FOUR-DIMENSIONAL TUBES 
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tivity can admit as being theoretically possible is one which 
finds its natural expression in terms of the four-dimensional 
continuum, the continuum in which the three dimensions of 
space and the one dimension of time enter as four equal part 
ners. There can hardly be an atomicity of the continuum itself, 
for, if there were, a universal constant of the physical dimen 
sions of space multiplied by time ought to pervade the whole 
of physical science. Nothing of the kind is even suspected, nor 
so far as I know, has ever been so much as surmised. Thus 
science can to-day proclaim with high confidence that both space 
and time are continuous.” 
Jeans suggests that the new atomicity may conceivably be 
an atomicity of the metric properties of the continuum, such as 
determine its curvatures. 
It is clear from what has already been said that the view 
taken of the quantum must be profoundly affected by the prin 
ciples of relativity. It will be well therefore to consider some 
what more carefully the nature and the consequences of these 
principles. 
3. Relativity and the Space-Time World 
In its simplest form the “ restricted,” or as it is sometimes 
called the “ special,” theory of relativity asserts that when we 
are dealing with uniform rectilinear motion, we can only speak 
of the mutual or relative motion of bodies. This statement is 
little more than an expression of the kinematic conception of 
motion, as signifying the alteration in the position of a body, 
and this can only be fixed by its distance from other bodies. 
But the statement may be extended so as to include the physical 
idea of motion, as a certain condition of the body which might 
conceivably be determined without reference to other bodies. 
We may then assert that it is impossible by means of observa 
tions made within a closed system (i.e. without reference to the 
surroundings) to ascertain whether or not the system is in uniform 
rectilinear motion.* 
Einstein employed a second principle, deduced from the re 
sults of the Michelson-Morley experiment, which he called “ the 
principle of the constancy of the velocity of light.” This asserts 
that the velocity of light is an “invariant ” of nature, always 
the same from whatever standpoint it is measured. 
These two principles lead to a well-known set of equations 
(generally referred to as the “ Lorentz transformation ”) by 
* See Thirring, The Ideas of Einstein’s Theory, pp. 2 and 166 (Methuen, 
1921).