1 2 0 D O C . 3 1 I D E A S A N D M E T H O D S
7. The Relativity of
Simultaneity[17]
The idea which led out of the dilemma explained under (5) is connected to the fol-
lowing question. Let and be two points of the coordinate system . Let a sud-
den event take place in each one of these points. We also state that these two events
occur simultaneously. Does this statement have a definite meaning? If yes, what is
this meaning?
At first, everybody believes that the statement of simultaneity would make im-
mediate sense; but this certainty rests on a deep-rooted prejudice suggested by ex-
perience. 〈When we want to clarify what we understand under the term simultane-
ity of both events.〉 Because for most purposes it is sufficient to agree that: two
events are simultaneous if one observer sees them simultaneously. For if the loca-
tions of both events are not too far distant from each other, then the simultaneous
viewing is nearly independent of the location of the observer; light has a speed of
propagation that in most experiences is equivalent to a velocity of infinite magni-
tude. Light practically provides instantaneous signals; it embodies simultaneity
with sufficient precision for everyday experience. For this reason alone we are in-
clined to connect immediate sense with simultaneity of spatially distant events.
On the other hand, it would be impossible to chronologically link the processes
at with those at if there were no physical interaction between the locations
and . It is therefore clear that we can get a physical definition of simultaneity only
if our definition uses processes that establish a connection between the two loca-
tions considered. For such processes we select light signals in a vacuum because
we are especially well informed about the law of light propagation, as was ex-
plained above. We define simultaneity on the basis of the principle of the constancy
of the speed of light.
Let and be two points of the inertial system , say at the end points of a
rod, at rest relative to , and be the midpoint of the rod. A light signal shall be
sent from in all directions. The principle of the constancy of the speed of light
forces us to state that the arrival 〈time〉 of the light signal in is simultaneous with
the arrival in . With this we have won a physically meaningful definition of si-
multaneity.1[18]
However, it is to be well noted that this definition uses the system of reference
. We do not know if two distant events that are simultaneous in reference to
1
The following is necessary in order to keep the definition free of contradiction. If the
〈pair
of
events〉
and are pairs of simultaneous events with respect to ,
then and too are simultaneous. If this were not the case, the principle of the constancy
of the speed of light could not be maintained.
A B K
[p. 7]
A B A
B
A B K
K M
M
A
B
α β) , ( α γ) , ( K
β γ
K