Universe: Expansion

Universe: Expansion

Published: May 2, 2008, 12:00 am
Updated: April 21, 2009, 8:43 pm
Lead Author: Sten Odenwald
Topics: Cosmology The Universe

Fundamental Idea – Stretching Universe

All Big Bang cosmologies have a common non-intuitive ingredient; they predict that 3-D space grows larger as the universe grows older. It does this not by appropriating new volumes of space at its periphery, but by stretching. We can countenance the idea the universe may have had a beginning in time, we can even accept that the universe may one day re-collapse in a blaze of fire. But the mind will simply not accept that the expansion effect described in Big Bang cosmology is not simply the movement of galaxies away from each other in space like the glowing embers of a fireworks display. The mind seems to have an easier time accepting space being infinite that it does with the prospect that space may be capable of stretching. Let's see where this fundamental idea emerges in both observations and theory.

Observations & Theory

For over 65 years the cosmological redshift discovered by Edwin Hubble (1889 - 1953) has endured as one of the most persuasive proofs that our universe is expanding. But at the same time, it is one of the most misunderstood and poorly explained features to our universe. By an unfortunate historical accident, the cosmological redshift is almost always confused with the more well-known Doppler Effect.

Soon after Christian Doppler's (1803 - 1853) 1842 discovery that a moving source of sound produces a measurable change in pitch, 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 (1875 - 1969), Edwin Hubble and Milton Humason (1891-1972) on the so-called "spiral nebulae" — distinctly non-stellar objects that also seemed to display star-like 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 to Willem De Sitter in 1931, Edwin Hubble 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."

Despite this cautionary note, the fact of the matter was that the redshifts measured at the telescope for the distant galaxies looked like Doppler shifts. The terms 'recession velocity' and 'expansion velocity' were quickly brought into service by astronomers and by popularizers, to describe the physical basis for the redshift.

Misunderstanding of Big Bang Cosmology

For decades no one really bothered to distinguish between 'cosmological redshift' and 'Doppler shift'. This has in the years since Hubble's work led to an unfortunate misunderstanding of Big Bang cosmology, obscuring one of its most mysterious beauties. As noted with a hint of frustration by renowned cosmologists such as Steven Weinberg, 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."

Although cosmologists unanimously agree that cosmological redshifts are distinct from Doppler shifts, popularizers of cosmology have a long tradition of not emphasizing this distinction. By referring 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 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 superluminal speed, 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. The adoption of the special relativistic Doppler formula by many educators has led to a peculiar 'hybrid' cosmology which purports to describe big bang cosmology using general relativity, but which is still firmly mired in the rubrik 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. This has now become the accepted way of explaining redshifts now used, for example, in the 1991 editions of undergraduate astronomy textbooks.

Expansion – Inferred

The expansion of the universe 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. Although we can intuitively imagine galaxies moving about like balls on a billiard table, astronomers have absolutely NO conventional evidence that galaxies move. This may surprise you, but consider this: although astronomers can, over the course of years, show that the positions of stars in the sky actually change, the shifts in the positions of galaxies over the course of a human lifetime and even a million years, is impossible to detect.

Cosmological expansion 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. Here is what the expansion predicted by general relativity looks like.

General Relativity – Expansion

Imagine two galaxies permanently located at the positions identified by their Gaussian coordinates, (x_1 , y_1 , z_1 ) and (x_2 , y_2 , z_2 ) at one moment in Cosmic time. Using the form of the FLRW metric* appropriate to that age, we determine that they are one billion light-years apart. Then a few billion years later while located at the same coordinates, we re-determine their distances and find that they are now 3 billion light years apart. The Gaussian coordinates of the galaxies have not changed, 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.

Motion of Space – Volume of Space Increasing

It is NOT a motion THROUGH space because the coordinates of the galaxies do not change,
instead it is a motion OF space.

This is why some popularizers like to use the expanding balloon or raisin bread analogy. It is not the raisins or spots on the balloon that move, but the stretching of the dough or rubber membrane that causes separations to increase. What general relativity proposes, and the balloon analogy attempts to show, is that all of 3-D space at a given instant in cosmic time is contained within a larger object: the 4-D spacetime manifold. This manifold may be sliced along a defined time axis to form 3-D, spatial cross sections. Each of these cross sections represents all of the physical 3-D space that constitutes the universe at any particular instant in Cosmic time.

If we were to look at two adjacent cross sections through the manifold, they would be represented by a volume of space seen at two different times, but in which one is larger than the other due to the expansion of the universe. If we were to represent the locations of the galaxies in such a space with Gaussian coordinate addresses (pure numbers) then those addresses would remain the same, but because of the expansion, their physical separations measured, say, by the length of a ray of light, would be different between the two time intervals. The increase in their separations has occurred, not because they moved in the Newtonian sense of changing their coordinates, but because the volume of space in the universe has increased.

Related EoC Articles

Further Reading

  • FLRW Metric - The Friedmann-Lemaître-Robertson-Walker (FLRW) metric is an exact solution of Einstein's field equations of general relativity; it describes a simply connected, homogeneous, isotropic expanding or contracting universe... Wikipedia.

External Links

  • Wilkinson Microwave Anisotropy Probe (WMAP) - A NASA Explorer mission that launched June, 2001 to make fundamental measurements of cosmology – the study of the properties of our universe as a whole. WMAP has been stunningly successful, producing our new Standard Model of Cosmology. NASA.
  • WMAPs Universe - Universe 101, NASA.
  • WMAP Images - Universe 101, NASA.
  • WMAP Image Topics - Universe 101, NASA. ("Drill-down" into the various topics where there is an interesting collection of appropriate images.)

Preview Image

"Timeline of the Universe" - A representation of the evolution of the universe over 13.7 billion years. The far left depicts the earliest moment we can now probe, when a period of "inflation" produced a burst of exponential growth in the universe. (Size is depicted by the vertical extent of the grid in this graphic.) For the next several billion years, the expansion of the universe gradually slowed down as the matter in the universe pulled on itself via gravity. More recently, the expansion has begun to speed up again as the repulsive effects of dark energy have come to dominate the expansion of the universe. The afterglow light seen by WMAP was emitted about 380,000 years after inflation and has traversed the universe largely unimpeded since then. The conditions of earlier times are imprinted on this light; it also forms a backlight for later developments of the universe.  View full-size image.  (Source: NASA/Wilkinson Microwave Anisotropy Probe (WMAP) Science Team.)

Citation

Odenwald, Sten, Ph.D. (Contributing Author); Bernard Haisch (Topic Editor). 2009. "Universe: Expansion." In: Encyclopedia of the Cosmos. Eds. Bernard Haisch and Joakim F. Lindblom (Redwood City, CA: Digital Universe Foundation). [First published May 2, 2008].
<http://www.cosmosportal.org/articles/view/138898/>

 

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