148 Thermal History of the Universe
On the other hand, following the observation of Villata [6], if one of the momenta
refers to a particle and the other one to an antiparticle, the momentum vector of
the antiparticle must be (C)PT-transformed, thus acquiring a minus-sign. This then
reverses the sign of the four-acceleration so that it becomes repulsive. As he points
out, there are two possible interpretations for the existence of antimatter. The more
conventional one is that antiparticles really exist as entities distinct from their matter
counterparts, and that they travel forward in time, as all ordinary particles. The other
interpretation is that antiparticles do not really exist as distinct particles, but that they
are nothing else than the corresponding particles that are traveling backwards in time
(BIT).
The most convincing argument in favor of the BIT interpretation is just the CPT
symmetry of physical laws, since it offers a physical explanation to the need of cou-
pling C with T (and P) for describing the behavior of antimatter: if antimatter were
not traveling back in time, why should we apply the time inversion? In other words,
according to the BIT interpretation, CPT is the operation that transforms events, par-
ticles and fields from one time direction to the other: the role of T is obvious, since
it inverts time intervals, P is needed to get a proper Lorentz transformation (T and P
alone are improper), and C provides the needed charge reversals to see time-reversed
matter as antimatter.
Problems
- Show that an expansion by a factor푎leaves the black-body spectrum (6.10)
unchanged, except that푇decreases to푇∕푎. - The flow of total energy received on Earth from the Sun is expressed by the
solar constant 1. 36 × 103 Jm−^2 s. Use Equation (6.41) to determine the surface
temperature of the Sun,
푏=휆푇. (6.120)
Using this temperature and the knowledge that the dominant color of the Sun
is yellow with a wavelength of휆= 0. 503 μm. What energy density does that flow
correspond to?- A line in the spectrum of hydrogen has frequency휈= 2. 5 × 1015 Hz. If this radi-
ation is emitted by hydrogen on the surface of a star where the temperature is
6000K, what is the Doppler broadening [7]? - A spherical satellite of radius푟painted black, travels around the Sun at a distance
푑from the center. The Sun radiates as a black-body at a temperature of 6000K. If
the Sun subtends an angle of휃radians as seen from the satellite (with휃≪1), find
an expression for the equilibrium temperature of the satellite in terms of휃.To
proceed, calculate the energy absorbed by the satellite, and the energy radiated
per unit time [7]. - Use the laws of conservation of energy and momentum and the equation of rela-
tivistic kinematics [Equation (3.9)] to show that positronium cannot decay into
a single photon.