Environmental Engineering Reference
In-Depth Information
6
Relativistic Kinematics
6.1 TIME DILATION, LENGTH CONTRACTION AND SIMULTANEITY
In the next section we shall find the new equations which will replace the Galilean
transformation equations (5.1) and (5.2), but before that let us derive perhaps the
two most remarkable results in Einstein's theory: the fact that time passes at dif-
ferent rates in different inertial frames and that it doesn't make sense to speak of
the length of a metre rule without also stating the frame in which it is at rest.
Historically people have regarded distance and time as fundamental units. For
example, as defined by a standard length of material and an accurate periodic
device. Speed is then a derived quantity determined by the ratio of distance travelled
and time taken. Nowadays, the scientific community has stopped thinking of the
metre as fundamental. Instead the metre is defined to be the distance travelled in
a vacuum by light in a time of exactly 1/2,9979,2458 seconds. This might look
like a rather arbitrary definition but that particular sequence of numbers in the
denominator means that the metre so defined corresponds to the length of the
old standard metre, which was a metal bar kept locked in a vault in Paris. The
advantage of defining the metre in terms of the speed of light and the unit of time
means that we no longer have to worry about the fact that the metal bar is forever
changing as it expands and contracts. By defining the metre this way we have
chosen a value for the speed of light in a vacuum, i.e.
c
10
8
m/s.
There is nothing particularly special about using the speed of light here, strictly
speaking one could define the metre to be the distance travelled by an average snail
in 15 minutes. Then the snail speed would be fundamental. However, given the
variability in snail speeds, this would not consitute a very reliable measure. Light
speed is much more preferable and it has the particular advantage that it is the only
speed which everyone agrees upon (by Einstein's 2nd postulate); all other speeds
require the specification of an associated frame of reference.
=
2
.
99792458
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