Logical Causality in Quantum Mechanics

Principal Investigator: Michael Epperson. Co-Investigators: David Finkelstein, Professor, Department of Physics, Georgia Institute of Technology; Henry P. Stapp, Lawrence Berkeley National Laboratory; Timothy Eastman, NASA-Goddard. Click here for Project Description. Supported by a grant from the Fetzer-Franklin Fund (Grant D11C36).

This project explores the mutually implicative relationship of the causal and logical orders in quantum mechanics and its connection to the mutually implicative relationship of subject and object (viz. contextualized measurement and measured system).

The logical structure of quantum theory emphasizes the importance of the non-unitary, contextualized evolution of the density matrix via von Neumann’s Process 1. The effects of Process 1 are specified by the orthodox von Neumann rules, but the process by which the measurement basis restricts the evolution and fixes a particular projection operator is not specified by any yet-known law or rule. The principle of the causal closure of the physical is thus not validated by the known rules of contemporary quantum physics. 

Von Neumann’s Process 1 was a crucial attempt to render explicit the non-classical, contextualizing effect of the measuring apparatus (‘subject’) upon the measured system (‘object’) in a way that at once preserved the traditional meanings of ‘subject’ and ‘object’ and made possible their coherent application to quantum mechanics. By this framework, the objective state of a classically-conceived ‘measuring subject’ actively, contextually conditions the superposition of potential outcomes states constitutive of the classically conceived ‘object measured.’ Prior to the measurement outcome, the potential objective qualifications of the ‘object-in-process’ always conform to ‘subjective’ contextualization via the measuring apparatus according to its orthonormal basis. The measured system is thus best understood not as a ‘classical object’ but rather a quantum physical ‘object-in-process’—i.e., a history of contextual quantum ‘measurement relations’ or, more generally, ‘quantum praxes.’

Executive Summary

With the advent of quantum theory, the philosophical distinction between ‘what appears to be’ and ‘what is reasoned to be’ has once again, after several centuries of easy dismissal by classical mechanistic materialism, become an important feature of physics. In recent well-regarded interpretations of quantum physics that give focus to the concept of 'quantum decoherence,' interpretations including those proposed by Robert Griffiths, Roland Omnès, and Nobel laureate Murray Gell-Mann among several others, we have seen careful investigations into the physical (i.e., not ‘merely philosophical’) distinction between the order of contingent causal relation and the order of necessary logical implication. Each of these interpretations, in its own way, makes an explicit appeal to the logical order as somehow ‘physically efficacious’ in or ‘governing of’ processes such as quantum decoherence and non-local, EPR-type quantum mechanical measurement interactions, among many other associated quantum processes.

The familiar classical conceptions of ‘subject,’ ‘object,’ ‘epistemology,’ and ‘ontology’ find no fully coherent mapping onto these recent advances in quantum physics, apart from their casual, practical application.  In the same way that the causal and logical orders are treated as mutually implicative in these modern interpretations of quantum physics, so too are the pairings of ‘subject and object,’ ‘epistemology and ontology.’

Principal Investigator Michael Epperson has argued that a careful philosophical exploration of the function of the logical order in modern interpretations of quantum physics yields an ineluctable re-casting of the classical, dualistic understandings of ‘subject-object,’ ‘epistemic-ontological’: The ‘subjective’ and ‘objective’ features of nature described by quantum physics are not best seen as fundamental, complementary, mutually exclusive features of reality as suggested by Bohr; rather, they are more coherently understood as mutually implicative features of fundamental units of relation (cf. Michael Epperson, Quantum Mechanics and the Philosophy of Alfred North Whitehead, Fordham University Press, 2004).  The Aristotelian infimae species are not material quanta related as ‘subject’ and ‘object’; the infimae species are, rather, the quantum relation-events (praxes) themselves, and their logical ordering into serial quantum histories (cf. Robert Griffiths, “Consistent Histories and the Interpretation of Quantum Mechanics.” Stat. Phys. 36: 219-272, and Robert Griffiths, Consistent Quantum Theory. Cambridge University Press, 2002).

Whereas quantum physics was initially lamented for the intrusion of ‘subjectivity’ into ‘objective’ physics, the explicit accounting of the role of the logical order in quantum physics reveals that it is not fundamental subjectivity that is evinced, but rather fundamental relativity, whose ultimate physical units are quantum praxis-events and their serial, logically ordered histories. Problematic phenomena such as EPR-like, nonlocal quantum causality can be more coherently accounted for in such a holistic framework, and not merely tolerated as an odd dispensation from classical, local causal mechanics.  But at the same time, classical, local mechanics are not merely dismissed or ‘explained away’ as epistemic artifacts of an underlying, fundamentally holistic quantum ontology, for the universe is not ‘sheerly’ holistic by this interpretation of quantum physics, which further leaves space for both epistemological and ontological emergence.

Unlike other interpretations of quantum mechanics (the various local and non-local ‘hidden variables’ interpretations, for example), local causality is not here cast as an epistemic illusion reducible to a fundamental ontological, sheerly nonlocal (holistic) causality; and neither is nonlocal causality cast in similar fashion, reducible to fundamental, merely local, classical causality.  Instead, the speculative philosophy of Relational Realism proposed herein, with its praxiological interpretation of the quantum theory, depicts the local and nonlocal features of these quantum relation-events (quantum praxes) as mutually implicative features of reality.  For example, causal relations that are locally restricted by their respective light cones and the constancy of the speed of light are, nevertheless, governed by their associated logical relations, which are not locally restricted by c (consistent with Einstein’s special and general theories of relativity.)  Thus, nonlocal EPR-type experimental results can be properly understood not as ‘non-local causality at a distance’ via some superluminal transfer of energy in violation of classical mechanics (as given in the various hidden variables interpretations, for example), but rather as causal quantum mechanical relations among spatially well-separated but logically ordered quantum praxes.

By this interpretation, the mechanics of physical causal relation given in the orthodox quantum theory is explicitly characterized as 'logically governed' by virtue of the logial presuppositions inherent within the formalism. At the conceptual level, for example, one could point to the presupposition of the laws of Boolean logic within probability theory--at least in the particular way the latter is employed in quantum theory. At the level of the physics, this is especially well-reflected in the concept of quantum decoherence, such that the latter can be understood as evincing a physically significant effect of this logical governance--a logical 'conditioning' of physical causality. Beyond its pertinence to familiar problems in physics, such as temporal asymmetry in thermodynamics, the thesis of logical causality explored by this research program has special relevance to philosophy as well, in that it might shed new light on the ages-old problem of correlating the order of causal relation and the order of logical implication. In this regard, the program's study of logical causality in quantum physics entails a modern re-exploration of the relationship between 'conceptual' and 'physical' first introduced by Plato and revisited continuously over the centuries since.

Within the past few decades, a confluence of key scientific and technological developments has set the stage for an historic rehabilitation of speculative, scientifically informed metaphysics; and it is this rehabilitation that will most likely provide the most sure-footed bridge in any fruitful dialogue among science, philosophy, and theology. This new reintegration of metaphysics and modern science, particularly as instantiated in modern interpretations of quantum physics, has led to promising new strategies for forging substantive advances in four primary areas: 1.  Reductionism, determinism, and causal closure; 2.  The mind-body problem; 3.  The ‘hard’ problem of consciousness; 4.  The relationship between quantum indeterminacy and free will.  Our proposed approach combines the following multi-disciplinary features:

1. Leveraging key results of modern physics, especially quantum theory, to convert some key elements of past philosophical debates into substantive, testable hypotheses.
2. Explicitly incorporate key philosophical distinctions (such as causal-logical, epistemic-ontological, subject-object), which are often left merely implicit in the science.
3. Develop recommendations for rigorous experimental protocols that will yield clear, reproducible results.

By the speculative philosophical program of Relational Realism outlined herein, with its praxiological interpretation of quantum mechanics, the causal-logical, subject-object, and epistemic-ontological 'dualisms' emblematic of conventional substance-based accounts (i.e., dualisms derived from fudamental material quanta) are recast as mutually implicative features of fundamental quantum praxes or relation-interaction events. Our investigation will be unique in that we shall proceed both from the ‘bottom up’ science of fundamental physics, and from the ‘top down’ sciences of more complex systems. From the bottom up, our investigations of the fundamental physics will be grounded in the work of co-investigator David Finkelstein at Georgia Tech, who has proposed new insights such as characterizing classical logic as merely a singular limit of quantum kinematics, and an emphasis of ‘actions’ (praxes) versus ‘objects’ in quantum physics.

From the top down, our investigation will include the work of co-investigator Henry Stapp, who has studied the ways in which large, complex systems such as the human mind exemplify these mutually implicative concepts—subject/object, logical/causal, epistemic/ontological—and their underlying quantum physical formalism. Dr. Stapp’s theoretical work on ‘quantum neuroscience’ applies an effect of well-tested standard quantum theory (the quantum Zeno effect) to obtain testable predictions about how the body can act in accord with the conscious intent of a human observer. Our goal with respect to this aspect of the research will be to identify ways in which the metaphysical principles undergirding our non-materialistic, non-dualistic, ‘event-ontological’ (‘praxiological’) interpretation of quantum physics might be exemplified in modern neuroscience and other important applications. (It is important to note here that a neuroscientific exemplification of the quantum theoretical framework in no way implies a reduction of mind or consciousness to quantum mechanics.) Rather, as a metaphysical desideratum, it is expected that logical causality as the a priori foundation of a ‘reasonable,’ quantum mechanically describable universe will have its reflection in the functioning of the ‘reasoning’ human brain to the extent that it, too, is quantum mechanically describable.  If quantum physics can be shown to be demonstrably applicable to a neuroscientific description of the brain—even in a limited sense—then it could be argued that the key role of the logical order in our approach to interpreting quantum mechanics will be reflected in the logic underlying human reason. 

Building on his previous work on the philosophical implications of the quantum theory (Epperson 2004), the program of Relational Realism introduced herein is grounded upon the notion that a coherent correlation, in the language of physics, of the causal and logical orders—one that includes a careful distinction between causal (i.e., efficient causal) efficacy and ‘logical efficacy’ or ‘logical governance’—is of first importance in modern physics and in modern science and philosophy more generally. Such a correlation might ultimately reveal deeper levels of systematic distinctiveness among the manifold competing modern interpretations of quantum physics—distinctiveness that is at once metaphysical and demonstrably physical.  More broadly, the speculative philosophical program of Relational Realism is intended to exemplify a novel two-way-rapprochement of physics and philosophy that could advance an understanding of nature in ways that transcend the conventional separation of these two disciplines.

Perhaps most important, the speculative philosophical program of relational realism proposes a novel means of bridging the centuries-long proliferation of disconnected worldviews by which ‘science’ is variously interpreted as exemplifying mutually antithetical ‘ultimate’ meanings and cosmological implications—reductionism versus holism, objectivism versus subjectivism, cosmogonic creation versus cosmological evolution, among many others. This proliferation has markedly impeded progress toward the evolution of scientifically informed worldviews capable of coherently accommodating fundamental features of experience that lie beyond the restricted scope of scientific description.

    “The proposition, foisted upon us by a materialism based on classical physics—that we human beings are essentially mechanical automata, with every least action and thought fixed from the birth of the universe by microscopic clockwork-like mechanisms—has created enormous difficulties for ethical theory. Quantum physics, joined to a natural embedding ontology, brings our human minds squarely into the dynamical workings of nature...”

    Co-investigator Henry Stapp
    Mindful Universe: Quantum Mechanics
    and the Participating Observer
    Springer Verlag, Berlin, 2007 p.117

    Logical Causality in Quantum Mechanics

    The fall of Aristotelian physics and the rise of modern science sparked the ignition of two vital engines that have carried modern Western philosophy of nature to eminence in the 20th century. The first engine, technological innovation, is often mistaken as the primary engine driving this ascent because its roar has, over the centuries, generated the most attention; but its less-regarded twin engine of mechanistic-substance metaphysics has contributed equally to the overall momentum. Indeed, even a cursory look at the history of western philosophy of science reveals that a major role for each engine has been to carry the weight of the other. And with occasional adjustments of balance and attunement over the past four centuries, mechanistic-materialism has contributed steadily and surely to the rise of modern science and philosophy.

    With the advent of quantum mechanics early in the 20th century, however, the engine of mechanistic-materialism has begun to sputter noticeably. In just the past few decades, classical philosophy of nature, with its comfortably understood components of ‘ontology,’ ‘epistemology,’ ‘objectivity’ and ‘subjectivity,’ has fallen so far out of alignment with the engine of technological innovation that the wobbling can no longer be ignored. Superconducting quantum interference devices, experimental demonstrations of quantum nonlocality, quantum transistor technology… These and other innovations have not been so easily borne by mechanistic-materialism as were the classical technological innovations of centuries past.

    Even so, the desire to keep classical mechanistic-materialism in service has easily trumped most efforts to modernize—perhaps because its coming of age back in the 17th century was such a triumph; for beyond the technological innovations it helped to power, mechanistic materialism was the first proven bridging of a chasm that had dominated philosophy for over 2000 years—the Platonic chasm separating description and explanation of phenomena—the wide gulf between what appears to be and what is reasoned to be. With classical science, a seemingly secure pathway from appearance to truth, from contingency to necessity, had finally been discovered; for proof, one need look no further than the technological breakthroughs fostered by this science, and the scientific breakthroughs that would, in turn, result from these new technologies.

    David Hume was perhaps the last empiricist of the early modern period to warn that cyclical progress of this kind, no matter how exhilarating, was no proof of crossing the Platonic chasm—that even the most careful empiricism could never demonstrate a real bridging of the orders of necessary logical implication and contingent causal relation. The mathematical and philosophical first principles associated with the logical order could, Hume argued, never be found within fundamental, ultra-reductive physical descriptions of phenomena associated with the causal order. The certainty of an objective logical conception such as ‘if p then q’ can neither be deduced from nor demonstrated by a subjective causal perception such as ‘p (seemingly) causes q.’  Logical necessity can never be soundly derived from causal contingency, no matter how carefully, or to whatever reductive depth, the latter is measured.

    Despite such admonitions from Hume and others to follow, the twin engines of modern technology and mechanistic-materialism pushed forward steadily and unimpeded well into the 20th century, carrying with them what have become conventional, “modernist” conceptions of ‘subject,’ ‘object,’ ‘epistemology,’ and ‘ontology.’ But after several decades of attempts to map these concepts onto quantum physics in a manner consistent with their familiar mapping onto classical physics, the old, steady trajectory of classical, reductive empiricism, borne by the heretofore well-proven engines of technological innovation and mechanistic-materialism, has slowly begun to degenerate.  The drive toward confident crossing of the Platonic chasm via the route of sheer reductionism—unification of the sciences via scientism—has, since the advent of quantum mechanics, instead degenerated into a divergence of barely-paved ‘interpretations’ of quantum physics, with no easy metric by which these ever-branching routes to truth might be evaluated. Indeed, ‘The Truth’ as science’s final goal is no longer the clear destination it once had seemed to be. The chasm separating fundamental descriptions of nature and fundamental explanations of nature remains unbridged. The familiar classical conceptions of ‘subject,’ ‘object,’ ‘epistemology,’ and ‘ontology’—the conventionally accepted foundations for all reasonable attempts at construction—simply have not been able to bear the weight of the new physics.

    The notorious ‘problem of measurement’ in quantum mechanics is perhaps the best exemplification of the difficulty in two key respects:

    1. Quantum theoretical descriptions of the ‘measurement’ of ‘objects’ by ‘subjects’ always yields a linear superposition of possible objective states; yet the actual measurement interaction always terminates with a unique ‘measured object’ in a definite state. Thus the logical principles of Non-Contradiction (PNC) and the Excluded Middle (PEM) are always satisfied in the practice of quantum mechanics; yet they are not in any way accounted for by the quantum theory itself.
    2) The classical separation of ‘subject’ and ‘object’ and the associated separation of ‘epistemology’ and ‘ontology’ are, at best, only clumsily applicable to quantum physics. ‘Objective’ states are not only subsequent to measurement by a ‘subject’ but consequent of such measurement, i.e., integrally part of measurement—a seeming intrusion of subjectivity into the classical conception of physical objectivity. And worse still, the ‘subject’ appears to play some physical role in qualifying possible outcome determinations, since these possible ‘objective’ qualifications are always expressed in terms of subjectively derived qualifications of the measurement process.

    Niels Bohr proclaimed on the first page of his 1934 book Atomic Theory and Human Knowledge that “The task of science is both to extend the range of our experience and reduce it to order.”  His point is that science needs to do more than merely codify what is already known; an important part of its task is also to expand the range of our experience.

    The development of quantum theory is an example of such an expansion. In the prior classical theory, the sense-data portion of our experience had been dealt with by effectively replacing all such ‘subjective’ experiential realities by corresponding ‘objective’ properties, which were assumed to be completely described in terms of mathematical properties attached to points in space-time. The theory conformed to the principle of ‘the causal closure of the physical,’ which asserted that at each moment t all physically defined future properties are completely determined  by the laws of physics in terms of physically defined properties of the past. Quantum theory extended that earlier theoretical structure by bringing the experiencing and acting observers explicitly into the conceptual and causal scientific structure.

    The omission from the earlier classical dynamics of any contribution from the experiential aspects of reality might reasonably have been seen from the start to be an expedient approximation destined eventually to be removed. Yet advances that broke away from the earlier one-sided theory were pursued by the founders of quantum theory not on philosophical grounds but, more importantly, in order to cope with the stubborn fact that the quantum generalization of the classical laws produced a putative ‘objective physical reality’ that was wildly out of synch with our sense perceptions. For example, a superposition of ‘Schrödinger cats’—some alive, some dead, some in between—is not given to our experience. That ‘defect’ was rectified by introducing into the dynamics what Bohr called “the free choice of experimental arrangement for which the mathematical structure of the quantum mechanical formalism offers the appropriate latitude” and what von Neumann, in his book Mathematical Foundations of Quantum Mechanics, called “Process 1.”

    According to the basic principles of quantum theory, all accessible knowledge pertaining to the input/preparation of a system S that is subject to our probing inquiries/actions is contained in a mathematical structure ρ, called the (probability) density matrix (or operator). In von Neumann’s non-relativistic formulation this operator ρ evolves in time, and ρ(t) represents the state of the system S at time t. The state S at time t is considered to exist over the subset of the set of space-time points (x’, y’, z’, t’) for which t’= t. The quantum dynamical law of evolution asserts that for an isolated system S, ρ(t’) = exp –iH(t’-t) ρ(t) exp iH(t’-t), where H is the Hamiltonian operator, here assumed to be time independent.  This dynamical law holds except at a discrete set of times at which a Process 1 intervention occurs, and at a discrete set of times at which answers to the queries posed at the Process 1 interventions are delivered. Each probing inquiry can be reduced to a set of ‘yes-no’ type questions. Each such question is associated with a pair of projection operators P and P’ = (1-P), and is represented mathematically by the Process 1 action ρ à ρ’ = PρP + P’ρP’. The probability that the delivered answer is ‘yes’ to the possible state PρP is Trace PρP/ Trace ρ. Tomonaga and Schwinger have generalized these von Neumann (vN) rules to relativistic quantum field theory (RQFT). Then ρ(t) gets replaced by ρ(σ), where σ is a continuous three-dimensional subset of space-time, having the property that for any pair of points p and p’ on σ  the separation between p and p’ is space-like (Stapp, 2007).

    The description of the logical structure of quantum theory given above emphasizes the importance in conventional orthodox quantum theory of Process 1 interventions. They are interventions from outside the scope of the dynamics described by the known mathematically described physical processes. The effects of these ‘interventions’ (as described by von Neumann) are specified by the orthodox vN rules, but the process that fixes the selected projection operator P is not specified by any yet-known law or rule. The principle of the causal closure of the physical is thus not validated by the known rules of contemporary quantum physics.

    Hence the question arises: How can we expand our thinking in a way that will convert these apparently causally effective interventions into elements of a logically coherent order? One of our objectives is to bring the combined resources of contemporary philosophy, cognitive science, neuroscience, and physics more effectively to bear upon this question.

    Von Neumann’s ‘Process 1’ was, in this spirit, a crucial attempt to render explicit the non-classical relationships between ‘subject’ and ‘object’ evinced by quantum mechanics in a way that both preserved their traditional meanings, and yet made possible their coherent application to modern quantum theory. The classical conception of objective ‘qualification by quality’ was re-written by Von Neumann into a model wherein the objective (quantum mechanical) facts constitutive of a classically-conceived ‘measuring subject’ actively conditioned the superposition of potential facts constitutive of the classically conceived ‘object measured.’ The latter is thus best understood not as a ‘classical object’ but rather a quantum physical ‘object-in-process.’

    Nevertheless, the classical conception of ‘subjective’ ‘secondary’ qualifications conforming to ‘objective’ ‘primary’ qualifications remains applicable in quantum mechanics—but only as regards the observation or registration of the actual measurement outcome (i.e., the object-as-actual) by a subsequent subject. Prior to the actualization of this measurement outcome, the potential objective qualifications of the ‘object-in-process’ must similarly conform to the (classically) ‘subjective’ qualifications of the measuring apparatus. Thus every classically conceived ‘object’ and ‘subject’ is, by the light of quantum mechanics, more fundamentally described as a chain of quantum ‘measurement interactions’ or, more generally, ‘quantum praxes.’

    By this description, the classical dualistic separation of ‘subject’ and ‘object’ is rendered a conceptual abstraction—as is the correlate classical dualistic separation of ‘ontology’ and ‘epistemology.’ If the fundamental constituents of nature are more accurately describable as ‘quantum praxes,’ from which we might abstract the classical conception of ‘objects known by subjects,’ we can similarly characterize the classical conceptions of ‘ontology’ and ‘epistemology’ as conceptual abstractions from a more fundamental quantum ‘praxiology.’

    Epistemology, Ontology, and The New Physics: Quantum Praxiology

    The term ‘praxiology’ (and its alternative spelling, ‘praxeology’) has traditionally referred to the study of human action, as rooted in the work of French philosopher and sociologist Alfred Espinas (1844-1922). It has since evolved into a number of related philosophical and sociological applications. In 1923 in the Polish academy, Tadeusz Kotarbinski (1886-1981), developed ‘praxiology’ as the theory of deeds, practice, and efficient action.  The term was later applied to theories of action in economics by several scholars, including Eugene Slutski (1926) and Ludwig von Mises (1933) among others, as well to the study of moral philosophy and ethics (cf. Mario Bunge, McGill University.)  Recent scholarship by the French and Polish academies, however, has traced the origins of praxiology to the work of philosopher of science Louis Bourdeau, who coined the term ‘praxeologie,’ defining it as a ‘science of functions’ (Théorie des Sciences: Plan de Science Integrale,Paris: Librairie Germer Baillière, 1882, v2).

    The conception of ‘praxiology’ given in the work of Bourdeau and his early French contemporaries is quite different from that seen in the later, more specialized applications developed by Espinas, Mises, Bunge, and others; the distinctiveness is so profound that today, there have developed two separate traditions of praxiology/praxeology, each adopting one of the two alternative spellings:

    Praxeology refers to the human action tradition and its applications to economics and ethics, rooted in the works of Ludwig von Mises and subsequent scholarship.
    Praxiology refers to the tradition whose roots go back to the origin of the term in the work of Bourdeau and the early French school. This is the tradition whose development continues with the French and Polish academies (cf. Praxiology: The International Annual of Practical Philosophy and Methodology. New Brunswick, N.J.: Transaction Publishers, 1992-present. NB: vol. 7, The Roots of Praxiology: French Action Theory from Bourdeau and Espinas to Present Days, V. Alexandre and W.W. Gasparski, eds., 2000.)

    Our application of the term ‘praxiology’ to quantum physics, particularly with respect to the work of von Neumann and the implications described above, exemplifies several of Bourdeau’s key conceptions of praxiology as ‘the science of functions.’ For example, Bourdeau writes:

    We give the name of "function" (from the Latin fungor, ‘I perform’) to a series of effects which are accomplished in a certain form under the influence of actions of the environment… Expressing the relationship between forms and the environment, it matches the condition of the former to those of the latter and relates each being to its habitat. Hence, it connects the parts to the whole, subordinates each detail to the entirety and completes the knowledge.
    …Taken as a whole, these functions makes up a truly unified category, despite the differences in their aspects. They are all caused by environmental actions modified in the forms and are refracted in a series of effects. Science has not yet systematized their order and even lacks the proper term to name the general force that produces them.
    Specific powers have of course been imagined to explain certain functions, such as life or vital forces and the soul or physical forces; but these imagined agents vested with partial functions arouse serious objections as did the discredited agents of early Physics. It would be in accordance with the methods of science to attribute all the functions to a single force of the same order as gravity, physical action and affinity. We shall give it the broadest name of ‘the force of activity.’ (The Roots of Praxiology: French Action Theory from Bourdeau and Espinas to Present Days, V. Alexandre and W.W. Gasparski, eds., 2000, p.21-23)

    When Bourdeau posits that diverse functions in nature are comprised by “a truly unified category, despite the differences in their aspects,” and that “they are all caused by environmental actions modified in the forms and are refracted in a series of effects,” one finds these notions echoed loudly in the works of many of the best-regarded quantum theorists of our time, including Nobel laureate Murray Gell-Mann, Roland Omnès, Robert Griffiths, and others. These physicists, despite their individual differences of approach, have each posited conceptions of quantum physics that aim at the very same unification described by Bourdeau, including the function of the environment in that unification.  These thinkers each attempt to unify quantum and classical descriptions of nature, for example, and stress the function of the environment in quantum measurement interactions. In addition, they all begin with von Neumann’s approach toward ‘quantum measurement,’ defined above as ‘quantum praxis,’ and similarly derive the classical notions of ‘subject’ and ‘object’ from this definition.

    Just as important to both the praxiology of Bourdeau and these modern interpretations of quantum physics, however, is the physical distinction between the order of causal relation and the order of logical implication.  Bourdeau writes:

    The work of function is quite specific and must not be mistaken, as is sometimes the case, for that of modality or composition. A function is characterized by the order of its developments owing to the unity of direction [i.e., an asymmetrical logical order] which the structure imposes upon concurrent forces. (Ibid.)

    And indeed, temporal and logical asymmetry must be a part of any coherent ontological interpretation of quantum mechanics. One finds, for example, a close connection between  Bourdeau’s quotation above and Heisenberg’s insistence that “every act of observation is by its very nature an irreversible process; it is only through such irreversible processes that the formalism of quantum theory can be consistently connected with actual events in space and time” (Heisenberg, 1958, 52). And similarly, the research programs of Gell-Mann et al. make explicit appeals to the logical order as somehow ‘physically efficacious’ in or ‘governing of’ processes such as decoherence and non-local, EPR-type quantum mechanical measurement interactions (cf. Roland Omnès. The Interpretation of Quantum Mechanics. Princeton, N.J.: Princeton University Press, 1994, and Robert Griffiths. Consistent Quantum Theory. Cambridge: Cambridge University Press, 2002 as examples.)

    Therefore, a coherent correlation, in the language of physics, of the order of causal relation and the order of logical implication—one that includes a careful distinction between causal (i.e., efficient causal) efficacy and ‘logical efficacy’ or ‘logical governance’—is of first importance in the proposed investigation of quantum praxis.

    Bridging Logic to Causality in Quantum Mechanics

    The relation between the logical and causal orders is illustrated most concretely in the simplest model, Peano’s. This is based on a successor operation ι converting any integer “moment” to the next, n to ι n = n + 1. Peano later generalized ι to the unit-set-generating operation ι in his set theory, converting any set s of any cardinality into the unit set ι s = {s}; we call this unition. The Peano causal order ι presupposes a logical order represented by the inclusion relation

    holding between any set

    regarded as defining a predicate or class of integers, and any subset s’of s (Finkelstein, 2002).

    The quantum theory of Bohr and Heisenberg was the first physical theory to transcend the mechanical notion of absolute truth implicit in mathematics; Heisenberg called it ‘non-objective.’ Like an integer, physical systems seem to have maximal descriptions. Unlike an integer, these are incomplete; every predicate has complementary ones. Bohr and Von Neumann respectively renounced and revised classical logic in formulating quantum theory. We see this as renouncing ontology (theory of being) for a praxiology (theory of acting); this is not an ‘interpretation’ of quantum theory but rather a ‘paraphrase.’ Since all actual observations make changes in the system beyond our control, we do not assume that a system has an absolute ontology, except as a singular limit

    but only an absolute praxiology, a network of quantum processes represented by an operator algebra associated with the system.

    Most quantum theory to date has retained the classical theory of the causal order and an absolute space-time, projecting these pre-quantum concepts into the quantum microcosm in what has long been recognized as unphysical and probably a failure of the theorist's imagination. Such mixed quantum/classical field theories are structurally unstable and singular as well as false to actual practice. They challenge us to reconstruct the physical theory of the causal order based on explicit linkages with the logical order.

      "The main idea of quantum theory is to talk about what you do, not about ‘things as they are’—to represent the whole process and use the theory to estimate whether it will happen. Heisenberg set up an algebra of observables in which the fundamental elements are operators, and could just as well be called ‘processes.’ They represent what we do, not what ‘is.’

      “...While it is impossible to fit quantum theory into classical understanding, it is possible to understand it on its own praxic terms.”

      Co-Investigator David R. Finkelstein
      Quantum Relativity: A Synthesis of
      the Ideas of Einstein and Heisenberg

      Springer Verlag, Berlin, 2002, p.35

      Just as classical unition ι (taken with union) generates classical set theory, a quantum unition operator ι  generates a quantum set theory rich enough for field theory. Like classical set theory, this quantum set theory comes with no manual for building a physical theory with its tools. This is provided by a correspondence principle generalizing Bohr’s, which is implicit in a suggestion by Irving Segal: Present-day singular physical theories are singular limits of a regular physical theory. Slight errors in the commutation relations have converted simple Lie algebras into nearby non-simple ones.

      This suggests that a suitable Lie algebraic (i.e. the algebra characterizing a physical theory’s transformations, as idealized in an infinitesimal limit) simplification can restore the hypothetical regular theory (i.e., a theory devoid of singularities which are denotive of a theory’s failure to give definite information.) This is an extension of canonical quantization; one may call it simplification quantization. One way to implement it is to move physical theories from their singular foundations in classical set theory onto the regular foundations of quantum set theory, which provides the necessary variety of simple Lie algebras. ‘Simplification quantization’ regularizes singularities that have eluded canonical quantization, while maintaining agreement with experiment. Simplification quantizations of gauge theory in general and of the gravitational theory of the causal order in particular are underway by co-investigators David Ritz Finkelstein and Mohsen Shiri. (See Appendix, “Transcendence of Physical Theories”)

      This hypothesis provides an origin for the important Lie algebras of quantum physics, including the Lorentz, Heisenberg, Poincaré, and unitary ones. The basic Lie algebras define the statistics of quantum aggregates. These then generate kinematical algebras—i.e., algebras characterizing all possible dynamical outcomes of a quantum system, as underwritten by the theory. Finally, the operators in kinematical algebras that are symmetries of organized modes like condensates make up the symmetry groups and Lie algebras. In this approach, there are no truly fundamental symmetries in nature. Empirical symmetries tell us about the symmetry of some organized substratum and are contingent upon that organization. Space-time curvature and classical gravity can now be regarded as residual effects of the quantum non-commutativity of a simple space-time-energy-momentum Lie algebra near the singular limit of classical space-time.

      These and other exemplifications of logical causality in fundamental physics might ultimately reveal deeper levels of systematic distinctiveness among recent interpretations of quantum mechanics; and at the same time, they might point to a broad unification of the sort proposed by Bourdeau—a unification that is at once metaphysical and demonstrably physical. In this context, the speculative philosophical program of Relational Realism will aim at exemplifying a novel two-way-rapprochement of physics and philosophy that could advance an understanding of nature in ways that transcend the conventional separation of these two disciplines.

        "…Temporal and logical asymmetry must be a part of any coherent ontological interpretation of quantum mechanics…  Heisenberg writes: ‘The transition from the “possible” to the “actual” is absolutely necessary here and cannot be omitted from the interpretation of quantum theory… ‘
             “The inability of quantum mechanics to account for the actualization of potentia or the temporally asymmetrical relations which obtain from such actualizations,is not problematic given that quantum mechanics presupposes and anticipates the existence of facts; this is evinced in the concepts of state evolution, probability, and history.  ‘One may consider,’  writes physicist Roland Omnès, ‘that the inability of the quantum theory to offer an  explanation, a mechanism, or a cause for actualization is in some sense a mark of its achievement. This  is because it would  otherwise reduce reality to bare mathematics and would correspondingly suppress the existence of time.’”

        Principal Investigator Michael Epperson
        Quantum Mechanics and the Philosophy of
        Alfred North Whitehead

        Fordham University Press, New York, 2004, p.94-95

        Just as Bourdeau’s definition of praxiology found its easy evolution into the more specialized applications of ‘praxeology’ seen in Espinas, Mises, Bunge, et al., we anticipate a similar cross-disciplinary application of quantum praxiology into several diverse areas of scientific inquiry, including neurophysiology and the ‘hard’ problem of consciousness.

        Quantum Praxiology: Additional Implications and Exemplifications

        The study of the logical order inherent in quantum theory has recently been advanced by Robert Griffiths in his introduction of the concept of (logically) consistent histories. Gell-Mann and Hartle, in an influential paper, have used this concept as a foundational part of their attempt to understand the origin, in a fundamentally quantum world, of the essentially ‘classical’ character of human experience. Gell-Mann and Hartle use Griffiths’ idea, and its developments by Roland Omnès, in conjunction with a major reinterpretation of Everett’s Many-Worlds proposal. Whereas Everett’s ‘many worlds’ are typically interpreted as equally real, ‘co-actual’ alternative universes, Gell-Mann and Hartle recast these ‘many worlds’ as ‘many alternative histories of the universe’:

        …The many worlds are all described as being ‘all equally real,’ whereas we believe it is less confusing to speak of ‘many [alternative] histories, all treated alike by the theory except for their different probabilities.’  To use the language we recommend is to address the familiar notion that a given system can have different possible histories, each with its own probability; it is not necessary to become queasy trying to conceive of many ‘parallel universes,’ all equally real. (Gell-Mann, 1994, p.138)

        Likewise, Griffiths in his book on consistent histories never mentions the ‘many-worlds’ idea, and Omnès is, in many places, explicitly contemptuous of the idea. Omnès also stresses a major deficiency of the Consistent Histories approach when considered as a full foundational structure: It deals with logically consistent ‘possibilities,’ but can give no accounting or explanation for the emergence or existence of actual facts. At the same time, however, Omnès writes that this ‘deficiency’ might be seen as “a mark of achievement” when properly understood as a necessary limitation of quantum mechanics (Omnès, 1994, 494)—a boundary that ends at the bridge between the logical and causal orders.  Crossing, for Omnès, with a nod back to Hume, cannot be accounted for by the physics alone. If quantum mechanics alone could account for the existence of facts, over and above merely providing a fundamental description of them, it would amount to a brute force assimilation of the causal order to the logical order—an unappealing and unwarranted reduction of “reality to bare mathematics.” (Ibid.)

        Gell-Mann and Hartle approach this problem of the generation of actual facts by introducing the concept of an IGUS, an Information Gathering and Utilizing System, the paradigmatic example of which is a human being. The general characteristics of such ‘complex adaptive systems’ is the subject of much ongoing research by Gell-Mann, Hartle, and their colleagues at the Santa Fe Institute. Our program can be viewed as an effort, from a different direction, to bring IGUSes, and associated facts, into quantum theory in a way that explicitly links logical order to causal order.  This goal—in line with the admonitions of Hume, revitalized by modern theorists like Omnès—will not be to fashion quantum mechanics into a fundamental explanation of actual facts in the sense of fully accounting for their existence. We propose, instead, to explore how quantum mechanics might provide a coherent and empirically adequate fundamental description of actualities as quantum actualization events or ‘quantum praxes.’

        Empirical evidence to support the sort of modeling for IGUSes that we intend to develop depends of course on the detailed model or models proposed. But the general characteristic will be macroscopic quantum effects in biological systems that appear to be beyond the capacity of classical-physics-based systems. A possible first example of such an effect may be in the harvesting of radiant energy by photosynthetic systems, introduced in the previous section of this proposal (p.13). The recent letter of Engel et. al. (2007), published in Nature, gives empirical evidence that photosynthesis uses a macroscopic quantum effect akin to Grover’s algorithm, a strictly quantum effect. If this basic biological process uses a macroscopic quantum process then it is plausible that macroscopic quantum effects will be used in other ways by biological systems. We plan to enlist the aid of biophysicists and neurophysiologists in our search for such effects.

        One of the models that we intend to scrutinize is the one proposed by co-investigator Henry Stapp, in collaboration with psychiatrist J. Schwartz, and neuroscientist M. Beauregard. Their proposal involves specific features such as cortical “Templates for Action” and a harnessing of the quantum Zeno effect. Those authors have cited significant evidence in their article in the Proceedings of the Royal Society. We shall endeavor, with the aid of neuroscience consultants, to identify in the recent literature other evidence, pro or con, and identify or propose more definitive experiments. One of these, currently underway, is Efstratios Manousakis’ experimental work on quantum mechanics and binocular rivalry.

        Summary and Outlook

        Given the current state of quantum theory as an arena of competing interpretations, the philosophical basis of any metaphysical preference—be it a dipolar praxiological scheme such as the one proposed by the philosophy of Relational Realism, a classical mechanical-material scheme, a positivist scheme, or any other—would beg as robust an exploration as the physical basis, at least insofar as ‘philosophy’ can serve as a valued conversation partner in such explorations. That is, if a physical theory can summarily trump a metaphysical theory via the desideratum of empirical adequacy, then the desideratum of logical coherence and consistency should similarly empower metaphysics, such that a metaphysical argument could entail a significant critique of some particular interpretation of quantum mechanics. If, for example, one presupposes the neo-classical dualism of actuality and potentiality as foundational to the interpretation of quantum physics, one might further wonder: Can the advantages, suggested by Heisenberg, of understanding actuality and potentiality (or the causal and logical orders) as connected yet mutually exclusive features of reality, be preserved within a more coherent monistic/quantum praxiological scheme, such as the one given in the speculative philosophical program of Relational Realism outlined herein?  For by such a scheme, actuality and potentia, causal relation and logical implication, are not conceived of as mutually exclusive (bipolar) features of reality, but rather mutually implicative (dipolar) features of fundamental, unified, quantum praxis events.The crucial question then becomes: Can such quantum praxis events be described as the Aristotelian infimae species—the elusive ‘final real thing’?

        This is the interpretation of quantum physics suggested by Alfred North Whitehead, who developed his event-ontological metaphysics during the same years that Heisenberg, Bohr, and their colleagues were developing the quantum formalism. Recent work has proposed a close compatibility between Whitehead’s metaphysical scheme and modern interpretations of quantum mechanics (Frank Hattich, Quantum Processes: A Whiteheadian Interpretation of Quantum Field Theory, Agenda Verlag 2004; Michael Epperson, Quantum Mechanics and the Philosophy of Alfred North Whitehead, Fordham University Press 2004).

        It might be argued that ontological dualisms such as the one proposed by Heisenberg (and the associated epistemic dualism proposed by Bohr) provide for ‘cleaner’ accommodations of the physics—such that, for example, causal relation in physics enjoys its status as a ‘concrete,’ ontological, ‘physical’ reality, and logical implication is restricted to an ‘abstract’ epistemic ‘conceptual’ reality. But it can also be said that a coherent dipolar monistic metaphysical scheme such as our quantum praxiological scheme, and the closely associated scheme proposed by Whitehead, each with its close correlation of ontological and logical first principles, is ‘cleaner’ than any such dualistic scheme (see, for example, co-investigator Timothy E. Eastman’s “Dualities without Dualism” in Physics and Whitehead: Quantum, Process, and Experience, SUNY Press 2004). The dipolar, monistic, quantum praxiological scheme may appear more complex insofar as it lacks any sharp speciation of reality into actuality and potentiality, concrete and abstract, physical and conceptual, causal and logical, as fundamentally mutually exclusive features of reality. But our praxiological scheme provides a coherent complexity, such that actuality and potentiality are seen as mutually implicative features of reality, as are the physical and conceptual features, and the causal and the logical features.

        In this regard, it can be argued that a dipolar, monistic, quantum praxiological scheme such as that given by the philosophy of Relational Realism proposed herein is ‘cleaner’ than any simply dualistic scheme that might be mostly coherent but nevertheless requires at least a few fundamental features that are mutually exclusive rather than mutually implicative. Our goal, as was Whitehead’s, is a physical and metaphysical scheme entirely free of such selective dispensations from coherence—especially those that would amount to foundational, ontological inconsistencies.  Information-based attempts to interpret quantum theory, for example, can be viewed as reflective of Whitehead’s dipolar event ontology, where ‘physical’ and ‘conceptual’ features of actuality are mutually implicative: ‘information,’ after all, is instantiated both physically and conceptually. Its formal structure has been precisely characterized by Shannon and von Neumann in terms of physical notions like entropy; and yet its content is nevertheless representational, i.e. irreducibly conceptual insofar as fundamentally exhibiting ‘aboutness’—that is to say, information is always information about.  

        If, indeed, a coherent praxiological, relational realist interpretation of quantum physics finds its way to fruition and is seen as exemplifying a Whiteheadian type (or any other type) of metaphysical scheme, the desideratum of empirical adequacy will be of paramount importance. The metaphysics must fit the empirically validated features of the physical formalism.  Interpretations of quantum physics such as those offered by Gell-Mann, Griffiths, and Omnès, for example, derive the logical order of classical causality, in part, from the decoherence effect, whereby potential facts constitutive of a quantum mechanical system are logically ordered into potential, mutually consistent histories. Decoherence is thus given by these interpretations as a derivation of classical logical causality from the quantum mechanical correlation of the causal and logical orders. And indeed, there have been experiments by which the logical order of classical causality can be seen as deriving from the logical integrations of potentia yielded by decoherence. Caldeira and Leggett (1983a Physica A121, 587) appear to have created a successful demonstration of such a derivation. Using the classical Lorentz oscillator model, they showed that the quantum interferences manifest by the oscillations were cancelled out via the decoherence effect. The latter, in other words, can be seen as introducing logical constraints upon the quantum system. Given sufficient time for decoherence to occur, the system becomes describable as a classical probability distribution in phase space. Moreover, observable consequences of co-investigator David Finkelstein’s theory (as characterized, for instance, in Finkelstein et al., [2001] “Clifford Algebra as Quantum Language,” J. Math. Phys 42, 1489-1502) are discussed in the model of the oscillator in Finkelstein and Shiri-Garakani, 2004c Finite Quantum Harmonic Oscillator. (https://www.physics.gatech.edu/people/faculty/finkelstein/FHO0410082.pdf)  

        But if fitness is to be tested and evaluated among competing physical-metaphysical interpretations of quantum mechanics—i.e., those that dualistically treat actuality and the causal order and potentiality and the logical order as separate or separable features of reality, versus the relational realist interpretation, which treats actuality and potentiality as dipolar, mutually implicative features of every quantum praxis event—it is equally crucial that the conception of experiment be sufficiently free of serious constraints imposed by any particular ontological commitment. This is especially important with respect to certain of these commitments that enjoy the status of ‘convention.’ Thus an emphasis on experimental testing, such as those discussed above, combined with reduced model-dependence, and a turn away from the typical conditioning influence of traditionally inherited ontological presuppositions, will be an important prescription for the development of metaphysically coherent interpretations of physical theories such as quantum physics. The EPR experiment, for example, was conceived by its authors via the conventional, inherited classical mechanistic-materialistic ontology. But more recent EPR-like tests of quantum nonlocality, rather than being conceived as constricted to this ontology, were conceived to test the limitations of this ontology.

        In Conclusion

        Our hypothesis is that any conception of ultimate reality that it is in any way fundamentally describable by physics must presuppose the order of logical implication as a necessary first principle.  Our investigations into quantum praxiology will build upon several modern interpretations of quantum physics that have begun to explore, in very small steps, the metaphysical notion of an explicit correlation of the order of efficient causal relation and the order of logical implication as physically, and not merely conceptually, significant.

        By ‘physically significant,’ we mean that the explicit correlation of the causal and logical orders is taken as useful to the solution of several notorious conceptual difficulties in quantum physics: Among these, the correlation of quantum theory and relativity theory, quantum non-locality, the measurement problem, and others. But as ‘philosophically significant,’ our program in quantum praxiology will exemplify an underlying ontology which grounds and makes possible the realities attended to by the natural sciences and the humanities.

        The speculative philosophical features of our research will be examined to the extent that they are exemplified by the physics; but this is merely the starting point of our work. Once explored carefully in this restricted arena, the metaphysical conceptions of potentiality and actuality, and the correlation of the logical and causal orders as evinced quantum mechanically can then find their application to other domains where comparable tests of empirical adequacy are not possible.

        “Any bridge intended to span the chasm separating classical and quantum mechanics must be constructed upon a sound ontological framework that is:
        1. coherent, in that its most fundamental concepts are incapable of abstraction from each other and thus free from self-contradiction; 2. logical; 3. empirically applicable; 4. empirically adequate, in that the ontology is applicable universally—both to the realm of familiar experience as well as that of theoretical experience.”
        Michael Epperson
        Quantum Mechanics and the Philosophy of Alfred North Whitehead, p.6

        Indeed, a physically substantiated metaphysical argument such asthat given in the philosophy of Relational Realism and its praxiological approach to quantum mechanics, briefly outlined herein, might thus find its way into the sciences as an important new metric for theory evaluation. Such a metric, we propose, may methodologically complement the formal and algebraic ‘Segal Doctrine,’ which aims to algebraically characterize fundamental physical theories as expansions into stable and simple groups (see, for example, Baugh, Finkelstein, Galiautdinov, & Shiri-Garakani, [2003] “Transquantum Dynamics,” Foundations of Physics, vol 33, n. 9, 1267-1275).   So long as the speculative metaphysical scheme includes empirical adequacy and logical coherence as key desiderata, it is difficult to argue against the possibility of such a metric becoming a non-trivial feature of the scientific enterprise; for both science and philosophy presuppose the same logical first principles, without which neither would be possible.


        Engel, G., Clahoun, T., Read, E., Ahn T.-K., Mancal, T., Cheng, Y.-C., Blankenship, R., & Fleming, G. (2007).  “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature, vol. 446 (April 12), 782-786.

        Epperson, Michael (2004) Quantum Mechanics and the Philosophy of Alfred North Whitehead,  New York: Fordham University Press

        Finkelstein, David (2002). Quantum Relativity: A Synthesis of the Ideas of Einstein and Heisenberg, Berlin: Springer-Verlag

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        Stapp, Henry (1993).  Mind, Matter, and Quantum Mechanics.  Berlin-Springer-Verlag.

        Stapp, Henry (2007).  The Mindful Universe.  Berlin: Springer-Verlag.

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