Dirac versus Teller on varying gravitational parameter G

General relativity fails to model the moment of creation because it tells you there the universe was then a singularity of zero size, infinite density, and infinite curvature.  I don’t believe that general relativity is any more than an approximation to a theory of quantum gravity, where there is no real curvature but instead a lot of little graviton interactions that produce accelerations that only appear to be a smooth curvature when seen on large scales.  It appears that cosmic inflation is wrong, because the flatness of the universe (the lack of lumpiness seen in the cosmic background radiation emitted at 300,000 years after the big bang, indicating little gravitational curvature at that time) is instead due to an increasing gravitational parameter G.  A variation of G with time is traditionally ruled out by Teller’s argument against Dirac in 1948, where Teller claimed that a variation in G would make the sun’s radiant power vary enormously so the seas would be boiling a billion years ago, preventing life.  However, Teller’s calculations implicitly assume that G is the only variable.  In fact, electromagnetic force coupling strength theoretically appears to vary in the same way as G, so the variation in the electromagnetic repulsion between protons in the sun would offset the effect of varying gravitational compression on the fusion rate.  As a result, fusion rates in stars and in the first minutes of the big bang don’t vary as Teller claimed when G varies.  I think that if full calculations could be done using the correct quantum field theory, they would indicate very clearly what the universe was like when it began (not a singularity!), and what it will evolve into in the distant future (because all fundamental force coupling strength parameters are rising, the result will be different to Dyson’s mainstream predictions which assume constant G etc.).

On the subject of the dispute between Dirac and Teller over varying G, I’ve just found a nice discussion by George Gamow in his book Gravity (Doubleday and Company, New York, 1962, pp. 138-141).  Notice that I’ve blogged elsewhere about how both Dirac and Teller were wrongly bigoted against and dismissive of Feynman’s path integral treatment of quantum electrodynamics in 1948, so they were not perfectly capable of judging ideas usefully.

Gamow starts off by explaining that the electromagnetic force of attraction between an electron and a proton is about 1040 times as strong as the gravitational force of attraction between the same particles, and then states that Dirac set out to explain why there was such a difference in fundamental force strengths. Dirac worked with the Hubble expanding universe and assumed that in the past at some point electromagnetism and gravity had the same strength, and that the ration has increased with time since then until attaining its present value of 1040. Gamow adds that Dirac thought that electric charge does not vary with time, so that G decreased with time (actually it increases with time, along with the coupling parameter for electromagnetism, etc.), ‘and that this decrease may be associated with the expansion of the Universe and the steady rarefaction of the matter filling it.

‘These views of Dirac were later [in 1948] criticized by Edward Teller (Father of the H-bomb), who pointed out that the variation of the gravitational constant G would result in the change of temperature of the Earth’s surface. Indeed, the decrease of gravity would result in the increase of the radii of planetary orbits, which (as can be shown on the basis of the laws of mechanics) would change in inverse proportion to G. The decrease would result also in the distortion of the internal equilibrium of the Sun, leading to the change of its central temperature, and of the rate of energy-producing thermonuclear reactions.

‘From the theory of internal structure and energy production of stars, one can show that luminosity (amount of light emitted per unit time) L of the Sun would change as G7.25. Since the surface temperature of the Earth varies as the fourth root of the Sun’s luminosity divided by the square of the radius of the Earth’s orbit, it follows that it will be proportional to (time)2.4, if G varies in inverse proportion to time. Assuming for the age of the solar system the value of three billion years, which seemed to be correct at the time of his publication, Teller calculated that during the Cambrian Era (a half billion years ago) the temperature of the Earth must have been some 50 oC above the boiling point of water, so that all water on our planet must have been in the form of hot vapor. Since, according to geological data, well-developed marine life existed during that period, Teller concluded that Dirac’s hypothesis concerning the variability of the gravitational constant cannot be correct. During the last decade, however, the estimates of the age of the solar system have been changed toward considerably higher values, and the correct figure may be five billion years or even more [it is 13.7 billion years, some 6.85 times as high as Hubble’s value of 2 billion years; Hubble exaggerated the estimate of the Hubble parameter because he confused two populations of Cepheid variable stars, which he used as yard-sticks to determine the distances of galaxies, and this error was only found in the 1950s]. This would bring the temperature of the primitive ocean below the boiling point of water and make the old Teller objection invalid, provided that the Trilobites and Silurian molluscs could live in very hot water. It may also help paleontological theories by increasing the rate of thermal mutations during the early states of the evolution of life, and supplying, during the still earlier periods, very high temperatures necessary for the synthesis of nucleic acids which, along with proteins, form the essential chemical constituents of all living beings. This the question of variability of the gravitational constant still remains open.’

On the next page, page 142, Gamow writes:

‘Are gravitational waves divided into discrete energy packets, or quanta, as electromagnetic waves are? This question, which is as old as the quantum theory, was finally answered two years ago [i.e. in 1960, since the book was published in 1962] by Dirac. He succeeded in quantizing the gravitational-field equation and showed that the energy of gravity quanta, or “gravitons”, is equal to Planck’s constant, h, times their frequency – the same expression that gives the energy of light quanta or photons.’

Gamow and the big bang

The name ‘big bang’ was coined by Sir Fred Hoyle in a dismissive attack on the idea of the expanding universe (Hoyle proposed a steady state model in which expansion is powered by the ongoing creation of matter at an unobservably small rate, an ad hoc epicycle-like belief system ‘theory’ that is no more than abject speculation and fails to predict the abundances of the light elements or the cosmic background radiation).

George Gamow (whose discussion in his 1962 book Gravity we quoted above) did a lot of early scientific work on the big bang theory.  In Leningrad in 1931 he wrote a text book, Atomic Nucleus, published in England by Oxford University Press.  Gamow’s major contribution to nuclear physics was proposing the liquid-droplet model of the nucleus, which is a useful model for heavy nuclei like uranium and was in 1938 used by Lise Meitner to successfully interpret the barium and other products in the neutron irradiation of uranium (by Hahn and Strassman) as indicating nuclear fission.  Gamow also collaborated in early calculations of the nuclear fusion rate in the sun and other stars.  In 1932 Gamow and his wife unsuccessfully attempted to escape from the Soviet Union by paddling a kayak 170 miles across the Black Sea to Turkey, but the next year he attended a physics conference in Brussels and was there offered a position as a lecturer in America.  He accepted, and as a result he was fired from the Academy of Sciences of the U.S.S.R.

With his student Ralph Alpher and Manhattan Project physicist Hans Bethe as proof-reader, Gamow calculated the abundances of the light elements created by nuclear fusion in the big bang in the classic Alpher-Bethe-Gamow paper ‘The Origin of the Light Elements’, published in 1948.  The abundances of elements predicted by the big bang theory corresponded to the observed abundances of light elements in the universe, the second major piece of evidence for the big bang after Hubble’s discovery of expansion in 1929 (which cannot be explained by ‘tired light’ speculations).  They assumed that the universe began with neutrons, which was a reasonable approximation at that time (more recent calculations of nucleosynthesis in the big bang are much more sophisticated, including an early quark era at very high energy densities).

Even more impressively, Gamow predicted that the big bang created a radiation flash still around today as a 5 K microwave background radiation (the prediction is slightly off because the Hubble constant wasn’t known well in 1948, see above).  Gamow’s argument was that initially the universe was ionized hydrogen gas with a small amount of other elements.  While the gas was ionized, the free electrons and positive ions (protons) would absorb radiation very effectively before re-emitting it.  So the temperature spectra of the matter and the radiation would be similar.  At around 300,000 years after the big bang, when the universe cooled to a temperature around 3000 K, the ions and electrons would combine to form electrically neutral hydrogen which is relatively transparent to radiation.  From then on, the radiation would propagate freely, and today we will continue to see that radiation, albeit that emitted from extremely redshifted receding ions at an age 300,000 years after the big bang, i.e., nearly 13,700 million light years away!  The redshift of this cosmic background radiation increases its wavelength and decreases its energy per photon so that it appears to us to have a temperature about 1000 times smaller than it had at 300,000 years after the big bang.  Hence, we see it as the 2.7 K microwave background radiation.  This microwave background radiation was discovered in 1965 (but Gamow was not awarded a Nobel Prize since his publications were ignored by the people who discovered it).

This microwave background radiation was the third major piece of evidence for the big bang, after the Hubble discovery of expansion, and the correctly predicted abundances of light elements in the universe due to nuclear fusion in the big bang fireball.  Heavy elements up to iron are created by fusion of lighter elements in stars, while elements heavier than iron are created during processes like star explosions, supernovae, by a two-stage process involving first the successive capture of neutrons by fusion products and then beta radioactive decay of those neutron-rich massive atoms.

‘Dr Edward Teller remarked recently that the origin of the earth was somewhat like the explosion of the atomic bomb…’– Dr Harold C. Urey, The Planets: Their Origin and Development, Yale University Press, New Haven, 1952, p. ix.


‘It seems that similarities do exist between the processes of formation of single particles from nuclear explosions and formation of the solar system from the debris of a supernova explosion. We may be able to learn much more about the origin of the earth, by further investigating the process of radioactive fallout from the nuclear weapons tests.’

– Dr P. K. Kuroda, ‘Radioactive Fallout in Astronomical Settings: Plutonium-244 in the Early Environment of the Solar System,’ Radionuclides in the Environment (Dr Edward C. Freiling, Symposium Chairman), Advances in Chemistry Series No. 93, American Chemical Society, Washington, D.C., 1970.

5 thoughts on “Dirac versus Teller on varying gravitational parameter G

  1. ‘But compared with a supernova a hydrogen bomb is the merest trifle. For a supernova is equal in violence to about a million million million million hydrogen bombs all going off at the same time.’ – Sir Fred Hoyle (1915-2001), The Nature of the Universe, Pelican Books, 1963, p. 75.

    ‘In fact, physicists find plenty of interesting and novel physics in the environment of a nuclear explosion. Some of the physical phenomena are valuable objects of research, and promise to provide further understanding of nature.’ – Dr Harold L. Brode, The RAND Corporation, ‘Review of Nuclear Weapons Effects,’ Annual Review of Nuclear Science, Volume 18, 1968, pp. 153-202.

    (These quotations are from http://glasstone.blogspot.com/2008/11/radiation-and-emp-chapters-from-dolans.html

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