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R. Barrett and P. P. Delsanto
explained later.) The magnitude of the frequency shift allows us to calculate
the velocity of the source away (or towards) us. Carrying out these measurements with galaxies, Hubble found that in almost all cases, the light was
red-shifted, which meant that practically all of the galaxies were receding away
from us. He also noticed, in cases where the distance to the galaxy was known,
that the red shift was proportional to the distance. The constant of proportionality is now known as Hubble’s constant. (Note the implicit assumption
here that the expansion is uniform.) From Hubble’s constant and the observed
red shift we can calculate the distance to the farthest astronomical objects. So
how do we estimate Hubble’s constant?
Fortunately, there is a region of overlap between where luminosity
measurements can be used to estimate distance, and where red shifts of the
closest galaxies can be measured. A comparison of the two sets of observations enables us to obtain an estimate of Hubble’s constant. It sounds simple,
but decades of work have been undertaken to refine the accepted value of this
constant. These estimates have fluctuated quite considerably. The estimated
age of the universe is directly related to the Hubble constant. 2
Measurement of the red-shift of galaxies became a turning point in the
history of Cosmology. Einstein abandoned his cosmological constant, and the
FLRW solution of the field equations of General Relativity lost its status as
a mathematical curiosity and became accepted fully-fledged into the domain
of physics. The expansion of cosmic space became generally accepted.
Earlier we considered a sphere as an analogy to the four dimensional
universe. We develop this analogy further by considering the sphere to
be an inflatable balloon, with the stars (and galaxies) as specks on the
balloon’s surface. As the balloon expands, the specks move further apart from
each other. Note that the specks do not move across the balloon’s surface,
but rather the surface expands between the specks. Similarly, in the fourdimensional universe, the galaxies do not move through space, but space
expands between them, making them further apart. This is what we meant
earlier when we said that the red shift of the expanding universe was analogous
to a Doppler shift, but not exactly the same. An important difference is that
whereas the Theory of Relativity (see Chap. 9) restricts the velocity of stars
moving through space to be less than the velocity of light, the stellar motion
resulting from the cosmic expansion of space itself faces no such limitation.
As we shall see in a later Section, this difference has important implications
in the early life of the universe.
2 Hubble’s law had been anticipated a couple of years earlier by Georges Lemaître, while analysing
the implications of his expanding universe.
R. Barrett and P. P. Delsanto
explained later.) The magnitude of the frequency shift allows us to calculate
the velocity of the source away (or towards) us. Carrying out these measurements with galaxies, Hubble found that in almost all cases, the light was
red-shifted, which meant that practically all of the galaxies were receding away
from us. He also noticed, in cases where the distance to the galaxy was known,
that the red shift was proportional to the distance. The constant of proportionality is now known as Hubble’s constant. (Note the implicit assumption
here that the expansion is uniform.) From Hubble’s constant and the observed
red shift we can calculate the distance to the farthest astronomical objects. So
how do we estimate Hubble’s constant?
Fortunately, there is a region of overlap between where luminosity
measurements can be used to estimate distance, and where red shifts of the
closest galaxies can be measured. A comparison of the two sets of observations enables us to obtain an estimate of Hubble’s constant. It sounds simple,
but decades of work have been undertaken to refine the accepted value of this
constant. These estimates have fluctuated quite considerably. The estimated
age of the universe is directly related to the Hubble constant. 2
Measurement of the red-shift of galaxies became a turning point in the
history of Cosmology. Einstein abandoned his cosmological constant, and the
FLRW solution of the field equations of General Relativity lost its status as
a mathematical curiosity and became accepted fully-fledged into the domain
of physics. The expansion of cosmic space became generally accepted.
Earlier we considered a sphere as an analogy to the four dimensional
universe. We develop this analogy further by considering the sphere to
be an inflatable balloon, with the stars (and galaxies) as specks on the
balloon’s surface. As the balloon expands, the specks move further apart from
each other. Note that the specks do not move across the balloon’s surface,
but rather the surface expands between the specks. Similarly, in the fourdimensional universe, the galaxies do not move through space, but space
expands between them, making them further apart. This is what we meant
earlier when we said that the red shift of the expanding universe was analogous
to a Doppler shift, but not exactly the same. An important difference is that
whereas the Theory of Relativity (see Chap. 9) restricts the velocity of stars
moving through space to be less than the velocity of light, the stellar motion
resulting from the cosmic expansion of space itself faces no such limitation.
As we shall see in a later Section, this difference has important implications
in the early life of the universe.
2 Hubble’s law had been anticipated a couple of years earlier by Georges Lemaître, while analysing
the implications of his expanding universe.