Science, Materialism, Mysticism

Probability in Microphysics:

Einstein brought about in 1905 a tremendous revolution in physics when he dethroned Newton's concept of a universal static space and a time flowing uniformly everywhere - an absolute space and an absolute time in terms of which there could be a measurement of absolute motion. The principle on which this revolution was based may be stated as follows: "None but observable factors - that is, factors definable by means of physical processes, factors distinguishable by experimental operations - can be considered to be in causal dependence." Einstein showed that scientific apparatus, even if developed to the utmost perfection and given the most favourable circumstances, could never measure Newton's absolutes and he ruled that these absolutes, there- fore, should never be invoked as the cause of anything in physics.

Twenty-two years later, Heisenberg brought about another revolution which struck scientists as still more tremendous. He declared that the very notion of causal dependence and relation, the very concept of causality was about an "unobservable" which no physical processes, no experimental operations by scientific apparatus could demonstrate! Einstein's revolution was in the realm of macrophysics - the large-scale world. Heisenberg's was the outcome of studying the small-scale sub-atomic world the realm of microphysics. The centre of study was the electron, one of the ultimate constituents of the atom of matter. An early picture of the atom, which solved several problems, Was that of Bohr: it took the atom to be a tiny solar system in which the electrons revolved round a nucleus of heavier particles. In this picture, the electrons were said to be travelling in definite orbits at a definite speed, and definite statements were made concerning their positions and their

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periods of rotation. But soon the solar-system conception broke down. A whole army of physicists, including R i11 himself, worked for more than twelve years and proved that such statements could only be made in macrophysics: subatomatic events were shown to fall outside them. The relation of the electrons to the orbits of rotation within the atom was so strange that the two magnitudes - position and velocity¹ could never be both stated accurately at the same time of any microphysical body.

Heisenberg summed up this fact in what he called the "Uncertainty Principle," known also as the "Principle of Indeterminacy." He said that the more certain is our measurement of the electron's position the more uncertain our measurement of its velocity, and vice versa. When both position and velocity are measured at the same time, there is always an uncertainty or inaccuracy in either and the margin of uncertainty is invariably a function of that small but positive number which is termed Planck's Constant (roughly .000000000000000000000000006624). To illustrate his principle with finality he suggested a simple crucial experiment which would convince us that the electron's position and velocity could not ever be observed at the same time with accuracy.

He declared that to observe anything we must illuminate it. To observe the electron's position or its velocity we must throw on the electron a beam of light. There is the well- known fact that nothing smaller than the shortest wave- length of visible light can be seen by human eyes. Visible light's shortest wave-length is of violet light, but the size of the electron is even smaller. Beyond violet light there is for us darkness. This, however, cannot stop observation, for we can replace our eyes by a photographic plate which is far more sensitive than they and which can record the action of light too short-waved for us to see. But, as the wave-length gets shorter and shorter, the radiation becomes more and more energetic. When we reach the wave-length which is so

' In physics Ac term "velocity" connotes direction as well as speed.

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short that the electron is not smaller than it - the wave-length of the "gamma rays" given off by radium - and we are able to illuminate the electron and observe it with the help of a photographic plate, we reach also such energy that in illuminating the electron we administer to it a big push. Thus, when the radiation can make the electron visible, the electron's velocity is disturbed. On the other hand, if we use light of the longest wave-length - red light - we have very poor energy in the beam and there is no disturbance, but the poor energy leaves the minute electron's position extremely hazy: we are as if trying to measure with a yardstick graduated to inches an object that is millions of times smaller than an inch. So, when the velocity is untouched, the position remains vague, and when the position might be ' clear the velocity is altered. There is no way to arrive at an accurate measurement of both position and velocity at once. The crucial experiment to find whether the two magnitudes can co-exist with definiteness gives a negative result.

And, mind you, this is not the result of any defect in our measuring instruments. It is the result of the very nature of things - the nature of the electron and of light. No matter what kind of instruments we use, the failure is inevitable. The constitution of the universe is such that scientific observation will never reveal to us an electron having a simultaneous definite position and velocity any more than scientific observation will reveal Newton's absolutes. To suppose such an electron is to suppose something that has no connection with any mathematical formula we actually use in physics. If physics is to be physics and not meta- physics, the supposition is fundamentally unacceptable. All that we have simultaneously are indefinite, indeterminate, uncertain position and velocity.

Now, the principle of causality, as the physicist under- stands it, may be formulated, in the words of Ernst Zimmer, as follows: "When the state of a 'system' - that is, the position and velocity of all its parts - is known at a given moment, together with the forces which are operative in it

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and on it, the state at any other moment of time can calculated." But, if our system consists of electrons or other sub-atomic bodies, Heisenberg's Uncertainty Principle immediately puts it beyond causality, for the initial position and velocity of not one single electron can be known. Heisenberg says: )'If we state the law of causality in the form: 'If we know the present, we can calculate the future,' it is not the conclusion but the premise which is false, for we can never know the present completely in full detail." And he adds that, since all experiments are subject to the laws of micro­physics, which is the science dealing with the world's final constituents, the universal invalidity of the causal law is proved as undeniably as the universal invalidity of Newton's absolute space, time and motion.

Lest it be thought that Heisenberg brings in complete irregularity in the physical world, we should point out that such irregularity would make physics quite impossible and that what he has done is only to replace, as Zimmer puts it, the causal law by a law of a more general character which allows us to predict from a state known to us with a specific degree of uncertainty what will happen within specific limits in the future. Instead of a strict calculus of certainty we have a strict calculus of probability.

If we like we may declare that the causal law does not consist merely in our being able to predict correctly from given data but in everything having an antecedent sufficient­ly accounting for its being such and such and that the substitution of probability for certainty does not do away with causal antecedents. Well, such causality is nothing else than the demand of the reason that a conclusion must have a premise. The calculus of probability is itself a system of causal antecedents: given a particular mathematical premise, a particular mathematical conclusion must follow. Similarly, a physical event cannot happen ex nihilo: it must have a sufficient reason in the form of a particular antecedent which provides the logical ground for it. Here is logical causality. Logical causality cannot be gainsaid and Heisenberg's principle

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does not negate it. But logical causality does not require that the world should be such as to enable us to make certain or accurate predictions. It leaves room not only for the probability calculus but also for the actual existence of factors in the world which would make certain or accurate predic­tion by us of physical events impossible. To take extreme examples, the factor of human freewill or the factor of God's secret presence. Given these factors, complete accuracy of prediction by us is out of the question: inaccuracy logically follows and it reflects an element of the unpredictable in physical events. Logical causality is complete here. And if we ask what logical causality there is for God's secret presence we can answer that it is the omnipotence of an infinite self-dependent Being. Similarly we can name the logical causality of freewill by saying that it is the human soul, a spark of the Divine Being. Philosophers may argue whether human freewill and God's infinite existence are facts or else whether they are compatible with each other, but we are not now concerned with this problem. What we are concerned with is that Heisenberg's Principle leaves the concept of causal antecedents in the logical sense untouched. That is precisely his meaning when he says that the premise and not the conclusion is at fault in the statement: "If we know the present, we can calculate the future." The conclusion follows by logical causality and, provided the premise is accepted, it Cannot be denied. To deny the premise is not to negate logical causality. It is simply to deny the confident deter­minism of classical physics which held that all the factors of the physical world are knowable, in principle if not in practice, by physicists and that ultimately these factors are particles with simultaneous definite position and velocity and that therefore on the basis of the combined knowledge of these two magnitudes accurate prediction can in principle be made, prediction which would lay down the future with a cast-iron physical fixity.

Science cannot do without logical causality, but the other kind - the deterministic - is a matter of taste, of predisposition.

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It is not a necessity for scientific thinking. Nor, we may add, has it any clear basis in macrophysics as distinguished from microphysics. There is a common error that macrophysics has nothing in it to throw doubt on determinism and that all macrophysical experiments confirm determinism. But Hans Reichenbach has a very pertinent passage on this point. "It is not at all true," he says, "that we ever find strict laws in nature. For all that we observe, each time, is that a law has been approximately fulfilled; a hurled stone, a flowing electrical current, a deflected ray of light, when exactly measured, will never show the course prescribed by the mathematical formula, but there will always be little deviations, so-called errors of observation, which may be decreased by better experimental devices but can never be fully eliminated. How far, however, such errors influence the result of advance calculations can never be told with certainty. It can only be said that the errors will very probably occasion but a slight disturbance - but that is already a statement containing the concept of probability. Thus the idea of probability unavoidably enters the formulation of all laws of nature, if these laws are to be stated with complete conceptual rigour."

Science tried to raise probability to certainty by two means. If we pass to a large number of cases we change the low probability of the single case into the high probability of average occurrence. Thus the physicist, unable to say almost anything about the motion of one molecule in a quantity of gas, could make pretty confident statements about the average motion of millions of molecules. Another way of bettering probability is to look for as many factors of influence as we can and take them into account in our forecast. Thus the astronomer, in order to foretell a planet's position, considers not only the planet's own velocity and the diameter of its own orbit round the sun but also the perturbations from the gravitational force exerted by neighbouring planets. But science never succeeded in changing probability into certainty. All it could achieve was practical certainty. An

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irreducible element of probability always remained and, philosophically, there was no ground for belief that an unbounded improvement of precision could always be possible. To quote Reichenbach again: "At bottom we have here a question of a property of nature; it might well be that there is an absolute limit, short of certainty, to the increase of accuracy. In that case it would be impossible, eventually, to arrive at the making of certain predictions (or even predictions of approximate certainty)."

So, we may dismiss the claim, anywhere or at any time in science, for an actually observed or observable operation of anything beyond very high probability. Causality, as scientifically understood, has been nothing more than a fond hope: no consideration on even macrophysical grounds can scientifically be adduced against Heisenberg's conclusion. As a matter of fact, what Heisenberg asserts is just what on the ground of available scientific evidence philosophical investigation - in contrast to dogmatic scientific thought - feared light be the case.

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We have now to inquire what sort of entity is the electron or any other sub-atomic unit which lacks simultaneous position and velocity and behaves according to probability instead of causality. The calculus of probability employed by physics today is in terms of a wave-function found by Schrodinger in 1926. At one time it was thought that the electron is both a particle and a wave. Even experimental evidence appeared to confirm this view. Prof. G.P. Thomson prepared a sheet of metal, crystalline in structure and one- millionth of an inch thick, and sent a stream of electrons through it upon a photographic plate on the other side: the pattern traced on the plate was of alternate bright and dark rings - a result which only wave-motion had been credited with producing, for the dark bands would be made by the crest of one wave coinciding with the trough of another,

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thereby cancelling each other, while the bright bands would be due to the crests of two waves coinciding. Here was evidence as reliable as that obtained by photographing tracks, which could only be of particles, in the device known as Wilson's Cloud Chamber or by bombarding with electrons a sheet of glass lightly powdered with zinc sulphide crystals and proving, by the sparks produced, the electrons to be like small bullets, like tiny particles.

Physics was in a quandary. How could an electron be a particle in some experiments and a wave or a "packet" of waves in others? It was pointed out that a universal property of waves is to scatter through space. Ehrenfest calculated that a packet of waves occupying the dimensions of a proton would double its linear dimensions in a ten-million-millionth part of a second, so that obviously such a system of waves would soon grow too big to show the spatial properties of an elementary particle. Even if a pattern of waves could be formulated which would not rapidly scatter while a single electron or proton was pursuing an undisturbed path, the waves would scatter as soon as the particle interacted with other matter: we have direct experimental evidence of this in the photographed patterns produced as if by wave-motion. Thus, if the waves represented, as Schrodinger had originally conjectured, the electric charge of a proton or electron, how would we account for the observational fact that this charge preserves itself intact and the proton and electron maintain their identity and there is not the least scattering?

Could it be that the wave-equation was merely a mathematical construction to correlate certain empirical observations in which particles somehow seemed to act like waves? The doubt was strengthened when it was dear that according to Schrodinger's wave-equation the wave of every single electron needed the whole of three-dimensional space! So two electrons need a space of six dimensions, three a space of nine dimensions and a small crowd of electrons a space of thousands of dimensions! Such waves can best be regarded as not existing anywhere except in a mathematician's conceptual

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space which can be allowed any number of dimensions. All considerations prompted a purely mathematical view of the waves.

Here two physicists. Born and Jordan, stepped forth and worked out the wave-equation on a statistical basis. Today no physicist ascribes to any action of actual physical vibrations the bright and dark rings photographically produced as if by wave-motion. Thus de Broglie, himself the first scientist to speak of matter-waves and start the train of thought which ended in Schrodinger's equation, remarks at the end of his book Matter and Light (page 256) that the waves have nothing except a symbolic character and only appear to be physical reality and that after years of discussion scientists have found it impossible to regard them as physical. Millikan has the same thing to say on pages 267-69 of Electrons (+ and —), Protons, Photons, Neutrons, Positrons and Cosmic Rays. Einstein and Infeld write on pages 305 and 307 of The Evolution of Physics: "The waves provide only the mathematical means of answering questions of a statistical nature.... The only physical significance is that they enable us to answer sensible statistical questions in the case of many particles as well as one." C. Molle and Ebbe Rasmussen in The World and the Atom (page 110) sum up succinctly the attitude of physicists towards the waves: "The waves are only a convenient method for expressing how the electrons behave while passing through a crystal, the different interference maxima (bright rings) being merely the places which in such an experiment are struck by the electrons, while the minima (dark rings) are the places where no electrons occur."

In general terms we may state the statistical view thus:

The concentration or diffusion of the waves is proportional to the greater or lesser probability of a particle being in a certain place. The concentration or diffusion is not of any "density of electric charge but of probability. Similarly, the uniform spreading of the waves is not such a spreading of electric energy but a uniform distribution of the probability that the particle may be anywhere. The waves are probability

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waves, an instrument of calculation, a symbolic representation of our knowledge. The reason why a symbolic wave can appear to behave like a physical entity is that, in all experiments in which it so appears, large numbers of particles are involved, and what we observe is a statistical distribution. To take an elucidatory comparison given by Dingle: we may assess the probability that a single individual will be found at a particular place in a street. Let us suppose the probability is greatest at the centre and falls off steadily away as we approach either end. The probability distribution can then be represented graphically by a wave curve but it will have no physical existence when only one individual is in the street. If 10,000 individuals are there, however, the wave will be visibly displayed by their distribution, and, taken as a whole, may be said to have a physical existence. Our knowledge by probability concerning the individual becomes by analogy from the crowd a physical characteristic of the man. But we must remember that the physical characteristic by analogy has only a statistical significance and is ultimately a mathematical invention and there is no actual wave 'out there'."

The explanation offered by Born and Jordan not only resolves the contradiction between wave and particle but shows itself to be just what one would expect on account of Heisenberg's Principle. If definite position leaves velocity utterly indefinite and vice versa, then in an experiment like Prof. Thomson's in which there is a crystalline sieve with holes just big enough to let one electron pass through each at a time and thus accurately define its position we can never know anything as to where the electron will strike the photographic plate since the speed and the direction - the two components of velocity - must become quite indefinite. Perforce we have to do with probability derived from studying the pattern formed by aggregates of electrons falling on the plate. The wave-equation describes the pattern, but Heisenberg's Principle is the rationale of the wave-equation and renders intelligible why it is an equation not about actual waves but about probabilities of particles.

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So what is "out there" is only the particle. However, let us not take this statement too simply. Since the laws of wave- mechanics relate fundamentally to crowds and not individuals and since the elementary laws about the particle cannot be formulated by specifying positions and velocities at any instant in the simple manner of classical physics, we are left eternally unable to describe as a precise happening in space and time what a particle does. The single particle, therefore, is not like the particle of classical physics. Some scientists hold that there is no real difference so far as position and velocity are concerned and that the particle of modem physics is always in a certain position and is moving at a certain velocity but only our knowledge of that position and velocity is not precise because any attempt we make to measure them necessarily interferes with them. These scientists would say that causality is really operative although we are confined to the probability calculus. But the bulk of opinion is against them: the whole methodology of physics runs counter to their assumption. The basis of modem physics - the rejection of what is "unobservable" in very principle - will give them no standing ground.

What the basis of modem physics permits is best indicated by an analogy employed by Whittaker on page 145 of From Euclid to Eddington. "Suppose," writes Whittaker, "that a child with a penny comes to an automatic machine which supplies chocolate when the penny is put in one slot, and sweets when the penny is put in the other slot. Since he has only one penny, he can get either chocolate or sweets, but not both; from the fact that he can get either at will, is he justified in concluding that they are both present in the machine? Not necessarily; for it is possible to imagine that there is a kind of paste in the machine which is converted into chocolate by his inserting the penny into one slot and into sweets by his inserting the penny into the other. If this latter explanation is correct, then it is possible to imagine the machine fitted with a number of other slots, such that by inserting the penny into any one of them a confection is

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obtained which is intermediate in some proportion between chocolate and sweets. This is analogous to the situation which exists in atomic physics. If we consider one of the elementary entities we can have an accurate knowledge of its position, combined with complete ignorance as to its velocity, or we can have an accurate knowledge of its velocity, combined with complete ignorance as to its position, or we can have a simultaneous partial knowledge of both, but there is no justification for assuming that the entity is a particle in the old sense, possessing simultaneously an exact position and an exact velocity. We have no right to postulate the existence of entities which lie beyond the knowledge actually obtainable by observation, and which have no part in the prediction of future events. Thus the classical concept of a particle must be discarded: in its stead there has been introduced a new fundamental element in the description of the external world, which is called a state."

On page 146 Whittaker has some further illuminating remarks to make: "The method of theoretical physics is essentially to analyse a complicated situation into an aggregate of elementary situations, each of which is governed by some simple law. Thus in the ordinary Newtonian mechanics of a system of bodies the interactions of the bodies are analysed into forces between pairs of particles; and indeed throughout classical theory the ultimate elementary bodies are generally conceived as particles, each occupying a particular point of space at a particular moment, so that the concepts by aid of which the resolution is effected are the concepts of space and time. The great discovery of the present century has been that in atomic physics this method of analysis is wrong: the blurring or imperfect definition, which has been described, simply expresses the fact that the true elementary constituents of nature have not the proper- ties characteristic of Newtonian particles. There are events which extend over more than one point of space and more than one instant of time and which yet are ultimate events: that is, they cannot be analysed into anything simpler than

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themselves. These are precisely the 'states' of quantum mechanics."

To distinguish the modem particle from the classical and invest it with the meaning of the term "state", we may coin the portmanteau word "staticle." This particle is inherently devoid of factors which would allow us to apply the law of causality to physical phenomena, and there is, within specified limits, an inherent indefiniteness in nature. The probability law must be accepted as primary: it cannot be superseded by a more fundamental law of a deterministic kind. To quote Whittaker again: "Kant said, quite justly, that regularity in occurrence is a necessary presumption of the science of physics. He supposed (erroneously) that these regularities must always be of the kind that we meet with in molar (macroscopic) physics, namely, that they must be deterministic as regards individual events; but this is not so. The regularities on which the science of physics is based are statistical regularities, and do not involve complete determinism."

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Now the question is: How are we to understand statistical regularities, how are we to conceive the probability calculus functioning? According to this calculus, when we are concerned with a large number of "staticles" the indefinitenesses or unpredictable variations of individual "staticles" reduce themselves to an average of uniformity so that what is a marked probability for one "staticle" becomes nearly a certainty for millions and the general indefiniteness becomes "imperceptible to the point nearly of non-existence. The Practical certainty that is the result is sought to be explained °n the analogy of the mathematics of coin-tossing. Provided the conditions of the toss remain the same throughout, if we toss a coin twice the odds are three to one against it coming "heads down both times; seven to one, if we toss it three times; fifteen to one, if four times; until, if we toss it a million time, the odds against it being always heads becomes

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almost inconceivably great and we shall have as good as equal chances of heads and tails. An average of uniformity will be attained - the uncertain variations will practically disappear by cancelling one another and also accurate prediction will be possible. Similarly, predictions such as of eclipses are said to be correctly made because, although the individual "staticles" composing the physical bodies taking part in an eclipse have an unpredictable nature, a huge crowd of these "staticles" are involved. In other words, large-scale phenomena seem to be governed practically by causal laws simply on account of an enormous quantity in them of indefinite "staticles".

This description of uncertainty getting metamorphosed into what seems its very opposite is open to serious criticism. But before we criticise, it may be mentioned that we are not talking of "subjective" probability. The abandonment of the causal law and the acceptance of indefiniteness in nature itself signify that the merely probable correctness of prophesies as to nature is here not due just to human ignorance failing to measure with accuracy a causal operation. Probability is "objective," and statistical regularities such as those of aggregates of electrons are a fundamental trend in natural events. But the fact that a statistical regularity, for all its apparent certainty, remains nothing else than a matter of extremely high probability means that at any moment what is assuredly predicted may not come to pass. Actually the million tosses of a coin might all in succession give us heads! This is always on the cards in a probability calculation. And it is so not because any outside forces might work on the situation. No matter if the conditions of the toss are the same throughout, the unexpected can happen. Probability never rules out the unexpected. Nor is there the least force in it to relegate the unexpected to some remote future and prevent it from occurring the very next minute. If probability by itself were the law of the universe, there would be no explanation of the large uniformities we observe in macrophysics. Automatically and without needing extraneous influence the

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predicted eclipses should on occasion show sudden non- occurrences and even the sun should be seen as not rising one time or another during the long procession of the ages. Why is there such marked regularity in nature? The probability calculus, as illustrated by coin-tossing, has no satisfying answer.

To explain the marked regularity in nature a comparison is also often drawn between it and the data on which life- insurance companies proceed. The actuary is able to predict that so many people of a given age will die each year, though the death of any individual is unpredictable. From a host of accidents a statistical law of probability emerges, by means of which prediction is possible. But would the actuary's generalisations hold good unless the individual deaths from road accidents, diseases and suicides, however unpredictable, were as a matter of fact somehow systematic? Is it logical to expect regularity in the mass without postulating regularity in detail? If we argue that human beings have freewill and that therefore the unpredictable of individual deaths is, in part at least, undeniable even though the actuary's general prediction is correct, we do not yet show how the partially unpredictable events get systematised on the whole. In forming a mass, individual events with some degree of unpredictable ness owing to freewill can only go on aggregating their degrees: there is no reason for practical certainty of forecast to result. The overall regularity must involve a process controlling the individuals. This logic is irrefragable - from human beings down to electrons. Of course, the phrase 'process controlling the individuals" or the phrase "regularity in detail" does not mean that every electron behaves altogether in the same manner, but it does mean that the electron has a behaviour not independent of a systematising and integrating factor, for which the concept of probability, as commonly advanced, has no place.

By analogy with neither coin-tossing nor insurance company procedure can the probability calculus serve to Provide a rationale for the marked regularity in nature. Must,

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then, the old causality come back - operating secretly? Must we endorse the opinion of D.J. Struik: "Statistical regularity is a result of causal relationships. No probability without causality"? Well, the old causal law cannot be accepted ~ unless we wish to negate the very principle on which modem physics is based. The negation would not only bring back the causal law but at the same time shut out both the confirmed contents of relativity theory and the proved findings of quantum study. A return to classical physics is impossible: a specific indefiniteness at the bottom of things has to be retained and also made to cope with the practical definiteness we meet with in the case of large aggregates of nature's fundamental constituents. But if the probability- concept in its usual form will not do and the causal law is taboo, what is to be postulated?

The only answer is that the probability-concept has to be infused with a new meaning. Into the initial indefiniteness as well as into the ultimate regularity a common factor is to be read by which they get connected - a strange factor X working both in the details and in the ensemble and some- how controlling the variations of the details so as to produce regularities in the ensemble although in the details there seems nothing to bring into being any limitation. Since probability is the law of the entire universe, X must be in operation everywhere with its dual function - it must be the single activity which by that dual function is responsible for our universe proceeding as it does. In the absence of determinism no less than of other logical alternatives on the purely physical level, X must be a free self-governing factor - an apparent randomness within a self-specified range, which is yet systematic and integrative by its own uncompelled nature. And this freedom implies that the regularities we observe are not themselves something we can always count upon: at any time X may cease to make predictability possible: the probability calculus is only our mathematical reading of its general process - this calculus cannot be a binding law.

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These are the terms to which modern physics will have to be reduced in the problem of probability. Without them the old deterministic causal law cannot be convincingly abandoned. Curious indeed are the terms and there may be a feeling that it would be better for science if the freely self- governing factor X could be avoided, for X unmistakably suggests some basic World-Will secretly deployed according to its own conscious plan. But, really, to accept this factor is nothing contrary to the temper of modem physics. All that we have to ensure is that the principle of rejecting the unobservable is not broken. That principle is upheld so long as no observable is denied. The law of causality can be brought in only by denying the essential unpredictable ness of observable primary phenomena. What we have done is just to supply the ground, the sufficient reason, for the observables concerned being what they are. They are correlated without being denied. Physics illegitimately becomes metaphysics when observables, instead of being explained, are explained away. If, without denying or quibbling over them, we correlate them by a concept whose full significance may not be compassed by scientific apparatus and may even involve a sort of mystical content, we do not act the meta- physician in a manner which the guiding principle of physics rules out - provided, of course, this concept can exclusively hold the field.

There seems to be no sign of any other concept adequately solving the difficulties we have raised. Thus quite legitimately we may say that modem physics suggests a universal Intelligence hidden at the very heart of things, acting elusively through all entities - obscurely in material forms and more overtly in organic nature and with a semi- 'revelation of itself in humanity.

The tracing of that universal Intelligence's elusive power through the probability calculus illuminates also the hints found of a mysterious presence through the postulate of the staticle". At once we realise the significance of the postulate. For, the elementary and primal body or event which

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bafflingly extends over more than one point of space and over more than one instant of time and thus escapes all final analysis by physical concepts of space-unit and time-unit - what else can this "staticle" with its inherent indefiniteness and natural indeterminacy be except a free transcendent Being's self-manifestation in the terms of microphysics -

A magic's process in a magical space,

An unintelligible miracle's depths

Whose source is lost in the Ineffable?

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