Environmental Engineering Reference
In-Depth Information
7
Relativistic Energy and
Momentum
7.1 MOMENTUM AND ENERGY
In classical theory, energy and momentum are conserved quantities, and are
therefore of particular significance. From a practical viewpoint, we can exploit
the conservation of energy and/or momentum in order to simplify calculations.
At this stage in our development of Einstein's theory we are led to contemplate
just how energy and momentum are to be defined if they are to be compat-
ible with Einstein's two postulates.
A priori
it might be that the concepts of
energy and momentum are only useful in the classical regime, where speeds
are small compared to light speed, in which case any attempt to extrapolate
into the relativistic regime would be doomed to fail. Fortunately, this is not the
case. Transcending relativity theory, it is now known that conservation laws often
have their origin in symmetry. Technically speaking, the law of conservation of
energy arises because physical phenomena are invariant under time translations,
which means that energy is conserved because, all other things being equal, it
does not matter whether one conducts an experiment today, tomorrow or at some
other time in history. Similarly, momentum is conserved because physical phe-
nomena are invariant under spatial translations. Again, in more down to earth
language, momentum conservation is a consequence of the fact that, all other
things being equal, it does not matter whether one conducts an experiment here
or over there. That said, and since we expect the same underlying symmetries
of space and time in Einstein's theory, we press on with our attempt to intro-
duce definitions of energy and momentum that do not conflict with Einstein's
postulates.
