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An Introduction To Non-aristotelian Systems And General Semantics.

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732
SUPPLEMENT I
by the strongest experimental evidence; it is generally accepted; if the strange element in the result concerning units of time is due to this postulate, it appears that we must accept it as being required by such experience as has already been tested with due care. Hence the conclusion seems to be inevitable that the strangeness in our result is due principally to postulate R.
We shall presently see that the same basis of postulates leads to the conclusion that corresponding units of length in the two systems are also different when taken in certain directions. From the transformations of time and space which result from the conclusions thus obtained the whole restricted theory of relativity may be deduced (as is shown in the book mentioned). Therefore this theory depends essentially on the principle of correspondence of units in two systems of reference and on the propositions set forth explicitly in the postulates; and all of these are either generalizations from experiment or statements of laws which have usually been accepted. Hence we conclude: The restricted theory of relativity may be developed by logical processes from the generalised results of certain experiments together with certain laws which have for a long time been accepted.
The main result concerning the relation of units of length may be put in the following form:
If two systems of reference Si and Ss move with a relative velocity v and if 0 is the ratio v/c of v to the velocity c of light as measured on either system, then to an observer on S\ the unit of length of Si along the line of relative motion appears to be in the ratio to that which is described to
him as a unit by an observer on St while to an observer on 52 the unit of length of St along the line of relative motion appears to be in the ratioto
that which is described to him as a unit by the observer on Si.
These remarkable conclusions concerning units of length in two systems of reference rest on just those postulates which led to the strange results as to the units of time.
What often impresses one as the most remarkable conclusion in the theory of relativity is one which implies that the notion of simultaneity of events happening at different places is indefinite in meaning until some convention is adopted as to how simultaneity is to be determined. In fact, there is no such thing as absolute simultaneity of events happening at different places. With respect to the measured time and space of physics we must conclude that time does not run its course independently of space. Measured time and space are indissolubly bound together. The theorem which sets this forth most concretely may be stated in the following way:
Let two systems of reference Si and 5g have an unaccelerated relative velocity v. Let an observer on Si place two clocks in the line of relative motion of Si and 52 and adjust them so that they appear to him to mark simultaneously the same time. Then to an observer on Si the clock on 52 which is forward in point of motion appears to be behind in point of time by the amount