"Though the character of time and space is not in any sense a
priori, the essential relatedness of any perceived field of events
to all other events requires that this relatedness of all events
should conform to the ascertained disclosure derived from the limited
field. For we can only know that distant events are spatio-temporally
connected with the events immediately perceived by knowing what
these relations are. In other words, these relations must possess a
systematic uniformity in order that we may know of nature as extending
beyond isolated cases subjected to the direct examination of individual
perception.... This doctrine leads to the rejection of Einstein's
interpretation of his formulæ, as expressing a casual heterogeneity of
spatio-temporal warping, dependent upon contingent adjectives."
Thus whereas Eddington seems to regard it as necessary to adopt
Einstein's variable space, Whitehead regards it as necessary to reject
it. For my part, I do not see why we should agree with either view: the
matter seems to be one of convenience in the interpretation of formulæ.
Nevertheless, Dr Whitehead's arguments deserve careful examination.
The main force of the above passages is epistemological: the question
involved is the Kantian one, How is knowledge possible? I do not wish
to deal with this question in its general form. But without going
into theory of knowledge, there is what may be called a common-sense
answer. Einstein enables us to predict what in fact can be predicted
about astronomical occurrences, and that seems all that ought to be
demanded of him. Dr Whitehead objects to the "casual" heterogeneity
of space-time in Einstein's system. In a sense, this adjective is
justified, since the character of space-time[Pg 79] in any region depends
upon circumstances which can only be ascertained empirically—namely,
the distribution of matter in the neighbourhood. But in another
sense the adjective is not justified, since Einstein's law of
gravitation gives the rule according to which space-time is affected
by the neighbourhood of matter. To say that we cannot, by the help
of this rule, know in advance the geometry of a region we have not
explored, seems an insufficient objection, since we also cannot know
what astronomical occurrences will take place unless we know the
distribution of matter. Einstein, like other people, assumes the
permanence of matter; this is a point to be considered in another
connection, but it has no particular relevance to the present issue.
The way the heavenly bodies move depends upon the distribution of
matter in their neighbourhood, which is, in Dr Whitehead's phrase,
"casual." Even by assuming Euclidean geometry we cannot make
astronomical predictions unless we assume that we know the important
facts about the distribution of matter in the region concerned. Whether
we put the consequences of these facts into our geometry or not does
not seem to make any real difference to the possibility of physical
knowledge.
Public-domain text, read in full here on John Shaqi.
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