Environmental Engineering Reference
In-Depth Information
As we have just seen, only in the limit of small
u/c
is the kinetic energy given
1
2
mu
2
. Since only the total energy is conserved we have the intriguing possibility
that mass is essentially just another form of energy and that kinetic energy might
be traded for mass (and vice versa) in physical processes.
Remarkably this is just what happens in Nature. The most striking examples
are to be found in particle and nuclear physics. For example, a nucleus at rest
can spontaneously transform into a system of lighter particles travelling with some
kinetic energy, leaving no trace of the original nucleus. In this case the total mass
of the lighter particles is less than the mass of the initial nucleus by an amount
that is exactly equal to the total kinetic energy of the particles (divided by
c
2
). Of
course this phenomenon lies behind the operation of nuclear fission reactors, where
an atomic nucleus breaks into two with the liberation of a significant amount of
energy. In particle physics, the LEP collider at CERN (the European Centre for
Particle Physics in Geneva) manufactured head-on collisions between electrons
and positrons. In a single collision, all of the kinetic energy and all of the mass
energy of the incoming particles was used to manufacture a single
Z
particle at
rest. In that way, the incoming kinetic energy was converted entirely into the mass
energy of a
Z
particle. In fact, one of the main motivations for building LEP
was to produce millions of
Z
particles this way in order to study the detailed
properties of the weak interactions and their unification with electromagnetism in
the so-called 'electroweak theory'. Apart from such striking examples of the way
Nature utilises the possibility to trade off mass and kinetic energy, the idea is
applicable in more everyday phenomena. For example, if one would burn a mass
of coal in a container sealed so that no material can enter or leave it then the mass
of the container after the coal has burnt (i.e. the mass of the remaining ash plus
gases) would be less than the initial mass of coal. The difference in mass being
equal exactly to the total energy radiated by the container divided by
c
2
.Thisis
clearly a very new idea, deviating essentially from the classical idea that there exists
some immutable atomic substructure. For chemical processes, the reduction in mass
is typically very small indeed
3
due to the largeness of the speed of light. That is
why the mass-energy equivalence was not demonstrated in a laboratory experiment
until long after Einstein's original conjecture using nuclear processes in which
the energies involved are much larger and changes in mass correspondingly much
more significant. Cockcroft and Walton are credited with providing the first direct
evidence in their work of 1932 wherein they studied the reaction p
by
+
→
+
α
and showed that the reduction in mass was balanced by an increase in kinetic
energy in accord with Einstein's expectations.
Before moving on, we pause to reflect upon an interesting symmetry which we
have accidentally uncovered.
Li
α
7.1.2 The hint of an underlying symmetry
Take a look at Eq. (7.20) and Eq. (7.22). They tell us that a particle travelling
in
S
with energy
E
and momentum components
(p
x
,p
y
)
has momenta
(p
x
,p
y
)
in
3
When expressed as a fraction of the total mass.
