Arthur Stanley Eddington
In the early 1920's, Arthur Stanley Eddington established himself as the leading interpreter of the new theories of relativity. His astronomical measurements of light bending as it passes the sun had confirmed Albert Einstein
's general relativity theory. And his popular interpretations of these difficult physical theories made Eddington, as well as Einstein, widely known to the general public.
Both special and general relativity are deterministic
theories. Special relativity is especially so, with some interpretations saying that the fourth dimension of time is like the other three, already there, so the future already exists. In his Gifford Lectures of 1927, Eddington had described himself as unable "to form a satisfactory conception of any kind of law or causal sequence which shall be other than deterministic
A year later, in response to Werner Heisenberg
's uncertainty principle, Eddington revised his lectures for publication as The Nature of the Physical World
. There he dramatically announced "physics is no longer pledged to a scheme of deterministic law
." He went even farther and enthusiastically identified indeterminism
with freedom of the will
"It is a consequence of the advent of the quantum theory that physics is no longer pledged to a scheme of deterministic law...we may note that science thereby withdraws its moral opposition to freewill." (The Nature of the Physical World, 1928, p.294-5)
"The indeterminacy recognised in modern quantum theory is only a partial step towards freeing our actions from deterministic control." (The Nature of the Physical World, 1928, p.313)
Eddington wrote an essay in 1932 on the role of indeterminism in the mind.
Mind and Indeterminism
I have, perhaps fortunately, left myself no time to discuss the
effect of indeterminacy in the physical universe on our general
outlook. I will content myself with stating in summary form the
points which seem to arise.
(1) If the whole physical universe is deterministic, mental decisions
(or at least effective mental decisions) must also be predetermined.
For if it is predetermined in the physical world, to which
your body belongs, that there will be a pipe between your lips on
January 1, the result of your mental struggle on December 31 as to
whether you will give up smoking in the New Year is evidently
predetermined. The new physics thus opens the door to indeterminacy
of mental phenomena, whereas the old deterministic physics
bolted and barred it completely.
(2) The door is opened slightly, but apparently the opening is not
wide enough. For according to analogy with inorganic physical
systems we should expect the indeterminacy of human movements
to be quantitatively insignificant. In some way we must transfer
to human movements the wide indeterminacy characteristic of
atoms instead of the almost negligible indeterminacy manifested by
inorganic systems of comparable scale. I think this difficulty is not
insuperable, but it must not be underrated.
(3) Although we may be uncertain as to the intermediate steps we
can scarcely doubt what is the final answer. If the atom has
indeterminacy, surely the human mind will have an equal indeterminacy;
for we can scarcely accept a theory which makes out the
mind to be more mechanistic than the atom.
(4) Is the human will really more free if its decisions are swayed
by new factors born from moment to moment than if they are the
outcome solely of heredity, training and other predetermining causes ?
On such questions as these we have nothing new to say. Argument
will no doubt continue " about it and about ". But it seems to me
that there is a far more important aspect of indeterminacy. It makes
it possible that the mind is not utterly deceived as to the mode in
which its decisions are reached. On the deterministic theory of the
physical world my hand in writing this address is guided in a predetermined
course according to the equations of mathematical
physics; my mind is unessential-a busybody who invents an
irrelevant story about a scientific argument as an explanation of
what my hand is doing-an explanation which can only be described
as a downright lie. If it is true that the mind is so utterly deceived
in the story it weaves round our human actions, I do not see where
we are to obtain our confidence in the story it tells of the physical
Physics is becoming difficult to understand. First relativity
theory, then quantum theory, then wave mechanics have transformed
the universe making it seem ever more fantastic to our
minds. Perhaps the end is not yet. But there is another side to
this transformation. Naive realism, materialism, the mechanistic
hypothesis were simple; but I think that it was only by closing our
eyes to the essential nature of experience, relating as it does to the
reactions of a conscious being, that they could be made to seem
credible. These revolutions of scientific thought are clearing up the
deeper contradictions between life and theoretical knowledge, and
the latest phase with its release from determinism marks a great step
onwards. I will even venture to say that in the present theory of
the physical universe we have at last reached something which a
reasonable man might almost believe.
In the mid-thirties, Eddington was a bit more circumspect, no doubt because some philosophers, led by L.Susan Stebbing
, had been quick to attack him. She argued in her book Philosophy and the Physicists
that a "free electron" has nothing to do with human freedom.
Eddington argued more cautiously,
"The revolution of theory which has expelled determinism from present-day physics has therefore the important consequence that it is no longer necessary to suppose that human actions are completely predetermined. Although the door of human freedom is opened, it is not flung wide open; only a chink of daylight appears." (New Pathways in Science, 1935, p.87)
"I would even say that in the present indeterministic theory of the physical universe we have reached something which a reasonable man might almost believe." (New Pathways in Science, 1935, p.91)
Eddington was apparently unaware of the work of William James
or Henri Poincaré
to make deliberation a two-stage process - first random possibilities, then a de-liberate
decision, first chance, then choice.
A decade after embracing indeterminism and just a few years before his death, Eddington in his 1939 book The Philosophy of Physical Science
reluctantly concluded there is no "halfway house" between randomness and determinism - an echo of David Hume
's "no medium betwixt chance and an absolute necessity."
"There is no half-way house between random and correlated behavior. Either the behavior is wholly a matter of chance, in which case the precise behavior within the Heisenberg limits of uncertainty depends on chance and not volition. Or it is not wholly a matter of chance, in which case the Heisenberg limits...are irrelevant." (The Philosophy of Physical Science, 1938, p.182)
The Cogito two-stage model
of human freedom is in many ways the "halfway house" that Eddington could not see, combining limited forms of determinism and indeterminism.
Eddington succumbed to the standard logical argument against free will
. He thus left himself open to the charge since Epicurus
’ time, that chance could not be identified with freedom. He was apparently unaware of the work of William James or Henri Poincaré to make deliberation a two-stage process
- first the random generation of alternative possibilities, then an adequately determined (by reasons, motives, etc.) choice.
In the end, Eddington may have considered some sort of dualistic
transcendent (metaphysical) explanation.
"There is in a human being some portion of the brain, perhaps a mere speck of brain-matter, perhaps an extensive region, in which the physical effects of his volitions begin,." (The Philosophy of Physical Science, 1938, p.182)
This sounds too much like the pineal gland of Descartes
' dualistic mind-body
distinction. Such metaphysics is unnecessary, as basic quantum physics is all that is needed for liberty
, and statistical regularity all that is needed for adequate determinism
The Nature of the Physical World, pp.74-75, 105
The practical measure of the random element which can increase in the universe but can never decrease is called
entropy. Measuring by entropy is the same as measuring by the chance explained in the last paragraph, only the unmanageably large numbers are transformed (by a simple formula) into a more convenient scale of reckoning. Entropy continually increases. We can, by isolating parts of the world and postulating rather idealised conditions in our problems, arrest the increase, but we cannot turn it into a decrease, That would involve something much worse than a violation of an ordinary law of Nature, namely, an improbable coincidence. The law that entropy always increases- the second law of thermodynamics - holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - then so much the worse for Maxwell's equations. If it is found to be contradicted by observation - well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation. This exaltation of the second law is not unreasonable. There are other laws which we have strong reason to believe in, and we feel that a hypothesis which violates them is highly improbable; but the improbability is vague and does not confront us as a paralysing array of figures, whereas the chance against a breach of the second law (i.e. against a decrease of the random element) can be stated in figures which are overwhelming.
I wish I could convey to you the amazing power of this conception of entropy in scientific research. From the property that entropy must always increase, practical methods of measuring it have been found. The chain of deductions from this simple law have been almost illimitable; and it has been equally successful in connection with the most recondite problems of theoretical physics and the practical tasks of the engineer. Its special feature is that the conclusions are independent of the nature of the microscopical processes that are going on. It is not concerned with the nature of the individual - it is interested in him only as a component of a crowd. Therefore the method is applicable in fields of research where our ignorance has scarcely begun to lift, and we have no hesitation in applying it to problems of the quantum theory, although the mechanism of the individual quantum process is unknown and at present unimaginable.
Primary and Secondary Law. I have called the laws controlling the behaviour of single individuals "primary laws", implying that the second law of thermodynamics, although a recognised law of Nature, is in some sense a secondary law. This distinction can now be placed on a regular footing. Some things never happen in the physical world because they are
impossible; others because they are
too improbable. The laws which forbid the first are the primary laws; the laws which forbid the second are the secondary laws...
Suppose that we were asked to arrange the following in two categories –
distance, mass, electric force, entropy, beauty,
I think there are the strongest grounds for placing
entropy alongside beauty and melody and not with the
first three. Entropy is only found when the parts are
viewed in association, and it is by viewing or hearing
the parts in association that beauty and melody are
discerned. All three are features of arrangement. It is
a pregnant thought that one of these three associates
should be able to figure as a commonplace quantity of
science. The reason why this stranger can pass itself
off among the aborigines of the physical world is, that
it is able to speak their language, viz. the language of
arithmetic. It has a measure-number associated with it
and so is made quite at home in physics. Beauty and
melody have not the arithmetical pass-word and so are
barred out. This teaches us that what exact science looks
out for is not entities of some particular category, but
entities - with a metrical aspect. We shall see in a later
chapter that when science admits them it really admits
only their metrical aspect and occupies itself solely with
that. It would be no use for beauty, say, to fake up a
few numerical attributes (expressing for instance the
ideal proportions of symmetry) in the hope of thereby
gaining admission into the portals of science and carrying
on an aesthetic crusade within. It would find that the
numerical aspects were duly admitted, but the aesthetic
significence of them left outside. So also entropy is
admitted in its numerical aspect; if it has as we faintly
suspect some deeper significance touching that which
appears in our conciousness as
purpose (opposed to
chance), that significance is left outside.
The Nature of the Physical World, pp.293-310
In the old conflict between freewill and predestination it has seemed hitherto that physics comes down heavily on the side of predestination. Without making extravagant claims for the scope of natural law, its moral sympathy has been with the view that whatever the future may bring forth is already foretold in the configurations of the past -
Yea, the first Morning of Creation wrote
I am not so rash as to invade Scotland with a solution of a problem which has rent her from the synod to the cottage. Like most other people, I suppose, I think it incredible that the wider scheme of Nature which includes life and consciousness can be completely predetermined; yet I have not been able to form a satisfactory conception of any kind of law or causal sequence which shall be other than deterministic. It seems contrary to our feeling of the dignity of the mind to suppose that it merely registers a dictated sequence of thoughts and emotions; but it seems equally contrary to its dignity to put it at the mercy of impulses with no causal antecedents. I shall not deal with this dilemma. Here I have to set forth the position of physical science on this matter so far as it comes into her territory. It does come into her territory, because that which we call human will cannot be entirely dissociated from the consequent motions of the muscles and disturbance of the material world. On the scientific side a new situation has arisen. It is a consequence of the advent of the quantum theory that physics is no longer pledged to a scheme of deterministic law. Determinism has dropped out altogether in the latest formulations of theoretical physics and it is at least open to doubt whether it will ever be brought back.
The foregoing paragraph is from the manuscript of the original lecture delivered in Edinburgh. The attitude of physics at that time was one of indifference to determinism. If there existed a scheme of strictly causal law at the base of phenomena the search for it was not at present practical politics, and meanwhile another ideal was being pursued. The fact that a causal basis had been lost sight of in the new theories was fairly well known; many regretted it, and held that its restoration was imperative.*
What the Last Dawn of Reckoning shall read.
In rewriting this chapter a year later I have had mingle with this attitude of indifference an attitude more definitely hostile to determinism which has arisen from the acceptance of the
Principle of Indeterminacy (p. 220). There has been no time for more than a hurried examination of the far-reaching consequences of this principle; and I should have been reluctant to include 'stop-press" ideas were it not that they appear to clinch the conception towards which the earlier developments were leading. The future is a combination of the causal influences of the past together with unpredictable elements— unpredictable not merely because it is impracticable to obtain the data of prediction, but because no data connected causally with our experience exist. It will be necessary to defend so remarkable a change of opinion at some length. Meanwhile we may note that science thereby withdraws its moral opposition to freewill. Those who maintain a deterministic theory of mental activity must do so as the outcome of their study of the mind itself and not with the idea that they are thereby making it more conformable with our experimental knowledge of the laws of inorganic nature.
Causation and Time's Arrow. Cause and effect are closely bound up with time's arrow; the cause must precede the effect. The relativity of time has not obliterated this order. An event Here-Now can only cause events in the cone of absolute future; it can be caused by events in the cone of absolute past; it can neither cause nor be caused by events in the neutral wedge, since the necessary influence would in that case have to be transmitted with a speed faster than light. But curiously enough this elementary notion of cause and effect is quite inconsistent with a strictly causal scheme. How can I cause an event in the absolute future, if the future was predetermined before I was born? The notion evidently implies that something may be born into the world at the instant Here-Now, which has an influence extending throughout the future cone but no corresponding linkage to the cone of absolute past. The primary laws of physics do not provide for any such one-way linkage; any alteration in a prescribed state of the world implies alterations in its past state symmetrical with the alterations in its future state. Thus in primary physics, which knows nothing of time's arrow, there is no discrimination of cause and effect; but events are connected by a symmetrical causal relation which is the same viewed from either end.
Primary physics postulates a strictly causal scheme, but the causality is a symmetrical relation and not the one-way relation of cause and effect. Secondary physics can distinguish cause and effect but its foundation does not rest on a causal scheme and it is indifferent as to whether or not strict causality prevails.
The lever in a signal box is moved and the signal drops. We can point out the relation of constraint which associates the positions of lever and signal; we can also find that the movements are not synchronous, and calculate the time-difference. But the laws of mechanics do not ascribe an absolute sign to this time-difference; so far as they are concerned we may quite well suppose that the drop of the signal causes the motion of the lever. To settle which is the cause, we have two options. We can appeal to the signalman who is confident that he made the mental decision to pull the lever; but this criterion will only be valid if we agree that there was a genuine decision between two possible courses and not a mere mental registration of what was already predetermined. Or we can appeal to secondary law which takes note of the fact that there was more of the random element in the world when the signal dropped than when the lever moved. But the feature of secondary law is that it ignores strict causation; it concerns itself not with what must happen but with what is likely to happen. Thus distinction of cause and effect has no meaning in the closed system of primary laws of physics; to get at it we have to break into the scheme, introducing considerations of volition or of probability which are foreign to it. This is rather analogous to the ten vanishing coefficients of curvature which could only be recognised if the closed system of the world were broken into by standards foreign to it.
For convenience I shall call the relation of effect to cause causation, and the symmetrical relation which does not distinguish between cause and effect causality. In
primary physics causality has completely replaced
causation. Ideally the whole world past and future is
connected into a deterministic scheme by relations of
causality. Up till very recently it was universally held
that such a determinate scheme must exist (possibly
subject to suspension by supernatural agencies outside
the scope of physics); we may therefore call this the
"orthodox" view. It was, of course, recognised that we
were only acquainted with part of the structure of this
causal scheme, but it was the settled aim of theoretical
physics to discover the whole.
This replacement in orthodox science of causation by causality is important in one respect. We must not let causality borrow an intuitive sanction which really belongs only to causation. We may think we have an intuition that the same cause cannot have two alternative effects; but we do not claim any intuition that the same effect may not spring from two alternative causes. For this reason the assumption of a rigid determinateness enforced by relations of causality cannot be said to be insisted on by intuition.
What is the ground for so much ardent faith in the orthodox hypothesis that physical phenomena rest ultimately on a scheme of completely deterministic laws? I think there are two reasons –
(1) The principal laws of Nature which have been discovered are apparently of this deterministic type, and these have furnished the great triumphs of physical prediction. It is natural to trust to a line of progress which has served us well in the past. Indeed it is a healthy attitude to assume that nothing is beyond the scope of scientific prediction until the limits of prediction actually declare themselves.
(2) The current epistemology of science presupposes a deterministic scheme of this type. To modify it involves a much deeper change in our attitude to natural knowledge than the mere abandonment of an untenable hypothesis.
In explanation of the second point we must recall that knowledge of the physical world has to be inferred from the nerve-messages which reach our brains, and the current epistemology assumes that there exists a determinate scheme of inference (lying before us as an ideal and gradually being unravelled). But, as has already been pointed out, the chains of inference are simply the converse of the chains of physical causality by which distant events are connected to the nerve-messages. If the scheme of transmission of these messages through the external world is not deterministic then the scheme of inference as to their source cannot be deterministic, and our epistemology has been based on an impossible ideal. In that case our attitude to the whole scheme of natural knowledge must be profoundly modified.
These reasons will be considered at length, but it is convenient to state here our answers to them in equally summary form.
(1) In recent times some of the greatest triumphs of physical prediction have been furnished by admittedly statistical laws which do not rest on a basis of causality. Moreover the great laws hitherto accepted as causal appear on minuter examination to be of statistical character.
(2) Whether or not there is a causal scheme at the base of atomic phenomena, modern atomic theory is not now attempting to find it; and it is making rapid progress because it no longer sets this up as a practical aim. We are in the position of holding an epistemological theory of natural knowledge which does not correspond to actual aim of current scientific investigation.
Predictability of Events. Let us examine a typical case of successful scientific prediction. A total eclipse of the sun visible in Cornwall is prophesied for 11 August 1999. It is generally supposed that this eclipse is already predetermined by the present configuration of the sun, earth and moon. I do not wish to arouse unnecessary misgiving as to whether the eclipse will come off. I expect it will; but let us examine the grounds of expectation. It is predicted as a consequence of the law of gravitation – a law which we found in chapter VII to be a mere truism. That does not diminish the value of the prediction; but it does suggest that we may not be able to pose as such marvellous prophets when we come up against laws which are not mere truisms. I might venture to predict that 2 + 2 will be equal to 4 even in 1999; but if this should prove correct it will not help to convince anyone that the universe (or, if you like, the human mind) is governed by laws of deterministic type. I suppose that in the most erratically governed world something can be predicted if truisms are not excluded.
But we have to look deeper than this. The law of gravitation is only a truism when regarded from a macroscopic point of view. It presupposes space, and measurement with gross material or optical arrangements. It cannot be refined to an accuracy beyond the limits of these gross appliances; so that it is a truism with a probable error – sma11, but not infinitely small.The classical laws hold good in the limit when exceedingly large quantum numbers are involved. The system comprising the sun, earth and moon has exceedingly high state-number (p. 198); and the predictability of its configurations is not characteristic of natural phenomena in general but of those involving great numbers of atoms of action – such that we are concerned not with individual but with average behaviour.
Human life is proverbially uncertain; few things are more certain than the solvency of a life-insurance company. The average law is so trustworthy that it may be considered predestined that half the children now born will survive the age of x years. But that does not tell us whether the span of life of young A. McB. is already written in the book of fate, or whether there is still time to alter it by teaching him not to run in front of motor-buses. The eclipse in 1999 is as safe as the balance of a life-insurance company; the next quantum jump of an atom is as uncertain as your life and mine.
We are thus in a position to answer the main argument for a predetermination of the future, viz. that observation shows the laws of Nature to be of a type which leads to definite predictions of the future, and it is reasonable to expect that any laws which remain undiscovered will conform to the same type. For when we ask what is the characteristic of the phenomena that have been successfully predicted, the answer is that they are effects depending on the average configurations of vast numbers of individual entities. But averages are predictable because they are averages, irrespective of the type of government of the phenomena underlying them.
Considering an atom alone in the world in State 3, the classical theory would have asked, and hoped to answer, the question, What will it do next? The quantum theory substitutes the question, Which will it do next? Because it admits only two lower states for the atom to go to. Further, it makes no attempt to find a definite answer, but contents itself with calculating the respective odds on the jumps to State 1 and State 2. The quantum physicist does not fill the atom with gadgets for directing its future behaviour, as the classical physicist would have done; he fills it with gadgets determining the odds on its future behaviour. He studies the art of the bookmaker not of the trainer.
Thus in the structure of the world as formulated in the new quantum theory it is predetermined that of 500 atoms now in State 3, approximately 400 will go on to State 1 and 100 to State 2 – in so far as anything subject to chance fluctuations can be said to be predetermined. The odds of 4 to 1 find their appropriate representation in the picture of the atom; that is to say, something symbolic of a 4 : 1 ratio is present in each of the 500 atoms. But there are no marks distinguishing the atoms belonging to the group of 100 from the 400. Probably most physicists would take the view that although the marks are not yet shown in the picture,they are nevertheless present in Nature; they belong to an elaboration of the theory which will come in good time. The marks, of course, need not be in the atom itself; they may be in the environment which will interact with it. For example, we may load dice in such a way that the odds are 4 to 1 on throwing a 6. Both those dice which turn up 6 and those which do not have these odds written in their constitution – by a displaced position of the centre of gravity. The result of a particular throw is not marked in the dice; nevertheless it is strictly causal (apart perhaps from the human element involved in throwing the dice) being determined by the external influences which are concerned. Our own position at this stage is that future developments of physics may reveal such causal marks (either in the atom or in the influences outside it) or it may not. Hitherto whenever we have thought we have detected causal marks in natural phenomena they have always proved spurious, the apparent determinism having come about in another way. Therefore we are inclined to regard favourably the possibility that there may be no causal marks anywhere.
But, it will be said, it is inconceivable that an atom can be so evenly balanced between two alternative courses that nowhere in the world as yet is there any trace of the ultimately deciding factor. This is an appeal to intuition and it may fairly be countered with another appeal to intuition. I have an intuition much more immediate than any relating to the objects of the physical world; this tells me that nowhere in the world as yet is there any trace of a deciding factor as to whether I am going to lift my right hand or my left. It depends on an unfettered act of volition not yet made or foreshadowed.* My intuition is that the future is able to bring forth deciding factors which are not secretly hidden in the past.
The position is that the laws governing the microscopic elements of the physical world – individual atoms, electrons, quanta – do not make definite predictions as to what the individual will do next. I am here speaking of the laws that have been actually discovered and formulated on the old quantum theory and the new. These laws indicate several possibilities in the future and state the odds on each. In general the odds are moderately balanced and are not tempting to an aspiring prophet. But short odds on the behaviour of individuals combine into very long odds on suitably selected statistics of a number of individuals; and the wary prophet can find predictions of this kind on which to stake his credit – without serious risk. All the successful predictions hitherto attributed to causality are traceable to this. It is quite true that the quantum laws for individuals are not incompatible with causality; they merely ignore it. But if we take advantage of this indifference to reintroduce determinism at the basis of world structure it is because our philosophy predisposes us that way, not because we. know of any experimental evidence in its favour.
We might for illustration make a comparison with the doctrine of predestination. That theological doctrine, whatever may be said against it, has hitherto seemed to blend harmoniously with the predetermination of the material universe. But if we were to appeal to the new conception of physical law to settle this question by analogy the answer would be: – The individual is not
predestined to arrive at either of the two states, which perhaps may here be sufficiently discriminated as State 1 and State 2; the most that can be considered already settled is the respective odds on his reaching these states.
The New Epistemological Outlook. Scientific investigation does not lead to knowledge of the intrinsic nature of things. "Whenever we state the properties of a body in terms of physical quantities we are imparting knowledge of the response of various metrical indicators to its presence and nothing more" (p. 257). But if a body is not acting according to strict causality, if there is an element of uncertainty as,to the response of the indicators, we seem to have cut away the ground for this kind of knowledge. It is not predetermined what will be the reading of the weighing-machine if the body is placed on it, therefore the body has no definite mass; nor where it will be found an instant, hence, therefore it has no definite velocity; nor where the rays now being reflected from it will converge in the microscope, therefore it has no definite position; and so on. It is no use answering that the body really has a definite mass, velocity, position, etc., which we are unaware of; that statement, if it means anything, refers to an intrinsic nature of things outside the scope of scientific knowledge. We cannot infer these properties with precision from anything that we can be aware of, because the breach of causality has broken the chain of inference. Thus our knowledge of the response of indicators to the presence of the body is non-existent; therefore we cannot assert knowledge of it at all. So what is the use of talking about it? The body which was to be the abstraction of all these (as yet unsettled) pointer readings has become superfluous in the physical world. That is the dilemma into which the old epistemology leads us as soon as we begin to doubt strict causality.
In phenomena on a gross scale this difficulty can be got round. A body may have no definite position but yet have within close limits an extremely probable position. When the probabilities are large the substitution of probability for certainty makes little difference; it adds only a negligible haziness to the world. But though the practical change is unimportant there are fundamental theoretical consequences. All probabilities rest on a basis of a priori probability, and we cannot say whether probabilities are large or small without having assumed such a basis. In agreeing to accept those of our calculated probabilities which are very high as virtually equivalent to certainties on the old scheme, we are as it were making our adopted basis of a priori probability a constituent of the world-structure – adding to the world a kind of symbolic texture that cannot be expressed on the old scheme.
On the atomic scale of phenomena the probabilities are in general well-balanced, and there are no "naps" for the scientific punter to put his shirt on. If a body is still defined as a bundle of pointer readings (or highly probable pointer readings) there are no "bodies" on the atomic scale. All that we can extract is a bundle of probabilities. That is in fact just how Schrodinger tries to picture the atom – as a wave centre of his probability entity ψ.
We commonly have had to deal with probabilities which arise through ignorance. With fuller knowledge we should sweep away the references to probability and substitute the exact facts. But it appears to be a fundamental point in Schrodinger's theory that his probabilities are not to be replaced in that way. When his ψ is sufficiently concentrated it indicates the point where the electron is; when it is diffused it gives only a vague indication of the position. But this vague indication is not something which ideally ought to be replaced by exact knowledge; it is ψ itself which acts as the source of the light emitted from the atom, the period of the light being that of the beats of ψ. I think this means that the spread of ψ is not a symbol for uncertainty arising through lack of information; it is a symbol for causal failure — an indeterminacy of behaviour which is part of the character of the atom.
We have two chief ways of learning about the interior of the atom. We can observe electrons entering or leaving, and we can observe light entering or leaving. Bohr has assumed a structure connected by strictly causal law with the first phenomenon, Heisenberg and his followers with the second. If the two structures were identifiable then the atom would involve a complete causal connection of the two types of phenomena. But apparently no such causal linkage exists. Therefore we have to be content with a correlation in which the entities of the one model represent probabilities in the second model. There are perhaps details in the two theories which do not quite square with this; but it seems to express the ideal to be aimed at in describing the laws of an incompletely causal world, viz. that the causal source of one phenomenon shall represent the probability of causal source of another phenomenon. Schrödinger's theory has given at least a strong hint that the actual world is controlled on this plan.
Principle of Indeterminacy. Thus far we have shown that modern physics is drifting away from the postulate that the future is predetermined, ignoring it rather than deliberately rejecting it. With the discovery of the Principle of Indeterminacy (p. 220) its attitude has become more definitely hostile.
Let us take the simplest case in which we think we can predict the future. Suppose that we have a particle with known position and velocity at the present instant. Assuming that nothing interferes with it we can predict the position at a subsequent instant. (Strictly the non-interference would be a subject for another prediction, but to simplify matters we shall concede it.) It is just this simple prediction which the principle of indeterminacy expressly forbids. It states that we cannot know accurately both the velocity and position of a particle at the present instant.
At first sight there seems to be an inconsistency. There is no limit to the accuracy with which we may know the position, provided that we do not want to know the velocity also. Very well; let us make a highly accurate determination of position now, and after waiting a moment make another highly accurate determination of position. Comparing the two accurate positions we compute the accurate velocity — and snap our fingers at the principle of indeterminacy. This velocity, however, is of no use for prediction, because in making the second accurate determination of position we have rough-handled the particle so much that it no longer has the velocity we calculated. It is a purely retrospective velocity. The velocity does not exist in the present tense but in the future perfect; it never exists, it never will exist, but a time may come when it will have existed. There is no room for it in Fig. 4 which contains an Absolute Future and an Absolute Past but not an Absolute Future Perfect.
The velocity which we attribute to a particle now can be regarded as an anticipation of its future positions. To say that it is unknowable (except with a certain degree of inaccuracy) is to say that the future cannot be anticipated. Immediately the future is accomplished, so that it is no longer an anticipation, the velocity becomes knowable.
The classical view that a particle necessarily has a definite (but not necessarily knowable) velocity now amounts to disguising a piece of the unknown future as an unknowable element of the present. Classical physics foists a deterministic scheme on us by a trick; it smuggles the unknown future into the present, trusting that we shall not press an inquiry as to whether it has become any more knowable that way.
The same principle extends to every kind of phenomenon that we attempt to predict, so long as the need for accuracy is not buried under a mass of averages. To every co-ordinate there corresponds a momentum, and by the principle of indeterminacy the more accurately the co-ordinate is known the less accurately the momentum is known. Nature thus provides that knowledge of one-half of the world will ensure ignorance of the other half—ignorance which, we have seen, may be remedied later when the same part of the world is contemplated retrospectively. We can scarcely rest content with a picture of the world which includes so much that cannot be known. We have been trying to get rid of unknowable things, i.e. ail conceptions which have no causal connection with our experience. We have eliminated velocity through aether, "right" frames of space, etc., for this reason. This vast new unknowable element must likewise be swept out of the Present. Its proper place is in the Future because then it will no longer be unknowable. It has been put in prematurely as an anticipation of that which cannot be anticipated.
In assessing whether the symbols which the physicist has scattered through the external world are adequate to predetermine the future, we must be on our guard against retrospective symbols. It is easy to prophesy after the event.
Natural and Supernatural. A rather serious consequence of dropping causality in the external world is that it leaves us with no clear distinction between the Natural and the Supernatural. In an earlier chapter I compared the invisible agent invented to account for the tug of gravitation to a "demon". Is a view of the world which admits such an agent any more scientific than that of a savage who attributes all that he finds mysterious in Nature to the work of invisible demons? The Newtonian physicist had a valid defence. He could point out that his demon Gravitation was supposed to act according to fixed causal laws and was therefore not to be compared with the irresponsible demons of the savage. Once a deviation from strict causality is admitted the distinction melts away. I suppose that the. savage would admit that his demon was to some extent a creature of habit and that it would be possible to make a fair guess as to what he would do in the future; but that sometimes he would show a will of his own. It is that imperfect consistency which formerly disqualified him from admission as an entity of physics along with his brother Gravitation.
That is largely why there has been so much bother about "me"; because I have, or am persuaded that I
have, "a will of my own". Either the physicist must leave his causal scheme at the mercy of supernatural interference from me, or he must explain away my supernatural qualities. In self-defence the materialist favoured the latter course; he decided that I was not supernatural — only complicated. We on the other hand have concluded that there is no strict causal behaviour anywhere. We can scarcely deny the charge that in abolishing the criterion of causality we are opening the door to the savage's demons. It is a serious step, but I do not think it means the end of all true science. After all if they try to enter we can pitch them out again, as Einstein pitched out the respectable causal demon who called himself Gravitation. It is a privation to be no longer able to stigmatise certain views as unscientific superstition ; but we are still allowed, if the circumstances justify it, to reject them as bad science.
Nature of the Physical World, pp.310-315
Volition. From the philosophic point of view it is of deep interest to consider how this affects the freedom of the human mind and spirit. A complete determinism of the material universe cannot be divorced from determinism of the mind. Take for example, the prediction of the weather this time next year. The prediction is not likely ever to become practicable, but " orthodox" physicists are not yet convinced that it is theoretically impossible; they hold that next year's weather is already predetermined. We should require extremely detailed knowledge of present conditions, since a small local deviation can exert an ever-expanding influence. We must examine the state of the sun so as to predict the fluctuations in the heat and corpuscular radiation which it sends us. We must dive into the bowels of the earth to be forewarned of volcanic eruptions which may spread a dust screen over the atmosphere as Mt. Katmai did some years ago. But further we must penetrate into the recesses of the human mind. A coal strike, a great war, may directly change the conditions of the atmosphere; a lighted match idly thrown away may cause deforestation which will change the rainfall and climate. There can be no fully deterministic control of inorganic phenomena unless the determinism governs mind itself.
Conversely if we wish to emancipate mind we must to some extent emancipate the material world also. There appears to be no longer any obstacle to this emancipation.
Let us look more closely into the problem of how the mind gets a grip on material atoms so that movements of the body and limbs can be controlled by its volition. I think we may now feel quite satisfied that the volition is genuine. The materialist view was that the motions which appear to be caused by our volition are really reflex actions controlled by the material processes in the brain, the act of will being an inessential side phenomenon occurring simultaneously with the physical phenomena. But this assumes that the result of applying physical laws to the brain is fully determinate. It is meaningless to say that the behaviour of a conscious brain is precisely the same as that of a mechanical brain if the behaviour of a mechanical brain is left undetermined. If the laws of physics are not strictly causal the most that can be said is that the behaviour of the conscious brain is one of the possible behaviours of a mechanical brain. Precisely so; and the decision between the possible behaviours is what we call volition.
Perhaps you will say, When the decision of an atom is made between its possible quantum jumps, is that also "volition"? Scarcely; the analogy is altogether too remote. The position is that both for the brain and the atom there is nothing in the physical world, i.e. the world of pointer readings, to predetermine the decision; the decision is a fact of the physical world with consequences in the future but not causally connected to the past. In the case of the brain we have an insight into a mental world behind the world of pointer readings and in that world we get a new picture of the fact of decision which must be taken as revealing its real nature — if the words real nature have any meaning.
For the atom we have no such insight into what is behind the pointer readings. We believe that behind all pointer readings there is a background continuous with the background of the brain; but there is no more ground for calling the background of the spontaneous behaviour of the atom "volition" than for calling the background of its causal behaviour "reason". It should be understood that we are not attempting to reintroduce in the background the strict causality banished from the pointer readings. In the one case in which we have any insight — the background of the brain — we have no intention of giving up the freedom of the mind and will. Similarly we do not suggest that the marks of predestination of the atom, not found in the pointer readings, exist undetectable in the unknown background. To the question whether I would admit that the cause of the decision of the atom has something in common with the cause of the decision of the brain, I would simply answer that there is no cause. In the case of the brain I have a deeper insight into the decision; this insight exhibits it as volition, i.e. something outside causality.
A mental decision to turn right or turn left starts one of two alternative sets of impulses along the nerves to the feet. At some brain centre the course of behaviour of certain atoms or elements of the physical world is directly determined for them by the mental decision - or, one may say, the scientific description of that behaviour is the metrical aspect of the decision. It would be a possible though difficult hypothesis to assume that very few atoms (or possibly only one atom) have this direct contact with the conscious decision, and that these few atoms serve as a switch to deflect the material world from one course to the other. But it is physically improbable that each atom has its duty in the brain so precisely allotted that the control of its behaviour would prevail over all possible irregularities of the other atoms. If I have at all rightly understood the processes of my own mind, there is no finicking with individual atoms.
I do not think that our decisions are precisely balanced on the conduct of certain key-atoms. Could we pick out one atom in Einstein's brain and say that if it had made the wrong quantum jump there would have been a corresponding flaw in the theory of relativity? Having regard to the physical influences of temperature and promiscuous collision it is impossible to maintain this. It seems that we must attribute to the mind power not only to decide the behaviour of atoms individually but to affect systematically large groups - in fact to tamper with the odds on atomic behaviour. This has always been one of the most dubious points in the theory of the interaction of mInd and matter.
Interference with Statistical Laws. Has the mind power to set aside statistical laws which hold in inorganic matter? Unless this is granted its opportunity of interference seems to be too circumscribed to bring about the results which are observed to follow from mental decisions. But the admission involves a genuine physical difference between inorganic and organic (or, at any rate, conscious) matter. I would prefer to avoid this hypothesis, but it is necessary to face the issue squarely. The indeterminacy recognised in modern quantum theory is only a partial step towards freeing our actions from deterministic control. To use an analogy — we have admitted an uncertainty which may take or spare human lives; but we have yet to find an uncertainty which may upset the expectations of a life-insurance company. Theoretically the one uncertainty might lead to the other, as when the fate of millions turned on the murders at Sarajevo. But the hypothesis that the mind operates through two or three key-atoms in the brain is too desperate a way of escape for us, and I reject it for the reasons already stated.
It is one thing to allow the mind to direct an atom between two courses neither of which would be improbable for an inorganic atom; it is another thing to allow it to direct a crowd of atoms into a configuration which the secondary laws of physics would set aside as "too improbable". Here the improbability is that a large number of entities each acting independently should conspire to produce the result; it is like the improbability of the atoms finding themselves by chance all in one half of a vessel. We must suppose that in the physical part of the brain immediately affected by a mental decision there is some kind of interdependence of behaviour of the atoms which is not present in inorganic matter.
I do not wish to minimise the seriousness of admitting this difference between living and dead matter. But I think that the difficulty has been eased a little, if it has not been removed. To leave the atom constituted as it was but to interfere with the probability of its undetermined behaviour, does not seem quite so drastic, an interference with natural law as other modes of mental interference that have been suggested. (Perhaps that is only because we do not understand enough about these probabilities to realise the heinousness of our suggestion.) Unless it belies its name, probability can be modified in ways which ordinary physical entities would not admit of.
This is Jaynes' theory of Bayesian MaxEnt probability
There can be no unique probability attached to any event or behaviour; we can only speak of "probability in the light of certain given information", and the probability alters according to the extent of the information. It is, I think, one of the most unsatisfactory features of the new quantum theory in its present stage that it scarcely seems to recognise this fact, and leaves us to guess at the basis of information to which its probability theorems are supposed to refer.
Looking at it from another aspect - if the unity of a man's consciousness is not an illusion, there must be some corresponding unity in the relations of the mindstuff which is behind the pointer readings. Applying our measures of relation structure, as in chapter XI, we shall build matter and fields of force obeying identically the principal field-laws; the atoms will individually be in no way different from those which are without this unity in the background. But it seems plausible that when we consider their collective behaviour we shall have to take account of the broader ünifying trends in the mind-stuff, and not expect the statistical results to agree with those appropriate to structures of haphazard origin.
I think that even a materialist must reach a conclusion not unlike ours if he fairly faces the problem. He will need in the physical world something to stand for a symbolic unity of the atoms associated with an individual consciousness, which does not exist for atoms not so associated — a unity which naturally upsets physical predictions based on the hypothesis of random disconnection. For he has not only to translate into material configurations the multifarious thoughts and images of the mind, but must surely not neglect to find some kind of physical substitute for the Ego.
Expansion of the Universe
(New Pathways in Science, 1935, pp.62-63, 66-68)
One way out of the difficulty of an abrupt beginning has sometimes found favour. I oppose it not through any desire to retain the present dilemma but because I do not think it is a genuine loophole. It depends on the occurrence of chance fluctuations. If we have a number of entities moving about at random, they will in the course of time go through every possible configuration; so that even the most orderly, the most non-chance configuration, will occur by chance if we wait long enough -
When the world has reached complete disorganisation (thermodynamic equilibrium) there is still infinite time ahead of it, and its elements will have the opportunity to take up every possible configuration again and again. If we wait long enough a number of atoms will, just by chance, arrange themselves as the atoms are now arranged in this room; and, just by chance, the same sound waves will come from one of the systems of atoms as are now emerging from my lips; they will strike other systems of atoms arranged, just by chance, to resemble you, and in the same stages of attention or somnolence. This mock delivery of the present course of Messenger Lectures will repeat itself many times over — an infinite number of times in fact — before t reaches ∞. Do not ask me whether I really believe, or expect you to believe, that this will happen —
There once was a brainy baboon
Compare Emile Borel
's idea of an infinite number of typing monkeys
Who always breathed down a bassoon
For he said "It appears
That in billions of years
I shall certainly hit on a tune".
Logic is logic. That's all I say.
So after the world has reached thermodynamic equilibrium the entropy remains steady at its maximum value, except that once in a blue moon an absurdly small chance comes off and the entropy drops appreciably below its maximum value. When this fluctuation has died out there will again be a very long wait for another coincidence giving another fluctuation. It will take multillions of years, but we have all eternity before us.
There is no limit to the possible amount of the fluctuation; and, if we wait long enough, there will be a fluctuation which will take the universe as far from thermodynamic equilibrium as it is at the present moment.
The suggestion is that we are now on the down-slope of one of these chance fluctuations. Is it an accident that we happen to be running down the slope and not toiling up the slope? Not at all. So far as the physical universe is concerned the direction of time has been defined to be that in which disorganisation increases, so that on whichever slope of the mountain we stand the signpost "To the Future" points downhill. In fact, on this theory, the going on of time is not a property of time in general but of the slope of the fluctuation on which we stand.
We can always argue that anything that can be done by arrangement or by specific cause can also be done by chance, provided that it is agreed not to count the failures. In this case the theory postulates a state of things involving an exceedingly rare coincidence, but it also provides an infinite time during which the coincidence might (or, it is suggested, must) occur. Nevertheless I feel sure that the argument is fallacious.
The irreversible dissipation of energy in the universe has been a recognised doctrine of science since 1852 when it was formulated explicitly by Lord Kelvin. Kelvin drew the same conclusions about the beginning and end of things as those given here—except that, since less attention was paid to the universe in those days, he considered the earth and the solar system. The general ideas have not changed much in eighty years; but the recognition of the finitude of space and the recent theory of the expanding universe now involve some supplementary considerations.
The conclusion that the total entropy of the universe at any instant is greater than at a previous instant dates from a time when an "instant" was conceived to be an absolute time-partition extending throughout the universe. We have to reconsider the matter now that Einstein has abolished these absolute instants; but it appears that no change is required. I think I am right in saying that it is not necessary that the instants should be absolute, or that the time t referred to in dS/dt should be a form of absolute time. For the first instant we can choose any arbitrary space-like section of space-time (smooth or crinkled), and for the second instant any other space-like section which does not intersect the first. One of these instants will be later throughout than the other; and the total entropy of the universe integrated over the later instant will be greater than over the earlier instant. This generalisation is made possible by the fact that the energy or matter which carries the disorganisation cannot travel from place to place faster than light.
The consequences of introducing the expansion of the universe are more difficult to foresee. Fundamental questions are raised as to the appropriate way of defining entropy when the background conditions are no longer invariable. I believe that the progress of the theory in other directions in the next few years will place us in a better position to treat the thermodynamical problem which it raises, and I prefer not to try to anticipate its conclusions.
Meanwhile it is important to notice that the expansion of the universe is another irreversible process. It is a one-way characteristic like the increase of disorganisation. Just as the entropy of the universe will never return to its present value, so the volume of the universe will never return to its present value. From the expansion of the universe we reach independently the same outlook as to the beginning and end of things that we have here reached by considering the increase of entropy. In particular the conclusion seems almost inescapable that there must have been a definite beginning of the present order of Nature. The theory of the expanding universe adds something new, namely an estimate of the date of this beginning. We shall see in Chapter X that from the scientific point of view it is uncomfortably recent — scarcely more than 10,000 million years ago.
In the expanding universe we can decide which of two instants is the later by the criterion that the later instant corresponds to the larger volume of the universe. (The instants are defined as before to be two non-intersecting space-like sections of space-time.) This provides an alternative signpost for time. But it is only applicable to time taken throughout the universe as a whole. The position of entropy as the unique local signpost remains unaffected. The fact that the direction of time for the universe, regarded as a single system, is indicated both by increasing volume and by increasing entropy suggests that there is some undiscovered relation between the two criteria. That is one of the points on which we may expect more light in the next few years.
By accepting the theory of the expanding universe we are relieved of one conclusion which we had felt to be intrinsically absurd. It was argued (p. 62) that every possible configuration of atoms must repeat itself at some distant date. But that was on the assumption that the atoms will have only the same choice of configurations in the future that they have now. In an expanding space any particular congruence becomes more and more improbable.
first suggested a fluctuation as the solution to the observed entropy increase of thermodynamics
The expansion of the universe creates new possibilities of distribution faster than the atoms can work through them, and there is no longer any likelihood of a particular distribution being repeated. If we continue shuffling a pack of cards we are bound sometime to bring them into their standard order — but not if the conditions are that every morning one more card is added to the pack.
The expansion creates new possibilities faster than atoms can adjust, the germ of David Layzer
's explanation for the growth of order
in the universe. Perhaps he did not read New Pathways?
So I think after all there will not be a second (accidental) delivery of these Messenger Lectures this side of eternity.
's (and Boltzmann
's) infinite universe view, there are an infinite number of Messenger lectures being delivered at this moment!