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Matters of Gravity: Relativity's Universes

In 1917, two years after developing the general relativity theory (GRT), Albert Einstein formulated a concept of a finite, static universe, into which he introduced the purely hypothetical quantity that he termed the "cosmological constant," a repulsive force increasing with the distance between two objects in the way that the centrifugal force in a rotating body increases with radius. This was necessary to prevent a static universe from collapsing under its own gravitation. (Isaac Newton was aware of the problem and proposed an infinite universe for that reason.) But the solution was unstable, in that the slightest expansion would increase the repulsive force and decrease gravity, resulting in runaway expansion, while conversely the slightest contraction would lead to total collapse.

Soon afterward, the Dutch astronomer, Willem de Sitter, found a solution to Einstein's equations that described an expanding universe, and the Russian mathematician Alexander Friedmann found another. Einstein's static picture, it turned out, was one of three special cases among an infinity of possible solutions, some expanding, some contracting. Yet despite the excitement and publicity that the General Theory had aroused—publication of Einstein's special relativity theory in 1905 had made comparatively little impact; his Nobel Prize of that year was awarded for a paper on the photoelectric effect—the subject remained confined to the circle of probably not more than a dozen or so specialists who had mastered its intricacies until well into the 1920s. Then the possible significance began being recognized of observational data that had been accumulating since 1913, when the astronomer V. M. Slipher (who, as is often the case in instances like this, was looking for something else) inferred from redshifts of the spectra of about a dozen galaxies in the vicinity of our own that the galaxies were moving away at speeds ranging up to a million miles per hour.

An Aside on Spectra and Redshifts

A spectrum is the range of wavelengths over which the energy carried by a wave motion such as light, radio, sound, disturbances on a water surface, is distributed. Most people are familiar with the visible part of the Sun's spectrum, ranging from red at the low-frequency end to violet at the high-frequency end, obtained by separating white sunlight into its component wavelengths by means of a prism. This is an example of a continuous, or "broadband" spectrum, containing energy at all wavelengths in the range. Alternatively, the energy may be concentrated in just a few narrow bands within the range.

 

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Changes in the energy states of atoms are accompanied by the emission or absorption of radiation. In either case, the energy transfers occur at precise wavelength values that show as "lines," whose strength and spacings form patterns—"line spectra"—characteristic of different atomic types. Emission spectra consist of bright lines at the wavelengths of the emitted energy. Absorption spectra show as dark lines marking the wavelengths at which energy is absorbed from a background source—for example, of atoms in the gas surrounding a star, which absorb certain wavelengths of the light passing through. From the line spectra found for different elements in laboratories on Earth, the elements present in the spectra from stars and other astronomical objects can be identified.

A "redshifted" spectrum means that the whole pattern is displaced from its normal position toward the red—longer wavelength—end. In other words, all the lines of the various atomic spectra are observed to lie at longer wavelength values than the "normal" values measured on Earth. A situation that would bring this about would be one where the number of waves generated in a given time were stretched across more intervening space than they "normally" would be. This occurs when the source of the waves is receding. The opposite state of affairs applies when the source is approaching and the wavelengths get compressed, in which case spectra are "blue-shifted." Such alteration of wavelength due to relative motion between the source and receiver is the famous Doppler shift. 43 Textbooks invariably cite train whistles as an example at this point, so I won't.

 

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A Universe in the Red and Lemaître's Primeval Atom

By 1924 the reports of redshifts from various observers had grown sufficiently for Carl Wirtz, a German astronomer, to note a correlation between the amounts of galactic redshift and their optical faintness, which was tentatively taken as a measure of distance. The American astronomer Edwin Hubble had recently developed a new method for measuring galactic distances using the known brightnesses of certain peculiar variable stars, and along with his assistant, Milton Humason, conducted a systematic review of the data using the 60-inch telescope at the Mount Wilson Observatory in California, and later the 100-inch—the world's largest at that time. In 1929 they announced what is now known as Hubble's Law: that the redshift of galaxies increases steadily with distance. Although Hubble himself always seemed to have reservations, the shift was rapidly accepted as a Doppler effect by the scientific world at large, along with the startling implication that not only is the universe expanding, but that the parts of it that lie farthest away are receding the fastest.

A Belgian priest, Georges Lemaître, who was conversant with Einstein's theory and had studied under Sir Arthur Eddington in England, and at Harvard where he attended a lecture by Hubble, concluded that the universe was expanding according to one of the solutions of GRT in which the repulsive force dominated. This still left a wide range of options, including models that were infinite in extent, some where the expansion arose from a state that had existed indefinitely, and others where the universe cycled endlessly through alternating periods of expansion and contraction. However, the second law of thermodynamics dictated that on balance net order degenerates invariably, one way or another, to disorder, and the process is irreversible. The organized energy of a rolling rock will eventually dissipate as heat in the ground as the rock is brought to a halt by friction, but the random heat motions of molecules in the ground never spontaneously combine to set a rock rolling. This carries the corollary that eventually everything will arrive at the same equilibrium temperature everywhere, at which point all further change must cease. This is obviously so far from being the case with the universe as seen today that it seemed the universe could only have existed for a limited time, and it must have arrived at its present state from one of minimum disorder, or "entropy." Applying these premises, Lemaître developed his concept of the "primeval atom," in which the universe exploded somewhere between 10 billion and 20 billion years ago out of an initial point particle identified with the initial infinitely large singularity exhibited by some solutions to the relativistic equations. According to this "fireworks model," which Lemaître presented in 1931, the primeval particle expanded and split up into progressively smaller units the size of galaxies, then stars, and so forth in a process analogous to radioactive decay.

This first version of a Big Bang cosmology was not generally accepted. The only actual evidence offered was the existence of cosmic rays arriving at high energies from all directions in space, which Lemaître argued could not come from any source visible today and must be a leftover product of the primordial breakdown. But this was disputed on the grounds that other processes were known which were capable of providing the required energy, and this proved correct. Cosmic-ray particles were later shown to be accelerated by electromagnetic forces in interstellar space. The theory was also criticized on the grounds of its model of stellar evolution based on a hypothetical process of direct matter-to-energy annihilation, since nuclear fusion had become the preferred candidate for explaining the energy output of stars, and Willem de Sitter showed that it was not necessary to assume GRT solutions involving a singularity. Further, the gloomy inevitability of a heat death was rejected as not being necessarily so, since whatever might seem true of the second law locally, nothing was known of its applicability to the universe as a whole. Maybe the world was deciding that the period that had brought about such events as the Somme, Verdun, and the end of Tsarist Russia had been an aberration, and was recovering from its pessimism. Possibly it's significant, then, that the resurrection of the Big Bang idea came immediately following World War II.

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