[The Concept of Nature by Alfred North Whitehead]@TWC D-Link bookThe Concept of Nature CHAPTER VIII 38/41
This fact is expressed by saying that the ten J's form a 'tensor.' It is not going too far to say that the announcement that physicists would have in future to study the theory of tensors created a veritable panic among them when the verification of Einstein's predictions was first announced. The ten J's at any event-particle E can be expressed in terms of two functions which I call the potential and the 'associate-potential' at E.The potential is practically what is meant by the ordinary gravitation potential, when we express ourselves in terms of the Euclidean space in reference to which the attracting mass is at rest. The associate-potential is defined by the modification of substituting the direct distance for the inverse distance in the definition of the potential, and its calculation can easily be made to depend on that of the old-fashioned potential.
Thus the calculation of the J's--the coefficients of impetus, as I will call them--does not involve anything very revolutionary in the mathematical knowledge of physicists.
We now return to the path of the attracted particle.
We add up all the elements of impetus in the whole path, and obtain thereby what I call the 'integral impetus.' The characteristic of the actual path as compared with neighbouring alternative paths is that in the actual paths the integral impetus would neither gain nor lose, if the particle wobbled out of it into a small extremely near alternative path.
Mathematicians would express this by saying, that the integral impetus is stationary for an infinitesimal displacement.
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