim of science—anaim to which quantum theory contributes onlyindirectly. Forexample, the Born Rule in the form of Equation \((\ref{ex2})\).

is less agent-specific than any probability assignments themselves.It’s a rule that any agent should pick up and use…. itlives at the level of the impersonal. And because of that, the BornRule correlates with something that one might want to call real.(Fuchs 2017: 119)

Fuchs thinks one thing quantum theory has taught us about the world isthat it is much richer than we may have thought: as agents usingquantum theory to make wise decisions we are not just placing bets onan unknown but timelessly existing future but activelycreating that future reality: “reality is more than anythird-person perspective can capture”. That is the sense inwhich he takes QBism to support a strong participatory realism, aboutthe world in and on which we act and about how science should describeit.

By contrast, Mermin 2019 draws related but possibly less radicalconclusions about science that (perhaps contrary to his intentions)some might interpret as a kind of instrumentalism or evenphenomenalism:

…science in general, and quantum mechanics in particular, is atool thateach of us uses to organize and make sense ofour own private experience. p.2
The fact is that my science has a subject (me) as well as an object(my world). Your science has a subject (you) as well as an object(your world). ... While each of us constructs a different world, theworld of science is our joint construction of the vast body ofphenomena that we try to infer, through language, to be common to ourown individual worlds. Science arises out of our use of language toindicate to each other our individual experiences out of which we eachconstruct our own individual worlds. p.5

2.3 Is QBist Quantum Theory Explanatory?

Realists often appeal to scientific explanation when arguing againstinstrumentalists. Quantum theory is generally acknowledged to provideus with a wide variety of successful explanations of phenomena wecan’t explain without it. Timpson (followed by Brown 2019)objects that QBists cannot account for its explanatory success.

… think of the question of why some solids conduct and someinsulate; why yet others are in between, while they all containelectrons, sometimes in quite similar densities…. Ultimately weare not interested in agents’ expectation that matter structuredlike sodium would conduct; we are interested inwhy it in factdoes so. (Timpson 2008: 600)

QBists face two problems here. In their view a user of quantum theorycan’t appeal to a description of objective, physical quantumstates in explaining the phenomena; and quantum theory’s Bornrule outputs subjective probabilities for each user independently thatbear not on what is objectively likely to happen but only on what(s)he should expect to experience, given her prior beliefs andexperiences.

Fuchs and Schack (2015) reply that explanations offered by quantumtheory have a similar character to explanations offered by probabilitytheory and give examples. This does not address the first problem. ButQBists could rationalize biting that bullet by pointing tolong-standing problems of measurement and non-locality faced byinterpretations that take quantum states to be physically real thatdon’t arise in their view. To respond to the second problem theycould try to develop a subjectivist view of scientific explanation asultimately a matter of making an economical and effective unity out ofall an agent’s beliefs and expectations.

2.4 Is the Born Rule a New Bayesian Norm?

Bacciagaluppi (2014) has raised an objection against the claim thatthe Born rule as formulated in Equation \((\ref{ex2})\) states anempirically motivated normative addition to Bayesian coherenceconditions. His basic objection is that QBism assumes the probability\(q(j)\) of an actual measurement outcome (as also the probability\(p(j)\) of a hypothetical measurement outcome) is independent of theprocedure by which this measurement is performed. That this is sofollows from the usual formulation of the Born Rule relating Bornprobabilities of measurement outcomes to quantum state assignments.But QBism cannot justify the procedure-independence of \(q(j)\) and\(p(j)\) in this way because it considers the Born Rule in the form ofEquation \((\ref{ex2})\) to be primitive, and so incapable ofempirical support from the relation between quantum states andoutcomes of laboratory procedures.

There are also technical problems with Equation \((\ref{ex2})\), whichassumes the existence of SICs in the relevant Hilbert space. Butinfinite as well as finite-dimensional Hilbert spaces are used inquantum theory, and SICs have not (yet) been shown to exist in everyfinite dimension.^[4] Informationally-complete (but not necessarily symmetric) POVMs doexist in all finite dimensional spaces. Fuchs and Schack (2015) give aschematic alternative to Equation \((\ref{ex2})\) that does notrequire symmetry of an informationally-complete POVM representing ahypothetical fiducial measurement.

2.5 Is QBism too Subjective?

The QBist approach to quantum theory is often criticized as toosubjective in its treatment of quantum states, measurement outcomes,and probabilities.

Many people assume a wave-function or state vector represents aphysical quantum state. On this assumption a quantum state isontic—a fundamental element of reality obeying the quantumdynamics that underlies classical dynamical laws. Bacciagaluppi (2014)urges QBists to accept this approach to dynamics even whilemaintaining a subjectivist or pragmatist interpretation ofprobability. But doing so would undercut the QBist account ofdiscontinuous change of quantum state on measurement as simplycorresponding to epistemic updating.

Most people take it for granted that a competently performed quantummeasurement procedure has a unique, objective outcome. QBists denythis, assimilating a measurement outcome to an agent’s personalexperience—including her experience of another agent’sverbal report of his outcome. QBists take a measurement outcome to bepersonal to the agent whose action elicited it. This tenet is key bothto QBist denial that quantum phenomena involve any nonlocal influence(Fuchs, Mermin and Schack 2014) and to the QBist (DeBrota, Fuchs andSchack 2020) resolution of the paradox of Wigner’s friend (seethe entry onEverett’s relative-state formulation of quantum mechanics). But their notions of experience and agency are broad enough toencompass personal experiences of agents other than individual,conscious humans.

By rejecting the objective authority of observation reports QBistschallenge what many have considered a presupposition of the scientificmethod. This rejection also threatens to undercut the standardpersonalist argument (see entry onBayesian epistemology, §6.2.F) that the opinions of agents with very different priordegrees of belief will converge after they have accumulated sufficientcommon evidence.

QBists consider a subjective view of quantum probability a corecommitment of the view, even when that probability is1 (Caves, Fuchs and Schack 2007). But Stairs (2011)and others have argued that QBist strategies for resolving conceptualproblems associated with non-locality may be co-opted by a qualifiedobjectivist about quantum probabilities.

QBists identify probability1 with an individualagent’s subjective certainty, in contrast to the objectivecertainty EPR took to entail the existence of a physical quantitywhose value could be predicted with probability1.Stairs (2011) referred to developments of David Lewis’s (1986:Appendix C) best systems analysis as providing an alternative notionof objective probability in which this entailment fails (see entry oninterpretations of probability, §3.6). So QBist subjectivism about probability is not necessaryto block the EPR inference to an element of reality (or beable, to useBell’s term) grounding the objective certainty of Bob’sdistant measurement outcome on his component of a non-separable systemfollowing Alice’s measurement on her component, therebyundercutting Bell’s proof that quantum theory is not locallycausal.

2.6 Should a QBist believe that an agent prepares a physically real state?

A QBist is convinced that an agent should take quantum mechanics as aguide for setting her subjective degrees of belief about the outcomesof future measurements. Myrvold (2020a,b) has used results of Pusey,Barrett and Rudolph (2012) and Barrett, Cavalcanti, Lal, and Maroney(2014) to argue that anyone with that conviction should also believethat preparations with which she associates distinct pure quantumstates result in ontically distinct states of affairs, a conclusionthat QBists reject.

His argument depends on results proved within the ontological modelsframework of Harrigan and Spekkens (2010). Myrvold defends thisframework as merely codifying a form of reasoning implicit in much ofscience and daily life which there is no good reason to reject whenapplied in the quantum domain. One reasons that an action on aphysical system affects what one will experience later only via thephysical transmission of that action’s effect from the system toevents one later experiences. If so, then the action of preparing asystem’s quantum state must affect some physical property of thesystem reflected in what the framework calls its ontic state.

In response, QBists insist that quantum states have no ontic hold onthe world and that the QBist notion of quantum indeterminism is a farmore radical variety than anything proposed in the quantum debatebefore because it says that nature does what it wants, without amechanism underneath (Fuchs 2017b, p. 272; 2018, p. 19). The QBistSchack rejects Myrvold’s form of reasoning in the quantum domainas follows (Schack 2018).

There are no laws that determine objective probabilities formeasurement outcomes. The world does not evolve according to amechanism.

2.7 Other Objections and Replies

Other objections to QBism may be found in Brown (2019) and Zwirn(forthcoming).

According to Brown (2019, p. 75) “…a variant ofBerkeleyan idealism suffuses QBism.” QBists insist on theexistence of a real world in which agents and their experiences areembedded, along with rocks, trees and everything else in the usualworld of common experience. But they deny that quantum mechanicsitself describes this world, while hoping eventually to infer moreabout it from our successful use of quantum mechanics to anticipateeach of our experiences when acting on it. Brown objects to thecurrently ineffable character of the world for a QBist, contrastingthis unfavorably with the way a realist about a quantum state can useit to describe the physical world and explain how it gives rise to ourexperiences by affecting our brains.

Brown also objects to the QBists’ understanding of theSchrödinger equation, assuming they consider this to trackchanges not in the physical state of a quantum system but in what anagent believes she is likely to experience were she to act on it. ButQBists understand this equation as a normative constraint on anagent’s belief state at a single time, not as a constraint onhow that state evolves (see§1.2).

Brown further questions QBist entitlement to divide up the externalworld, either into subsystems or spatiotemporally, complaining that“That part of QBism which relates to ‘a theory ofstimulation and response’ between the agent and the world is notgrounded in known physics.” (2019, p. 81)

Barzegar (2020) has replied to Brown’s objections. His replyincludes a defense of a claim by Fuchs (2017, p. 118) that Brown(2019) sought to refute––the claim that QBism is pursuingEinstein’s (1949) program of “the real”.

Following a largely sympathetic sketch of QBism, Zwirn (forthcoming,§10) highlights ways in which some of its key notions remainunclear. Regarding quantum mechanics as an extension of subjectiveprobability theory, QBists (DeBrota and Stacey (2019), seeOther Internet Resources) reject the demand to provide a reductive definition of the notion ofan agent. Zwirn presses this demand because in this context the agentis not merely a passive witness: “It is the interaction betweenan agent and the external world that creates a result. Without agent,there is no result.”

Zwirn (forthcoming) also challenges QBists to clarify their keyconcepts ofworld andexperience: “QBismendorses the existence of an external world independent of any agent,but it is not clear if the external world is unique and shared by allagents or if each agent has her own external world.”

Zwirn believes that his own view of Convivial Solipsism (Zwirn 2016,2020) improves on QBism because it provides clear answers to thesechallenging questions. In his view an agent is something whoseconscious experiences are produced by a common external physicalworld, but organized into that agent’s personal externalworld.

3. QBism and Pragmatism

Most QBists are physicists rather than philosophers. But Fuchs locatesQBism in the tradition of classical American pragmatism (see entry onpragmatism). While quoting Peirce and referring to Dewey, Fuchs (2011; 2016, OtherInternet Resources) acknowledges especially the influence of WilliamJames’s ideas of pure experience and an open and pluralisticuniverse in which “new being comes in local spots and patcheswhich add themselves or stay away at random, independently of therest” (2016, 9, Other Internet Resources). Mermin’s CBistintroduction of the “Now” into physics and Fuchs’schoice of title for his 2014 (Other Internet Resources) both showaffinity with James’s reaction against what he called theblock-universe (see entrybeing and becoming in modern physics). Moreover, they both credit the influence on QBism of Niels Bohr. Bohrhimself never acknowledged pragmatist influences on his view ofquantum theory. But in a late interview^[5] he expressed enthusiasm for James’s conception ofconsciousness, and he was almost certainly acquainted with some ofJames’s ideas by the Danish philosopher Høffding, afriend and admirer of James.

4. Pragmatist Views

Pragmatists agree with QBists that quantum theory should not bethought to offer a description or representation of physical reality:in particular, to ascribe a quantum state is not to describe physicalreality. But they deny that this makes the theory in any waysubjective. It is objective not because it faithfully mirrors thephysical world, but because every individual’s use of the theoryis subject to objective standards supported by the common knowledgeand goals of the scientific community. So an individual’sassignment of a quantum state may be correct (or incorrect) eventhough no quantum state is an element of physical reality; Bornprobabilities are similarly objective; and measurement is a physicalprocess with a unique objective outcome, albeitepistemically-characterized.

4.1 Stapp

In attempting to clarify the Copenhagen interpretation of quantumtheory, Stapp called it pragmatic and used James’s views ontruth and experience to provide an appropriate philosophicalbackground for the Copenhagen interpretation “which isfundamentally a shift to a philosophic perspective resembling that ofWilliam James” (1972: 1105).

The significance of this viewpoint for science is its negation of theidea that the aim of science is to construct a mental or mathematicalimage of the world itself. According to the pragmatic view, the propergoal of science is to augment and order our experience. (Stapp 1972:1104)

He follows Bohr (1958), Landau and Lifshitz (1977), and others ininsisting on the objective character of quantum measurements, taking“our experience” not as individual and subjective but asconstituted by physical events, on whose correct description in theeveryday language of the laboratory we can (and must) all agree ifphysical science is to continue its progress.

4.2 Bächtold

Bächtold (2008a,b) takes an approach to quantum theory he callspragmatist. Quoting C.S. Peirce’s pragmatic maxim, he offerswhat he calls pragmatic definitions of terms used by researchers inmicrophysics, including “preparation”,“measurement”, “observable”, and“microscopic system”. His “pragmatist”approach to interpreting a theory is to isolate the pragmaticfunctions to be fulfilled by successful research activity inmicrophysics, and then to show that quantum theory alone fulfillsthese functions.

While acknowledging that his interpretation has an instrumentalistflavor, in his 2008a he distinguishes it from the instrumentalism ofPeres (1995) and others, who all (allegedly) claim some metaphysicalideas but seek to remove the expression “microscopicsystem” from the vocabulary used by quantum physicists. Bycontrast, his “pragmatic definition” of that expressionlicenses this usage, taking “quantum system” to refer to aspecified set of preparations.

Bächtold (2008b: chapter 2) elaborates on his pragmatistconception of knowledge, appealing to a variety of philosophicalprogenitors, including Peirce, James, Carnap, Wittgenstein, Putnam,and Kant. But his overall approach to quantum theory has strongaffinities with operationalist approaches to the theory.

4.3 Healey

In recent work, Healey (2012a,b, 2017a,b, 2020) has also taken what hecalls a pragmatist approach to quantum theory. He contrasts this withinterpretations that attempt to say what the world would (or could) belike if quantum theory were true of it. On his approach quantum statesare objective, though a true quantum state assignment does notdescribe or represent the condition or behavior of a physical system.But quantum states are relational: Different agents may correctly andconsistently assign different quantum states to the same system in thesame circumstances—not because these represent their subjectivepersonal beliefs, but because each agent has access to differentobjective information backing these (superficially conflicting) stateassignments. Each such assignment may be said to correctly representobjective probabilistic relations between its backing conditions andclaims about values of magnitudes.

On this approach, quantum theory is not about agents or their statesof belief: and nor does it (directly) describe the physical world. Itis a source of objectively good advice abouthow to describethe world and what to believe about it as so described. This advice istailored to meet the needs of physically situated, and henceinformationally-deprived, agents like us. It is good because thephysical world manifests regular statistical patterns the right Bornprobabilities help a situated agent to predict and explain. But theadvice is available even with no agents in a position to benefit fromit: there are quantum states and Born probabilities in possible worldswith no agents.

Born probabilities are neither credences nor frequencies. They areobjective because they are authoritative. Setting credences equal toBorn probabilities derived from the correct quantum state for one inthat physical situation is a wise epistemic policy for any agent in aworld like ours. Born probabilities are equally objective even whenthey differ more radically from Lewis’s (1986) chances becausethey are based on more (physically) limited information.

Healey’s approach is pragmatist in several respects. Itprioritizes use over representation in its general approach to quantumtheory; its account of probability and causation is pragmatist, inquantum theory and elsewhere; and it rests on a theory of content thatBrandom (2000) calls inferentialist pragmatism. While not endorsingany pragmatist identification of truth with “what works”,in its deflationary approach to truth and representation it followsthe contemporary pragmatist Huw Price (2003, 2011). Healey (2020)argues for a conception of realism according to which this pragmatistapproach is realist rather than anti-realist.

4.3.1 Contrasts with QBism

Independently of similar suggestions by Bacciagaluppi (2014) andStairs (2011), Healey co-opts some QBist strategies for dissolving themeasurement problem and removing worries about non-locality, whilerejecting the accompanying subjectivism about quantum states, Bornprobabilities, and measurement outcomes.

While QBists take quantum state assignments to be subject only to thedemand that an agent’s degrees of belief be coherent and conformto Equation \((\ref{ex2})\), Healey takes these to be answerable tothe statistics of objective events, including (but not restricted to)outcomes of quantum measurements. This makes the objective existenceof quantum states independent of that of agents even though their mainfunction is as a source of good advice to any agents there happen tobe. And it makes quantum states relative, not to the epistemicsituation of actual agents, but to the physical situation of actualand merely hypothetical agents.

While QBists follow de Finetti in taking all probabilities to becredences of actual agents, Healey’s pragmatist takesprobabilities to exist independently of the existence of agents butnot to be physical propensities or frequencies, nor even to superveneon Lewis’s Humean mosaic (see entry onDavid Lewis §5). There are probabilities insofar as probability statementsare objectively true, which they may be when sensitive to though notdetermined by physical facts.

There is no measurement problem since reassignment of quantum state onmeasurement is not a physical process but corresponds torelativization of that state to a different physical situation fromwhich additional information has become physically accessible to ahypothetical agent so situated.

There is no instantaneous action at a distance in a quantum world,despite the probabilistic counterfactual dependencies betweenspace-like separated events such as (macroscopic) outcomes ofmeasurements confirming violation of Bell inequalities. On apragmatist approach, these dependencies admit no conceptualpossibility of intervention on one outcome that would alter (anyrelevant probability of) the other. So there is no instantaneousnon-local influence, in conformity to Einstein’s principle oflocal action.

4.3.2 Decoherence and Content

On Healey’s pragmatist approach, an application of the Born ruledirectly specifies probabilities for claims about the values ofphysical magnitudes (dynamical variables of classical physics as wellas new variables such as strangeness and color): it does notexplicitly specify probabilities for measurement outcomes. But theBorn rule is legitimately applied only to claims with sufficientlywell-defined content. The content of a claim about the value of aphysical magnitude on a system depends on how the system interactswith its environment. Quantum theory may be used to model suchinteraction. Only if a system’s quantum state is then stablydecohered in some basis (see entry onthe role of decoherence in quantum mechanics) do claims about the value of the associated “pointermagnitude” acquire a sufficiently well-defined content tolicense application of the Born rule to them. Because of thisrestriction on its legitimate application, the Born rule may beconsistently applied to claims of this form (not just to claims aboutthe outcomes of measurements) without running afoul of no-go resultssuch as that of Kochen and Specker (see entry onthe Kochen-Specker theorem).

What endows a claim (e.g., about the value of a magnitude) withcontent is the web of inferences in which it is located. Such a claimhas a well-defined content if many reliable inferences link it toother claims with well-defined content. It is the nature of asystem’s interaction with its environment that determines whichinferences to and from a magnitude claim about it are reliable.Quantum decoherence and inferentialist pragmatism work together hereto make objective sense of the Born rule with no need to mentionmeasurement: Though of course at some stage all actual measurements doinvolve interactions with an environment well modeled by quantumdecoherence.

Contra to Mermin’s view (see§1.6), concepts are not invented by each of us to make his or her experiencemore intelligible. They acquire content from the social practice oflinguistic communication about a physical world that perceptionrepresents (to humans as well as organisms with no capacity forlanguage) as independently existing.

4.3.3 Objections and Replies

Jansson (2020) challenges the claim of Healey’s pragmatistapproach to offer objective explanations of phenomena, whileacknowledging the attractions of a position that seeks to occupy themiddle ground between explanation seeking realism and predictionfocused instrumentalism. She concludes (2020: 165) that

Many explanations according to this approach to quantum theory seem toat least partially black-box crucial information about the physicalground for the appropriate assignment of quantum states orapplications of the Born rule. …neither quantum states nor theBorn rule can act as initial explanatory input. While this is aserious cost, it is not clear that a pragmatist approach to quantumtheory has to resist this conclusion.

One taking Healey’s pragmatist approach to quantum theory couldreply as follows (see Healey 2020, §7.7). The primary target ofan explanatory application of quantum theory is not a collection ofevents but a probabilistic phenomenon they manifest. A probabilisticphenomenon is a probabilistic data model of a statistical regularity.One explains the phenomenon by demonstrating how the probabilities ofthe model are a consequence of the Born rule, as applied to eventsthat manifest the regularity. Since theexplanandum is notitself a physical condition, it is inappropriate to demand a physicalexplanans (such as a physically real quantum state). But thedemonstration is explanatory only if each event manifesting theregularity itself depended on whatever physical conditions obtained,including whatever conditions backed assignment of the quantum stateinput to the Born rule. One can have good evidence for such backingconditions while unable to specify exactly what they are. The morecomplete the description of the physical conditions on which eachevent manifesting the regularity depended, the better the explanationof the probabilistic phenomenon they manifest.

Lewis (2020) raises concerns about Healey’s application ofinferentialist pragmatism to the content of claims in quantum theoryand its applications. His first worry concerns the distinction betweenthe prescriptive content of quantum claims (about the quantum state,for example) and descriptive non-quantum claims about magnitudes likeposition and energy.

But, as he notes, a claim’s having a distinctive prescriptivefunction does not show that it has no representational content. Apragmatist could reply that a quantum state represents something otherthan an “element of physical reality” while functioning toprescribe credences about such elements: Healey (2017a) suggests thata quantum state represents probabilistic relations between them.

Lewis’s second worry is that Healey’s position fails toadequately take into account the role of conditional or counterfactualinferences in conferring content both on quantum, and on non-quantummagnitude, claims. Through its prescriptive role in applications ofthe Born rule, Lewis maintains, a claim about a quantum state or amagnitude implies many counterfactual probabilistic claims aboutmagnitudes. For an inferentialist then, quantum claims and magnitudeclaims derive content from the corresponding inferences.

On Healey’s (2017, pp. 208–210) pragmatist approach, aclaim assigning a quantum state does derive much of its content frominferences involving counterfactuals. The inference is to acounterfactual whose antecedent is (or supervenes on) a claim aboutmagnitudes, and whose consequent specifies a probability as great as1 for a different magnitude claim that is meaningfulin these counterfactual circumstances. Healey could argue that themagnitude claims Lewis considers do not derive content from hiscorresponding counterfactuals, on the grounds that they do notmaterially imply those counterfactuals and so in quantum theory aninference from the claim to the counterfactual is not reliable.According to Healey’s inferentialist pragmatism, only reliablematerial inferences confer content. Magnitude claims about thetrajectory of a molecule might be meaningful and true according to analternative theory such asBohmian mechanics. But in Healey’s pragmatist view (2012b, pp. 1547–8), evenan imprecise claim about the location and velocity of a molecule istrue only in a situation that can be modeled by decoherence of a kindthat would block the inference to the counterfactual.

Lewis’s final worry is that this application of inferentialistpragmatism renders the content of a claim highly sensitive to thephysical environment of the system concerned. He correctly notes that,on this pragmatist approach, quantum theory requires acknowledgementof radical changes to physical concepts that do not flow from otherapplications of pragmatism.

One taking Healey’s pragmatist approach might respond to thisworry by noting that these conceptual changes are a straightforwardconsequence of the application of inferentialist pragmatism to quantumtheory. For an inferentialist pragmatist, a material inference cancontribute to the content of a claim only if it is reliable, but inthe quantum domain physical inferences of a sort we all make ineveryday life fail dramatically. The sensitivity of physical conceptsto a system’s physical environment is arguably the naturalresult of reconfiguring our physical concepts to restore thereliability of inferences involving them.

5. Related Views

The view that a quantum state describes physical reality is sometimescalled \(\psi\)-ontic, by contrast with a \(\psi\)-epistemic view thatit represents an agent’s incomplete information about anunderlying physical state. When Harrigan and Spekkens (2010)originally defined these terms they applied them only to what theycalled ontic models of quantum theory. But others have since used themmore broadly to classify alternative views of quantum states outsideof the ontological models framework. QBists and pragmatists are notthe only ones to adopt a view that is neither \(\psi\)-ontic nor\(\psi\)-epistemic in these broader senses. Other views share thepragmatist thought that quantum states aren’t a function of anyagent’s actual epistemic state because quantum state assignmentsare required to conform to objective standards of correctness. Thissection covers two such views.

5.1 Friederich

Friederich (2011, 2015) favors what he calls a therapeutic approach tointerpreting quantum theory, taking his cue from the later philosophyof Ludwig Wittgenstein. This approach grounds the objectivity ofquantum state assignments in the implicit constitutive rules governingthis practice. Those rules determine the state an agent has to assigndepending on her knowledge of the values of observables, perhapsobtained by consulting the outcome of their measurement on the system.Friederich agrees with Healey that differently situated agents maytherefore have to assign different states to the same system in thesame circumstances insofar as their situations permit some to consultoutcomes inaccessible to others, and makes the point by saying asystem is not \(in\) whichever quantum state it is assigned.

Friederich treats quantum probabilities as rational quasi-Lewisianconstraints on credence and, together with his relational account ofquantum states, this enables him to refute the claim that Bell’stheorem demonstrates instantaneous action at a distance. He uses (whathe calls) his epistemic conception of quantum states to dissolve themeasurement problem by denying that an entangled superposition ofsystem and apparatus quantum states is incompatible with theoccurrence of a definite, unique outcome. Like Healey, he appeals todecoherence in picking out the particular observable(s) a suitableinteraction may be considered to measure.

So far Friederich’s therapeutic approach parallelsHealey’s pragmatist approach (though there are significantdifferences of detail, especially as regards their treatments ofprobability and causation). But Friederich rejects Healey’sinferentialist account of the content of claims about the values ofphysical magnitudes, taking restrictions on legitimate applications ofthe Born Rule to follow directly from the constitutive rules governingits use rather than from the need to apply it only to magnitude claimswith well-defined content. And Friederich seriously explores thepossibility that a set of magnitude claims collectively assigning aprecise value toall dynamical variables may be not onlymeaningful but true together. His idea is that the constitutive rulesgoverning the Born Rule may forbid any attempt to apply the rule in away that would imply the existence of a non-contextual probabilitydistribution over their possible values, thus avoiding conflict withno-go theorems like that of Kochen and Specker.

5.2 Brukner and Zeilinger

Brukner and Zeilinger (2003), Zeilinger (2005) follow Schrödinger(1935) and many others in viewing a quantum state as a catalogue ofour knowledge about a system. Their view is not \(\psi\)-epistemicbecause it denies that the systemhas an ontic state aboutwhich we may learn by observing it. Instead, a system is characterizedby its information content. An elementary system contains informationsufficient to answer one question. For a spin ½ system, aquestion about spin component in any direction may be answered by asuitable observation. But the answer cannot typically be understood asrevealing the pre-existing value of spin-component in that direction,and answering this question by observation randomizes the answer toany future question about spin-component in different directions. Sothe catalog of knowledge takes the form of a probability distributionover possible answers to all meaningful question about a quantumsystem that contains only one entry with probability 1 that might beconsidered a property that would be revealed if observed.

Brukner (2018) has recently used an extension of Wigner’s friendparadox (Wigner 1962) to argue that even the answers to such questionsgiven by observation cannot be regarded as reflecting objectiveproperties of the devices supposedly recording them. If sound, such anargument provides a reason to modify this view of quantum states tomake it closer to that of QBists.

6. Conclusion

A variety of QBist and pragmatist views of quantum theory have beenproposed since quantum theory assumed close to its present form. Inrecent years this has been an active area of research especially byphilosophically aware physicists working in quantum foundations.Philosophers have tended to dismiss such approaches, objecting totheir instrumentalism and/or anti-realism. But there is much to learnfrom responses to such objections and goodphilosophicalreasons to take these views more seriously.

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Pusey, Matthew, 2016, “Is QBism 80% complete, or 20%?” (YouTube, 1:14:45), Annual Philosophy of Physics Conference, RotmanInstitute of Philosophy, Western University, Canada, June 11–12,2016.
Schack, Rüdiger, 2016, “Participatory realism” (YouTube, 1:14:35), Annual Philosophy of Physics Conference, RotmanInstitute of Philosophy, Western University, Canada, June 11–12,2016.
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Stacey, Blake, 2019, “Ideas abandoned en route to QBism”, manuscript at arxiv.org/abs/1911.07386

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