# Platonic Wholes and Quantum Ontology

Translated by Katarzyna Kretkowska

## Summary

## Excerpt

## Table Of Contents

- Cover
- Title
- Copyright
- About the author(s)/editor(s)
- About the book
- This eBook can be cited
- Contents
- Introduction
- PART ONE
- Chapter 1: Megiste mousike: The Hidden logos of Nature and Platonic Wholes
- 1.1 The relation of the whole and its parts in Plato’s ontology, the problem of the hidden structure and a new reading of the Parmenides
- 1.2 The division of the whole, Eleatic paradoxes and the Universal Principle of Relativity
- 1.3 The philocryptology of nature, internalistic compositionism and the hidden whole in microphysics
- Chapter 2: ‘The Adaptation of All Things’: Leibniz’s Series and the Foundations of Microphysics
- 2.1 Mathesis quaedam Divina: relational states, the Connection and a mathematizable process in the Leibnizian system
- 2.2 Action, the universal algebra of the process and the foundations of quantum physics
- 2.3 Quantum history as a hidden whole: the delayed choice quantum eraser experiment
- PART TWO
- Chapter 3: Nonseparability as the Ur-Phenomenon of Mechanics and Holism in Microphysics
- 3.1 Is quantum mechanics magic? Einstein’s Local Realism, the Bell–Kochen–Specker Theorem and quantum contextuality
- 3.2 The global nonseparability of nature: state holism, contextual realism and the hidden structure of the physical process
- Chapter 4: ‘Esse est percipi aut percipere’: The Quantum Principle of Relativity and Measurement as a Correlation
- 4.1 Quantum frames of reference: relativity, the blockworld and the universal relativization of the observer
- 4.2 Frames of reference, correlations and the breakdown of unitarity
- Chapter 5: The Relational Structure of Quantum Mechanics and Internalistic Compositionism
- 5.1 The Principle of Relativity, the internal consistency of quantum mechanics and the quantum thermodynamics of time
- 5.2 Carlo Rovelli’s relational quantum mechanics and internalistic compositionism in fundamental physics
- Bibliography
- General Index

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Composition has doubtlessly been one of the intensely discussed problems in the whole history of metaphysics, but the development of fundamental physics has placed it in a completely novel light. Niels Bohr, when developing his refined interpretation of the newly formulated quantum mechanics in the 1920’s, placed the category of ‘the indivisible wholeness of the quantum phenomenon’ at the very centre of the physical theory and thus triggered off another round of disputes within the philosophy of nature, which – though that might seem a bit surprising – have recently been more and more intensely pervading the foundations of physics in the context of quantum cosmology. The next round of speculation was set off by the more or less independent reflections of Heisenberg and Pauli, who strove to find a place for their own accounts of quantum holism in the shadow of Bohr’s influential semi-positivistic statements. But then, in the 1960’s, John Bell [1987a] opened new perspectives for the discussion of ‘quantum nonlocality’ and quantum entangled states, and Y. Aharonov, P. Bergmann and J. Lebowitz [1964] (later also [Aharonov, Vaidman, 1990] and [Aharonov *et al*., 2009]) disclosed a time-symmetrized structure of quantum theory with a timelike entanglement, relational states and a deep connection to the Kochen–Specker [1967] theoretical result, causing quantum mechanics to be even more astounding to metaphysicians (which, probably, was later stimulated by David Bohm’s daring ontological ideas subtly indebted to ‘Copenhagen’ holism). Quantum wholes became even more non-classical than in the pre-Bell era, the latter not having bothered itself too much with the then elusive ‘nonseparability’ and the physical meaning of entanglement, not to mention the geometry of quantum histories and the exotic quantum temporal-causal ‘paradoxes’. Mara Beller [1999] argued, perhaps rightly, that early ‘Copenhagen’ efforts concerning holism were at best somewhat foggy and philosophically dilettantish. However, the anything but trivial philosophical question, once provoked by Heisenberg and Pauli, can be boiled down to an attempt at judging how radical a holism we need to construe acceptable *quantum ontologies*, and not merely the pared-down epistemologies for quantum labs and quantum mechanics handbooks.

In the present book, I am going to put forward the view that the category of the hidden ‘primary whole’ has a fundamental meaning in quantum physics and allows us to speak reasonably about its radical, structural holism, which markedly differentiates it from all the earlier classical theories. The very concept of ‘holism’ is wide and unequivocal, hence the principal issue is to ascertain what we ← 9 | 10 → really mean by quantum mechanics being ‘radically holistic’. And further: why do the phenomena of microphysics and the structure of the theory itself force us to speak about a logically and ontologically primary ‘hidden whole’ at a cosmological level? Such reflections result in the need of a new, deeper understanding of the ontological sense of the quantum theory and such an attempt at its presentation shall be found at the end of the book, as its strictly relational interpretation, proposed in the 1990’s by Carlo Rovelli. The relational-informational approach (as a certain programme of formulating quantum theory as an Einsteinian ‘principle theory’ and at the same time the pediment of the future relational quantum cosmology, at least *in spe*) is sufficiently radical to totally transform an understanding of quantum mechanics as the theory of information transfers in the Universe, whose non-classical, irreducible properties are both relativity *and* the global nonseparability of physical states. I will argue that that global nonseparability is *the* fundamental, structural and irreducible feature of the quantum Universe, and every quantum ontology must acknowledge that fact. Sooner or later, a metaphysician is forced to cope with the nonseparability of quantum actions, which means a stormy divorce with the familiar, post-Aristotelian world of separable objects and their states as ‘elements of reality’. But one might ask: what are we supposed to do if those ‘elements of reality’ vanish into thin air and what about ontology itself? Even some adventurous ontologies of nature we sometimes probe have a frustratingly conservative core consisting of some form of noncontextual realism, preferred presentism with the ‘real becoming’ and/or thinking of wholes as secondary or derivative as if the lure of metaphysical atomism was literally irresistible. Hence, quantum phenomena in the world of Aristotle’s successors are doomed to be ‘paradoxes’ or ‘anomalies’, and that is of course why ‘commonsensical people’ like Karl R. Popper or David Lewis [1986b, p. xi] are inclined to complain about the quantum ‘doublethinking deviant logic’. I shall claim that as far as quantum theory is concerned, noncontextual realism is doomed to fail and a new kind of a Platonic-type compositionism is needed, which I call an ‘internalistic compositionism’, generating a kind of non-classical, internalistic logic and an internalistic (non-Boolean) theory of probability.

In Part I of the book, stress shall be put on the more historical-philosophical aspects of the problems in question. When reflecting on the category of the ‘hidden wholeness’ of nature, I have found it indispensable to limit the historical material directly concerning microphysics to two selected ontological models, key ones in the whole Western ontological tradition, namely those of Plato and Leibniz. In the case of the former, I shall concentrate on highlighting the model of the relations between the whole and the parts (intensional–internalistic), which has been rather seldom analyzed by historians of philosophy and which is competitive ← 10 | 11 → to the mereological (extensional) and Aristotelian ones (the latter being intensional, but at the same time ‘externalistic’). ‘Aristotelian (externalistic) wholes’ – considered not just as Aristotle’s concept but more broadly as a residuum of the post-Aristotelian imagery in metaphysics – are such irreducible wholes which presuppose a prior existence of the compositional ‘matter’ for them, i.e., some ‘elements’ (possessing definite, even if minimal properties) being combined and recombined, or primitive base individuals with solely some non-relational ‘thisness’, or any other pre-existing empirical ‘material’ being structured by some ‘forms’ and creating further empirical wholes. The key feature of that kind of compositionism is its association with the naïve intuitions concerning becoming and change – the secondary wholes arrange and rearrange ortochronally (along with the ‘flowing time’), come into being along history with the objective ‘now’ at the front, while the holistic structure of thus coming-into-being and dissolving objects is external to their supposed conditioning ‘pre-matter’. I shall thus conduct, following Verity Harte’s important study [2002a], a more detailed analysis of the *Parmenides* dialogue, to show how Plato attempted to justify the value of radical holism and the primacy of the ‘hidden whole’ over the phenomenal, apparently ‘becoming’ (‘as in a dream’ of the senses/sense perception, *Tim*. 52b) parts. I shall then, against the backdrop of the ancient debate on the relation of the ‘One’ and the ‘many’, present the problem of the relationship between contradiction and ‘absolute elements’ (the absolutes of cognition) in the conceptualization of nature, and propose a working formulation of the Universal Principle of Relativity as a postulate and at the same time a procedure of avoiding those contradictions and eliminating the absolutes from the theory. The Platonic model of holism and the postulate of relativizing empirical ‘elements’ will next be preliminarily used to modify the popular understanding of the nature of the quantum ‘state’. It turns out that it is possible, even at quite a preliminary level, to treat quantum mechanics as a theory of hidden, relational structures (atemporal wholes) of physical micro-processes. ‘Quantum states’ of the imagined, pre-existing ‘material systems’, which are usually said to be ‘measured’ and ‘registered’ as if they were classical, cannot be treated as ‘elements’ of mechanics, and, even less so, separable ‘elements of reality’; for if they are, a whole array of paradoxes, contradictions and physical deadlocks is produced. Quantum wholes are not composites of pre-existing elements (such as ‘states of the subsystems’), even the minimally simple ones, thus they are ‘Platonic wholes’.

In Chapter 2, I shall concentrate on the holistic aspect of Leibniz’s ontology, usually set aside in favour of his theory of substances (‘monadology’). I shall attempt to outline Leibniz’s interesting project of the ontology of nature’s hidden wholeness, construed upon the category of perspectival ‘action’, and I shall also show how Leibniz’s thesis on the processes of nature being ‘micro-actions’ ← 11 | 12 → corresponds to an important idea of ‘action physics’, put forward recently by David Finkelstein [1999a]. I shall also place particular stress on the connection between that ontology of the mathematizable process and Leibniz’s theory of representation in the context of the 20^{th} century theory of categories, used in recent years to construct relational quantum cosmology. One of the most fascinating facets of the Leibnizian project is its subtle interplay between the notions of the ‘process’ and complete (atemporal) ‘series of actions’, which preconditions the consistency of cosmology, hence Leibniz can be seen as a pioneer of the classical blockworld ontology with its built-in internal ‘dynamics’ and with all the tensions inherent in such a construction. That is the case since the Leibnizian ‘series’ (internalistic cosmological histories/atemporal functions defining blocks of local events) are an instance of Platonic wholes, and such a universe can be described by a general algebra of the process defined for fundamental, fully relational actions inside it, but nevertheless the condition of the consistency of histories (a predecessor of modern general covariance) enforces an acceptance of the blockworld cosmology. That is why Leibniz’s system is also so instructive for modern relational cosmologies as their *classical* toy model. Quantum experimental ‘paradoxes’ such as that of the delayed choice quantum eraser, seen in a cosmological context and not just as amusing lab effects, are especially interesting in that respect. Quantum wholes manifest themselves *fully locally* in the *apparent* causal-temporal ‘paradoxes’ forbidden by classical mechanics.

Chapter 3 opens the second part of the book, in which stress will be put not on the historical-philosophical aspects of the radical forms of holism, but on the foundational aspects of the ontology of microphysics as such. I shall begin with a presentation of the basic feature of microphysics – the nonseparability of quantum states which, I claim, is also at the core of almost all the philosophical controversies concerning the quantum theory (even if not recognized as such). I shall start with a concise analysis of the ontological assumptions of the Einstein–Podolsky–Rosen Gedankenexperiment, and I shall stress the fact that a simplistic reading of Einstein’s arguments against Bohr – too quickly reducing them to the former’s defence of relativistic (causal) locality – misses the point, since Einstein in fact always demanded, as has been rightly argued e.g. by Don Howard, that physical ontology should uphold the *strong principle of separability* and have separable ‘elements of reality’ as the classical ‘states of affairs’, thus Bohr was right when he insisted that it was *not* spatiotemporal locality itself which was of prime importance in the foundational dispute between them. Bohr’s local contextuality and Kochen–Specker contextuality, as implied in the (Bell)–Kochen–Specker theorem, have a deep connection with quantum nonseparability, which is a much more general ← 12 | 13 → and fundamental property and makes quantum entanglement itself more primitive than spatiotemporal relations. The EPR argument does not work, because all the quantum ‘states’ of the subsystems of the Universe are nonseparable, *hence* inherently contextual. The famous Bell theorem does not indeed list nonseparability among its independent conditions, but the latter is deeply ingrained in it as its general metaphysical underpinning and cannot simply be ignored as a purely philosophical issue, thus the problem of determining which of the Bell conditions is/are being violated, gets even more complex. I shall argue that Einsteinian fully noncontextual, i.e., separable quantum ‘states of affairs’ indeed cannot exist, and quantum ontology must acknowledge that fact by recognizing nonseparability as *the* ur-phenomenon of mechanics, which obviously constitutes a great challenge for metaphysicians: a new, more general kind of realism must be accepted and it is an immediate consequence of the failure of externalistic compositionism. It turns out that the most natural alternative is the radical, yet still local Contextual Realism, which is – true to Bohr’s simple intuitions – relativity working at the fundamental layers of mechanics/dynamics. Quantum ‘states’ as quantum actions within global histories are purely relational and contextual, thus Einstein’s hopes cannot hold and Bell-type inequalities must be violated. The question remains what the global physics/cosmology underlying that is.

The consistent relativization of quantum mechanics has serious consequences, among which the most important one is the full relativization of quantum ‘states’/actions and quantum ‘observers’ themselves. *Quantum wholes do not possess any non-relational base elements*, because their internal structure itself obeys the Universal Principle of Relativity. In Chapter 4, I am going to analyze the consequences of adopting such a model of internalistic compositionism in quantum cosmology if we wish to understand the correlations of the EPR or GHZ-type on cosmological scales. Treating quantum histories as ‘Platonic wholes’, inaccessible to internal subsystems of the Universe, requires an acceptance of quantum blockworld ontology as a deepening of the block ontology of spacetime in the relativity theory. I am persuaded by David R. Finkelstein’s [1996, p. IX] slogan: ‘Quantum theory is above all an extended kind of relativity’, which eventually makes a generic quantum blockworld inevitable. The argumentation in favour of the block universe is stronger than is usually claimed by conservative analytical metaphysicians (as is clearly shown e.g. by Petkov [2006, 2009]) and it is *not* true that that is an ontology excluded by quantum mechanics, often being falsely depicted as time-asymmetric and pro-presentist. An idea of spacelike (signal) nonlocality or nonlocal ‘action-at-a-distance’ is the direct outcome of a naïve, quasi-classical interpretation of the quantum ‘state’ and the ‘state function’, but seems unnecessary if we allow the mechanical ‘elements of reality’ together ← 13 | 14 → with presentism to disappear and treat quantum correlations between entangled subsystems as the atemporal global structure of the nonseparable blockworld, and not the properties of some imagined, coming-into-being micro-entities. ‘Aristotelian wholes’ and ‘Aristotelian parts’ may be desirably intuitive when one is accustomed to think about cats, stones and cells, but are useless when there are no base entities placed in the ‘points of space’ and no intrinsic properties changing ‘in time’. Finally, I shall present the very important idea of quantum frames of reference and of the fundamental connection between the Heisenberg–von Neumann cut and the logical paradoxes of self-reference in the context of quantum measurement. The quantum (action) frame is a fundamental concept for the foundations of quantum information theory and the basic ingredient of the ontology of contextual realism in a quantum blockworld.

In the final chapter, I am going to argue, following Carlo Rovelli, that a conspicuous property of quantum mechanics is its immanently relational structure making it a type of metatheory which ascribes different descriptions to different observers without the loss of an inner consistency. I shall thus systematically present Rovelli’s time-symmetric relational interpretation of quantum mechanics and the way in which it solves the EPR paradox without abandoning causally local interactions. A consistent relational (and atemporal) interpretation of the ‘quantum state’ is much more radical than might seem at first glance and it is to Rovelli’s merit that his proposal is ontological, which differentiates it from ones that are similar in spirit, but one-sidedly epistemological or, even more disappointingly, constantly drifting towards the baroque many-worlds ontology. It is obvious that, as in the case of the relativistic blockworld, the principal resistance to the *quantum blockworld* and time-symmetric quantum theory has its roots in presentism and the ideology of objective ‘coming-into-being’, thus the problem of time (and probabilities) in quantum theory comes to the fore. I shall argue, as in Ch. 4, in favour of quantum ‘Parmenidean (or Platonic) physics’ without any irreducible time flow which cannot be consistently injected into the fundamental, changeless layer of physics, composed of global, atemporal histories. Quantum mechanics is deeply time-symmetric (which feature manifests itself in almost all its pecularities, strangely invoking a banned spectre of teleology in physics), but in a quite different way than classical mechanics, and that makes any relational quantum cosmology even more non-intuitive in the case when the initial and final boundary conditions of the history of the Universe should be seen as relationally ‘conjugated’ or coupled. The issue concerning mathematical formalism, which would be able to describe such a generalized, internalistic time-symmetric causality is quite interesting, since it might need purely global notions as in noncommutative geometry and view spacetime histories with local relational events ← 14 | 15 → as derivative. In any case, Rovelli’s relational paradigm, consistently eliminating time flow from the foundations of physics is perfect for construing any quantum blockworld ontology, even if one does not interpret quantum mechanics itself as the principle theory in Einstein’s sense (as e.g. Rovelli does). I shall argue that it is exactly that quantum time-symmetry which makes quantum mechanics *fully relational* and the ‘quantum states’ of arbitrarily singled-out subsystems of the Universe obey the Universal Principle of Relativity. Quantum wholes are atemporal ‘Platonic wholes’.

Philosophy is sometimes unable to keep apace with new developments in physics, but since ancient times it has also in a number of ways created the basic paradigms of ontological thinking realized by theoretical physics itself (for example ‘atomism’ as a general conceptual scheme). Modern metaphysics, dominated by post-Aristotelian imagery and discussing spatial ‘things’, the becoming ‘objects’ and ‘bare individuals’ as if nothing had changed much since the Middle Ages, seems to be estranged in the world of quantum theory and there are good reasons to assume that it has been destined to that alienation from the very beginning. One can pinpoint many reasons of that but I shall claim that one of the most important ones is not only the conservative, but plainly false model of composition or the whole–parts relation. That is the reason of the stress I shall be placing on the alternative paradigms of holistic thinking (Platonic and Leibnizian) and their non-zero value for theoretical physics, at the cost of a wider evaluation of different, competitive standpoints (particularly the more conservative ones) which, I claim, are disappointingly impotent in the field of quantum ontology. In a sense, the book is to encourage philosophers to experiment with some radical ontologies, which from the perspective of standard discussions appear to be definitely exotic. I have attempted to construe all of my presentation in such a way so as not to weigh it down with physical-theoretical details (excluding Ch. 4 and 5, where I have included more technical subject matter), but instead to analyze the foundational problem of compositionism from the perspective of a metaphysican grappling with the challenges brought on by the development of fundamental physics and the new ways of solving particular theoretical problems (particularly in quantum mechanics and quantum cosmology). It has been my particular concern to present purely metaphysical subject matter in a pronounced way, one which is sometimes overshadowed by technical discussions on the details of physical theories, so important in the philosophy of physics.

## Details

- Pages
- 290
- Year
- 2015
- ISBN (PDF)
- 9783653053425
- ISBN (ePUB)
- 9783653951134
- ISBN (MOBI)
- 9783653951127
- ISBN (Hardcover)
- 9783631666296
- DOI
- 10.3726/978-3-653-05342-5
- Language
- English
- Publication date
- 2015 (May)
- Keywords
- Holism Relational ontology post-Aristotelian externalistic compositionism Quantum blockworld
- Published
- Frankfurt am Main, Berlin, Bern, Bruxelles, New York, Oxford, Wien, 2015. 290 pp., 7 graphs