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HISTORY OF PHYSICS: EINSTEIN AND THE COSMOLOGICAL CONSTANT

The following points are made by Steven Weinberg (Physics Today 2005 November):

1) The mistakes made by leading scientists often provide a better insight into the spirit and presuppositions of their times than do their successes. In thinking of Einstein's mistakes, one immediately recalls what Einstein (in a conversation with George Gamow) called the biggest blunder he had made in his life: the introduction of the cosmological constant. After Einstein had completed the formulation of his theory of space, time, and gravitation -- the general theory of relativity -- he turned in 1917 to a consideration of the spacetime structure of the whole Universe. He then encountered a problem. Einstein was assuming that, when suitably averaged over many stars, the Universe is uniform and essentially static, but the equations of general relativity did not seem to allow a time-independent solution for a universe with a uniform distribution of matter. So Einstein modified his equations, by including a new term involving a quantity that he called the cosmological constant. Then it was discovered that the Universe is not static, but expanding. Einstein came to regret that he had needlessly mutilated his original theory. It may also have bothered him that he had missed predicting the expansion of the universe.

2) This story involves a tangle of mistakes, but not the one that Einstein thought he had made. First, the author (Weinberg) does not think that it can count against Einstein that he had assumed the Universe is static. With rare exceptions, theorists have to take the world as it is presented to them by observers. The relatively low observed velocities of stars made it almost irresistible in 1917 to suppose that the universe is static. Thus when Willem de Sitter (1872-1934) proposed an alternative solution to the Einstein equations in 1917, he took care to use coordinates for which the metric tensor is time-independent. However, the physical meaning of those coordinates is not transparent, and the realization that de Sitter's alternate cosmology was not static -- that matter particles in his model would accelerate away from each other -- was considered to be a drawback of the theory.

3) It is true that Vesto Melvin Slipher (1875-1969), while observing the spectra of spiral nebulae in the 1910s, had found a preponderance of redshifts of the sort that would be produced in an expansion by the Doppler effect, but no one then knew what the spiral nebulae were; it was not until Edwin Hubble (1889-1953) found faint Cepheid variables in the Andromeda Nebula in 1923 that it became clear that spiral nebulae were distant galaxies, clusters of stars far outside our own galaxy. The author (Weinberg) does not know if Einstein had heard of Slipher's redshifts by 1917, but in any case he knew very well about at least one other thing that could produce a redshift of spectral lines: a gravitational field.

4) It should be acknowledged here that Arthur Eddington (1882-1944), who had learned about general relativity during World War I from de Sitter, did in 1923 interpret Slipher's redshifts as due to the expansion of the Universe in the de Sitter model. Nevertheless, the expansion of the Universe was not generally accepted until Hubble announced in 1929 -- and actually showed in 1931 -- that the redshifts of distant galaxies increase in proportion to their distance, as would be expected for a uniform expansion. Only then was much attention given to the expanding-universe models introduced in 1922 by Alexander Friedmann (1888-1925), in which no cosmological constant is needed. In 1917 it was quite reasonable for Einstein to assume that the Universe is static.

Physics Today http://www.physicstoday.org

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ON QUINTESSENCE AND THE EVOLUTION OF THE COSMOLOGICAL CONSTANT

The following points are made by P.J.E. Peebles (Nature 1999 398:25):

1) Contrary to expectations, the evidence is that the Universe is expanding at approximately twice the velocity required to overcome the gravitational pull of all the matter the Universe contains. The implication of this is that in the past the greater density of mass in the Universe gravitationally slowed the expansion, while in the future the expansion rate will be close to constant or perhaps increasing under the influence of a new type of matter that some call "quintessence".

2) Quintessence began as Einstein's cosmological constant, Lambda. It has negative gravitational mass: its gravity pushes things apart.

3) Particle physicists later adopted Einstein's Lambda as a good model for the gravitational effect of the active vacuum of quantum physics, although the idea is at odds with the small value of Lambda indicated by cosmology.

4) Theoretical cosmologists have noted that as the Universe expands and cools, Lambda tends to decrease. As the Universe cools, symmetries among forces are broken, particles acquire masses, and these processes tend to release an analogue of latent heat. The vacuum energy density accordingly decreases, and with it the value of Lambda. Perhaps an enormous Lambda drove an early rapid expansion that smoothed the primeval chaos to make the near uniform Universe we see today, with a decrease in Lambda over time to its current value. This is the cosmological inflation concept.

5) The author suggests that the recent great advances in detectors, telescopes, and observatories on the ground and in space have given us a rough picture of what happened as our Universe evolved from a dense, hot, and perhaps quite simple early state to its present complexity. Observations in progress are filling in the details, and that in turn is driving intense debate on how the behavior of our Universe can be understood within fundamental physics.

Nature http://www.nature.com/nature

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Notes by ScienceWeek:

Active vacuum of quantum physics: This refers to the idea that the vacuum state in quantum mechanics has a zero-point energy (minimum energy) which gives rise to vacuum fluctuations, so the vacuum state does not mean a state of nothing, but is instead an active state.

If a theory or process does not change when certain operations are performed on it, the theory or process is said to possess a symmetry with respect to those operations. For example, a circle remains unchanged under rotation or reflection, and a circle therefore has rotational and reflection symmetry. The term "symmetry breaking" refers to the deviation from exact symmetry exhibited by many physical systems, and in general, symmetry breaking encompasses both "explicit" symmetry breaking and "spontaneous" symmetry breaking. Explicit symmetry breaking is a phenomenon in which a system is not quite, but almost, the same for two configurations related by exact symmetry. Spontaneous symmetry breaking refers to a situation in which the solution of a set of physical equations fails to exhibit a symmetry possessed by the equations themselves.

In general, the term "latent heat" refers to the quantity of heat absorbed or released when a substance changes its physical phase (e.g., solid to liquid) at constant temperature.

The inflationary model, first proposed by Alan Guth in 1980, proposes that quantum fluctuations in the time period 10^(-35) to 10^(-32) seconds after time zero were quickly amplified into large density variations during the "inflationary" 10^(50) expansion of the Universe in that time frame.

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COSMOLOGY: ON THE COSMOLOGICAL CONSTANT PROBLEM

The following points are made by Thomas Banks (Physics Today 2004 March):

1) Since the mid-1980s, astronomers and astrophysicists have been accumulating evidence that the expansion of the universe is accelerating. The simplest way to incorporate that acceleration into the description of cosmology, within the framework of general relativity, is to add a cosmological constant (CC) term to the Einstein equations. Before Edwin Hubble discovered the expansion of the universe, Albert Einstein had originally introduced such a term to obtain a static solution of his cosmological equations. After the cosmic expansion was discovered, Einstein considered his introduction of the CC to be the greatest mistake of his career.

2) Many physicists were reluctant to consider the CC as an explanation for astronomical data, because the value it would need to have is ridiculously small compared to current theoretical expectations -- some 10^(120) times too small. Theorists interpreted that discrepancy as an indication that they would one day find an elegant explanation for why the parameter was exactly zero. Although some still cling to that hope, the author concludes that observation has once again upset the expectations of overconfident theorists.

3) The framework that gives rise to the enormous mismatch between calculation and observation is called "effective quantum field theory in background spacetime", or EFT for short. EFT always involves a short distance cutoff scale below which the approximations of EFT break down. The natural length scale introduced by quantum gravity (QG) is the Planck length -- the combination of Newton's gravitational constant, Planck's constant, and the speed of light that has units of length. Naive dimensional analysis and explicit calculations in EFT suggest that the cosmological constant should be proportional to the fourth power of the corresponding Planck energy of about 10^(28) eV. That is 10^(120) times too big.

4) Any dynamical solution of the CC problem within EFT should involve particles whose mass is on the order of the energy scale of the CC, about 10^(-3) eV. There have been many published attempts to resolve the problem by invoking such particles, but all of them have failed. EFT does provide a loophole for resolving the CC problem: Apart from calculable contributions, there are contributions from energy scales higher than those corresponding to the cutoff. In principle, those two types of contributions can cancel, but from the EFT point of view, the cancellation to 1 part in 10^(120) would be incredibly fortuitous. The author believes that the resolution of the CC problem does not involve some clever trick in EFT. Rather, QG will force on theorists a fundamental revision of the rules of the game. This belief is not yet the accepted dogma of the field. There are as many ideas about how to solve the CC problem as there are theorists who think about it.(1-5)

References (abridged):

1. G. 't Hooft, in Salamfestschrift: A Collection of Talks From the Conference on Highlights of Particle and Condensed Matter Physics, A. Ali, J. Ellis, S. Randjbar-Daemi eds., World Scientific, River Edge, NJ (1994), available at http://www.arXiv.org/abs/gr-qc/9310026; L. Susskind, J. Math. Phys. 36, 6377 (1995)

2. J. H. Schwarz, in Quantum Aspects of Gauge Theories, Supersymmetry, and Unification, A. Ceresole, C. Kounnas, D. Loest, S. Theisen, eds., Springer-Verlag, New York (1999), available at http://www.arXiv.org/abs/hep-th/9812037

3. T. Banks, in Strings, Branes, and Gravity: TASI 99, J. Harvey, S. Kachru, E. Silverstein, eds., World Scientific, River Edge, NJ (2001), available at http://www.arXiv.org/abs/hep-th/9911068; D. Bigatti, L. Susskind, http://www.arXiv.org/abs/hep-th/9712072; O. Aharony et al., Phys. Rep. 323, 183 (2000)

4. L. Susskind, in The Black Hole: 25 Years After, C. Teitelboim, J. Zanelli, eds., World Scientific, River Edge, NJ, (1998), available at http://www.arXiv.org/abs/hep-th/9309145; A. Sen, Nucl. Phys. B 440, 421 (1995); A. Strominger, C. Vafa, Phys. Lett. B 379, 99 (1996)

5. J. Bekenstein, Phys. Rev. D 7, 2333 (1973); 9, 3292 (1974); S. Hawking Phys. Rev. D 13, 191 (1976)

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