The Concept of Nature: The Tarner Lectures Delivered in Trinity College, November 1919Whitehead, Alfred North
Philosophy
The Concept of Nature: The Tarner Lectures Delivered in Trinity College, November 1919
Whitehead, Alfred North
Knowledge, Theory of; Nature; Science -- Philosophy
In order to answer our question we put the idea of the attracting masses
in the background and concentrate attention on the field of activity of
the events in the neighbourhood of the path. In so doing we are acting
in conformity with the whole trend of scientific thought during the last
hundred years, which has more and more concentrated attention on the
field of force as the immediate agent in directing motion, to the
exclusion of the consideration of the immediate mutual influence between
two distant bodies. We have got to find the way of expressing the field
of activity of events in the neighbourhood of some definite
event-particle E of the four-dimensional manifold. I bring in a
fundamental physical idea which I call the 'impetus' to express this
physical field. The event-particle E is related to any neighbouring
event-particle P by an element of impetus. The assemblage of all the
elements of impetus relating E to the assemblage of event-particles in
the neighbourhood of E expresses the character of the field of
activity in the neighbourhood of E. Where I differ from Einstein is
that he conceives this quantity which I call the impetus as merely
expressing the characters of the space and time to be adopted and thus
ends by talking of the gravitational field expressing a curvature in the
space-time manifold. I cannot attach any clear conception to his
interpretation of space and time. My formulae differ slightly from his,
though they agree in those instances where his results have been
verified. I need hardly say that in this particular of the formulation
of the law of gravitation I have drawn on the general method of
procedure which constitutes his great discovery.
Einstein showed how to express the characters of the assemblage of
elements of impetus of the field surrounding an event-particle E in
terms of ten quantities which I will call J_{11}, J_{12}
(=J_{21}), J_{22}, J_{23}(=J_{32}), etc. It will be noted that
there are four spatio-temporal measurements relating E to its
neighbour P, and that there are ten pairs of such measurements if we
are allowed to take any one measurement twice over to make one such
pair. The ten J's depend merely on the position of E in the
four-dimensional manifold, and the element of impetus between E and
P can be expressed in terms of the ten J's and the ten pairs of the
four spatio-temporal measurements relating E and P. The numerical
values of the J's will depend on the system of measurement adopted,
but are so adjusted to each particular system that the same value is
obtained for the element of impetus between E and P, whatever be the
system of measurement adopted. 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.
Public-domain text, read in full here on John Shaqi.
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