Inconstant

The funniest April Fools prank was definitely the one about time variation of $\pi$. That idea is of course absurd because the Bible unambiguously sets the value of $\pi$ to be equal three. But the physical constants like the QCD scale or the Fermi constant are not mentioned in the Bible which suggests that they might not be constants. Recently, Harald Fritzsch put on ArXiv a neat status report of various theoretical and experimental pursuits of varying fundamental constants.

For almost a century the idea of varying fundamental constants has been attracting most brilliant minds and complete crackpots alike. At the theoretical level the mechanism is easy to imagine: the physical constants can be set by a vacuum expectation value of a scalar field that evolves on cosmological timescales. In high-energy theory we already have one evolving scalar field for inflation and sometimes another one for quintessence, so that introducing yet another one for varying constants is not that difficult to swallow.

At the beginning of this century the idea has received renewed attention due to some experimental claims that the electromagnetic constant $\alpha$ may vary in time. A group of astrophysicists studying absorption spectra of very distant quasars concluded that 10 billion years ago $\alpha$ was smaller than today by $\Delta \alpha/\alpha \sim 10^{-5}$, corresponding to a time variation of order $10^{-15}$ per year. This claim is very controversial because of various assumptions involved in the determination $\alpha$ and, most of all, because other groups did not confirm this result. A more recent claim that the proton-to-electron mass ratio was different 10 billion years ago also remains highly controversial.

Yet another reason why the above claims are taken with a huge grain of salt is that the so-called Oklo bounds imply a slower variation of $\alpha$. 2 billion years ago, when the Earth was young and beautiful, the uranium-235 isotope was five times more abundant than today. Thanks to that fact and some other lucky coincidences, near the river Oklo in today's Gabon nature could create a fully organic nuclear reactor which operated for 100 million years. The uranium fission produced many rare isotopes, and the particular ratio of Samarium-149 to Samarium-147 can be used to constrain variation of the fundamental constants. The point is that the cross-section for the neutron capture on Samarium 149 is accidentally enhanced by a presence of resonance just 0.1 eV above the threshold. From the fact that the position of this resonance could not migrate by more than 0.1 eV one can set the bound $\Delta \alpha/\alpha \sim 10^{-7}$ (assuming that only the electromagnetic constant is varied) corresponding to a time variation $10^{-16}$ per year. If $\alpha$ was changing faster than that (as suggested by some astrophysical results) it had to stabilize at least two billion years ago.

In the neat future there is hope for more progress from precision measurements in a controlled laboratory environment. Experiments in quantum optics have recently reached a similar sensitivity to varying constants as the astrophysical observations. In particular, Theodor Haensch's group in Munich is running an experiment that studies time variation of the frequency of the 1s-2s transition in atom hydrogen (review here). The measurements from different years are related to the hyperfine transitions of Cesium-133 and to another precision measurement of quadrupole transitions in Mercury, which allows them to constrain the variation of both the electromagnetic constant and the QCD scale. The results published several years ago constrain the variation of both at the level of few times $10^{-15}$ per year.

Actually, Harald Fritzsch is spreading wild rumors that the most recent results from Munich imply the time variation of the QCD scale at the level of $3 \cdot 10^{-15}$ per year. Well, I'd rather bet that at the end of the day the constants will once more turn out to be constants. But who knows...in the end the Hubble constant has changed since the nucleosynthesis by some 17 orders of magnitude.