6 From Newton to Hubble
motion’ was to be understood as motion relative to the whole Universe. Although
Mach clearly realized that all motion is relative, it was left to Einstein to take the full
step of studying the laws of physics as seen by observers in inertial frames in relative
motion with respect to each other.
Einstein published his General Theory of Relativity in 1917, but the only solution he
found to the highly nonlinear differential equations was that of a static Universe. This
was not so unsatisfactory though, because the then known Universe comprised only
the stars in our Galaxy, which indeed was seen as static, and some nebulae of ill-known
distance and controversial nature. Einstein firmly believed in a static Universe until he
met Hubble in 1929 and was overwhelmed by the evidence for what was to be called
Hubble’s law.
Immediately after general relativity became known,Willem de Sitter(1872–1934)
published (in 1917) another solution, for the case of empty space-time in an expo-
nential state of expansion. In 1922 the Russian meteorologistAlexandr Friedmann
(1888–1925) found a range of intermediate solutions to the Einstein equation which
describe the standard cosmology today. Curiously, this work was ignored for a decade
although it was published in widely read journals.
In 1924 Hubble had measured the distances to nine spiral galaxies, and he found
that they were extremely far away. The nearest one, M31 in the Andromeda, is now
known to be at a distance of 20 galactic diameters (Hubble’s value was about 8) and
the farther ones at hundreds of galactic diameters. These observations established that
the spiral nebulae are, as Kant had conjectured, stellar systems comparable in mass
and size with the Milky Way, and their spatial distribution confirmed the expectations
of the cosmological principle on the scale of galactic distances.
In 1926–1927Bertil Lindblad(1895–1965) andJan Hendrik Oort(1900–1992) ver-
ified Laplace’s hypothesis that the Galaxy indeed rotated, and they determined the
period to be 10^8 yr and the mass to be about 10^11 푀⊙. The conclusive demonstration
that the Milky Way is an average-sized galaxy, in no way exceptional or central, was
given only in 1952 by Walter Baade. This we may count as the third breakdown of the
anthropocentric world picture.
The later history of cosmology up until 1990 has been excellently summarized by
Peebles [3].
To give the reader an idea of where in the Universe we are, what is nearby and
what is far away, some cosmic distances are listed in Table A.1 in the appendix. On
a cosmological scale we are not really interested in objects smaller than a galaxy!
We generally measure cosmic distances inparsec(pc) units (kpc for 10^3 pc and Mpc
for 10^6 pc). A parsec is the distance at which one second of arc is subtended by a
length equalling the mean distance between the Sun and the Earth. The parsec unit is
given in Table A.2 in the appendix, where the values of some useful cosmological and
astrophysical constants are listed.
1.2 Inertial Frames and the Cosmological Principle
Newton’s first law—the law of inertia—states that a system on which no forces
act is either at rest or in uniform motion. Such systems are calledinertial frames.