The nature of the physical world

by Sir Arthur Stanley Eddington

This is not a casual difficulty; it is a cunningly arranged plot—a plot to prevent you from seeing something that does not exist, viz. the locality of the electron within the atom. If I use longer waves which do no harm, they will not define the electron sharply enough for you to see where it is. In shortening the wave-length, just as the light becomes fine enough its quantum becomes too rough and knocks the electron out of the atom.

Other examples of the reciprocal uncertainty have been given, and there seems to be no doubt that it is entirely general. The suggestion is that an association of exact position with exact momentum can never be discovered by us because there is no such thing in Nature. This is not inconceivable. Schrödinger’s model of the particle as a wave-group gives a good illustration of how it can happen. We have seen ([p. 217]) that as the position of a wave-group becomes more defined the energy (frequency) becomes more indeterminate, and vice versa. I think that that is the essential value of Schrödinger’s theory; it refrains from attributing to a particle a kind of determinacy which does not correspond to anything in Nature. But I would not regard the principle of indeterminacy as a result to be deduced from Schrödinger’s theory; it is the other way about. The principle of indeterminacy, like the principle of relativity, represents the abandonment of a mistaken assumption which we never had sufficient reason for making. Just as we were misled into untenable ideas of the aether through trusting to an analogy with the material ocean, so we have been misled into untenable ideas of the attributes of the microscopic elements of world-structure through trusting to analogy with gross particles.

A New Epistemology. The principle of indeterminacy is epistemological. It reminds us once again that the world of physics is a world contemplated from within surveyed by appliances which are part of it and subject to its laws. What the world might be deemed like if probed in some supernatural manner by appliances not furnished by itself we do not profess to know.

There is a doctrine well known to philosophers that the moon ceases to exist when no one is looking at it. I will not discuss the doctrine since I have not the least idea what is the meaning of the word existence when used in this connection. At any rate the science of astronomy has not been based on this spasmodic kind of moon. In the scientific world (which has to fulfil functions less vague than merely existing) there is a moon which appeared on the scene before the astronomer; it reflects sunlight when no one sees it; it has mass when no one is measuring the mass; it is distant 240,000 miles from the earth when no one is surveying the distance; and it will eclipse the sun in 1999 even if the human race has succeeding in killing itself off before that date. The moon—the scientific moon—has to play the part of a continuous causal element in a world conceived to be all causally interlocked.

What should we regard as a complete description of this scientific world? We must not introduce anything like velocity through aether, which is meaningless since it is not assigned any causal connection with our experience. On the other hand we cannot limit the description to the immediate data of our own spasmodic observations. The description should include nothing that is unobservable but a great deal that is actually unobserved. Virtually we postulate an infinite army of watchers and measurers. From moment to moment they survey everything that can be surveyed and measure everything that can be measured by methods which we ourselves might conceivably employ. Everything they measure goes down as part of the complete description of the scientific world. We can, of course, introduce derivative descriptions, words expressing mathematical combinations of the immediate measures which may give greater point to the description—so that we may not miss seeing the wood for the trees.

By employing the known physical laws expressing the uniformities of Nature we can to a large extent dispense with this army of watchers. We can afford to let the moon out of sight for an hour or two and deduce where it has been in the meantime. But when I assert that the moon (which I last saw in the west an hour ago) is now setting, I assert this not as my deduction but as a true fact of the scientific world. I am still postulating the imaginary watcher; I do not consult him, but I retain him to corroborate my statement if it is challenged. Similarly, when we say that the distance of Sirius is 50 billion miles we are not giving a merely conventional interpretation to its measured parallax; we intend to give it the same status in knowledge as if someone had actually gone through the operation of laying measuring rods end to end and counted how many were needed to reach to Sirius; and we should listen patiently to anyone who produced reasons for thinking that our deductions did not correspond to the “real facts”, i.e. the facts as known to our army of measurers. If we happen to make a deduction which could not conceivably be corroborated or disproved by these diligent measurers, there is no criterion of its truth or falsehood and it is thereby a meaningless deduction.

This theory of knowledge is primarily intended to apply to our macroscopic or large-scale survey of the physical world, but it has usually been taken for granted that it is equally applicable to a microscopic study. We have at last realised the disconcerting fact that though it applies to the moon it does not apply to the electron.

It does not hurt the moon to look at it. There is no inconsistency in supposing it to have been under the surveillance of relays of watchers whilst we were asleep. But it is otherwise with an electron. At certain times, viz. when it is interacting with a quantum, it might be detected by one of our watchers; but between whiles it virtually disappears from the physical world, having no interaction with it. We might arm our observers with flash-lamps to keep a more continuous watch on its doings; but the trouble is that under the flashlight it will not go on doing what it was doing in the dark. There is a fundamental inconsistency in conceiving the microscopic structure of the physical world to be under continuous survey because the surveillance would itself wreck the whole machine.

I expect that at first this will sound to you like a merely dialectical difficulty. But there is much more in it than that. The deliberate frustration of our efforts to bring knowledge of the microscopic world into orderly plan, is a strong hint to alter the plan.

It means that we have been aiming at a false ideal of a complete description of the world. There has not yet been time to make serious search for a new epistemology adapted to these conditions. It has become doubtful whether it will ever be possible to construct a physical world solely out of the knowable—the guiding principle in our macroscopic theories. If it is possible, it involves a great upheaval of the present foundations. It seems more likely that we must be content to admit a mixture of the knowable and unknowable. This means a denial of determinism, because the data required for a prediction of the future will include the unknowable elements of the past. I think it was Heisenberg who said, “The question whether from a complete knowledge of the past we can predict the future, does not arise because a complete knowledge of the past involves a self-contradiction.”