Elements of Modern Physics
414
Radio Source Counting
Radio telescopes can detect sources at enormous distances and hence can be
used to obtain informations about the number of ratio sources with apparent
brightness (related to the radiation energy received) l > l 0 . Now, for a
homogeneous distribution of sources, since l = a/r
2
, the number of sources with
l > l 0 is related to l 0 by
N =
3
0
br
=
3/2
0
/
b l
′
(11.96)
where l 0 =
2
0
/
a r , and a, b, b′ are constant. This implies that
ln N =
3
2
− ln l 0 + d
(11.97)
Observationally, the number of faint sources appears to be larger,
ln N ~ – 2.0 ln l 0 + d′
(11.98)
This is an interesting result. In the big-bang theory, it only means that since
the radiation from far away sources was emitted earlier, there must have been
(i) more numerous radio sources and/or (ii) brighter radio sources, at early times.
Particle Physics and Cosmology
Finally, we note the important role that our knowledge of particle properties, is
playing in our understanding of the universe. Two recent, though tentative,
developments are mentioned here.
The preponderance of matter over antimatter has been one of the puzzles in
cosmology. The solution to this puzzle may be in the difference in the properties
of baryons and antibaryons. The recent attempts at grand unification of strong,
weak and electromagnetic interactions (see Sec. 10.5), allow for differences in
the properties of matter and antimatter. Estimations based on these theories,
and also in rough agreement with the observed ratio of 10
–9
for the number of
baryons (essentially protons and neutrons) to the number of photons.
There has been a question about the missing mass in the universe (apart
from the mass of the galaxies). Some recent experiments appear to suggest that
neutrinos may have nonzero mass. If this is confirmed, the neutrinos of the
universe may contribute a substantial amount of mass to the galaxies and the
universe.
A striking characteristic of recent developments in modern physic is that
observations in such diverse fields as elementary particles, nuclear physics,
atoms and molecules, solid state physics and astrophysics, are interrelated and
414
Radio Source Counting
Radio telescopes can detect sources at enormous distances and hence can be
used to obtain informations about the number of ratio sources with apparent
brightness (related to the radiation energy received) l > l 0 . Now, for a
homogeneous distribution of sources, since l = a/r
2
, the number of sources with
l > l 0 is related to l 0 by
N =
3
0
br
=
3/2
0
/
b l
′
(11.96)
where l 0 =
2
0
/
a r , and a, b, b′ are constant. This implies that
ln N =
3
2
− ln l 0 + d
(11.97)
Observationally, the number of faint sources appears to be larger,
ln N ~ – 2.0 ln l 0 + d′
(11.98)
This is an interesting result. In the big-bang theory, it only means that since
the radiation from far away sources was emitted earlier, there must have been
(i) more numerous radio sources and/or (ii) brighter radio sources, at early times.
Particle Physics and Cosmology
Finally, we note the important role that our knowledge of particle properties, is
playing in our understanding of the universe. Two recent, though tentative,
developments are mentioned here.
The preponderance of matter over antimatter has been one of the puzzles in
cosmology. The solution to this puzzle may be in the difference in the properties
of baryons and antibaryons. The recent attempts at grand unification of strong,
weak and electromagnetic interactions (see Sec. 10.5), allow for differences in
the properties of matter and antimatter. Estimations based on these theories,
and also in rough agreement with the observed ratio of 10
–9
for the number of
baryons (essentially protons and neutrons) to the number of photons.
There has been a question about the missing mass in the universe (apart
from the mass of the galaxies). Some recent experiments appear to suggest that
neutrinos may have nonzero mass. If this is confirmed, the neutrinos of the
universe may contribute a substantial amount of mass to the galaxies and the
universe.
A striking characteristic of recent developments in modern physic is that
observations in such diverse fields as elementary particles, nuclear physics,
atoms and molecules, solid state physics and astrophysics, are interrelated and