The "Compton effect" provided real support for the wave-particle duality of radiation (which Einstein had proposed as early as 1909) and matter (proposed by Louis de Broglie in 1924. Compton himself initially denied that his experiment supported Einstein's idea of light quanta (later called photons). Compton was awarded the Nobel Prize in Physics in 1927 for this "Compton effect," the year that Werner Heisenberg discovered quantum indeterminacy.

Compton scattering is "inelastic," because the energy hν (or hc / λ) of the incident photon is different from that of the scattered photon hν' (or hc / λ').

Compton's experiments confirmed the relation

The wavelength shift λ' - λ varies from nothing to twice h/mc, which is known as the Compton wavelength. For a derivation, see Compton scattering on Wikipedia.

Wolfgang Pauli objected to Compton's analysis. A "free" electron cannot scatter an electron, he argued. A proper analysis, confirmed by Einstein and Ehrenfest the same year (1923), is that scattering should be interpreted as a two-step process, the absorption of a photon of energy hν followed by the emission of a directed photon hν', where the momentum of the photon hν' / c balances the momentum of the scattered electron mv.

In his very excellent presentation of the uncertainty principle, published in a recent number of SCIENCE,² Professor Darwin concludes with a comment regarding the significance of this principle in connection with the problem of "free will," which should not be allowed to pass without comment. He may be correct in his view that "the question is a philosophic one outside the thought of physics." Yet the reason that he offers to show that the uncertainty principle does not help to free us from the bonds of determinism is inadequate.

Darwin's argument is that "physical theory confidently predicts that the millions of millions of electrons concerned in matter-in-bulk will behave .. . regularly, and that to find a case of noticeable departure from the average we should have to wait for a period of time quite fantastically longer than the estimated age of the universe." He apparently overlooks the fact that there is a type of large-scale event which is erratic because of the very irregularities with which the uncertainty principle is concerned. I refer to those events which depend at some stage upon the outcome of a small-scale event.

As a purely physical example, one might pass a ray of light through a pair of slits which will so diffract it that there is an equal chance for a photon to enter either of two photoelectric cells. By means of suitable amplifiers it may be arranged that if the first photon enters cell A, a stick of dynamite will be exploded (or any other large-scale event performed); if the first photon enters cell B a switch will be opened which will prevent the dynamite from being exploded. What then will be the effect of passing the ray of light through the slits? The chances are even whether or not the explosion will occur. That is, the result is unpredictable from the physical conditions.

Professor Ralph Lillie has pointed out³ that the nervous system of a living organism likewise acts as an amplifier, such that the actions of the organism depend upon events on so small a scale that they are appreciably subject to Heisenberg uncertainty. This implies that the actions of a living organism can not be predicted definitely on the basis of its physical conditions.

Of course this does not necessarily mean that the living organism is free to determine its own actions. The uncertainty involved may merely correspond to the organism's lack of skill. Yet it does mean that living organisms are not subject to physical determinism of the kind indicated by Darwin.

1. A. H. Compton, SCIENCE, 74, 1911, August 14, 1931.
2. C. G. Darwin, SCIENCE, 73, 653, June 19, 1931.
3. Ralph Lillie, SCIENCE, 66, 139, 1927. Lillie draws much the same conclusion as that found here.

There is no way in which we can be sure. We have found that light has the dual aspect of waves and particles. The photon (particle) follows the light wave, and if we try to make its path more definite by using a smaller hole to transmit the ray, we merely make the transmitted beam of waves more diffuse by diffraction. Though the first photon may enter one cell, with the initial conditions identical as far as any test can show, the next photon may enter the other cell. The result is thus not reproducible. It is, as far as we can see, truly a matter of chance. That is what we mean by saying that the law of causality does not hold: knowledge of the initial conditions does not enable us to predict what will happen, for with the same initial conditions we cannot consistently produce the same effect.

We might connect one of our amplifiers with an electrical device which will explode a stick of dynamite, and the other amplifier with a switch which will open the circuit. Now what will happen when the shutter transmits a photon? If it enters one cell the dynamite will explode, and the apparatus will be blown to bits. If the photon enters the other cell, the switch will be pulled and the apparatus is no longer in danger. Both events are equally probable. Similarly any event which depends at some stage upon the outcome of a small-scale event is essentially unpredictable on the basis of previous history.

A daemon controlling the shutter might be conscious of their qualities. The daemon controlling the shutter might consider a photon which would enter the photoelectric cell that would result in exploding the dynamite a "bad" photon, and one which would enter the cell where it would prevent the catastrophe a "good" photon. Being directly conscious, of these nonphysical characteristics which will determine their direction, the daemon may then close the shutter to all approaching "bad" photons until a "good" photon has passed through and saved the day. Has the daemon in this way contravened any physical laws?

The point is that the event under consideration is really an individual act, to which, since it can be performed but once, the laws of statistics do not apply. Whether the switch is opened or the dynamite exploded by the first photon, in either case the experiment is complete. This corresponds closely to human action, considered in the light of habit. An experiment involving deliberation can be performed on a person only once; for afterwards his condition is not the same. Habit will now enter into the determination of his action. Thus deliberate actions likewise are individual events, and are not therefore predictable from laws of probability. Faced by the necessity for an individual decision, all one's physiological structure, his environment, and previous history determine what Warren Weaver describes as a "spectrum of action probability," within which "spectrum" it is possible for any action to be chosen. There will be greater probability for certain modes of action than others; but these probabilities do not specify the choice of the individual act.

It would be easy to outline a closely parallel scheme whereby consciousness could select the desirable brain current, even though the undesirable one might be equally probable from statistical considerations, thus leading to the performance of the desirable act rather than its alternative. It is not necessary to elaborate any particular brain mechanism for performing the selection, for the example just given shows that it is possible to select one of a number of physically possible acts without violating or modifying any physical law. In this way the determination of a man's actions by his will is, I believe, shown to be consistent with the principles of physics is they are now understood.

TODAY'S PHYSICS HAS ROOM FOR FREEDOM

The fault in the theory of mechanical determinism was not discovered until about thirty years ago. It was then found that the laws of Newton do not describe what happens to the atoms of which matter is composed. It was found instead that the properties of these atoms are such that prediction of what happens to them can only be made within certain limits. The amount of this uncertainty is fixed in the very nature of matter itself.

On my laboratory desk I have two simple devices. The first is a freely swinging pendulum. Its beats are regular, repeating themselves uniformly at equally timed intervals. This pendulum is typical of the objects with which the physicists of Laplace's time were familiar.

The second device is a Geiger counter, responding with a click to each ray that enters it from a nearby capsule of radium. The clicks occur at irregular intervals. It may be that about 100,000 clicks will occur each day. But several seconds may pass without any clicks, while during the next second two or three will occur. Whether in the following second a ray will be counted cannot be foretold. This device responds to the action of individual atoms. Nothing of this kind was known until near the end of the nineteenth century.

The pendulum swings back and forth according to a precise law. The clicks of the counter occur at random.

If such a pair of experiments had been known in Newton's time, it is doubtful whether the idea that events must happen according to precise laws would ever have been formulated. It would have been evident that only under special conditions can one predict definitely what will occur. These conditions are that what we observe shall be the average of a very large number of individual events.

Consider what happens when an atom of radium disintegrates. This event can be recorded by such an instrument as a Geiger counter. The average life of a radium atom is about two thousand years. That is, in any one year from the time the radium atom is first formed, the chance is about one in two thousand that it will disintegrate. It may disintegrate during the present year, but there is roughly one chance in eight that it will remain unchanged six thousand years from now. What the physicists of the twentieth century have shown is that there is no kind of observation that can be made which will tell in what particular year the radium atom will disintegrate. If the atom was in existence six thousand years ago, it was then identical with what it is today. The possibility of disintegration has always been there. Whether it will in fact disintegrate in this particular year is, as far as physics is concerned, a matter of chance—a likelihood of one in two thousand.

There is something comparable with this example in the case of every atomic or molecular event. Thus when light falls on a photographic emulsion, under its stimulus there is a certain chance that any particular grain of silver bromide will be changed so that it can be developed to silver. With a given light exposure, this chance may be one in ten, so that on the average about one-tenth of the grains will be transformed. But which particular grain will thus be changed is by the very nature of the process unpredictable.

These examples illustrate a point of critical importance in today's interpretation of the physical world. Nature provides nothing whose precise measurement would make possible the exact prediction of an atomic event. On this limitation that nature sets on our knowledge both experiment and theory are agreed. The average of large numbers of atomic events does indeed follow exact laws. In a large lump of radium in one year almost precisely one part in two thousand will have disintegrated. In a square inch of the photographic emulsion, almost exactly one tenth of the silver bromide, after the light exposure, will be reduced to silver. The number of atoms in my laboratory pendulum is huge, roughly a million billion billion. The statistics of the action of such numbers of particles are very precise — even more so when one observes the moon's regular revolution around the earth.

Not all large-scale events, however, are thus precisely predictable. If at any stage the big event depends on some atomic process, the end result shares in the uncertainty of this small event.

A typical large-scale event of this kind is the explosion of an atomic bomb. Such an explosion is triggered by the appearance of a neutron during the particular fraction of a microsecond when the chain reaction must be started. But this neutron comes from a radioactive process, which cannot be precisely foretold. If the chances were only even that during the critical time interval a neutron would appear, there would likewise be only even chances that the bomb would explode. In order that the bomb shall be sure to fire, it is arranged that during the critical time interval some thousands of neutrons will probably be present. Thus the chance of failure becomes practically zero.

Now most of life's processes are like such an atomic chain reaction. They begin with some very small event and grow. They are in fact chemical chain reactions. What starts these reactions in living organisms is not known in detail, but we do know that the beginning is on a molecular, or in certain cases on a submolecular, scale. Thus when I touch something hot and quickly withdraw my finger, the nerve currents that stimulate the muscular contractions are themselves small-scale reactions. The events that are involved when choices and decisions are made have so far defied physical identification; but in all probability they are reactions involving such small numbers of particles that definite prediction on a physical basis is by the nature of things impossible.

As far as physics is concerned, a person's actions which we think of as free would thus appear to occur simply according to the rules of chance. We find nevertheless that in practical life such actions can be predicted when we know the person's intentions. This implies that something additional to the physical phenomena is involved. What we actually note is that in such a case the person has a kind of firsthand knowledge of his own situation that is not gained from any physical observation. This additional knowledge is the awareness of his own intentions. When he acts he feels that he is acting freely. That is, his action corresponds with what he intends.

Thus, for example, I told the editor that I would have this article prepared in time for the present issue of the Atlantic. How could I confidently give him this assurance? Was it on the basis of physical data? Only to the extent that it appeared physically possible that the article could be prepared in time. As a physical event an immense number of other possibilities were equally likely to occur. Was not the primary basis of my prediction rather that I knew my own intention? And this I knew, not through any kind of observation, but by an inner awareness; not through a deduction from data, but because of a choice that I was making from among the various possibilities before me.

After thousands of years of discussion among scientists and philosophers, the place of free acts in a world that follows physical law has thus become clarified. There is nothing known to physics that is inconsistent with a person's exercising freedom.

Is this our two-stage model for free will?

A set of known physical conditions is not adequate to specify precisely what a forthcoming event will be. These conditions, insofar as they can be known, define instead a range of possible events from among which some particular event will occur. When one exercises freedom, by his act of choice he is himself adding a factor not supplied by the physical conditions and is thus himself determining what will occur. That he does so is known only to the person himself. From the outside one can see in his act only the working of physical law. It is the inner knowledge that he is in fact doing what he intends to do that tells the actor himself that he is free.

Let me then summarize how a physicist now views man's freedom. It is not from scientific observation that we know man is free. Science is incapable of telling whether a person's acts are free or not. Freedom is not something that one can touch or measure. We know it through our own innermost feelings. The first essential of freedom is the desire to attain something that one considers good. But desire lies outside the realm of science — at least outside of physics. You can't locate desire as somewhere in space. Similarly our recognition that within limits we can do what we try to do is not a matter of measurement or of external observation. It is a matter of immediate awareness. There is nothing in such awareness of freedom that is inconsistent with science. Freedom does, however, involve the additional determining factor of choice, about which science tells us nothing.

For myself, at least, this answer satisfies. Yes, I am free. I say this because I have found in my inner experience that the world does in fact respond to my efforts. And the findings of science, in particular the findings of physics, which at one stage so sharply denied that freedom had any meaning, are completely consistent with this experience.

Thus the way is cleared for our great task. We are free to shape our destiny. Science opens vast new opportunities, greatly enlarging man's freedom. Let us look to see what kind of world we want for ourselves and our fellows. Let us learn what we must do to create such a world. Let us put our hearts, our minds, and our combined strength — everything we've got — into making that better world a reality. In this undertaking we will find our greatest freedom.

2. Reprinted in The Cosmos of Arthur Holly Compton, Compton 1967.

A set of known physical conditions is not adequate to specify precisely what a forthcoming event will be. These conditions, insofar as they can be known, define instead a range of possible events from among which some particular event will occur. When one exercises freedom, by his act of choice he is himself adding a factor not supplied by the [random] physical conditions and is thus himself determining what will occur.

We can see Compton's quantum randomness contributing to the "range of possible events," which he says Warren Weaver called the "spectrum of action probability," within which "spectrum" it is possible for any action to be chosen.