Disentangling entanglement
Version 2018-09-30
Antony R. Crofts
Department of Biochemistry and Center for Biophysics and Computational Biology
University of Illinois at Urbana-Champaign, Urbana IL 61801
Correspondence:
A.R. Crofts
Department of Biochemistry
University of Illinois at Urbana-Champaign
419 Roger Adams Lab
600 S. Mathews Ave
Phone:(217) 333-2043
Fax:(217) 244-6615
Email:
Introduction
Since the birth of quantum mechanics with Planck’s explanation for the ultraviolet catastrophethrougha Boltzmann treatment of discrete oscillators that revealed the famous E=hν,andthe extension throughde Broglie’s suggestion that objects of mass in the quantum range should show detectable wavelike properties, the discussion has evolved into the idea that quantum objects sometimes behave like particles and sometimes likewaves. The problems raised by that “particle/wave duality” have remained at the core of philosophical debates about quantum mechanics.Because of the difficulties pointed out by Heisenberg, the behavior in the wave-like regime cannot be measured without uncertainty, and, althoughsome properties of this domain can be assayed, complete ‘information’ comes only from measurement of interactions in the particle-like domain. As is well recognized, these propertiesintroduce both epistemological and ontological problems.In this commentary, I address some of these difficulties in the context of the entanglement question. I do not claim the mathematic expertise needed for any detailed treatment, and it might seem presumptuous for a biologist to venture views in this area. My perspective comes from attempts to bring a consideration of information transfer in the biosphere into the standard thermodynamic1 framework. This has uncovered some interesting properties, and has led me to propose a demarcation, in which propositions that require semantic transmission without a physical framework (transmitter, carrier, receiver) accessible to direct thermodynamic measurement are outside science(1). This raises questions in the context of the transfer of information in physical systems, - in some interpretations of entanglement experiments, this is suggested to occur faster than light.
The EPR paradox
In his argument with Bohr in the mid 1930s on what is now known as the EPR paradox (2), Einstein was concerned about the apparent contradictions between the “spooky actions at a distance” (non-locality) implied by quantum mechanical interpretations of correlations between quantum entities (entanglement), and the limitation on energy flux to the speed of life implicit in special relativity, which constrained the spatial range of interaction (locality). The problem was that the quantum mechanical treatment required a description in terms of a wavefunction encompassing two or more quantum objects that extended through space to arbitrary distance. The measurement of one object, in terms of properties (location, polarization orientation or spin) that reflect the energy content of the system, seemed to determine similar but complementary properties of an entangled remote object. The state of a distant physical entity was claimed to be established in some way by measurement of the properties of an entangled partner performed locally; ; - in Shimony’s words, “the quantum state probabilistically controls the occurrence of actual events”(3). This seemed to require that energy or information be exchanged faster then light. Either the superluminal constraint of relativity was wrong, or quantum mechanics did not provide a complete description (in a deterministic sense) of what was happening (in the physical sense)during the temporal evolution of the “entangled” states. Einstein later summarized his position in a letter to Max Born(4, 5), as follows:
“…the paradox forces us to relinquish one of the following two assertions:
(1) the description by means of the ψ-function is complete
(2) the real states of spatially separate objects are independent of each other.”
The ambiguities explored in (2)were extended to complementary spin states by Bohm (6, 7), and received a seminal restatement by Bell (8), who analyzed the expectations arising from a quantum mechanical treatment of entangled states andfrom a ‘local realistic’ treatment, and proposed inequalities that were in principle open to test(9). Subsequent experiments of increasing sophistication and accuracy have confirmed the results anticipated from the quantum mechanical treatment (cf. (10, 11). These results have engendered a continuing discussion ofentanglement, superposition, coherence, and collapse of the wavefunction. The superposition of entangled states, the collapse of the wavefunction, and the “actions at a distance” seen in entanglement experiments, seemed to require interpretations implying that something moves faster than light, but whether that is so, and what that “something” is, have become matters of contention.
The philosophical background
In the standard “Copenhagen interpretation” of Bohr and Heisenberg(12-14), the ambiguities were dealt with in the context of a prevailing philosophical view, influenced perhaps by the arguments between the “atomists” and “energists”, and Boltzmann’s ideas on the centrality of measurement as the ontological underpinning of hypothesis(15). Since measurement provided the link between the quantum mechanical and a classical physicalinterpretation, a complete treatment was taken as demanding a formal description of the evolution between states accessible to measurement. The initiating and final states were accessible, but the evolving wave-like state was not, so the treatment was thought to require a wavefunction that encompassed the evolution from the initiating transition. In the case of entangled entities, this required a common wavefunction that therefore “evolved” in the intervening space as the particles separated.The wavefunction was claimed to provide a “complete description”, but it was unclear what was meant by this. The Schrödinger equation for the hydrogen atom was developed in the context of a time-independent treatment ofelectron energy levels,made realistic because of standing-wave and conservation constraints. The ‘quantum’ part of quantum mechanics comes into play in the quantized behavior of transitions between energy levels. This was extended toinclude spin states, requiring treatment of conservation of angular momentum, arising from the Pauli principle. The wavefunctioncontains classical energy terms in the Hamiltonian, but Heisenberg uncertainty considerations require a probabilistic treatment, so that these are modified by the ψ-function(through |ψ|2) so as to representspatial probabilities(16). In the extrapolation to time-dependent systems, the quantized states are ‘borrowed’ from the description of the transition, and embedded in a Hilbert-space treatment (17)to deal with the temporal evolution in the wave-like domain. The wavefunction of the evolving system used to describe the entangled entitiesretains the probabilistic property, but constraints relating to conservation laws are implicitly included, and serve to introduce a realistic element. However, these constraints are taken to come into play only on measurement, and the intermediate wave-like state itself is characterized by an indeterminacy that allows degrees of freedom that are much less constrained, elegantly handled by the Hilbert-space treatment. As a consequence, measurement appears to serve the function of a selection of the states permitted by conservation laws from a more or less infinite set of possibilities allowed in Hilbert space,in the so called “collapse of the wavefunction”. However, there seems to be confusion between the thermodynamic realism introduced by constraints, and the presence of energy terms in the Hamiltonian, so that the latter have been taken to imply a more causal description that, despite the epistemic problems, embraced a thermodynamic status for the wavefunction, such that the measurement of one state determines the other.
Although Bohr is usually represented as championing the view that quantum theory provided a complete description, what he advocated was more subtle(13):
“The entire formalism is to be considered as a tool for deriving predictions, of definite or statistical character, as regards information obtainable under experimental conditions described in classical terms and specified by means of parameters entering into the algebraic or differential equations of which the matrices or the wave-functions, respectively, are solutions. These symbols themselves, as is indicated already by the use of imaginary numbers, are not susceptible to pictorial interpretation; and even derived real functions like densities and currents are only to be regarded as expressing the probabilities for the occurrence of individual events observable under well-defined experimental conditions.”
In the words of Jeffrey Bub “…the import of the state then lies in the probabilities that can be inferred (in terms of the theory) for the outcomes of possible future observations on the system” (18).
An alternative approach was that of David Bohm (19, 20) (see Goldstein(21) for a recent review). Bohmian dynamics defines the evolution of the physical configuration of the quantum entity in terms of two functions, a Schrödinger equation, with a Hamiltonian containing appropriate energy terms that account for all interactions, and a first-order evolution equation, - the so-called Guiding Equation. In this, the particle velocity is represented in terms of the quantum probability (current/density), so that the probability gradient given in terms of the wave function has a “guiding” role for the evolution of the particle. In Bohmian dynamics, the explanatory power of classical quantum dynamics is retained, but the wavefunction has a less ambiguous function, - the trajectory of a constrained quantum object appears to be directed by the probability function through a quantum potential field. This treatment has the advantage of avoiding some difficulties of the collapse of the wavefunction; - in informal terms, the quantum object always has a defined position and momentum, but only goes where the wavefunction “says” it can, so that the collapse “is a pragmatic affair” (21). However, the wavefunction appears to have at the same time both a more causal role and a more nebulous ontological status.
The paradoxical properties of entangled states have generated extensive speculation about their philosophical and mechanistic status; for example, Herbert (22) discusses eight distinct interpretations, with different treatments of the nature of the underlying quantum-reality, all of which account for the experimental data satisfactorily. However, all these hypotheses fail, in Popper’s sense (23),since none provides any experimental test that would allow a distinction between them; - hardly a satisfactory state of affairs.All start from the assumption of a common wavefunction, and hence have to deal with the appearance of superluminal problems.
Since my own interest is from the ‘information’ perspective, I will follow,for the purposes of discussion,a comprehensive account by Shimony (3)whichcovers philosophical aspects of Bell’s theorem and entanglement. Shimony provides this view, presented as an acceptable physical interpretation (though not his favored one):
“Yes, something is communicated superluminally when measurements are made upon systems characterized by an entangled state, but that something is information, and there is no Relativistic locality principle which constrains its velocity.”
Shimony quotes Zeilinger as an eloquent champion of this view (24) to the effect that
“…If we accept that the quantum state is no more than a representation of the information we have, then the spontaneous change of the state upon observation, the so-called collapse or reduction of the wave packet, is just a very natural consequence of the fact that, upon observation, our information changes and therefore we have to change our representation of the information, that is, the quantum state.”
This is an odd choice of quotation, because the statement is, at face value, quite consistent with a realistic view, and could be interpreted simplyas recognizing that the quantum mechanical description of the evolution of the wave-like state is just a mental picture, our “representation of…the quantum state”. However, some of Zeilinger’s more recent views seem to be more metaphysical, and to better reflect Shimony’s interpretation(25):
“…Thus, ifinformation is the most fundamental notion in quantum physics, a very natural understanding ofphenomena like quantum decoherence or quantum teleportation emerges. And quantum entanglementis then nothing else than the property of subsystems of a composed quantum systems to carryinformation jointly, independent of space and time…”.
Fine (5) haspointed out that the distinction between thermodynamic and informational aspects, and the notion that information transmission is not constrained by the speed of light, can be traced back to Bohr(12).
Information transmission and its relation to physical states
There are several aspects of this discussion I want to address; some of these have certainly been rehearsed in previous discussions(22).
Firstly, what do we mean by information?In the everyday usage, information implies a communication context, in which the message has a meaning, - it’s semantic content. The use of this term in physics is more ambiguous. In the classical realistic view, as framed by Galileo (26) for example, “Nature never…cares a whit whether her abstruse reasons and methods of operation are understandable to men…”. In this realistic view (i), the information content of a physical system is intrinsic to the state of the system; - there is no intentional semantic content. We can measure properties that provide clues from which we can infer the behavior of the underlying reality. The consistency of this behavior gives us the Laws of physics. Another usage (ii) is in terms of distinguishable states, and their manipulation in encoding of information. This usage is essentially thermodynamic, - either the intrinsic physical properties allow a reading of an existing non-equilibrium condition (a usage synonymous with negentropy, more or less as in (i)), or the states can be reordered to give local gradients that allow encoding of information. Shannon’s information theory (iii) comes into this class, but is used in the context of communication, which includes encoding of a semantic component. Shannon was careful to note that the engineering aspects,involving manipulation of physical states,were distinct from the semantic components. The usage in the quantum context is less obvious. For example, as noted above, the first quote from Zeilinger could be interpreted as recognizing that the outcome of entanglement experiments is simply ascribableto the intrinsic physical properties of the quantum objects, and that the resolution through measurement was of the observer’s uncertainty. However, Shimony’s gloss, and the later quote from Zeilinger seem to imply that an additional semantic component is imbedded in the physical state. Similar interpretations extend to higher levels of philosophical discussion. Even in the classical Copenhagen interpretation, the underlying state was taken to have no reality until measured, leading some to suggest that reality is dependent on measurement by conscious beings. This idea has also evolved. For example, the quantum character of all physical entities has been invoked in a renaissance of Plato’s Forms,captured in the entangled states. The permeation of information, coded in the entangled state, through space and time has been postulated as providing an explanatory basis for many of life’s mysteries, including the emergence of consciousness(27, 28).This ‘Platonic’ interpretation gives an oddly anthropocentric bent to the term ‘information’, implying that the universe performsan intentional transmitter function, with a semantic component encoded for reception by the human species. This is far removed from the classical interpretation in which ‘information content’ is intrinsic to the physics. Shimony’s description, the quotes from Zeilinger, and the quantum Platonic perspective, all beg the question of what is meant by “information” in this context.
This question can be clarified by recognizing explicitly the differences between the usages in physics ((i) to (iii) above) and in communication. In everyday cultural exchanges, or in evolution,for example, an encoded semantic component is always implicit, and we have to considerinformation transmission as involving bothsemantic and thermodynamic components. However, as Shannon(29) pointed out in his seminal paper, the whole apparatus of Information Theory pertains to the “engineering aspects” of encoding and transmission, but says nothing about the semantic content or ‘meaning’ of the message. This raises the question of the thermodynamic status of the semantic component. I have argued elsewhere (1)that the value of semantic content is not measurable in thermodynamic terms, but only becomes apparent though translational processing in a specific context. Although the semantic content confers no additional thermodynamic burden, the message itself is always realized in the context of encoding, transmission, and of a translational and interpretational machinery at the receiver end, each with a physical context. Since the semantic content has no thermodynamic status, it might be considered as unconstrained by superluminal considerations. However, all componentsof information transmission, - the several physical components of the engineering side, and the semantic contentof the message, - are needed if communication is to result.Whether information transmission(and itssemantic component) is involved in collapse of the wavefunction, or information read on measurement is intrinsic to the physical state, the outcome is the same. In either case, the something in Shimony’s statement is constrained by ‘Relativistic locality principles’. The only escape is to suggest that‘information’ has an alternative meaning, in which semantic content can be transferred without a thermodynamic vehicle. However, this wouldseem to open all sorts of possibilities for what my colleague Mike Weissman calls “science-fiction hell”. In line with this, the “impossibility of superluminal information transfer” has been suggested as “one of three fundamental information-theoretic constraints from which the basic kinematic features of a quantum description of physical systemscan be derived”(30).
As already noted, philosophical difficulties have been widely recognized in previous discussions, but some points deserve emphasis. Bohr suggests that the “entire formalism is to be considered as a tool for deriving predictions”, and “functions like densities and currents are only to be regarded as expressing the probabilities”, appropriate for the status of the quantum mechanical account of the evolution of the entangled stateas hypothesis. Like all hypotheses, it is a mental construct with a semantic component, and its epistemic status depends on how tightly this is tied to observation. Obviously, its predictions relate to the thermodynamic world, and these can be tested by measurement. However, the question of mechanism, of how to interpret theontological status of thewavefunction in terms of an intermediate state whose properties cannot be adequately determined by measurement, remains ambiguous(22). The limitations imposed by the uncertainty principle require a probabilistic treatment, divorced from direct measurement except in terms of the initial state and the outcome measurement. Bohr’s emphasis on “the measurement” was inrecognition of this difficulty. In terms of entanglement, the evolution of thewavefunction is a probabilistic representation of our knowledge of possible outcomes arising from a transition in which complementary quantum objects are generated. The physical state carrying the information is derived from the initial state of the system and the characteristics of the transition, including properties such as vectorial components arising from theorientation of polarization or spin. The wavefunction is also an expression of ignorance (or uncertainty) as to the specific evolution of the entities, - both in terms of spatial location, and in terms of which particular complementary properties are attributable to which entities. In any treatment, both the complementary properties, and the uncertainty of location, must be represented. The Hilbert-space representation handles both neatly, but the number of possible states in the evolutionary phase is very large. So long as the system is in this uncertain transitional state, it has been be taken as necessaryin most interpretations to represent the evolution of the entangled entities by a single wavefunctiondefining probabilities for evolution starting from the initial transition, - the last tie to the phenomenalworld.However, this is a philosophical, not a physical requirement; it does not seem required that one should assign a causal functionto the states described by the wave function. The thermodynamic reality comes from the conservation law constraints; the wavefunction itself, although it may containenergyterms,is modified by the |ψ|2term so as to take on aprobabilistic role.The interpretation of the wavefunction as having some deterministic role seems to be at the root of much of the weirdness arising from the quantum mechanical treatment of the evolution in the wave-like domain. The extensive discussion about the “collapse of the wavefunction”, superposition, and the role of measurement, is predicated onan interpretation ofthe spatially extended wavefunction as thermodynamically real, and that is whatbrings it into conflict with superluminal limitations.