685 :....N....:A...:..T.:.U.:..;R.:.E_V_:O:...:L:...... :.33:....7....:2.:..3.:..F.::::E.:._B_R.:._U_:A.:._R_Y_l_98:....9 ______NEWS AND VI EWS------Einstein's much delayed little joke When Einstein invented the cosmological constant in 1917, and promptly disowned it, he cannot have known that the concept would be bothering his successors more than 70 years later.

EINSTEIN had very few reasons to be may mean, is more vividly alive now than underlying equations of ashamed of any of his work, but his inven­ sixty years ago. must include a 'cosmological constant' tion of what is called the cosmological The bare bones of the issue are easily whose value is exactly cancelled by that constant seems to have been one of them. understood. Einstein's picture of the simulated by the fluctuations of the And it is a curious business. Having de­ geometry of space-time turns on the set of . And the cancellation must be veloped the theory of gravitation called 16 coefficients defining the relativistic extraordinarily exact. the General Theory of Relativity, equivalent of distance (or time) by means The net effect of the 'real' and 'simu­ Einstein embarked in 1917 on an attempt of a quadratic form called a metric; only lated' constants can be related to to apply his equations to the as a 10 of these coefficients are independent, Hubble's constant, which determines the whole. On the principle that the motions because the form is symmetric, but rate at which the Universe is expanding, of the most distant objects in the Universe general relativity differs from special rela­ and which serves as an upper bound, while - the first galaxies to be recognized as tivity in that the coefficients are functions the value of the constant simulated by such were being measured at the time­ of position. The original field equations vacuum fluctuations can be estimated are uniformly much less than the velocity relate these coefficients at any place-time from the properties of quantum systems. of light , Einstein set out to find solutions to the curvature at the same place-time, Weinberg concludes that the two lines of of his equations that might be taken to which is a function of the same coeffi­ argument are consistent only if the true represent a , but could not. cients. (This is why the equations are not and simulated values of the cosmological So, with a daring that must have seemed linear and are thus not soluble systemati­ constant cancel each other out to 118 natural to one who had just used pure cally.) decimal places (although, on another thought to put the then laws of on The physics of general relativity is estimate of the quantum fluctuations, he a rational foundation, he invented the embodied in the way in which the metric estimates that the cancellation may extend cosmological constant and promptly coefficients are related to the density of to only 41 decimal places). For practical reached a solution of the desired form- a energy (which includes mass) and momen­ purposes, this is simply another way of spherical fixed universe filled with tum in the system. The effect of Einstein's saying that the numbers are equal. of uniform density. But within a few introduction of his cosmological constant Weinberg's objective is to consider how months, Einstein had withdrawn the is dimensionally and in every other way the extraordinary coincidence implied by notion of the cosmological constant. equivalent to the arbitrary addition of these estimates can be rationally ex­ Legend has it that Einstein's disillusion energy and momentum to empty space, in plained. He flirts with several possibili­ sprang from Hubble's discovery that the quantities determined by the size of the ties, only to dismiss them. The supersym­ Universe is expanding (so that the search constant. That explains why the constant metric world in which (electrons, for a static solution would have seemed a should have turned an expanding into a say) and bosons (say photons) are identi­ wild goose chase), but , static universe. In the distant early 1920s, cal might arrange for the cancellation if writing from the University of Texas at it is understandable that Einstein should the supersymmetric world were like the Austin, tells a different story in an elegant first have taken the liberty of introducing real world (which it is not). The super­ review article just published (Rev. Mod. the cosmological constant and then, when of particle fields (in which six Phys. 61, I; 1989). it seemed no longer necessary, the liberty of ten dimensions are made to disappear, Serious accounts of the dilemma make of discarding it. giving entities which are elastic strings in it plain that the difficulty that gave Quantum mechanics has put a stop to ten dimensions, the properties of the Einstein pause was de Sitter's demonstra­ that. That is Weinberg's starting point. particles we know in only four) appears to tion a few months later that there is a static The essence of his case is that, whatever have offered hope at first, but to have solution of Einstein's equations with the Einstein's pros and cons may have been, proved a disappointment. uncomfortable property that the Universe nobody can now hide from the truth that The anthropic view, that people are it represents is entirely devoid of matter. even empty space is filled with energy­ able to observe the stars and galaxies only This may have seemed a body blow, for it to say the least of it, the zero-point if the Universe in which they find them­ cast doubt on Einstein's guiding principle energy of all the oscillators corresponding selves is one in which the cancellation is that mechanical inertia is a consequence to radiation of different frequency with exact is plainly seductive, but Weinberg of the distribution of mass within the which even a vacuum must be filled but, eventually dismisses it in each of half a Universe. more tangibly perhaps, because pairs of dozen varieties. His own clear favourite is In the event, as Weinberg puts it, the particles (such as electrons and positrons) that the cancellation will spring naturally need for the cosmological constant was can be created out of nothing anywhere from the attempts being made to develop entirely undermined by the emergence in and any time by what are called the fluctu­ a quantum theory of , but there the 1920s of the family of due ations of the vacuum. may be as many opinions as there are to A. Friedman, which allowed for an From this observation springs the di­ people qualified to write about the expanding or a contracting Universe lemma that now perplexes people. If the problem. simply by the appropriate choice of a effect of the unavoidable fluctuations of Meanwhile, it is clear that Einstein was parameter. Yet the irony remains that, the vacuum are logically equivalent to a even more perceptive than he knew. It despite Einstein's disavowal of his own cosmological constant different from cannot be often that the notions a person invention, the question of whether the zero, and if the observation of the real discards turn out to be crucial to a conun­ cosmological constant exists, and is dif­ Universe shows that Einstein's cosmologi­ drum that perplexes his successors the ferent from zero, and of what precisely it cal constant is unnecessary, then the best part of a century later. John Maddox