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Philosophy of Science

Quantum Holism as Consequence of the Relativistic Approach to the Problem of Quantum Theory Interpretation

Kharkov State University

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ABSTRACT: In modern physics the common relational approach should be extended to the concepts of element and set. The relationalization of the concepts of element and set means that in the final analysis the World exists as an indivisible whole, not as a set (of one or another kind of elements). Therefore, we have to describe quantum systems in terms of potentialities and probabilities: since quantum systems cannot be analyzed completely into sets of elements, we can speak only of the potentialities of isolating elements and sets within their structure. On the other hand this quantum property of the world as an indivisible whole accounts for the astonishing logical properties of the structure of the potentialities of quantum systems which it brings forth. This has been confirmed by quantum-correlation experiments (A.Aspect and oth.). These effects have a relational nature, not a physical-causal or material one, and they are brought forth by the changes (resulting from measurement or physical interaction) in the structure of the relations of the mutually complementary sides of reality. One of these sides expresses an actually existing structure of the system as a real (and physically verifiable) but only relatively separable set, and the other expresses the sets of potentialities in it which arise from the astonishing property of finite non-analyzability of the system into elements and sets (i.e. by the quantum property of the world as an indivisible unit).

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Known physicist D.Bohm have successfully used the holistic idea in modern physics. (1) Besides that it is necessary to call reader's attention to the fact that Bohm had never got from idea of Holism the necessity of probability description of quantum systems, and never got to the explanation of quantum correlations as logical by their nature. There is nothing in common about usage of term "implicate" in the works of D.Bohm and term "implicative" (or "implicative-logical") which is strictly equal to the term "logical". Considering the term "implicate order" D.Bohm understands hidden, internal meaning order that could be illustrated by the following example, given by Bohm himself. Let us take a piece of paper and make a sphere of it by crumpling. Let us then pierce it by a needle. Then when we unfold the paper, we'll see the implicate order of the points' sequence that was hidden in the paper sphere. This is exactly the implicate order, that Bohm expected to understand with a little help of the theory of hidden variables, quantum potentials etc. The term "implicative" is uzed here in quite different sense: as "logical" (or as we could say "implicative-logical"). This turning to the term "logical" ascends to the known Russian physicist V.A.Fock, (2) who was the first to characterize (in the 1958) the quantum-correlative relation (like Einstein-Podolsky-Rosen-paradox, or so called EPR-paradox) as logical and in no way mechanical or physically-caused. This new idea of logical type of relation in base of physical world (which convincingly demonstrate EPR-experiments) follows from the finite indivisibility so called pure quantum state into elements and sets of any kind, that imply essentially probabilistic description of it. The probabilities or potential possibilities of the quantum system that has been introduced this way, appears to be essentially logical related and correlated with the property of ultimate wholeness itself (i.e. quantum system). From this point of view there is no necessity in the hidden parameters in the explanation of the quantum correlation effects.

The Common Relational Approach

At the Symposium on the Foundations of Modern Physics in Singapore in 1985, Simon Kochen (3) suggested that the paradoxes of quantum physics could be overcome by developing the common relational approach which was needed at one time to solve the paradoxes of relativistic physics (the Lorentz reduction of length, etc.) It is interesting to compare the special theory of relativity (STR) and quantum mechanics (QM) to see how successfully the relational approach can be applied to the interpretation of quantum theory.

In spite of substantive differences in the content of the two physical theories, there are remarkable similarities in their methodological foundations:

(1). STR introduces the constant C as the maximum speed of the propagation of physical signals and this limits the measuring procedures for determining space-temporal relations.

QM introduces the constant h as the minimum quantity of action and this limits the physical operations for specifying the state of a physical system.

(2). STR rejects absolute space and time.

QM rejects the universality and absoluteness of the concepts of element and set in describing physical reality.

(3). STR relativizes the concepts of simultaneity, length, time, etc. because of their operational nature, i.e., considering the finite speed of the propagation of physical signals that figures in the physical procedures by which these concepts are defined.

QM relativizes the concepts of separate object, element, and set of elements because of their operational nature, i.e., considering the finite value of the constant h in the physical procedures by which these concepts are defined.

(4). STR introduces a new invariant - the four-dimensional interval in space-time.

QM introduces the finite and undivided cell h power N (where N is the number of dimensions of the system) as an absolute invariant in the phase space of the system. The cell h power N makes it impossible to describe the system in terms of elements and sets because in any experiment cell h power N always remains whole and indivisible. Therefore, we must describe the quantum system in terms of potentialities and probabilities. The wholeness and indivisibility of the cell h makes potentialities and probabilities fundamental for describing nature.

(5). The object of description in STR are space-temporal relations in sets of objects with a finite rest-mass.

The object of description in QM are sets of the potentialities of the system.

(6). STR asserts that in the transitions from one reference system to another the relativistic invariant four-dimensional space-time interval acts as a unique determining factor and sets the exact correlations between different sections of the single space-time depending on the reference system selected.

QM asserts that in the transitions from one macroscopically given actual state of multiplicity of the system to another, as a result of the act of measurement or physical interaction, cell h power N (i.e. unique property of the world as ultimate wholeness or unit), which always remains indivisible and whole, acts as a determining factor which transforms one set of quantum system's potentialities into another.

(7). In STR the Lorentz transformation of mechanical quantities becomes just a kinematics effect based on changes in space-temporal relations which are produced by the transition from one reference system to another.

In QM the reduction of wave function and the quantum-correlative effects are purely relational, not physic-causal or substantial in nature. These effects are the natural consequences of the changes in the structure of relations of mutually complementary sides. One of these sides is the macroscopically given actual ensemble side of the system and the other side is the system of potentialities arising from the physical impossibility of the system's complete analysis into elements and sets.

Preliminary Conclusions

1. All that we can know in nature are relations and in the final analysis any kind of knowledge is just knowledge of relations. Any possible objects or elements that we introduce into our picture of nature are simply intersections of relations or 'knots' in the net of relations. These objects or elements which are introduced initially as undefined become finally defined through the totality of relations connected with them (the idea of the bootstrap, etc.). Here lies the essence of the relational approach in the epistemology of physics.

2. QM assumes that in the final analysis the World exists as an indivisible whole, not as a set . This quantum property of the World as an indivisible unit gives rise to the implicative-logical structure of potentialities in quantum systems.

Quantum Holism as a Theory of Implicative-Logical Structure of Probabilities in Quantum Systems

The formulation of the famous Bell inequalities presupposes that physical objects exist as elements and sets that are fully determined and independently existent. Therefore, the properties which are covered by Bell's inequalities characterize objects as they are in themselves. Thus, any relation that is not physically caused is excluded form a set of such objects. This means that a system of which Bell inequalities are true can and must be represented as an actual set of objects-elements which are characterized by certain properties belonging to each of them by itself. This can be shown by deriving any one of the Bell inequalities. (4)

Let there be an object characterized by three parameters A, B, and C, which assume the values +1 or -1. If we assume that every particle exists as a fully determinate element of a set of such objects, then it follows that every particle has definite simultaneous values for all three parameters A, B, and C. Let us denote the case when A takes the value +1 as A*, and the case when A takes the value -1 as A'. Similarly for B and C. Then for any ensemble of such particles with any values for A, B, and C the following equation will hold:

N (A*B') = N (A*B'C*) + N (A*B'C'), where N is the number of particles with the corresponding properties.

Let us write the remaining equations:

N (B'C*) = N (A*B'C*) + N (A'B'C*)

N (A*C') = N (A*B*C') + N (A*B'C')

From the last two equations it follows that N (A*B') < or = N (B'C*) + N (A*C'), which is one of the Bell inequalities.

It is clear from this example that the very possibility of formulating the Bell inequalities presupposes that objects of which these inequalities are true exist in themselves as quite determinate objects characterized by the indicated properties and that any kind of link or dependence among them except a causal one is excluded from sets of such objects. The physic-causal link can hold among the elements, sets or hidden variables. The usefulness of the Bell inequalities lies in this: they are the means of verifying the purely pluralist structure of reality. If the world is just a set of some elements then the Bell inequalities have to be true.

It is possible to treat the parameters A, B, and C in these inequalities as three mutual-perpendicular projections of particle spin which in the case of photons take exactly the values +1 or -1. It remains to test the Bell inequalities by the real distribution of the spin values of photons which arise from the disintegration of a quantum state according to the pattern of the well-known EPR experiment. Such experiments were done and they have refuted the Bell inequalities. Thus experimental evidence refutes the pluralistic structure of reality. The only alternative is quantum holism.

The essence of quantum holism lies in translating the idea of wholeness into the fundamental property of the finite indivisibility of quantum systems into any kind of elements or sets. In the final analysis a quantum system as well as the entire world exists as one whole, not as a set. This fact leads to many non-trivial consequences.

Suppose we have a quantum system consisting of two particles with a total spin of zero. The system exists in a pure quantum state described by the unit wave function. Since at bottom the system is indivisible into sets and exists as one whole, we should speak about the particles it contains in terms of probability. This means that the structure of the system is formed by sets of the potential states of its separate particles. Not one of these states is real and at the same time each of them as a possible state contributes to the probability structure of the system. Actually, there are no particles as such but only sets of probabilities of the separation of such entities as the first or the second particle. The ontological basis for such a probability description of quantum systems and of primary importance of the probabilities themselves is the finite indivisibility of the system into elements or sets and the non-universal nature of the concept of set in the description of the world.

The existence of the world not as a set but as an indivisible whole is the most significant, real, and confirmed objective fact.

This wholeness is formally introduced into quantum mechanics by means of the Planck constant h. It is manifested in every physical system through the existence of the indivisible cell h power N (where N is the number of dimensions of the system) in the phase space of the system.

Insofar as the space of any real physical measuring always becomes just a particular section of phase space, the permanent existence of the whole and indivisible cell h power N in phase space obviously makes it impossible to get precise and complete results in any real physical measurement. The wholeness and finite indivisibility of a quantum system into elements or sets that is secured by the cell h power N, makes us describe its structure in terms of the probabilities of its fragmentation in experiment into this or that kind of elements. Consequently, probabilities are primary (and indispensable) in observations. But in relation to the unobservable but logically attainable and absolutely objective phenomenon of wholeness probabilities are secondary because they are derived from the property of the finite indivisibility of quantum systems into elements or sets.

The fundamental property of wholeness is the source of the potentialities of quantum systems and at the same time secures their mutual coordination and correlation. The definition of the spin projection of one of the particles after the disintegration of system implies the simultaneous transition of the other particle into a state with a corresponding (and reliable) expected result for the analogous spin projection.

This quantum correlation of the states of particles (demonstrated in the EPR experiment) is a trivial consequence of the implicative-logical organization of the probability structure of the initial state of the common system, a structure which follows from its quantum property of wholeness and its finite indivisibility into sets of elements. At the same time the quantum correlations that appear in response to our arbitrary choice to measure this or that observable prove the remarkable directive role of the phenomenon of the system's wholeness. This shows that even after a system's disintegration the particles are not absolutely separated from one another. On the sub-quantum level both particles and together with them the whole world exist as an indivisible unit. Another example of implicative structure are the structures of thought and consciousness which are directed by the phenomenon of wholeness intrinsic to the psyche or consciousness.

Final Conclusions

The holistic idea should be clearly articulated by bringing out the relativity and non-universality of the concept of set in the description of quantum systems. The probabilities of separation of these or those elements out of a fully specified state of a system are mutually coordinated and correlated by the phenomenon of the system's wholeness and constitute the implicative-logical structure controlled by the wholeness phenomenon.

The idea of the implicative-logical organization of the probability structure of a quantum system in the pure state and of the controlling role of the wholeness phenomenon (in the redistribution of probabilities depending on this or that real experiment) is confirmed by the results of quantum-correlation experiments (for example, A. Aspect's experiments).

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(1) D.Bohm. Wholeness and the implicate order. L., 1984.

(2) V.A.Fock. Uspekhi fizicheskikh nauk, , 66, 592 (1958) (foot-note on this page).

(3). S. Kochen, Symposium of the Foundations of Modern Physics: 50 Years of the Einstein-Podolsky-Rosen Gedankenexperiment, (World Scientific Publishing Co., Singapore, 1985), pp. 151-69.

(4). A.A.Grib, "Uspekhi fizicheskikh nauk", 142, 621(1984).

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