MODERN PHYSICS — JEANS 91 



particle-picture and supported the wave-picture — not merely, be it 

 noted, as a picture of our knowledge of nature, but as a picture of 

 nature itself. The particle-parable is useful as a concession to the 

 materialistic habits of thought which have become ingrained in our 

 minds, but it can no longer claim to fit the facts, and, so far as we 

 can at present see, the truth about nature must lie very near to the 

 wave-parable. 



Let me digress again to remind you of two simple instances of 

 such conflicts and of the verdicts which observation has pronounced 

 upon them. 



A shower of parallel-moving electrons forms in effect an electric 

 current. Let us shoot such a shower of electrons at a thin film of 

 metal, as your own Prof. G. P. Thomson did. The particle-parable 

 compares it to a shower of hailstones falling on a crowd of umbrellas ; 

 we expect the electrons to get through somehow or anyhow and come 

 out on the other side as a disordered mob. But the wave-parable 

 tells us that the shower of electrons is a train of waves. It must 

 retain its wave-formation, not only in passing through the film, 

 but also when it emerges on the other side. And this is what actually 

 happens; it comes out and forms a wave-pattern which can be pre- 

 dicted — completely and perfectly — from its wave-picture before it 

 entered the film. 



Next let us shoot our shower of electrons against the barrier 

 formed by an adverse electromotive force. If the electrons of the 

 shower have a uniform energy of 10 volts each, let us throw them 

 against an adverse potential difference of a million volts. According 

 to the particle-parable, it is like throwing a handful of shot up into 

 the air; they will all fall back to earth in time — the conservation of 

 energy will see to that. But the wave-parable again sees our shower 

 of electrons as a train of waves — like a beam of light — and sees the 

 potential barrier as an obstructing layer — like a dirty window pane. 

 The wave-parable tells us that this will check, but not entirely 

 stop, our beam of electrons. It evens shows us how to calculate 

 what fraction will get through. And just this fraction, in actual 

 fact, does get through; a certain number of 10-volt electrons sur- 

 mount the potential barrier of a million volts — as though a few 

 of the shot thrown lightly up from our hands were to surmount the 

 earth's gravitational field and wander off into space. The phenom- 

 enon appears to be in flat contradiction to the law of conservation 

 of energy, but we must remember that waves of knowledge are not 

 likely to own allegiance to this law. 



A further problem arises out of this experiment. Of the mil- 

 lions of electrons of the original shower, which particular electrons 

 will get through the obstacle? Is it those who get off the mark 



