June 18, 1914] 
NATURE 
409 
. 
this way of ordering the idea of simultaneous 
events at different places is essential. 
Now the very. first thing that appears, if we 
accept the hypothesis of relativity, is that it is 
impossible for us to determine uniquely whether 
two events are or are not simultaneous. This can 
be best illustrated by a simple ideal experiment. 
Retaining for the present the conception of a 
unique stationary zther, let us suppose that two 
points A, B, are moving relative to it with the 
same velocity v, and let c be the velocity of light. 
Now imagine a ray of light to be sent out from 
A at,an instant ¢,, in the direction AB. Let this 
ray arrive at B at the instant f,. Let it then be 
reflected back to A, arriving there at the instant 
t,. - Now if the distance A B is J, since the relative 
velocity of the light on the outward journey is 
(c—v), we have . 
i, —t, =1/(c —2), 
and similarly since the relative velocity on the 
return is (c+v), 
ts—tg=1/(c +). 
From these equations we obtain 
tp=t, + ts/2+lu/(c?—v"). 
Now if the velocity v were zero, we should 
have the result that the moment of reflection at 
B is simultaneous with the moment 3(t,+ts), that 
is, with the moment at A midway between those 
of emission and return of the ray. But if the 
velocity v is unknown, which is the hypothesis 
with which we are dealing, then we cannot say 
from this experiment what instant at A is simul- 
taneous with the instant ft, at B. 
Now no man of science should say, of course, 
that because he does not know, or cannot deter- 
mine a thing, that, therefore, it does not exist. 
We have no right to say that, because we cannot 
determine our velocity relative to the «ther that 
therefore the ether cannot exist. So we do not 
say that the conception of “simultaneity” is an 
absurdity ; what we do say is that the notion is not 
an intuitive one, forced upon us with a unique 
significance apart from all material phenomena; 
but that it is a convenient element in our ways 
of thinking about phenomena, and is really in- 
separable from the whole body of thought about 
them, that is, from the laws by which we con- 
veniently describe their sequences. 
In the light of the simple experiment described 
above, therefore, we find that the conception of 
“simultaneity ”’ does not become definite until we 
have assigned a definite velocity to a certain 
point, which may conveniently be our own point 
of observation. 
The next thing we may notice is that the notion 
of the “length of a body” becomes indefinite 
along with the term “simultaneous.” For in our 
usual ways of thinking, the length of a body is 
the same as, is in fact defined to be, the distance 
between two points of our universal frame of 
reference, with which the ends of the -body 
““simultaneously coincide.” Until we have made 
the last phrase definite, the length of a body is 
either indefinite, or else it must be defined in some 
NO. 2329, VOL. 93] 
other way, in which case we might have a con- 
tradiction between the definition of length and the 
derived concept of measurable space. 
In the light of these difficulties we may be pre- 
pared to reconsider our preconceived notions of ' 
the measures of space and time and what is 
implied in respect of them by the laws which we 
find to be the best expression of the order which 
we have disentangled from the complex of physical 
phenomena, including among those laws the 
principle of relativity. 
As was stated at the beginning, this includes 
the statement that it is impossible for an observer 
to detect a difference between the velocities of 
light in different directions, whatever may be his 
own motion. In other words, the propagation of 
light through space is supposed to be expressible 
as a uniform propagation in all directions with 
velocity c whatever velocity the observer supposes 
himself to have. This is a_ self-contradictory 
assumption if we adhere to the space and time 
which we use in Newtonian dynamics, where the 
relative velocity of two points is just their dif- 
ference. But if we grant that our measures of 
space and time are, as has been suggested above, 
modes of thought inseparable from the laws into 
which they enter, then we realise that what we 
have been in the habit of looking upon as assured 
and permanent elements in our thought may, 
with the development of our knowledge of the 
physical world, come to require modification, 
If now we start from the fundamental law that 
there is a definite physically-determined velocity, 
that of light, an invariant element in the physical 
world, we can proceed by an algebraic process 
to examine what variety is possible in the quan- 
tities by which we measure space and time. This 
is a problem capable of complete solution, and 
when it is carried out we find that there is a 
large degree of. arbitrariness. It appears that 
out of all the possible systems of measurement 
so obtained we can always find one such that 
all points at rest in this system have an arbi- 
trary uniform velocity in any other given system. 
If this velocity is v and if two simultaneous 
events as estimated in the time variable of the 
first system occur at two points at distance 1 
apart on a line parallel to v, then. as estimated 
in the second space-time system, they occur at 
instants separated by a time lIv/c(c?—v?)?, at 
points the distance apart of which is cl/(c?—v?)}. 
The remarkable thing is that when we have 
developed this infinite number of ways of measur- 
ing space and time out of the single hypothesis 
of the universal value of the velocity of light, we 
are able to show further that the whole set of 
laws of the electromagnetic field may be retained 
in the same form whichever of the systems of 
measurement we adopt. Thus we find that not 
only space and time, but the physical quantities, 
electric and magnetic intensity, and the force on 
“ec 
a charged body, are quantities which are “re- 
lative,” that is, which are only uniquely defined 
after the choice of the system of reference has 
} been made; that is, after we have stated in ad- 
