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Work by Dyson and Alex Shlyakhter on the fine-structure constant

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Work by Dyson and Alex Shlyakhter on the fine-structure constant

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Could gravity vary with time?

Freeman Dyson
Scientist

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The question was raised by Dirac, I think in 1936 or thereabouts: Could gravity be varying with time as the universe evolves? And the motivation for Dirac was he didn't like the fact that gravitational interaction is so weak as compared with other kinds of interactions, so if you take a dimensionless ratio which is Gm^{2}/hc, where G is the gravitational constant of Newton, m is the mass of a proton, h is Planck's constant, and c is the velocity of light - that's a dimensionless number; it happens to have the value 10^{-39}, and Dirac considered that to be ugly; that in the laws of physics there's this enormously small quantity which appears to be just arbitrary and put in by God into the laws of physics, and he said any self-respecting god wouldn't have done that, so that there must be some reason for this very small number appearing. So Dirac's argument was that if you assume that gravity goes down with time, like 1/T from the beginning of the universe, and you measure time in units of the proton Compton wave length, which is sort of the natural unit of time - no, not the Compton wavelength but the Compton frequency, the Compton wave length divided by velocity of light - then the unit of time is about 10^{-22} seconds, and the universe has existed for about 10^{17} seconds, so the ratio between the present age of the universe and the natural unit of time is 10^{39}. So that's an interesting fact. So Dirac's hypothesis was that - so this small number merely is indicating the particular age at which we live in the history of the universe; in the natural units we are 10^{39} units from the beginning of time. So if you assume that gravity goes like 1/T, then you don't need to write this small number into the laws of physics. Well that was a very attractive notion to Dirac. He had this very strong belief in the power of aesthetics to divine the laws of nature, but then it's a question whether that's experimentally true. Well after that, then... Dirac's hypothesis remained a hypothesis for 40 years. Nobody had good enough observational data either to confirm it or to contradict it. So it remained quite possible that Dirac was right. In the meantime I think it was Edward Teller who proposed that the same thing might be true for the fine-structure constant, since that's also a rather small number, not as small as the gravitational coupling constant, but it's still... it's e^{2}/hc, that's 1/137, and that looks like a logarithm. If you take the logarithm of Dirac's number, the natural logarithm of 10^{39} is about a 100, so it's about a 100 powers of e, so you might imagine that 137 is the logarithm of the time. And so Teller proposed the hypothesis that the electromagnetic interaction is also weakening with time, but going like 1 over logarithm. So that was also a very interesting question and that... Teller proposed that, I think - I don't remember exactly when, around 1950 or so - I mean it was some time after Dirac. And that was clearly much easier to test because we have much more accurate information about the electromagnetic interaction than we do about gravity. So... attention then was immediately concentrated on the fine-structure constant rather than on gravitation. And the first response to Teller, I think, came from Denys Wilkinson and he showed that in fact Teller couldn't be right, and he did that by looking simply at the decay rate of uranium in ancient rocks. That if you observe isotopes of uranium and isotopes of lead into which they decay in ancient rocks you can... by - it's a fairly circular argument, but you can in fact more or less prove by looking at these different kinds of rocks that the decay rates have remained pretty constant over the last 10^{9} years or so, within 10%, something like that. I mean, there hasn't been a huge variation in the decay rate. Well, if you take the rate of the outer decay of uranium 238, it's actually extremely sensitive to the fine-structure constant because it... the alpha particle has to come out of the nucleus over a very high Gamow barrier, and the Gamow formula for the lifetime has an exponential with the fine-structure constant in it, since the fine-structure constant determines the Coulomb interaction between the alpha particle and the rest of the nucleus. So you... the lifetime goes like the exponential of something proportional to the fine-structure constant with a big coefficient. And so if you change the fine-structure constant by a small fraction, you change the lifetime by the 500th power of the fine-structure constant. So it's actually a very sensitive test for variation of the fine-structure constant, and so that by itself was enough to demolish Teller.

Freeman Dyson (1923-2020), who was born in England, moved to Cornell University after graduating from Cambridge University with a BA in Mathematics. He subsequently became a professor and worked on nuclear reactors, solid state physics, ferromagnetism, astrophysics and biology. He published several books and, among other honours, was awarded the Heineman Prize and the Royal Society's Hughes Medal.

**Title: **Could gravity vary with time?

**Listeners:**
Sam Schweber

Silvan Sam Schweber is the Koret Professor of the History of Ideas and Professor of Physics at Brandeis University, and a Faculty Associate in the Department of the History of Science at Harvard University. He is the author of a history of the development of quantum electro mechanics, "QED and the men who made it", and has recently completed a biography of Hans Bethe and the history of nuclear weapons development, "In the Shadow of the Bomb: Oppenheimer, Bethe, and the Moral Responsibility of the Scientist" (Princeton University Press, 2000).

**Tags:**
Planck's constant, Compton frequency, fine-structure constant, Paul Dirac, Edward Teller, Denys Wilkinson

**Duration:**
6 minutes, 10 seconds

**Date story recorded:**
June 1998

**Date story went live:**
24 January 2008