exploring philosophical implications of quantum decoherence

Philosophy Compass 8/9 (2013): 875–885, 10.1111/phc3.12058

Exploring Philosophical Implications of QuantumDecoherence

Elise M. Crull*University of Aberdeen

AbstractQuantum decoherence is receiving a great deal of attention today not only in theoretical and exper-imental physics but also in branches of science as diverse as molecular biology, biochemistry, and evenneuropsychology. It is no surprise that it is also beginning to appear in various philosophical debatesconcerning the fundamental structure of the world. The purpose of this article is primarily to acquaintnon-specialists with quantum decoherence and clarify related concepts, and secondly to sketch itspossible implications – independent of particular interpretations of quantum mechanics – for broaderphilosophical debates. For example, decoherence shows that any method of parsing nature into levelsor parts cannot be in principle but instead derives from our perception of the world as classical, aperception that is itself sustained by the process of decoherence.

1. Introduction

Quantum decoherence is receiving a great deal of attention today not only in theoretical andexperimental physics but also in branches of science as diverse as molecular biology, chemistry,and even neuropsychology. It is no surprise that it is also beginning to appear in various philo-sophical debates concerning the fundamental structure of the world. The primary purpose ofthis article is to acquaint philosophers of science with quantum decoherence and the relevantphysical concepts, including necessary assumptions involved. After the physics is presented, Idiscuss its possible implications for broader philosophical debates; a sufficient grasp of the sciencenot only rearranges the philosophical terrain but furthermore suggests new avenues of inquiry.There is an important sense in which the project carried out below is unlike much of the

extant philosophical literature on decoherence, and that is in its principled avoidance of issuestraditionally considered the central problems in philosophy of quantum mechanics: I bypassquestions about the measurement problem (i.e., why do we get definite outcomes for quantummechanical measurements when the theory describes outcomes only probabilistically?) and I donot engage in the debate concerning interpretations of quantum theory. As for the measure-ment problem, what decoherence says on the matter has been amply discussed; excellentoverviews of the problem and relevant literature are found in the work of Bacciagaluppi(2007), Schlosshauer (2005), and Wallace (2010). As for the interpretation question, philoso-phers may quite reasonably ask why they should bother with complicated quantum phenomena– despite claims about their extreme relevance for a wide variety of philosophical projects –when those who know the physics themselves cannot agree on what it means. However, manyof the interesting aspects of the dynamics of objects as revealed by decoherence can beunderstood independently of a specific interpretational approach to quantum mechanics, andit is my aim in what follows to highlight these aspects.1 Although these two canonical issuesin philosophy of quantum mechanics do not enter into what follows, a basic familiarity withthe general landscape of quantum mechanics (and the philosophy thereof ) is assumed.

© 2013 The AuthorPhilosophy Compass © 2013 John Wiley & Sons Ltd

876 Exploring Philosophical Implications of Quantum Decoherence

One last introductory note: I follow the predominant scientific literature in definingquantum decoherence (hereafter ‘decoherence’) to be a physical phenomenon broughtabout by a system’s entanglement with its environment. Decoherence is not an interpretationof quantum mechanics, nor is it new physics. It is just the consequence of incorporating inour calculations the fact that no physical system is truly isolated (or isolate-able) fromquantum mechanical interactions. When we drop such assumptions, a fascinating dynamicalstory arises. Because decoherence is so quick and its consequences nigh impossible to undo inmost scenarios, understanding this process both theoretically and experimentally proves acrucial component of our general conception of physical bodies and their interactions.And this new knowledge of the physical world surely affects a variety of philosophicalinquiries in which material bodies play a central role.

2. The Physics

2.1. PREREQUISITE CONCEPTS

In order to understand the process of decoherence, one must first understand quantumcoherence. In order to understand coherence, one must be familiar with related conceptssuch as entanglement, phase relations, quantum superpositions, and interference phenomena.Thus, I begin with a brief overview of these terms.2

Quantum superpositions

Quantum mechanics is done not in ordinary space, but in a Hilbert space – an abstract,complex multidimensional space in which all possible states (constituting possible valuesfor degrees of freedom) of a given quantum system are represented by vectors. A linearlyindependent and complete set of vectors in this multidimensional Hilbert space defines abasis. The (ideal) measurement of a system is done with respect to some basis, and thus,measurements select a certain point of view within which to observe a given system. In whatfollows, ‘system’ can, if one chooses, be read so weakly as to refer to independent degrees offreedom. For example, a single electron can be treated as two separate systems: oneconstituted by the electron’s spin degree of freedom and the other by the electron’s translationaldegrees of freedom.It is a mathematical property of Hilbert spaces that not only the vectors representing

possible states of a particular system exist within that Hilbert space, but any linear superposi-tion of those states also represents a state of that system. This consequence of the linearity ofHilbert space is referred to as the superposition principle, and it is a fundamental feature ofquantum mechanics. To explain how the superposition principle manifests itself physically,consider the double-slit experiment. A single particle is sent through a barrier with two slitsand then detected on a screen. The superposition principle implies that since it is possible forthe particle’s trajectory to be a vector corresponding to passage through slit 1 or through slit2, then it is also possible that the particle’s state be a superposition of ‘trajectories’ throughslits 1 and 2. Thus, the total wave function for a particle traversing a double-slit apparatusis written as the sum of both component states, each with a coefficient for probabilisticweighting: |Ψi= (1/√2) (cslit 1 +cslit 2). This generalizes to

Ψj i ¼X

ncn cnj i:

In a world without superpositions, the only possible states for a particle in the double-slitapparatus would be classical trajectories through either slit. Sending many quanta through the

© 2013 The Author Philosophy Compass 8/9 (2013): 875–885, 10.1111/phc3.12058Philosophy Compass © 2013 John Wiley & Sons Ltd

Exploring Philosophical Implications of Quantum Decoherence 877

apparatus one at a time would then result in a Gaussian distribution centered behind each slit,indicating a statistical ensemble of non-superposed states. However, when we actuallyperform this experiment, we obtain interference patterns. This means that particles hit thescreen in places given zero probability by classical states but nonzero probability whensuperposed states are allowed, as in quantum theory.While quantum theory does not provide a straightforward physical interpretation of

superpositions, what is clear from the occurrence of interference phenomena is that a particlewithin this apparatus cannot be described in terms of a classical statistical ensemble – i.e., itcannot be described as following a classical trajectory, in which case our ignorance prior tomeasurement as to which trajectory will be actualized leads us to write the particle’s stateas a weighted distribution of all probable outcomes. Instead, entirely new situations arisefrom superpositions. This is evident in cases where superposed states are observationallydistinct from individual component states, as with the K meson. When measured in asuperposition with its antiparticle, the K meson becomes an entirely new particle – eitherthe Klong or Kshort meson.3

Phase relations and coherence

In analogy with classical wave mechanics, phase relations mathematically express the degreeto which amplitudes can combine between individual waves constituting a superposition.4

That this occurs already within a single particle’s Hilbert space explains why we detect spatialinterference patterns when particles are sent one at a time through a double-slit apparatus(self-interference). If the phase relations are constant with respect to one another – in whichcase the wave packet as a whole does not disperse – the system will exhibit interferenceeffects (constructive or destructive) whose strength depends on the exact character of thephase relations. Phase relations that are well-defined with respect to each other are calledcoherent; a state with such phase relations is a coherent superposition.When a quantum system in a coherent superposition interacts with external degrees of

freedom (say, those of the environment), the result is to delocalize the system’s phaserelations, which in turn leads to the suppression of interference phenomena. This just isdecoherence: the process of smearing, or de-cohering, the phase relations between compo-nents of a system’s wave function. The character of these components is basis-dependent, andthus the basis in which decoherence becomes manifest will depend on the specific nature of agiven system-environment interaction.5

Consider the images below (Fig. 1), which intuitively model the decoherence of a Schrödingercat state in a fictional alive–dead basis: initially, the components ‘alive’ and ‘dead’ of thesuperposition are large Gaussian curves in the cat’s phase space, the smaller peaks being interferencebetween these components. As the cat state interacts with environmental parameters, interferenceterms are increasingly damped until trivial at the scale of the component peaks, which remainlargely intact through evolution. Hence, when we measure the cat’s state after decoherence hasoccurred (and it occurs extremely quickly, usually many orders of magnitude more rapidly thanthe measurement process itself), the probability of measuring what is effectively rendered anon-superposed state (‘dead’ or ‘alive’) is extremely large compared to the probability ofmeasuring a strange superposed dead–alive state. These strange states still exist, but have beenrendered practically immeasurable by decoherence.

Entanglement

A quantum state is entangled when it cannot be factorized into states of its constituentsystems. Defined in this way, entanglement can occur within a single system between


Figure 1. Decoherence of a cat-like state caused by increasing interaction with an environment, modeled using two Gauss-ian functions (representing ‘alive’ and ‘dead’ states) evolving in classical phase space. Scale in units of phase space (‘cells’).


independent degrees of freedom; the existence of two previously non-interacting systems is nota necessary requirement for entanglement (this is what allows us to define a system so weakly).6

Any given system will inevitably and intensely interact quantumly with its environment.7 Theconsequence of this is entanglement, and the consequence of entanglement is not only ourinability to describe the initial system independently of the environment, but additionally thephase relations of that system become smeared out, or decohered, into the new degrees offreedom provided by the environment.



Not only is decoherence caused by entanglement, but decoherence itself begets furtherentanglement: a system interacts and becomes entangled to environmental degrees offreedom. This entanglement combines their respective Hilbert spaces, allowing the coherenceof the initial system to leak or smear into the joint Hilbert space. Thus, the initial system losescoherence while the composite system gains it. Immediately, the new composite system willinteract and become entangled with further environmental degrees of freedom, causing itsdecoherence (and the coherence of the new composite system), and so on, in a perpetualcascade of decoherence begetting entanglement begetting further decoherence.

2.2. THE APPEARANCE OF CLASSICALITY

The issue of the emergence of an apparently classical world from a fundamentally quantum oneseems to have found its resolution in decoherence, though to explain exactly how this happensdepends on what one means by classicality. Below are two common ways of conceiving ofclassicality and a brief explanation from decoherence as to how such classicality arises.8

1. ‘Classicality’ as Newtonian motion9: in classical mechanics, the state of a system is repre-sented by a single point in phase space (the space formed by momentum and position axes).The closest analogue in quantum mechanics is a Gaussian distribution as narrow in everydimension of phase space as is possible given Heisenberg’s uncertainty relations; suchdistributions are called minimum uncertainty peaks. Each component of a superposed stateis represented in phase space by a (usually notminimum uncertainty) peak, with interferenceterms (phase relations) between peaks. For most macroscopic systems, environmentalinfluence leads to strong decoherence in the momentum and position bases, driving systemsinto states wherein all peaks effectively become minimum uncertainty peaks by suppressinginterference terms (see Fig. 1 above). In other words, through decoherence, each peak is ren-dered functionally non-superposed and so each traces out a quasi-Newtonian trajectory. Re-peated measurements will thus yield classical motion independent of which component isultimately measured.

2. ‘Classicality’ as lack of interference: given the fact that all quantum states are superposedstates in some basis, one might wonder why evidence of superpositions at the macroscale(usually qua interference phenomena) is rare – so rare that ‘classical’ is understood as ‘non-superposed’. Since, as stated, macroscopic objects typically interact with the environmentmost strongly in position and momentum bases, decoherence occurs most effectivelythere. Hence, the likelihood of measuring a macroscopic object in a superposition ofposition (obtaining interference patterns) or of momentum is extraordinarily small. Thelonger one keeps decoherence at bay, the more likely one is to measure interferenceeffects. A group of experimentalists at the Institute for Quantum Optics and QuantumInformation in Vienna has succeeded in obtaining interference patterns using very large(C70) molecules by delaying decoherence of these systems.10

2.3. ASSUMPTIONS: UNITARY SCHRÖDINGER EVOLUTION, THE BORN RULE AND WIDESPREADENTANGLEMENT

The Schrödinger equation is the basic dynamical equation used to describe evolution of aquantum system. It is not entirely truthful to say that everywhere and always unitary evolutionof the Schrödinger equation is preserved, and the reason for this is due to entanglement. Unitaryevolution is destroyed locally when a system becomes entangled with another system. At thescale of the newly created entangled system, unitary evolution is preserved; it is only whenone is interested in tracking the dynamical evolution of an individual subsystem that the



mathematical description becomes non-unitary and in most cases frighteningly complicated.There do exist mathematical methods for approximately following the evolution of one ofthe entangled pair, in particular, the methods of reduced density matrices and of restricted pathintegrals. These methods allow studies of decoherence to bypass the complicated state of affairscontinually created by entanglement and to describe the measurement statistics of a systemindependently of its environment.11

There is one axiom of standard quantum mechanics – the Born rule – that is typicallybound up with various interpretations of quantum mechanics and considered possiblycontentious. The Born rule assigns a probability to each possible value obtainable throughthe measurement of a quantum system in a particular basis. That is all. The question ofhow the Born rule works is a different sort of question that may or may not have an answer.12

In order to establish the prevalence of decoherence, one must argue that the scope ofentanglement is universal. Hopefully this is old news. While some have argued for a speciesof holism from universal entanglement (cf. Esfeld 2001; Joos 2007; Zeh 2004), all that isrequired to establish the ubiquity of decoherence is that each system be interacting or haveinteracted with at least one external degree of freedom and thereby exist in an entangled state.This is trivially true. Even a particle in the far reaches of the universe has interacted or isinteracting with vacuum fluctuations in space or with cosmic microwave background radiation.One might worry that if every system is entangled with some other system, then the

assumption necessary for modeling decoherence that the investigated system be initiallyun-entangled is untenable. However, we know that any given system generally has beeninteracting with an environment long enough that by the time we perform a measurement,it is so decohered that it behaves in all practically measurable bases like an un-entangledsystem. To clarify this point, consider Bohr’s early atomic model. In it, the electron alwaysoccupied definite energy states, performing quantum jumps to transition instantaneouslyfrom one energy level to the next. The model’s assumption that electrons always occupynon-superposed energy states (called eigenstates) succeeded despite being false because bythe time an electron’s energy was measured, it had been interacting with its environment,become entangled, and lost coherence in the energy basis. The electron’s superposed energystates became prodigiously damped by environmental influence while its energy eigenstatesremained largely unaffected – this robustness toward environmental influence translating intoincreased measurability. Recall the cat state discussed above: the phase relations betweencomponents in the cat’s fictional ‘life basis’ became quickly randomized through environmentalinteraction, leaving the cat in a state that was incredibly unstable (and thus unlikely to bemeasured) with respect to superposed states but extremely stable (thus likely to be measured)with respect to the eigenstates ‘alive’ and ‘dead’.

2.4. THE ROLE OF DECOHERENCE IN OTHER SCIENCES13

Let us pause for a moment to consider the import of all this: only by incorporating decoherenceinto our explanation of a system’s evolution do we understand why we got away with incorrectassumptions about isolatedness, closedness, and unitary Schrödinger evolution for so long(as with electrons in Bohr’s model). To strengthen this point, one needs only look to thefascinating experimental work being done in biological research, e.g., investigating the effectsof decoherence on molecules and proteins. In the work of Briegel and Popescu (2009), theauthors predicted that many biological systems of interest (which are, by virtue of beingbiological, surrounded by very hot, noisy environments that nontrivially influence the system)can nevertheless be relaxed into energy ground states, a process effectively resetting the system-environment entangled state to idealized pre-interaction, un-entangled states. This allows one



to assume initially un-entangled systems, and so successfully apply decoherence models formapping dynamical evolution.This theoretical work has led the way for the application of decoherence models in study-

ing the migratory sensitivity of birds, the hypothesis being that decoherence might explainthe precise physical orientation of molecules in the avian brain whose polarity aligns withearth’s magnetic orientation (thus allowing the establishment of migration patterns) – statesof molecules that should be, but are effectively not, highly entangled (Cai et al. 2010).Or consider chemical research initiated by Senthilkumar et al. (2005) and Zilly et al.

(2009), wherein the incorporation of decoherence models in the study of DNA allows oneto measure the suppression of entanglement between particular base pairs and their environ-ment (including the remainder of the DNA helix) to such a degree that experimenters canassign the base pair of interest a local energy distribution rather than a nonlocal one. Thisin turn allows closer examination of bonding behavior within specific segments of a DNAstrand, an experimental feat hitherto considered impossible.That the models of decoherence are spectacularly successful in describing and predicting such

diverse phenomena lends empirical weightiness to this insight it affords: it is the thorough-goingquantumness of a thing that explains the apparent non-quantumness of that thing.14

3. Philosophical Implications

Space limitations have prevented me from giving enough details regarding decoherence tofully substantiate some of the claims made in this section; the aim has been to provide enoughof an understanding of the physics to encourage further work on the topics suggested below.What is novel here, again, is that the following sketch of implications is not directly depen-dent upon the measurement problem or any particular interpretation of quantum mechanics.That entanglement ought to play a substantive role in material ontological schema is a

point that has been stressed by Esfeld (2001, 2004), French and Krause (2006), Howard(2007), Ladyman et al. (2007), Silberstein and McGeever (1999), and Teller (1986), amongothers. What decoherence adds to these considerations is an explanation of why we thoughtwe could get away with ignoring entanglement in our philosophizing: despite all thisentanglement, the world still appears to have classical properties like being divisible,spatially-temporally well located, and so on. But decoherence teaches us that due to the sizeof everyday objects and their inevitable interaction with environmental degrees of freedom,while we may observe these objects to have certain so-called classical properties, the mostaccurate description of the said objects nevertheless contains extremely nonclassical states ofaffairs. We know this because in experiments where decoherence is thwarted (albeit briefly),we can measure objects of varying size and energy behaving quantumly.15 Though this physicsseriously challenges atomistic ontologies, it remains to be explored whether these considerationscount as support for atomless gunk theories or something else altogether.Decoherence also ought to cure us of the notion that the world is truly divisible – an

assumption necessary for theories of material constitution and atomistic ontologies. Onecan slice the material world in myriad ways and get away with it because those slices haveno ontological grit – divisions that appear to be ontically derived are contingent on the sizeand energy scale of the physical contents of each division, and on the fact that these contentsare immersed in environments. In modeling decoherence, we impose a division betweensome subsystem and all the rest, and through various clever mathematical means are ableto treat them as separate things. That interactions among various degrees of freedom behavequantumly and we can provide cohesive dynamical explanations from decoherence for the



behavior of the resultant subsystems irrespective of whatever divisions have been made illustrates thede dicto nature of such divisions.It follows that there are no more- or less-fundamental degrees of freedom. Among other

things, this implies that spatial-temporal definiteness cannot be considered a fundamentalfeature of the world since our usual observation of objects in, say, an eigenstate and not asuperposition of position is due to our inability to observe all those still-extant but extremelydamped superpositions in which the object could in principle be measured. This is a significantproblem for the sorts of metaphysical schema Paul (2012, p. 222) labels spatiotemporalist –schema that consider spatiotemporalism to be a fundamental category of the world’sstructure and typically begin with considerations dependent upon the existence of (presumablywell-defined) spatiotemporal regions.A world in which all material being is done quantumly (that is, all things can be given a

more fundamental description at the quantum level) will not lend itself to usual interlevelrelations like emergence, reduction and supervenience between physical objects, all of whichrequire at least two relata and usually some ontic hierarchy. Of course, this point had alreadybeen made using entanglement (particularly strongly by those advocating ontic structuralrealism, e.g., French 1998; French and Krause 2006; Ladyman et al. 2007); there is certainlyno ignoring it in light of decoherence. This is not just a problem for interlevel relationswherein both relata are material objects. For example, consider arguments in philosophy ofmind requiring that mental states supervene on physical brain states: investigations ofdecoherence reveal that there only apparently exist well-defined brain states and so onecould, in principle, experience something highly nonclassical. How supervenience relationswith a nonlocal physical base can retain ontological import is thus an open question.Hopefully, it is clear despite the brevity of the above suggestions that rich philosophical

work remains to be done that makes essential (and correct) use of decoherence and relatedconcepts like entanglement and superpositions, and which can be carried out despite themaelstrom concerning interpretations of quantum mechanics and the measurement problem.

Acknowledgements

The images in Figure 1 were generated using a programwritten by Christopher Ferrie (Institutefor Quantum Computing and Department of AppliedMathematics, University of Waterloo); Ithank Chris for the kind permission to borrow and modify his code for this article. My thanks toGuido Bacciagaluppi and Franz Berto for valuable comments on early drafts, and also toKatherine Brading and an anonymous reviewer for helpful suggestions.

Short Biography

Elise Crull received a BSci (2005) in Physics from Calvin College but soon found that her truepassion lay in exploring the historical and philosophical aspects of physics and science more gen-erally. She went on to receive an MA (2008) and a PhD (2011) in History and Philosophy ofScience from the University of Notre Dame. In Fall 2011, she began a post-doctoral researchfellowship at the University of Aberdeen in Scotland, where she is writing a book jointly withGuido Bacciagaluppi provisionally titled ‘The Einstein Paradox’: The debate on nonlocality and in-completeness in 1935 (forthcoming, CUP). The book explores both historical and philosophicalaspects of quantummechanics as conceived by the theory’s primary contributors (including, butnot limited to, Schrödinger, Heisenberg, Einstein, Bohr, Pauli, and Born). Crull andBacciagaluppi are recipients of a three-year Leverhulme Trust research grant for this project.Aside from foundational issues in quantum mechanics, she is interested in considering more



broadly the philosophical import of quantum decoherence, a work began in her dissertation,Decoherence and Interlevel Relations. Since much of her work is deeply interdisciplinary, Crulllooks forward to a career of monitoring and engaging in evolving meta-issues arising betweenphilosophy of science andmetaphysics, as well as in the arenas of science, technology and values,science and religion, and the perception of science in the public sphere.

Notes

* Correspondence: University of Aberdeen, Philosophy, School of Divinity, History and Philosophy, King’s College,Aberdeen, UK, AB24 3UB. Email: [email protected].

1 For bits that do require further interpretation, one needs only to note that most viable candidates for interpretationalschemes can be classed in one of two categories: theories in which the wave function collapses and those in which it doesnot. While both categories have distinct consequences, one can proceed by making a choice between collapse theoriesand no-collapse theories without having to adopt a more specific approach.2 The discussion of such terms is necessarily kept quite brief; for a fuller introduction to quantum mechanics written forthe non-specialist, see Albert (1992).3 For more on the K meson, see chapters 2 and 3 of Joos et al. (2003). Chapter 3 (‘Decoherence Through Interactionwith the Environment’) provides another interesting example of observed superpositions involving optical isomers likethe ammonia molecule. Ammonia is a chrial (‘handed’) molecule often observed in a superposition of both its left- andright-handed states.4 Bear in mind that this analogy with classical wave mechanics is just that – an analogy. In classical mechanics, a wavepacket is analyzable in terms of a superposition of the aggregate individual waves (e.g., electromagnetic field strength isjust the sum of wave amplitudes at a space-time point). But in quantum mechanics, although mathematically thesuperposed state is still described as a sum of the individual component states, the resultant physical state can be a differentthing than an aggregate (e.g., a new particle in the case of K mesons).5 It is in this sense that decoherence explains how certain bases emerge as ‘preferred’ or ‘pointer bases’: the specificnature of dynamical interaction between a given system and environment comes down to the interaction of certain(commuting) degrees of freedom over others, and on different time scales. Degrees of freedom of both system andenvironment that commute and do so most rapidly will become most quickly entangled with one another, and there-fore, most quickly (and robustly) decohered with respect to those degrees of freedom. Since a system is then measuredin approximately non-superposed states within such a basis, it is labeled the ‘preferred’ basis of measurement for thatsystem, in that environment. For a fuller discussion of decoherence and pointer bases, consult the early chapters ofSchlosshauer (2007) or Zurek (2003).6 Again, ‘environment’ can be understood entirely generally as all or any degrees of freedom except those underconsideration. Recalling the above example, the system of interest could be an electron’s spin, in which case that sameelectron’s spatial coordinates might be considered the environment; likewise, in an entangled pair of particles, oneparticle may be treated as the system and the other as the environment.7 Note that I am not making the (false) claim that all entanglement results from interaction, only that if interaction, thenentanglement.8 For more thorough examinations of the question of emergent classicality, see one of the earliest papers ondecoherence by Joos and Zeh (their 1985), as well as Zurek’s seminal 1991 paper. More recent discussions can be foundin the work of Joos et al. (2003), Schlosshauer (2007), and Stamp (2006).9 This understanding of classicality is characterized by Ehrenfest’s theorem. Ballentine, Yang, and Zibin argue in their1994 paper that one’s ability to apply Ehrenfest’s theorem to a system is neither a necessary nor sufficient conditionfor its being defined as classical.10 The group has generated a suite of papers on molecular interferometry, including Arndt et al. (2002), Brezger et al.(2002), Hackermüller et al. (2003), and Hornberger et al. (2003).11 Excellent introductions to these methods can be found in the work of Schlosshauer (2007) for the reduced densitymatrix method and in the work of Mensky (2000) for the reduced path integral approach.12 There have been some attempts to derive the Born rule from more basic principles (cf. Rae 2009 for an overview ofsuch derivations). At the end of the day, however, the dubious nature of many of these investigations lends credence tothe belief that the Born rule is what it is, and what it is is an axiom of an extraordinarily well-confirmed theory. Physicistsmust bite the bullet at some point; perhaps the Born rule is that point.13 The experimental corpus in just the last five years has become immense for decoherence in biology, chemistry,genetics, and other non-physics arenas – one need only type ‘decoherence’ and ‘biology’ or ‘chemistry’, etc., into a



search engine to verify this. The interested reader might begin with the more general considerations provided in thework of Arndt et al. (2009), Brändas (2011), and chapter 9 of Schlosshauer (2007).14 For an introduction to the canonical models of decoherence and the various assumptions involved, see chapter 3 ofCrull (2011), chapter 5 of Schlosshauer (2007), and Stamp (2006).15 Such experiments notably include the creation of Schrödinger ‘kittens’ (a gentle introduction to this sort of experi-mental work is given in the work of Raimond and Haroche 2005) and the experiments in molecular interferometryreferenced above in Section 2.4.

Works Cited

Albert, D. Z. Quantum Mechanics and Experience. Harvard: Harvard UP, 1992.Arndt, M., Juffmann, T., and V. Vedral. ‘Quantum Physics Meets Biology.’ HFSP Journal 3.6 (2009): 386–400.——, Nairz, O., and A. Zeilinger. ‘Interferometry with Macromolecules: Quantum Paradigms Tested in the MesoscopicWorld.’Quantum [Un]Speakables: From Bell to Quantum Information. Eds. R. Bertlmann and A. Zeilinger. Berlin: Springer,2002. 333–351.

Bacciagaluppi, G. ‘The Role of Decoherence in Quantum Mechanics.’ The Stanford Encyclopedia of Philosophy. 2007.Retrieved 8 June 2012. <http://plato.standford.edu/entries/qm-decoherence>.

Ballentine, L., Yang, Y., and J. Zibin. ‘Inadequacy of Ehrenfest’s Theorem to Characterize the Classical Regime.’Physical Review A 50 (1994): 2854–2859.

Brändas, E. ‘Some Comments on the Problem of Decoherence. ’International Journal of Quantum Chemistry 111.2 (2011):214–224.

Brezger, B., Hackermüller, L., Uttenthaler, S., Petschinka, J., Arndt, M. and A. Zeilinger. ‘Matter-wave Interferometerfor Large Molecules.’ Physical Review Letters 88 (2002): 100404.

Briegel, H. J. and S. Popescu. ‘Entanglement and Intra-molecular Cooling in Biological Systems? A Quantum Thermo-dynamic Perspective.’ 2009. Preprint available at: <http://arxiv.org/abs/0806.4552v2>.

Cai, J., Guerreschi, J., and H. J. Briegel. ‘Quantum Control and Entanglement in a Chemical Compass.’ Physical ReviewLetters 104.22 (2010): 220502(4).

Crull, E. ‘Quantum Decoherence and Interlevel Relations.’ Diss. U of Notre Dame, 2011. Available online at:<http://etd.nd.edu/ETD-db/theses/available/etd-04152011-145851/>.

Esfeld, M. Holism in Philosophy of Mind and Philosophy of Physics. Dordrecht: Kluwer, 2001.——. ‘Quantum Entanglement and a Metaphysics of Relations.’ Studies in History and Philosophy of Modern Physics 35B(2004): 601–617.

French, S. ‘On the Withering Away of Physical Objects.’ Interpreting Bodies: Classical and Quantum Objects in ModernPhysics. Ed. E. Castellani. Princeton: Princeton UP, 1998. 93–113.

French, S. and D. Krause. Identity in Physics. Oxford: Oxford UP, 2006.Hackermüller, L., Uttenthaler, S., Hornberger, K., Reiger, E., Brezger, B., Zeilinger, A., and M. Arndt. ‘Wave Natureof Biomolecules and Fluorofullerenes.’ Physical Review Letters 91 (2003): 090408.

Hornberger, K., Uttenthaler, S., Brezger, B., Hackermüller, L., Arndt, M. and A. Zeilinger. ‘Collisional DecoherenceObserved in Matter Wave Interferometry.’ Physical Review Letters 90.16 (2003): 160401(4).

Howard, D. ‘Reduction and Emergence in the Physical Sciences: Some Lessons from the Particle Physics andCondensed Matter Debate.’ Evolution and Emergence: Systems, Organisms, Persons. Eds. N. Murphy and W. R. Stoeger,S. J. Oxford: Oxford UP, 2007. 141–157.

Joos, E. ‘Dynamical Consequences of Strong Entanglement.’ Quantum Decoherence. Eds. B. Duplantier, J.-M. Raimond,and V. Rivasseau. Basel: Birkhäuser Verlag, 2007. 177–192.

Joos, E. and H. Zeh. ‘The Emergence of Classical Properties Through Interaction with the Environment.’ Zeitschrift fürPhysik B59 (1985): 223–243.

Joos, E., Zeh, H. D., Kiefer, C., Giulini, D., Kupsch, J. and I.-O. Stamatescu. eds. Decoherence and the Appearance of aClassical World in Quantum Theory. 2nd ed. Berlin, Heidelberg: Springer, 2003.

Ladyman, J., Ross, D., Spurrett, D., and J. Collier. Every Thing Must Go. Oxford: Oxford UP, 2007.Mensky, M. B. Quantum Measurements and Decoherence: Models and Phenomenology. Dordrecht, Boston & London:Kluwer, 2000.

Paul, L. A. ‘Building the World from its Fundamental Constituents.’ Philosophical Studies 158.2 (2012): 221–256.Rae, A. I. ‘Everett and the Born rule.’ Studies in History and Philosophy of Modern Physics 40.3 (2009): 243–250.Raimond, J.-M. and S. Haroche. ‘Monitoring the Decoherence of Mesoscopic Quantum Superpositions in a Cavity.’Séminar Poincaré 2 (2005): 25–64.

Schlosshauer, M. ‘Decoherence, the Measurement Problem, and Interpretations of Quantum Mechanics.’ Reviews ofModern Physics 76.4 (2005): 1267–1305.



——. Decoherence and the Quantum-to-Classical Transition. 2nd ed. Berlin: Springer, 2007.Senthilkumar, K., Grozema, F. C., Fonseca Guerra, C., Bickelhaupt, F. M., Lewis, F. D., Berlin, Y. A., Ratner, M. A. andL. D. A. Siebbeles. ‘Absolute Rates of Hole Transfer in DNA.’ Journal of the American Chemical Society 127.42 (2005):14894–14903.

Silberstein, M. and J. McGeever. ‘The Search for Ontological Emergence.’ The Philosophical Quarterly 49.195 (1999):182–200.

Stamp, P. ‘The Decoherence Puzzle.’ Studies in History and Philosophy of Modern Physics 37 (2006): 467–497.Teller, P. ‘Relational Holism and Quantum Mechanics.’ The British Journal for the Philosophy of Science 37 (1986): 71–81.Wallace, D. ‘Decoherence and Ontology.’Many Worlds? Everett, Quantum Theory, & Reality. Eds. S. Saunders, J. Barrett,A. Kent, and D. Wallace. Oxford: Oxford UP, 2010. 53–72.

Zeh, H. ‘The Wave Function: It or Bit?’ Science and Ultimate Reality: Quantum Theory, Cosmology and Complexity. Eds.J. Barrow, P. Davies, and C. J. Harper. Cambridge: Cambridge UP, 2004. 103–120.

Zilly, M., Ujsághy, O., and D. E. Wolf. ‘Statistical Model for the Effects of Dephasing on Transport Properties of LargeSamples.’ The European Physical Journal B 68.2 (2009): 237–246.

Zurek, W. ‘Decoherence and the Transition from Quantum to Classical.’ Physics Today 44 (1991): 36–44.—— ‘Decoherence, Einselection, and the QuantumOrigins of the Classical.’ Reviews of Modern Physics 75 (2003): 715–775.

Further Reading

Anglin, J., Paz, J., and W. Zurek. ‘Deconstructing Decoherence.’ Physical Review A 55.6 (1997): 4041–4053.Bitbol, M. ‘Decoherence and the Constitution of Objectivity.’Constituting Objectivity: Transcendental Perspectives onModern Physics. Eds. M. Bitbol, P. Kerszberg, and J. Petitot. Berlin: Springer, 2009. 347–357.

Blanchard, P., Giulini, D., Joos, E., Kiefer, C. and I.-O. Stamatescu. eds. Decoherence: Theoretical, Experimental, and Con-ceptual Problems. Berlin: Springer, 2000.

Bokulich, A. ‘Can Classical Structures Explain Quantum Phenomena?’ The British Journal for the Philosophy of Science 59.2(2008): 217–235.

Camilleri, K. ‘A History of Entanglement: Decoherence and the Interpretation Problem.’ Studies in History and Philosophy ofModern Physics 40.4 (2009): 290–302.

Duplantier, B., Raimond, J.-M., and V. Rivasseau, eds. Poincaré Seminar 2005: Quantum Decoherence. Vol. 48. Basel:Birkhäuser Verlag, 2007.

Hines, A. P. and P. Stamp. ‘Decoherence in Quantum Walks and Quantum Computers.’ Canadian Journal of Physics 86(2008): 541–548.

Janssen, H. ‘Reconstructing Reality: Environment-induced Decoherence, the Measurement Problem, and the Emergenceof Definiteness in Quantum Mechanics.’ 2008. Available online at: <http://philsci-archive.pitt.edu/4224/>.

Lo, H.-K., Popescu, S., and T. Spiller, eds. Introduction to Quantum Computation and Information. Singapore: WorldScientific, 1998.

Paz, J. and W. Zurek. ‘Quantum Limit of Decoherence: Environment Induced Superselection of Energy Eigenstates.’Physical Review Letters 82 (1999): 5181–5185.

Schlosshauer, M. ‘Classicality, the Ensemble Interpretation, and Decoherence: Resolving the Hyperion Dispute.’Foundations of Physics 38 (2008): 796–803.

Wallace, D. ‘Decoherence and Its Role in the Modern Measurement Problem.’ Philosophical Transactions of the RoyalSociety A 370.1975 (2012): 3476–4593.

Zeh, H. ‘On the Interpretation of Measurement in Quantum Theory.’ Foundations of Physics 1 (1970): 69–76.Zurek, W. and J. Paz. ‘Why We Don’t Need Quantum Planetary Dynamics: Decoherence and the CorrespondencePrinciple for Chaotic Systems.’ Quantum Classical Correspondence: Proceedings of the 4th Drexel Symposium on QuantumNonintegrability, 1994. Eds. B. Hu and D. Feng. Cambridge, MA: Drexel University International Press, 1997.367–379.


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