Principle of Indeterminacy. My apprehension lest a fourth version of the new quantum theory should appear before the lectures were delivered was not fulfilled; but a few months later the theory definitely entered on a new phase. It was Heisenberg again who set in motion the new development in the summer of 1927, and the consequences were further elucidated by Bohr. The outcome of it is a fundamental general principle which seems to rank in importance with the principle of relativity. I shall here call it the “principle of indeterminacy”. The gist of it can be stated as follows: a particle may have position or it may have velocity but it cannot in any exact sense have both. If we are content with a certain margin of inaccuracy and if we are content with statements that claim no certainty but only high probability, then it is possible to ascribe both position and velocity to a particle. But if we strive after a more accurate specification of position a very remarkable thing happens; the greater accuracy can be attained, but it is compensated by a greater inaccuracy in the specification of the velocity. Similarly if the specification of the velocity is made more accurate the position becomes less determinate. [Pg 221] Suppose for example that we wish to know the position and velocity of an electron at a given moment. Theoretically it would be possible to fix the position with a probable error of about ¹⁄₁₀₀₀ of a millimetre and the velocity with a probable error of 1 kilometre per second. But an error of ¹⁄₁₀₀₀ of a millimetre is large compared with that of some of our space measurements; is there no conceivable way of fixing the position to ¹⁄₁₀₀₀₀ of a millimetre? Certainly; but in that case it will only be possible to fix the velocity with an error of 10 kilometres per second. The conditions of our exploration of the secrets of Nature are such that the more we bring to light the secret of position the more the secret of velocity is hidden. They are like the old man and woman in the weather-glass; as one comes out of one door, the other retires behind the other door. When we encounter unexpected obstacles in finding out something which we wish to know, there are two possible courses to take. It may be that the right course is to treat the obstacle as a spur to further efforts; but there is a second possibility—that we have been trying to find something which does not exist. You will remember that that was how the relativity theory accounted for the apparent concealment of our velocity through the aether.