SCIENTIFIC CORRESPONDENCE that the coincidence in phase rela­ one would expect for the planetary inter­ flict with observation. tionship between the Earth's orbit pretation, in the absence of any dispers­ Olbers' paradox has climaxed this cen­ around the Sun and that of the planet ing clouds. tury with the realization that the sky is around the pulsar is not explained by the Two other aspects of this model also covered not by redshifted stars, but by model of Helfand and Hamilton, but worry me. First, it seems most unlikely the redshifted Big Bang. At night we rather argues against it. that the structure of the cloud should look out between the stars to immense There is further relevant observational give rise to an integrated density profile distances and far back in time before the evidence, concerning the frequency de­ that produces such a closely sinusoidal formation of galaxies and stars. We look pendence of the amplitude of the sinu­ form in the observed time delay. out and back to the limit of the visible soid formed by the timing residuals. The Second, such a large, dense plasma Universe, and almost every line of sight data set used in ref. 2 contains observa­ cloud so close to the Sun would be terminates in the early Universe. The tions at frequencies around 1,408 MHz expected to produce substantial Hex Big Bang covers the entire sky, but its and 1,630 MHz. Independent fits at emission, which to my knowledge is not brilliance is mercifully redshifted by the these frequencies give amplitudes of observed. expansion of the Universe into an in­ 7.7±0.3 ms and 7.4±0.6 ms respectively, ANDREW LYNE frared gloom invisible to the naked eye. whose ratio is 1.04±0.08. This is signifi­ University of Manchester, EDWARD HARRISON cantly different from the value of 1.34 Nuffield Radio Astronomy Laboratories, Physics and Astronomy Department, that would be expected if the dispersing Jodre/1 Bank, University of Massachusetts, cloud were a cold plasma, because the Macclesfield, Cheshire SK11 9DL, UK Amherst, magnitude of any delay will depend on 1. Helfand. D. J. & Hamilton. T. T. Nature 352. 481 Massachusetts 01002, USA (1991). the inverse square of the observing fre­ 2. Bailes, M .. Lyne. A. G. & Shemar. S. L. Nature 352, quency. A ratio of 1 is of course what 311-313 (1991). 1. Maddox, J. Nature 349, 363 (1991) 2. Wesson, P. S. Astrophys. J. 367, 399-406 (1991) 3. Thomson. W. Phil. Mag. Ser. 6, 2, 161-177 (1901) 4. Bondi. H. Cosmology (Cambridge University Press. Another look at the Big Bang 1952). 1 5. Harrison. E. R. Nature 204, 271-272 (1964). SIR- In a discussion on the resolution density is usf (1 + ), or u = Us (1 + 6. Harrison. E. R. Darkness at Night: A Riddle of the of Olbers' paradox, prompted by Wes­ q)/(2 + q), where us is the radiation Universe (Harvard University Press. Cambridge, Mas· 2 sachusetts, 1987). son's article , Maddox compares the energy density in the static universes, 7. Harrison. E. R. Nature 322, 417-418 (1986). effects of the age and expansion of the and the deceleration term q is constant. B. Olbers. W. H. Astronomisches Jahrbuch 1826 (ed. Bode. Universe. The age limits the light emit­ J. E.) (Spathen. Berlin, 1823). (Trans. in ref. 6.) In all decelerating universes of q > 0, 9. Bonnor, W. Mon. Not. R. astr. Soc. 128, 33-47 (1964). ted by stars, and expansion redshifts the expansion reduces the radiation to a starlight. The age limit was first calcu­ level never less than 0.5 of that in the lated by Lord Kelvin3 in 1901, who static universe. Thus, in the standard Rhythms of war showed that the night sky is dark be­ model (density parameter equal to uni­ cause the visible Universe, having a size ty), q = 0.5, hence u = 0.6us. Bondi's SIR- We decided to examine whether determined by the finite speed of light, redshift solution, applied to a Big Bang seasonal rhythms exist in the opening contains too few stars to cover the whole universe, reduces the radiation field by a dates of wars. Our analysis is based on a sky. Bondi in 1952 attributed darkness4 factor not less than 0.5, whereas Kelvin's total of 2,131 acts of hostility, appearing 13 1 of the night sky to expansion and argued solution limits the radiation field to 10- as entries in Laffin's monograph , for that the darkness is direct proof of the of that needed to create a bright sky. which a defined opening month date is expansion of the Universe. Bondi's The age effect clearly dominates. given. Each act of hostility was assigned popular argument, true in a steady-state The visible Universe has a radius both its opening month date and its line universe of infinite age, fails in an evolv­ roughly 1010 light years. Stars in a sphere of latitude. ing universe of finite age. For, if Kelvin's of radius 1010 light years cover geometri­ In the Northern Hemisphere, latitudes solution applies in a static universe uni­ cally (not diffractionally) lQ-13 of the sky. 30-60° N, the annual rhythm in the formly populated with stars, then it also Insufficient stars exist in the visible uni­ opening dates of wars shows a peak in applies in an expanding universe of gala­ verse to cover the sky. In the long August and a nadir in January (a in the 6 xies, and expansion, absorption, and history of the paradox , Kelvin was the figure). An inverse pattern in the annual clustering of stars serve only to make the only person to relate the radiation densi­ rhythm of wars with a peak in 7 night sky darker. ty of starlight to the sky-cover fraction , December-February and a nadir in July I discussed5 the age limit in 1964, and thereby proving the aptness of Olbers' was found in the Southern Hemisphere, 8 showed that to fill a static universe with geometic line-of-sight argument . latitudes 30-60° S (c in the figure). The starlight in thermodynamic equilibrium When the effect of expansion domin­ circannual rhythms in the acts of aggres­ with stars requires that stars shine con­ ates, as in Bondi's steady-state solution, sion, both in the Northern and the tinuously for 1lf3 years. The energy the sky is covered with stellar disks, Southern hemispheres, have a statistical­ density of starlight in a static universe most of which cannot be seen because of ly significant positive correlation with only 1010 years old is 10-13 of that large redshift. When the effect of age the annual rhythm of the photoperiod needed to create the bright sky of 01- dominates, as in Kelvin's solution, the duration in the same geographical re­ bers' paradox. Even in a much older sky is not covered with stellar disks; stars gions. The results in the Northern universe, the sky remains dark because in the visible Universe must increase in Hemisphere suggest that there is a the lifetime of luminous stars is typically number by 1013 to cover the sky and phase-shift of about one month between 1010 years. come into equilibrium with starlight. the two rhythms. We found a constant I also showed5 that the effect of ex­ Olbers' paradox is full of intricacy and rate of acts of hostility throughout the pansion is usually small. Two universes subtlety, which explains why it continues year around the line of the Equator (bin of equal age, one static and the other to fascinate, if only for theoretical the figure). expanding, with stars in identical states, reasons. Substitution of galaxies for stars Barbara Tuchman2 designates affec­ contain equal numbers of photons emit­ changes the name of the game: a more tiveness and irrationality as dominant ted by stars. In the expanding universe suitable name would be 'Bonnar's contributory factors in the series of wars 9 the average redshift of photons is = paradox' , were it not that a sky tiled from Troy to Vietnam. Elongation of the (1 + q)-1 and the radiation energy with galaxies is not in paradoxical con- daily photoperiod may induce increases 574 NATURE· VOL 352 · 15 AUGUST 1991