Numerology in the skies

Maurizio Gasperini, the co-father of pre-big-bang string cosmology (with Gabriele Veneziano) has a very intriguing essay called

• A new scale in the sky

on the hep-th archive tonight. His goal is to present some evidence of the gravity-is-the-weakest-force conjecture whose blog description was provided by Jacques Distler. The assertion not only makes string theory falsifiable but also trivially rules out all models of pure gravity, for example all existing competitors of string theory.

Note that the statement that gravity is the weakest force, when properly defined with some mathematical equations, is arguably one of the universal predictions of string theory. Why do I find Gasperini's essay intriguing?

He bravely combines some rather abstract arguments in string theory and quantum gravity with real-life astrophysical observations. In fact, one of his main sources include a paper of Baliunas, Sokoloff, and Soon.

Incidentally, Sallie Baliunas and Willie Soon are rather famous climate sceptics from the Harvard-Smithsonian Center for Astrophysics who can't really exist because, as you have heard from Al Gore, climate sceptics don't really exist in the scientific community and if they do, they certainly don't work at any well-known places. And if they do, it is certainly impossible that you would ever hear about these marginal individuals, or at least not from a source of information composed at a well-known university, and so forth. ;-)

As Steve McIntyre would say: Take a Ritalin, Al.

Anyway, what are the intriguing points in the essay? As you know, we have conjectured the existence of a new scale

• g.M_Planck

for every gauge coupling "g". This is one starting point. The other starting point are phenomenological power laws satisfied by many astronomical objects. The first one is

• J = beta M^delta

in the Planck units that relates the angular momentum and the mass and where all observations seem to be consistent with the exponent

• delta = 2.

Some sources give "beta = 0.0007" although other sources seem to lead to a higher value "beta = 0.003". Another relation is between the angular moment "J" and the magnetic moment "Mag":

• J = gamma^-1/2 Mag^epsilon

in the natural units. Again, all observations are marginally consistent with the exponent

• epsilon = 1

and the experimental determinantion of "gamma" leads roughly to "gamma = 0.009". Now the key, breath-taking hypothesis of the author, and be ready for a miracle, is

• alpha = beta = gamma = 1/137.036,

i.e. both of these constants from the prefactors, "beta" and "gamma", in the laws above are the the fine structure constant and these relations could be derived by saturating the weak-gravity inequalities. Wow. That's what I call a bold claim. A nearly perfect unification of the Greek alphabet. Alpher, Bethe, and Gamow would be proud, together with Eddington who used to explain all numbers by the fine structure constant. The author seems to view these astrophysical observations as experimental circumstantial evidence not only for the "nearly saturated form" of our conjecture but also for string theory. I would indeed be thrilled if such things could be true.

We report, you decide. ;-)

However, it seems that the people are unable to determine what I think about similar ideas. Well, frankly, I don't believe a word of it. The weak gravity conjecture is about the very high-energy physics. The astrophysical observations are about very low-energy physics. It seems unlikely that there would be any direct link between these two. While it's plausible that the Universe tends to prefer some power laws between various quantities describing localized macroscopic celestial bodies, this rule is unlikely to be connected with fundamental physics: it's kind of emergent and therefore independent of the fundamental laws of Nature.

Moreover, the high-energy physics regime where the weak gravity conjecture is relevant describes not only the electromagnetic interaction but also the strong and weak forces. In fact, we must replace electromagnetism by the electroweak force. The occurrence of the low-energy fine-structure constant - that otherwise runs - in the weak-gravity setup would be a shock.

Also, I seem to disagree with some factors of "4 pi", "8 pi", and others, and the numerical evidence looks unconvincing.