MODERN CONCEPTS IN PHYSICS — LANGMUIR 237 



them. If we make an experiment which proves that an electron 

 has a very definite position, then it Nvoukl seem to prove that it is a 

 particle. In that case, however, according; to the uncertainty prin- 

 ciple, we are not able to determine accurately the velocity and there- 

 fore can not predict where the particle will <^o. • 



Bohr has emphasized that the essential reason that the classical 

 theory falls down in any detailed description of atomic phenomena 

 is that our knowledge of such atomic systems can only be obtained 

 throujLrh an act of observation which makes the observer inherently a 

 part of the system. On the classical theory we assume that we 

 could have knowledge of a completely closed system as though it 

 were possible to know anything of what would go on in a strictly 

 closed system. In order to make an observation some signal must 

 be transmitted from the system to ourselves, and if we take this 

 interaction completely into account we are forced to the quantum 

 theory with its uncertainty principle. 



An interesting feature of this new quantum mechanics is that 

 the original conception of the relation between cause and effect 

 which was universally accepted in science has lost its meaning. 

 Atomic processes seem to be governed fundamentally by the law 

 of probability. It has no meaning to ask when a particular radium 

 atom will disintegrate, for no operation is conceivable by which such 

 an event could be predicted. The same is true of every individual 

 quantum process. We have no guarantee whatever that the expul- 

 sion of an a-particle from an atom of radium has any immediate 

 cause. In chemistry the formation of nuclei in supercooled liquids, 

 etc., must be essentially quantum phenomena in which no cause can 

 be assigned for the formation of the individual nucleus. By vary- 

 ing the conditions we may alter the probability that a nucleus will 

 appear at a given point, but in no absolute sense can we ever make a 

 nucleus form through a direct cause. 



By a deeper analysis of this question of causality Bohr concludes 

 that we have an option af two alternative descriptions of natural 

 phenomena. If we choose to describe phenomena in terms of ordi- 

 nary space and time then we must abandon causality. We may, 

 however, retain the conception of causality if we are willing to 

 describe atomic phenomena in terms of what the mathematician calls 

 configuration space. Consider, for example, a helium atom with its 

 two electrons. If we attempt to give the position of both of these 

 electrons in space wo would need a set of 3 coordinates, x, y. /, for 

 each of the electrons, that is, G coordinates in all, 3 of which belong 

 to one and '^ to the other electron. The mathematician, however, 

 finds that the 2 electrons in general could also be described by 1 

 point in G-dimensional space, for such a point has G coordinates. 



