Abstract
Although the present paper looks upon the formal apparatus of quantum mechanics as a calculus of correlations, it goes beyond a purely operationalist interpretation. Having established the consistency of the correlations with the existence of their correlata (measurement outcomes), and having justified the distinction between a domain in which outcome-indicating events occur and a domain whose properties only exist if their existence is indicated by such events, it explains the difference between the two domains as essentially the difference between the manifested world and its manifestation. A single, intrinsically undifferentiated Being manifests the macroworld by entering into reflexive spatial relations. This atemporal process implies a new kind of causality and sheds new light on the mysterious nonlocality of quantum mechanics. Unlike other realist interpretations, which proceed from an evolving-states formulation, the present interpretation proceeds from Feynman’s formulation of the theory, and it introduces a new interpretive principle, replacing the collapse postulate and the eigenvalue–eigenstate link of evolving-states formulations. Applied to alternatives involving distinctions between regions of space, this principle implies that the spatiotemporal differentiation of the physical world is incomplete. Applied to alternatives involving distinctions between things, it warrants the claim that, intrinsically, all fundamental particles are identical in the strong sense of numerical identical. They are the aforementioned intrinsically undifferentiated Being, which manifests the macroworld by entering into reflexive spatial relations.
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Notes
There is further evidence that quantum mechanics is essentially a probability calculus or a calculus of correlations. If one accepts the existence of “ordinary” objects, defined as objects that (1) have spatial extent (they “occupy” space), (2) are composed of finite numbers of objects that lack spatial extent, and (3) neither collapse nor explode as soon as they are formed, then one needs the uncertainty principle to stabilize these objects, and the “uncertainties” \(\Delta x\) and \(\Delta p\) must be measures of an objective indeterminacy or fuzziness. This is because what “fluffs out” ordinary objects cannot be anyone’s ignorance of the exact values of their internal relative positions and momenta; it can only be an objective indeterminacy. We describe this objective indeterminacy by assigning probabilities to the possible outcomes of measurements. If we then look for an appropriate probability calculus—for how the probabilities of the possible outcomes of a measurement depend on actual outcomes, and how they depend on the time of the measurement to the possible outcomes of which they are assigned—what we find is the formal apparatus of quantum mechanics. This argument is set forth in Mohrhoff (2009b) and in greater detail in Mohrhoff (2011, Chapter 8).
The notion that a Bare Quantum Formalism can be separated from the quantum-mechanical probability calculus is also suggested by the manner in which the axioms of standard quantum mechanics are routinely stated. This is because the first several axioms tend to be stated without explicit reference to probabilities; only the last couple of axioms refer to probabilities. Yet every single axiom makes perfect sense only as a feature of a probability calculus, as has been argued in Mohrhoff (2009b; 2011, Section 16.1).
Here Peres echoes Bohr’s insistence that what happens between the preparation of a system and a measurement is a holistic phenomenon, which cannot be decomposed into the unitary evolution of a quantum state and a subsequent “collapse” of the same: “all unambiguous interpretation of the quantum mechanical formalism involves the fixation of the external conditions, defining the initial state of the atomic system concerned and the character of the possible predictions as regards subsequent observable properties of that system. Any measurement in quantum theory can in fact only refer either to a fixation of the initial state or to the test of such predictions, and it is first the combination of measurements of both kinds which constitutes a well-defined phenomenon.” (Bohr 1939)
Another misconception muddying the interpretive waters is the so-called eigenvalue–eigenstate link, a postulate that Dirac (1958, pp. 46–47) formulated thus: “The expression that an observable ‘has a particular value’ for a particular state is permissible ... in the special case when a measurement of the observable is certain to lead to the particular value, so that the state is an eigenstate of the observable.” If the time a quantum state depends on is the time of the measurement to the possible outcomes of which it serves to assign probabilities, then the time at which an observable has a particular value can only be the time of an actual measurement.
If the existence of “ordinary” objects (as defined in note 1) is a fact, then a teleological or anthropic demonstration of what is entailed by it can go a long way towards explaining why the laws of physics have the form that they do (Mohrhoff 2002, 2009b, 2011). The question for pure metaphysics is then why “ordinary” objects, which have spatial extent, are composed of finite numbers of objects lacking spatial extent. For a possible answer see the final section and Mohrhoff (2014b).
If the indicated values of a supposedly macroscopic position turned out to be inconsistent with a classical law of motion, then this particular position would not actually be a macroscopic position.
According to Falkenburg (2007, p. XII), “quantum mechanics and quantum field theory only refer to individual systems due to the ways in which the quantum models of matter and subatomic interactions are linked by semi-classical models to the classical models of subatomic structure and scattering processes. All these links are based on tacit use of a generalized correspondence principle in Bohr’s sense (plus other unifying principles of physics).” This generalized correspondence principle, due to Heisenberg (1930), serves as “a semantic principle of continuity which guarantees that the predicates for physical properties such as ‘position’, ‘momentum’, ‘mass’, ‘energy’, etc., can also be defined in the domain of quantum mechanics, and that one may interpret them operationally in accordance with classical measurement methods. It provides a great many inter-theoretical relations, by means of which the formal concepts and models of quantum mechanics can be filled with physical meaning” (Falkenburg 2007, p. 191).
Because we are here concerned with the particle’s position, the question of parts does not arise, for a position isn’t a thing that can have parts. It can only be indefinite or fuzzy.
For a significantly more detailed presentation of this argument see Mohrhoff (2014, Sec. 4).
There is a philosophical position according to which there are no things—there are only bundles of properties. Whenever we apply quantum mechanics to a physical system, there is, however, always one thing: the physical system as a whole. We may not be able to think of it as being “made up” of “smaller” things, but we are always in a position to think of it as the thing we study experimentally, and we are always able to attribute to it the properties we observe.
I am not the first to put forth this preposterous idea. In his Nobel Lecture on December 11, 1965, Feynman recalled: “I received a telephone call one day at the graduate college at Princeton from Professor Wheeler, in which he said, ‘Feynman, I know why all electrons have the same charge and the same mass.’ ‘Why?’ ‘Because, they are all the same electron!’”
There is an extensive literature on the subject of individuality in quantum theory. See French (2011) for an overview and French and Krause (2006) for a comprehensive review. French sums up the situation by stating that quantum mechanics is “compatible with two distinct metaphysical ‘packages,’ one in which the particles are regarded as individuals and one in which they are not.” I rather agree with Esfeld (2013), who does not consider it “a serious option to regard quantum objects as possessing a primitive thisness (haecceity) so that permuting these objects amounts to a real difference.”
Does this mean that the material world is unreal, as some illusionistic philosophies assert? By no means, for the material world owes its existence to an intrinsically undifferentiated Being and a multitude of reflexive relations, and these are real.
When physicists reflect on the motives for their research, they nonetheless often claim (especially on TV, in press releases, and in grant applications) that their aim is to discover the elementary building blocks of the universe and the processes by which these interact with each other—a rather schizoid state of affairs.
Generations of students have been puzzled by the special role that the z axis plays in descriptions of the stationary states of atomic hydrogen. If a stationary state were to describe an atom as it is by itself, the question would have no answer. A stationary state, however, is a probability algorithm predicated on a particular preparation. In describing the atom’s stationary states we assume that a particular component of its angular momentum has been measured, along with its energy and its total angular momentum.
A hundred years ago it seemed obvious to many that life could not have emerged from utterly lifeless matter, just as today it seems obvious to many that experience cannot have emerged from utterly non-experiential matter. Yet today no one appears to seriously doubt that life did emerge from utterly lifeless matter; the seemingly insuperable “hard problem of life” simply dissolved. So why should it not be the same with the “hard problem of consciousness” (Chalmers 1995), a hundred years from now? As Strawson (2006) has pointed out, one cannot draw such a parallel unless one considers life completely apart from conscious experience. If consciousness is essential to life, as it may well be, one cannot reduce life to physics via chemistry if one cannot reduce consciousness along with it.
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Mohrhoff, U.J. Quantum Mechanics in a New Light. Found Sci 22, 517–537 (2017). https://doi.org/10.1007/s10699-016-9487-6
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DOI: https://doi.org/10.1007/s10699-016-9487-6