PRINCIPLE OF INDETERMINACY 223 



sponding momentum, the necessary uncertainty of our 

 knowledge of q multiplied by the uncertainty of p is of 

 the order of magnitude of the quantum constant h. 



A general kind of reason for this can be seen without 

 much difficulty. Suppose it is a question of knowing 

 the position and momentum of an electron. So long as 

 the electron is not interacting with the rest of the uni- 

 verse we cannot be aware of it. We must take our 

 chance of obtaining knowledge of it at moments when it 

 is interacting with something and thereby producing 

 effects that can be observed. But in any such interaction 

 a complete quantum is involved; and the passage of this 

 quantum, altering to an important extent the conditions 

 at the moment of our observation, makes the information 

 out of date even as we obtain it. 



Suppose that (ideally) an electron is observed under 

 a powerful microscope in order to determine its position 

 with great accuracy. For it to be seen at all it must be 

 illuminated and scatter light to reach the eye. The least 

 it can scatter is one quantum. In scattering this it re- 

 ceives from the light a kick of unpredictable amount; 

 we can only state the respective probabilities of kicks 

 of different amounts. Thus the condition of our ascer- 

 taining the position is that we disturb the electron in an 

 incalculable way which will prevent our subsequently as- 

 certaining how much momentum it had. However, we 

 shall be able to ascertain the momentum with an uncer- 

 tainty represented by the kick, and if the probable kick 

 is small the probable error will be small. To keep the 

 kick small we must use a quantum of smali energy, that 

 is to say, light of long wave-length. But to use long 

 wave-length reduces the accuracy of our microscope. 

 The longer the waves, the larger the diffraction images. 

 And it must be remembered that it takes a great many 



