1 6 4 D O C . 1 7 0 O N O V E R D E T E R M I N A T I O N

must examine whether one should indeed conclude from former endeavors and

data that it is impossible to make do with partial differential equations. Anyone

who fully appreciates the wonderful certainty with which the wave theory inter-

prets the geometrically much-convoluted phenomena of interference and diffrac-

tion of light will have difficulty believing that partial differential equations are, in

the final instance, unsuited to doing justice to the observed facts.

Taking a critical look at the Maxwell-Lorentz theory, one realizes that its foun-

dation consists of two formal, only loosely connected parts, namely, the differential

equations of the electromagnetic field and the equations of motion of the (positive

and negative) electron. The phenomena of diffraction and interference which are so

well confirmed by experiment are essentially formally governed by the field equa-

tions alone; the processes of absorption, on the contrary, which theory is unable to

render faithfully in accord with observation, are mainly defined by the laws of mo-

tion of the

electron.1)

It is hence an obvious (often expressed) thought that one

should retain the field equations but should abandon the equations of motion for

electrons. This would, of course, also entail that one can not retain the customary

theory for localizing energy within the field. This theoretical possibility was not

pursued further for the simple reason that hitherto no tractable path toward a for-

mulation of different laws of motion for the electron was found. Mie’s attempt to

extend the field equations in such a way that they also apply to the interior of elec-

trons has hitherto led to no useful

result.[6]

This method could have led to a unifi-

cation of the foundations in that it would have made special equations of motion

for electrons superfluous. Why this approach cannot contribute decisively toward

a solution to the problem of quanta either, however, will emerge from the following

consideration, which in my view leads us to the most essential point of the whole

problem.

According to existing theories, the initial state of a system can be freely chosen;

the differential equations then deliver the temporal continuation. According to our

knowledge about quantum states, as it has been developed particularly in connec-

tion with Bohr’s theory during the last decade, this feature of the theory does not

correspond to reality. The initial state of an electron moving around a hydrogen nu-

cleus cannot be freely selected. Rather, this choice must meet the quantum condi-

tions. Generally: not only the temporal continuation but also the initial state is sub-

ject to laws.

1)

The foundation of mechanics in itself contradicts already the quantum facts (failure

of the equipartition theory). The equations of motion for material points therefore have to

be abandoned, regardless of the question as to whether one can hold on to the field

theory.[9]

[p. 360]