Science, Materialism, Mysticism

Heisenberg's Principle of Indeterminacy

Q: Heisenberg's principle of uncertainty or indeterminacy has it that we can never measure with accuracy both the position and the velocity of an elementary particle. Why is this principle regarded as most revolutionary?

Not all scientists regard this principle as effecting a fundamental revolution. All agree that it marks an absolute physical limit to the measurement of two basic quantities together and that, since correct predictions demand the knowledge of both of them at the same time, we can never have anything except a play of probability at the core of our knowledge in microphysics. From these admissions it can further be said that the law of causality which in physics would make for correct predictions from an accurate calculation of the "state" of a system - that is, the position and velocity of all its parts - has no role in the description of elementary particles.

Having agreed so far, scientists start differing. Some hold the law of causality to be still in operation although we cannot make any use of it in our ultimate description. They declare: "No probability without causality." Others take probability to be an ultimate condition. The former believe that position and velocity are associated quantities which are definitely there but we cannot measure them together with definiteness. The latter say that such belief is quite arbitrary, "e basic particle being not at all one to which these associated quantities can be ascribed as in the old physics.

Several scientists argue: "If with our instruments we fail measure two quantities accurately, how does it prove them to be non-existent together in a definite form? The answer is "No refinement in our instruments will ever take ., us nearer accuracy. For the inaccuracy depends on the size of the elementary particle and on the nature of light. The universe is so made that When the light is powerful the c e s velocity is disturbed by the radiant energy and

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when it is weak we cannot observe the particle sufficiently to note its position. So, when the velocity is untouched, the position remains vague, and when the position may be clear the velocity is altered. There is no way, because of the very constitution of matter and light, to get past this dilemma. So far as observation in physics is concerned, the dilemma is irremediable. The very constitution of matter and light debars us from asserting that beyond a certain point definite position and velocity co-exist. To speak of failing with our instruments to measure them is irrelevant."

The next stage in the argument is: "The co-existence of definite position and velocity is necessary for our thought." To this the answer is: "At one time it was considered necessary for our thought to believe in a space and a time uniform throughout the universe and in a rate of motion which can be called absolute in relation to a perfectly static frame. Einstein showed that in very principle and not only in practice such concepts were for ever removed from observational verification. The constitution of the world put them beyond observation and, since physics has finally to be tested by observation or by observability in principle if not in practice, such concepts are superfluous and have no place in physical formulas. Similarly the co-existence of definite position and velocity is a concept useless in physics: it can have no function in any of our physical formulas."

At this juncture the line of argument runs as follows: "Einstein's relativity theory never did away with causality. Causality is at the bottom of all physics. Even when Heisenberg concludes from his hypothetical experiment with a particle like the electron that position and velocity cannot with definiteness be measured together he is doing it causally, for he is proceeding from premises to a conclusion. So even where causality is unobservable on account of the constitution of things, it must be posited."

Here there is a mix-up between logical causality and physical causality. Logical causality insists that there must be a sufficient reason for every statement and that certain

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antecedents being given certain inferences must be drawn. All discourse, scientific or philosophic, is based on it. But there is nothing in it to weigh the scales either for or against simultaneous definite position and velocity. What it rules is simply this: "If such position and velocity are there, then calculations of physical causality can be made; but if they are not there, then only the calculus of probability can be employed in physics." Logical causality insists that both accurate calculation and probable calculation should be thought of as resulting from a state of affairs which is sufficient ground for them. In the one case, co-existent definite velocity and position; in the other, definite velocity and indefinite position or vice versa. What actually is in nature cannot be decided by merely logical causality: where physics is concerned physical observation is the deciding factor. Logical causality is neutral as between the statements of the two conflicting schools vis-a-vis Heisenberg's principle. It is not violated by the dropping of physical causality - and by jettisoning physical causality we do not cease to be scientific, for what is at the bottom of all thought in physics is only the causality that is logical."

Heisenberg's principle is really most revolutionary. The reason why its true character is not at once understood is that its organic connection with the physical research that went before it is not properly seized. Most books start with it the topic whether definite position and velocity co-exist. But this topic did not actually arise from it. We should be mistaken in holding that prior to Heisenberg's hypothetical experiment nobody had wondered whether those two quantities could co-exist in a definite form. In fact, as soon as the inadequacy was seen of the early picture of the atom which took the atom 0 be a tiny solar system with electrons travelling in definite orbits at a definite speed around a nucleus of heavier Particles, the question came up: "Can definite statements be made concerning the position of the electrons and their velocity around the nucleus?" A whole army of physicists, "including Bohr himself who had proposed the first solar-

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system model, worked for more than twelve years and proved that such statements could only be made in macro physics: sub-atomic 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 quantities - position and velocity - could never be both stated accurately at the same time of any microphysical body. All that Heisenberg did was to sum up this discovery with mathematical precision: he said that the margin of the inaccuracy or uncertainty which is always present is invariably a function of that small but positive number which is termed Planck's Constant (roughly .000000000000000000000000006624). It is this summing up that is really his principle of uncertainty or indeterminacy.

And the experiment which he imagined with gamma rays to observe velocity and with red light to observe position is not the foundation of his principle. When people look on it as the foundation they begin asking why the mere failure of an experiment should lead to a basic revolution. Their line of argument, even so, is erroneous: we have already pointed out the error. But the error would not be committed at all if one realised that the experiment was suggested by Heisenberg to satisfy the plea that lack of observational apparatus made us conclude from those twelve years of atomic study the incompatibility of simultaneous exact position and velocity. Heisenberg defined the needed apparatus and with his experiment illustrated with finality the principle he had enunciated. The very conditions required for an appeal to observation were proved to be unobtainable in the nature of things. Resort to observation was convincingly shown to be fruitless and meaningless.

Thus, if the experiment is considered in its organic connection with physical research before it, it comes as the last and clinching step of that research and not as the firs1 and opening theme of a possible controversy. It is not a subject for fresh discussion: it resolves an old problem.

The extreme revolution which the resolution of that

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problem by Heisenberg's principle represents is our complete inability to formulate about the elementary particles the basic laws by specifying positions and velocities at any instant in the manner of classical physics: we are left eternal- , unable to describe as a precise happening in space and time what a particle does. The particle of modern physics does not occupy a particular point of space at a particular moment; it has an inherent indefiniteness which makes it escape to a small degree from the spatio-temporal scheme of our universe. Physics can still deal with it but by a new under- standing of the term "state": a "state" in the realm of quanta is an ultimate event which concerns a particle yet extends over more than one point of space and more than one instant of time and can be measured only by probabilities. The introduction of a fundamental probability amounts to an admission that in regard to the elementary particles the spatio-temporal scheme of our universe with its implication of physical causality is exceeded to a small degree.

Could we interpret this admission to mean that the physical universe is no longer a closed and self-contained system and that there is a minute yet highly significant pointer - highly significant because at the sheer basis of things - to a beyond with which physics cannot deal? Most physicists would be disposed to say No - and yet...1

POSTSCRIPT

Cosmological Uncertainty

(From "Scientific American", September 1960)

On the very largest scale, as on the smallest, man's effort to "Discover the detailed workings of nature may be frustrated

Recently Bohm has made out a plausible case for a sub-electronic world which would hold the cause of the sub-atomic, even though the indeterminacy "principle would be valid on the level of the latter. But no experimental grounds e been offered and scientists have been impressed but not convinced. Action, in science, cannot come independently of experiment - and, in the domain of theory itself, Bohm is not so cogent yet as to impress all scientists.

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by an essential principle of uncertainty. So argues the British mathematician and cosmologist William H. McCrea n recent issue of Nature.

He begins by assuming that every part of the universe interacts with every other part, and that all interacts propagate at the speed of light. If so, the form in which see distant parts of the universe is the form in which they now exerting all their influence on our local region. "Therefore we can, in principle, predict the immediate future behaviour of our own part of the universe."

The situation is quite different for regions remote from us and from each other. McCrea considers two regions, P and Q, each a billion light years from the earth and in opposite directions. We see both P and Q as they were a billion years ago. But the influence that each was exerting on the other at that time depends on their respective states two billion years earlier, about which we have no information whatever. If the universe were finite, the difficulty could eventually be overcome by continuing observations for a sufficiently long time and then making predictions for still later times. How- ever, "we almost certainly have to regard the universe as unbounded....It thus appears that there is an uncertainty in cosmology... occasioned by the fact that the speed of light is not infinite, that is complementary to the uncertainty in c atomic physics... occasioned by the fact that the quantum of action is not zero."

McCrea has calculated that the differences between the predictions of "evolutionary" and "steady-state" cosmologies lie within the limits of this uncertainty. Therefore, h suggests, the question of which cosmology is correct is inherently unanswerable. In general, we can assert almost nothing about what the universe is like at great distances ( space or time). This view "seems more satisfactory than the recent trend toward a belief that the nature of the 'whole universe has already been discovered."

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Materialism and Sense-Perception

The scientific account of the complex of agencies involved in sense- perception is worth viewing in its correct bearings on the question whether materialism is a valid doctrine.

There is a tendency today in certain scientific quarters to , . "Matter is only the version which sense-perception gives of an unknown reality. An impact comes upon the sense-organs; the nerve-terminals are stimulated; nerve- currents start moving; they reach the brain-cells and there is sense-perception as of actual objective matter existing. Now, evidently, the perception is an image. What proof have we that this image is true? Verification, in science, is always by seeing, hearing, tasting, smelling or touching. Yet, whether we see, hear, taste, smell or touch, we have nothing except sense-perception: that is, an image, in the broad connotation of the term. So there is no means of verifying sense- perception. At most we may aim at correlating the various sides of it. We cannot get beyond it. Hence we have on the one hand an image of the world and on the other the unknown world itself. Scientifically, we can be said to work not on the world itself but on an image of it produced by sense-organs, nerve-terminals, nerve-currents and brain- cells, and therefore there is no proof of the world being matter rather than a non-material reality which is imaged by us as material."

What shall be our comment on this declaration? Only one thing: it is capital balderdash. We cannot with logical consistency talk of an unknown world acting on the sense-organs Meeting the nerve-terminals and sending messages in e form of nerve-currents to the brain-cells, when clearly those very organs and terminals and currents and cells involve actual objective material existence of the precise sort which is said to be in doubt! We as good as say: "The material world as a real entity comes to be in doubt only if sense-organs' nerve-terminals, nerve-currents and brain-cells ^h are part of the same world really exist to receive the

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