Since its discovery
nearly 65 years ago, the cosmological redshift has endured
as one of the most persuasive 'proofs' that our universe is
expanding. The steps leading to its discovery are well known.
Soon after Christian Doppler discovered that motion produces
frequency shifts in 1842, astronomers began an aggressive
spectroscopic program to measure the velocities of stars and
planets using their Doppler shifts. This continued through
the first few decades of the 20th century 'culminating' in
the work by Vesto Slipher, Edwin Hubble and Milton Humason
on the socalled spiral nebulae  distinctly non stellar
objects that also seemed to display starlike Doppler shifts.
So long as velocities of only a few hundred kilometers per
second were measured, no one questioned that the frequency
shifts for the spiral nebulae indicated relative motion just
as they had for stars and planets.
But, during the 1920's and 30's spiral nebulae with Doppler
shifts of over 34,000 kilometers per second were discovered.
In a letter by Hubble to the Dutch cosmologist Willem De Sitter
in 1931, he stated his concerns about these velocities by
saying "... we use the term 'apparent velocities' in
order to emphasize the empirical feature of the correlation.
The interpretation, we feel, should be left to you and the
very few others who are competent to discuss the matter with
authority." Dispite this cautionary note, the fact of
the matter was that the redshifts measured for the distant
galaxies LOOKED like Doppler shifts. The terms 'recession
velocity' and 'expansion velocity' were quickly brought into
service by astronomers at the telescope, and by popularizers,
to describe the physical basis for the redshift.
As astronomers
explored the universe to greater depths, galaxies and quasars
appeared to be rushing away at faster and faster speeds. It
seems to be a completely natural consequence of the outrushing
of matter from the big bang. Like a sparkling display of fireworks
on a warm summer evening, we imagine ourselves standing on
one of those galactic 'cinders', watching the others rush
past us into the dark void of infinite space. Upon closer
examination, however, this intuitivelycompelling and seductive
mental image is both inadequate and misleading.
The Mysteries of Relativity
Big bang cosmology is based on Einstein's general theory of
relativity. It is a theory transcending both Newton's mechanics
and Einstein's special theory of relativity, introducing us
to concepts that do not exist within the older theories. Nor
are these concepts easily comprehensible by our common sense
which has been honed by organic evolution to see the world
only through a narrow set of glasses.
For example,
special relativity is based on the difficulttofathom postulate
that the speed of light is absolutely constant when measured
in reference frames moving at a constant speed. From this
emerges the concept of 'spacetime' which then becomes the
arena for all phenomena involving time dilation, length contraction
and the Twin Paradox. Beyond special relativity lies the incomparably
more alien landscape of general relativity. Gravitational
fields now become geometric curvatures of spacetime. This
has no analog in special relativity based as it is on a perfectly
flat spacetime that remains aloof from any influence on it
by matter or energy.
Just as the
constancy of the speed of light led to the Twin Paradox, the
curvature of spacetime leads to its own menageri of peculiar
phenomena. One of these involves the slowingdown of clocks
in the presence of a strong gravitational field. Related to
this is the "gravitational redshift" which occurs
when the frequency of light sent from the surface of a body
is shifted to lower frequencies during the journey to the
observer. This redshift is not related to the famous Doppler
shift since the observer is not in motion relative to the
body emitting the light signal!
A second phenomenon
predicted by general relativity that also has no analog in
special relativity is the cosmological redshift. Simply stated,
the cosmological redshift occurs because the curvature of
spacetime was smaller in the past when the universe was younger
than it is now. Light waves become stretched en route between
the time they were emitted long ago, and the time they are
detected by us today.
The
Doppler shift and cosmology
It is tempting to refer to cosmological redshifts as Doppler
shifts. This choice of interpretation has in the years since
Hubble's work led to an unfortunate misunderstanding of big
bang cosmology, obscurring one of its most mysterious beauties.
As noted with a hint of frustration by cosmologists such as
Steven Weinberg and Jaylant Narlikar and John Wheeler, "The
frequency of light is also affected by the gravitational field
of the universe, and it is neither useful nor strictly correct
to interpret the frequency shifts of light...in terms of the
special relativistic Doppler effect.".
By refering
to cosmological redshifts as Doppler shifts, we are insisting
that our Newtonian intuition about motion still applies without
significant change to the cosmological arena. A result of
this thinking is that quasars now being detected at redshifts
of Z = 4.0 would have to be interpreted as traveling a speeds
of more than V = Z x c or 4 times the speed of light. This
is, of course, quite absurd, because we all know that no physical
object may travel faster than the speed of light.
To avoid such
apparently nonsensical speeds, many popularizers use the special
relativistic Doppler formula to show that quasars are really
not moving faster than light. The argument being that for
large velocities, special relativity replaces Newtonian physics
as the correct framework for interpreting the world. By using
a special relativistic velocity addition formula the quasar
we just discussed has a velocity of 92 percent the speed of
light. Although we now have a feeling that Reason has returned
to our description of the universe, in fact, we have only
replaced one incomplete explanation for another. The calculation
of the quasar's speed now presupposes that special relativity
( a theory of flat spacetime) is applicable even at cosmological
scales where general relativity predicts that spacetime curvature
becomes important. This is equivalent to a surveyor making
a map of the state of California, and not allowing for the
curvature of the earth!
The adoption
of the special relativistic Doppler formula by many educators
has led to a peculiar 'hybrid' cosmology which attempts to
describe big bang cosmology using general relativity, but
which is still firmly mired in the ruberik of special relativity.
For instance, under the entry 'redshift' in the Cambridge
Encyclopedia of Astronomy it is explicitly acknowledged that
the redshift is not a Doppler shift, but less than two paragraphs
later, the special relativistic Doppler formula is introduced
to show how quasars are moving slower than the speed of light!
It is also common for popularizers of cosmology to describe
how 'space itself stretches' yet continue to describe the
expansion of the universe as motion governed by the restrictions
of special relativity. What's going on here?
General relativity to the rescue
By adopting general relativity as the proper guide, such contradictions
are eliminated. General relativity leads us to several powerful
conclusions about our cosmos: 1) special relativity is inapplicable
for describing the larger universe; 2) the concepts of distance
and motion are not absolutely defined and 3) Preexisting spacetime
is undefined. Each of these conclusions are as counterintuitive
as the Twin Paradox or as the particle/wave dualism of quantum
mechanics. As Nobel Physicist John Wheeler once put it "If
you are not completely confused by quantum mechanics, you
do not understand it" The same may be said for general
relativity.
The first conclusion
means that we cannot trust even the insights hard won from
special relativity to accurately represent the 'big picture'
of the universe. General relativity must replace special relativity
in cosmology because it denies a special role to observers
moving at constant velocity, extending special relativity
into the arena of accelerated observers. It also denies a
special significance to special relativity's flat spacetime
by relegating it to only a microscopic domain within a larger
geometric possibility. Just as Newtonian physics gave way
to special relativity for describing high speed motion, so
too does special relativity give way to general relativity.
This means that the special relativistic Doppler formula should
not, in fact cannot, be used to quantify the velocity of distant
quasars. We have no choice in this matter if we want to maintain
the logical integrity of both theories.
Distance and motion
The second conclusion is particularly upsetting because if
we cannot define what we mean by distance, how then can we
discuss in meaningful terms the 'motion' of distant quasars,
or a Hubble Law interpreted as a distance versus velocity
relation? In a small region of spacetime, we can certainly
define motion as we always have because space has a static,
flat geometry. When a body moves from point x to point y in
a time interval, T, we say it is moving with a speed of S
= (x  y)/T. There are also specific experimental ways of
measuring x, y and T to form the quotent S by using clocks
and rulers. The crucil feature behind these measurements is
that nothing happens to the geometry of space during the experiment
to change the results of the measuring process.
In the cosmological
setting which we believe is accurately described by general
relativity, we have none of these luxuries! Astronomers cannot
wait millions of years to measure quasar proper motions. They
cannot, like Highway Patrol officers, bounce radar beams off
distant galaxies to establish their relative distances or
speeds. Unlike all other forms of motion that have been previously
observed, cosmological 'motion' cannot be directly observed.
It can only be INFERRED from observations of the cosmological
redshift, which general relativity then TELLS US means that
the universe is expanding.
In big bang
cosmology, galaxies are located at fixed positions in space.
They may perform small dances about these positions in accordance
with special relativity and local gravitational fields, but
the real 'motion' is in the literal expansion of space between
them! This is not a form of movement that any human has ever
experienced. It is, therefore, not surprising that our intuition
reels at its implication and seeks other less radical interpretations
for it including special relativity. But even the exotic language
and conundrums of special relativity cannot help us. Instead
we are forced to interrogate the mathematics of general relativity
itself for whatever landmarks it can provide. In doing so,
we are left, however, with a riddle as profound as that of
the Twin Paradox, and equally challenging to explain.
Two galaxies
permanently located at positions (x1 , y1 , z1 ) and ( x2
, y2 , z2 ) at one time find themselves one billion light
years apart. Then a few billion years later while located
at the same coordinates, they find themselves 3 billion light
years apart. The galaxies have not 'moved', nevertheless,
their separations have increased. In fact, when the universe
was only one year old, the separations between these galaxies
were increasing at 300 times the speed of light! Space can
expand faster than the speed of light in general relativity
because space does not represent matter or energy. The displacements
that arise from its dilation produce an entirely new kind
of motion for which even our special relativisticallytrained
intuitions remain profoundly silent. Like that gentleman from
Main once said "You can't get there [to general relativity]
from here [special relativity]". To the extent that general
relativity has been tested and found correct, we have no choice
but to accept its consequences at face value.
Space, time and matter
The last conclusion drawn from general relativistic cosmology
is that, unlike special relativity, it is not physically meaningful
to speak of spacetime existing independently of matter and
energy. In big bang cosmology, both space and time came into
existence along side matter and energy at 'time zero'. If
our universe contains more than a critical density of matter
and energy, its spacetime is forever finite and bounded, in
a shape analogous to a sphere. Beyond this boundary, space
and time simply do not exist. In fact, general relativity
allows the Conservation of Energy to be suspended so that
matter and energy may be created quite literally from the
nothingness of curved spacetime. General relativity provides
a means for 'jumpstarting' Creation!
Big bang cosmology
is both a profoundly beautiful, and disturbing, model for
our universe, its shape and its destiny. It contains many
surprises which have yet to be completely workedout. But
one feature of the evolving universe seems absolutly clear,
the big bang was not some grand fireworks display, but an
event of a completely different order. It resembled more an
expanding soap bubble film upon which galactic dust motes
are carried along for the ride. This film represents the totality
of all the space and matter in our universe, and it expands
into a mysterious primordial void which is itself empty of
space, dimension, time or matter.
In the future
it is hoped that a death knell will finally have sounded for
the last vestage of the older thinking. With the Doppler interpretation
of the cosmological redshift at last reconsidered, and rejected,
we will finally be able to embrace the essential beauty and
mystery of cosmic expansion as it was originally envisioned
by its discoverers.
