28 SECTIONAL ADDRESSES 



Acting on a hint given by the theory of refraction, Heisenberg was led 

 to the suggestion that the contradictions of atomic theory would dis- 

 appear if one adopted the idea of non-commutative algebra in deahng 

 with the motions of electrons in an atom. Then the floodgates broke 

 and the whole New Quantum Theory burst forth. It would of course 

 be an incomplete account of it not to mention the quite different approach 

 made independently by de Broglie and Schrodinger. If we are to trace 

 this to its origin we must go back a century to Hamilton, for it was his 

 work in geometrical optics which showed how a wave of short wave- 

 length could be treated as a ray. It was de Broglie who worked out 

 the modern analogies, but it was Schrodinger who succeeded in giving 

 its full form, and by the invention of the zuave-fuiiction placed in the 

 hands of the mathematicians the most powerful of weapons for the 

 technical discussion of atomic problems. 



At first the work was of a formal kind, obviously right, and a complete 

 synthesis of the rival doctrines of particle and wave mechanics, but there 

 is a very interesting point that has gradually emerged in connection 

 with the discovery. In his first paper Heisenberg laid great stress on 

 the idea of building theory only on directly observable quantities. It 

 is not very clear how the distinction was drawn. The electron's orbit 

 is certainly not observable, but is it less so than the electric force which 

 is the amplitude in the light-wave emitted by the atom ? It has seemed 

 to me that it was not this idea of using the observable that was the merit 

 of his work, but rather the contrary — the capacity for carrying through 

 a formal mathematical analogy without ever asking what it all meant 

 in terms of observable things. However that may be, it was only a year 

 later that he remedied the defect by making a picture of his process by 

 means of the Uncertainty Principle. I may remind you that the Un- 

 certainty Principle asserts that it is impossible simultaneously to measure 

 the position and velocity of any body, because the measurement of either 

 inevitably produces a change of indeterminate amount in the other. 

 The subject has been so often discussed that I am not going into it now, 

 but as it concerns the centre of my argument, I want to emphasise its 

 negative side, which as I think is much the most important. In this 

 role the Uncertainty Principle is to be regarded as the argument used 

 to defeat the old-fashioned physicist who claims that there is at any rate 

 ideally no limit to the accuracy with which both position and velocity 

 can be simultaneously measured. He has to admit the correctness of 

 experiments such as the Compton effect, and we show him that by his 

 own admission he will be defeated. On the positive side the principle is 

 not so useful, because once we have seen the reason for the failure of 

 classical ideas, we had better take advantage of the full technique of the 

 quantum mechanics. Here my point is that the Uncertainty Principle 

 showed up a fallacy in the old arguments about causality, and it was a 

 fallacy about which we were so unconscious that we did not even know 

 we were making it. It is now easy to see that there was nothing wrong 

 with the old inference that if I know all about the present I can forecast 

 the future exactly ; the trouble was the impossibility of knowing the 

 present. Once this is seen the whole argument becomes obvious, but 

 nobody saw it until Heisenberg. We had somehow to avoid the com- 



