MATTER, A MODE OF MOTION 363 



as one factor in the description of an interference pattern which results from 

 the superposition of component progressive waves of different frequencies, 

 each of which travels with velocity c. This difference in viewpoint leads to 

 other differences. 



One of these has to do with the possibility of describing accurately both 

 the position and velocity of a particle, which is ruled out from the wave 

 mechanics viewpoint. An ether wave pattern, however, may have its posi- 

 tion accurately described by its envelope, while at the same time the pattern 

 moves with a definite velocity. The particle velocity may here be regarded 

 as a group velocity derived from two waves progressing in opposite direc- 

 tions, but does not depend on the presence of dispersion as does that for 

 waves in the same direction. It is not to be concluded from this that the 

 position and velocity can be measured with this accuracy, for we have still 

 to deal with the disturbing effect of the measurement. 



From the ether viewpoint, one of the limitations of wave mechanics is 

 to be expected, its inability to calculate directly the position of a particle. 

 The information regarding this position is contained in the expression for 

 the envelope, while the wave factor depends only on its state of motion. A 

 calculation based on a solution which involves the wave factor without the 

 envelope would be expected to be indefinite regarding position. We should 

 expect, however, that it would give information as to the probability of the 

 presence of the particle in a given region, since this is derivable from its 

 state of motion. 



Returning to the comparison with experiment, while wave patterns based 

 on the linear equations have shown close agreement so far, the next experi- 

 ment upsets the applecart. It has been observed that the motion of one 

 particle is modified by the presence of other particles in its neighborhood. 

 So long as the assumed equations are linear, the law of superposition holds, 

 and every solution is independent of every other one. So any wave pattern, 

 when once set up, will continue in its state of rest or of uniform motion 

 indefinitely, and will not be influenced by the presence of other patterns or 

 of free progressive waves. But these together comprise all other matter and 

 radiation. Hence, while we have provided for the property of inertia, there is 

 nothing which tends to alter the state of motion of a body, that is, there 

 are no forces. In this respect the present linear treatment is similar to the 

 special theory of relativity. So, in order to represent the interactions between 

 particles, account must be taken of those between patterns which result 

 from the non-linearity and time dependence of the ether. 



Reactions between Patterns 



The general problem of the effect of one pattern on another is even more 

 intricate than that of the stable state of a single pattern, which it includes. 



