10 How the World Began
205
An immediate consequence of the expansion of space was the finite age
of the universe, the current estimate of which is 13.8 billion years. If we
could go backwards in time in such an expanding universe, we would
find the mass/energy of all galaxies becoming increasingly squeezed by the
reduced space that was available to it at these earlier times. The density of
matter/energy would steadily increase until at the origin of the universe we
would presumably encounter an infinite density condition, which we might
call a space–time singularity.
Before moving on, it is opportune to discuss in more detail what we mean
by singularity. Singularities in mathematics arise when some variable takes an
infinite value. For instance, consider the reciprocal 1/x of a number x. The
smaller the number, the larger the reciprocal. The reciprocal of 0.1 is 10, of
0.01 is 100, of 0.0001 is 10,000, and so on. Try taking the reciprocal of 0
with your calculator and you will obtain an error message; this is the calculator’s way of saying the answer is infinity and handling infinities is outside
its job description, thank you very much.
Singularities are common enough in mathematics, but physicists don’t like
them. Remember Einstein introduced his cosmological constant to avoid the
very singularity that we are discussing above. Sometimes singularities bound
a region that we cannot enter. For instance, we have seen in Chap. 6 that
when we increase our speed, the closer we get to the velocity of light, the
greater our mass becomes. If we could ever travel at the velocity of light our
mass would become infinite, which indicates that it is impossible for us ever
to attain that speed. In other cases, as we get closer to a singularity, the laws
of physics that we are applying break down, and we need to find new laws
that are applicable in this particular domain.
Upon hearing that the universe has an origin, the first naïve question that
comes to mind is “what happened before the origin?” Such a question does
not make sense, and is contradictory. The word “before” implies time, but
the singularity is the origin of time, as well as of space. There is no “before”.
Of course, physicists did not (and still do not) feel at ease with the idea of an
origin of time, since it invokes scenarios outside the domain of science. This
point is discussed further in Part 3.
Although the red shift has now become a routine tool in Astronomy,
not everybody accepted its interpretation in terms of the expansion of the
universe, and several scientists proposed alternative explanations, since abandoned. In 1948 British scientist, Fred Hoyle, proposed a mechanism that
would have guaranteed, in his opinion, a steady state for the universe. (Independently, similar ideas were also considered by Hermann Bondi and Thomas
Gold.) Hoyle accepted that the cosmic red-shift was due to an expansion,
205
An immediate consequence of the expansion of space was the finite age
of the universe, the current estimate of which is 13.8 billion years. If we
could go backwards in time in such an expanding universe, we would
find the mass/energy of all galaxies becoming increasingly squeezed by the
reduced space that was available to it at these earlier times. The density of
matter/energy would steadily increase until at the origin of the universe we
would presumably encounter an infinite density condition, which we might
call a space–time singularity.
Before moving on, it is opportune to discuss in more detail what we mean
by singularity. Singularities in mathematics arise when some variable takes an
infinite value. For instance, consider the reciprocal 1/x of a number x. The
smaller the number, the larger the reciprocal. The reciprocal of 0.1 is 10, of
0.01 is 100, of 0.0001 is 10,000, and so on. Try taking the reciprocal of 0
with your calculator and you will obtain an error message; this is the calculator’s way of saying the answer is infinity and handling infinities is outside
its job description, thank you very much.
Singularities are common enough in mathematics, but physicists don’t like
them. Remember Einstein introduced his cosmological constant to avoid the
very singularity that we are discussing above. Sometimes singularities bound
a region that we cannot enter. For instance, we have seen in Chap. 6 that
when we increase our speed, the closer we get to the velocity of light, the
greater our mass becomes. If we could ever travel at the velocity of light our
mass would become infinite, which indicates that it is impossible for us ever
to attain that speed. In other cases, as we get closer to a singularity, the laws
of physics that we are applying break down, and we need to find new laws
that are applicable in this particular domain.
Upon hearing that the universe has an origin, the first naïve question that
comes to mind is “what happened before the origin?” Such a question does
not make sense, and is contradictory. The word “before” implies time, but
the singularity is the origin of time, as well as of space. There is no “before”.
Of course, physicists did not (and still do not) feel at ease with the idea of an
origin of time, since it invokes scenarios outside the domain of science. This
point is discussed further in Part 3.
Although the red shift has now become a routine tool in Astronomy,
not everybody accepted its interpretation in terms of the expansion of the
universe, and several scientists proposed alternative explanations, since abandoned. In 1948 British scientist, Fred Hoyle, proposed a mechanism that
would have guaranteed, in his opinion, a steady state for the universe. (Independently, similar ideas were also considered by Hermann Bondi and Thomas
Gold.) Hoyle accepted that the cosmic red-shift was due to an expansion,