Contents of this paper

III. Quantum Correlation viewed from the Philosophy of Organism

The peculiarity of quantum correlation is caused by the so-called "the collapse of the wave function". One of the unsolved problems of quantum mechanics is about the nature of this discontinuous phenomenon. The usual framework of quantum theory does not describe the process of collapse itself but simply accepted it as the result measurement in the statistical data of observation. In other words the collapse of the wave function belongs, not to the object language of quantum formulae, but the meta-language of quantum mechanics which correlates mathematical formula and experimental data. Many physicists tried to enlarge the framework of quantum mechanics enough to give a unified description of observer and observed, i.e. microscopic measured system and the macroscopic measuring apparatus, but there seems not to be an unanimous resolution of this conundrum.

d'Eespagnat pointed out the enigma of the "collapse of the wave function" follows : ⁽²²⁾

The puzzle with which we have to struggle is constituted by the fact that, since the wave function is a non-local entity, its collapse is a non-local phenomenon. According to the formalism, this phenomenon propagates instantaneously. In that sense we may say that the wave packet reduction is a non-covariant process. Again, this would create no difficulty if, like the reduction of probabilities in classical phenomena, this collapse were of a purely subjective nature. But we have seen quite strong arguments in favor of the thesis that it is not.

d'Espagnat's comment that the wave collapse is not to be solved by a subjective interpretation of probability is important, for it excludes an easy "solution" of the conundrum by appealing to our ignorance of initial conditions. Certainly, if we get a new information about the system, then the probability distribution of quantities which characterize the system changes discontinuously. The discontinuous change of quantum physics cannot be explained away by this kind of probabilistic arguments. Such general arguments are unsatisfactory because they do not take into consideration the peculiar characteristics of quantum mechanical algorithm of probability. The probability wave and the probability amplitude represented by a complex number were totally unknown before quantum physics. They behave in the very inconceivable way as if they violated classical logic.

For example, the famous double slit experiment shows that even in the case of only one particle, say a photon, the interference occurs between two mutually exclusive possibilities i.e. the possibility of the same particle's going through one slit A and the alternative possibility of its going through another slit B. So if we represent the third event, say the effect of the photon on the photographic plate with C, then has been experimentally confirmed, which violates the distributive law of classical logic.

Finkelstein stresses the need of quantum logic as a non-Aristotelian logic in the description of the microscopic world just as we need a non-Euclidean geometry in the theory of general relativity.⁽²³⁾ I prefer to say that if we need quantum logic, then it must be a kind of modal logic with the distinction of real (objective) possibility and actuality. In the above example of the double slit experiment, describes not an actuality but a real possibility whereas both and describe two actualities which are mutually exclusive. In the Whiteheadian terminology, the transition from the disjunctive many to the conjunctive one does not follow classical logic because the interference of alternative possibilities really occurs.

This phenomenon of probability interference shows that we have to face objective probability reflecting the experimental situation rather than subjective one reflecting only our ignorance of the determinate fact. In other words real possibility and actuality are inseparable with each other in quantum physics, and we must treat the collapse of the wave function as the objective transition from real possibility to actuality.

The next Problem is about the quantum transition itself. If the collapse of wave function is an objective phenomenon, then is it "an action at a distance" i.e. a non-covariant phenomenon which happens instantaneously This problem is crucial to our consideration of the Bell correlation and the theory of relativity. In the section II we confirmed the fact that quantum correlation and the principle of relativity are compatible, and we need not explain quantum correlation as the unilateral causal effect with the superluminous speed. Einstein's theory of relativity was more progressive than Lorentz's theory of aether in that Einstein introduced into physics a radically new perspective in which space and time are non-separable with each other.

It is regrettable that many discussions of physicists about the collapse of the wave function presuppose only non-relativistic framework. The "simultaneous" correlation would be meaningless in the relativistic framework, because such a terminology implicitly assumes that there exists only one time-system of classical physics. The non-relativistic quantum physics does not treat space and time in their non-separable unity. Time appears only in the form of a parameter and does not take the role of operator corresponding to an observable quantity whereas spatial coordinates are permitted status of operators which characterize the quantum system. So if we describe the collapse of the wave function in the non-relativistic framework, we must say that it happens instantaneously, i.e. non-locally with respect to space.

The dubious scenario roughly runs as follows : if the quantum system prepared at the time t₁ is measured at t₂ , it changes its states continuously and causally between t₁< t < t₂ according to Schroedinger's equation, but at the moment of t₂ the discontinuous irreversible event called "the collapse of the wave function" happens and its effects propagates instantaneously with the super-luminous speed. The above picture is not relevant to the relativistic concept of space-time, because the very concept of simultaneity and instantaneous transmission does not make sense. The non-separability of time from space means that non-locality of the collapse should be accepted, not only with respect to space but also with respect to time. The reason why temporal non-locality, more exactly spatio-temporal non-locality has been ignored may be simply that the collapse of the wave function has been discussed mainly in the non-relativistic framework. Einstein himself seemed to anticipate the problematic of spatio-temporal non-locality in his criticism of the indeterminacy principle, for he pointed out that "if we accept quantum physics, then it becomes impossible to restrict the indeterminacy principle to the future ; we must admit the indeterminacy of the past as well."⁽²⁴⁾

This criticism was not so famous as the EPR argument, but it is of decisive importance when we discuss the collapse of the wave function as a non-local phenomenon in space-time.

An example of the indeterminate past was given by Wheeler in his famous discussion of the "delayed choice" experiment.⁽²⁵⁾ We may use the same diagram to explain this experiment. In this diagram we assume that the present choice is made at A₃. The experimenter at A₃ can choose for one photon either the mode of non-interference or the mode of self-interference even after the photon has passed through A_l or A₂. In this experiment, whether the photon has passed through (either A_l or A₂) as a particle, or through (both A₁ and A₂) as a wave depends on the present choice made at A₃. Before the decision at A3 the location of the particle was essentially indeterminate. What we can say of past space-time and past events is decided by choices made in the near past and now. Wheeler discussed the possibility that the phenomena called into being by the present decision can reach backward in time, even to the earliest days of the universe. The above example shows that it makes sense to state that events occur in the four dimensional framework of space-time. This occurrence itself does not take place in time as the fourth coordinate of space-time.

In Einstein's theory of relativity the concept of events is static in the sense that an event simply is and occupies a determinate location without any regard to other regions of space-time sub specie aeternitatis. In the quantum indeterminism, on the other hand, the modified concept of events is dynamic in the sense that an event happens in the extensive continuum of space-time. We need not postulate, as Stapp did, that all events of the whole universe constitute the well-ordered sequence with respect to this kind of happening in space-time, because it would make geneses of events subordinate to space-time coordination to make becoming of events the fifth coordinate. The delayed choice experiment cannot be explained away by the introduction of anything like absolute time-order because any theory compatible with relativity must retain the order of causality within a light cone.

We cannot call the delayed-choice "retroactive causality" because it does not make sense to say that we can "change" the past if we mean by the past something determinate ; rather we should say that the past in the level of quantum description cannot be considered as totally determinate. The following analysis of quantum correlation is similar to that of Whitehead's analysis of "symbolic reference" though Whitehead seems to use this term to explicate the structure of perception only in the high-grade organisms such as a human being. As the wave function is an essentially non-local relational entity, the world itself has the structure of symbolism as well as that of causality.

The main difference of the proposed model from the Whiteheadian ontology is that this model does not take a single quantum event as the totally determinate individual. The specificity of any attribute of the quantum event is, as Shimony clearly showed,⁽²⁶⁾ always attained at the price of indefiniteness of other attributes on account of the indeterminacy principle. Every event is complementarily described as an entity with respect its actuality, and as a locus with respect to its potentiality. An event is a spatio-temporal entity, and a material body corresponds to the nexus of events (world-tube) which has various characteristics such as energy, momentum, and other observable physica quantities. It is essential in this organic model that observables are adjectives of event-nexus with alternative selective patterns of perspectives.

Two "elementary particles of the same kind are not two separate substances, but the same adjective which can have two contexts of actualization in different events. The fundamental relation of events is called "self-projection". This term i introduced for the purpose of explaining both objective and subjective aspects which necessarily emerge in quantum organism, but it should not be understood in psychological sense in which the self-projection of an observer has no objective correlate. The self-projection which I mean is a physical relation between events and signifies the organic unity between the observer and the observed. We cannot observe microscopic events without their self-projections in the macroscopic measuring apparatus. What we observe, however, is not a mere shadow of the separate self-existing substance, but in one sense a thing itself because every thing can exist only in the complex network of self-projections of events. What we observe depends on our choice of measuring apparatus which reciprocally projects itself in the microscopic events by influencing the possible pattern of actualized contingency.

First I will sketch the formal structure of self-projection ; a, b, c, signify events which, as loci, "mirror" the universe according to their own perspectives, and as entities, project themselves in every loci in the universe. There are two modes of self-projection : causal efficacy and mutual immanence.

a < b : a projects itself into b in the mode of causal efficacy

: a projects itself into b in the mode of mutual immanence

The mode of causal efficacy is cumulative ; it is non-reflexive, non-symmetrical and transitive :

(1) (a)(a<a)
(2) (a,b)(a<bb<a)
(3) (a, b, c) ((a<b)(b<c)(a<c))

The mode of mutual immanence is reflexive, symmetrical, and transitive ;
(4) (a)(aa) (5) (a,b)(abba) (6) (a, b, c) ((ab)(bc)(ac))

Let a, b, g signify classes of events. We can define the relativistic concept of the past, the future, and the contemporaries of an given event in terms of the self-projection in the mode of causal efficacy :

Def. P(a)={x | x<a}	P(a) is called the (causal) past of a
Def. F(a)={x | a<x}	F(a) is called the (causal) future of a
Def. aCb(a<b)(b<a)	a is contemporaneous with b

As the relation of contemporaneity is not always transitive, the existence of the uniquely-defined present of a given event is not guaranteed by the theory of relativity. We can introduce something like a cosmological "present" in terms of a maximum class of mutually contemporary events instead

Def. If a class d of events satisfies the following conditions, it is called a contemporary duration of the universe :

(1) (a, b) (adbdaCb (2) (a, b) (adaCbbd)

The relativity of simultaneity means that there are an infinite number of possibilities for a contemporary duration of the universe. As the arrow of local causality always passes from the past to the future in every frame of reference, it cannot explain the quantum correlation of the Bell experiment which holds between two contemporaries. The contemporaneity as defined above is essentially a negative (derivative) relation and also irrelevant to the explanation of positive correlation in quantum physics. The experimental test of Bell's theorem requires something positive to cover such a correlation. Self-projection in the mode of mutual immanence is introduced to satisfy this requirement. This mode should be non-causal in the sense that it does not pass immediately from the past to the future, but signifies a kind of mutual interpenetration among events in terms of which a composite system behaves as if it were one individual. Causal efficacy ranges from causal immanence to causal influence.

Causal immanence holds between two temporally separated events in the isolated microscopic system with a small number of degrees of freedom, when the causal influences from the outside are negligible. The relation of causal immanence is the basis of a deterministic description of the microscopic system before its interaction with the measuring apparatus.

The causal efficacy from the macroscopic system with a great number of degrees of freedom is called causal influence. It is practically impossible to give a deterministic description of the system on the basis of the exact control of causal influences, which only permit statistical treatment of complex thermo-dynamical processes with an increasing entropy. The irreversible process of quantum measurement, however, cannot be identified with the entropy-increasing process of thermodynamics, as Wigner showed in his argument against Daneri-Loinger-Prosperi's theory of measurement.⁽²⁷⁾ When a and b project themselves into each other in the mode of mutual immanence, they behave as if they were one individual on account of mutual immanence (the non-separability of quantum events). Even when the two loci of a and b are spatially separated, these two loci as potentialities have an internal relation with each other with regard to certain characteristics (e.g. polarization or spin).

The mutual immanence disappears when the system is causally influenced from the outside system. The collapse of the wave function of a composite system may give a distant simultaneous correlation when self-projections between contemporary parts of the system pass from the mode of mutual immanence to that of mutual transcendence (the disappearance of the term of phase interference between them). Every event is organically related with the whole universe by symbolic correlation which integrates the two modes of self-projection. The distant correlation h quantum physics holds between two contingent events with the same causal past immanent in both. This correlation does not mean the superluminous sending o information in terms of causality. but signifies the relation of mutually self projecting events which constitute the organic system. This system integrates two different modes of self-projection in the presented duration defined by the measuring apparatus. The whole setting of the measuring apparatus determines the kind o simultaneous correlation which holds between contingent patterns of physical value, measured in both parts. Each of two events with the same immanent causal past can be seen as the symbol of the other as if they were two sides of the same coin.