## Tuesday, April 15, 2014

### How Variable Is alpha, the Fine Structure Constant?

The fine structure constant or 'alpha' is introduced to every first year student in quantum mechanics or modern physics. It was originally introduced in 1916  by A. Sommerfeld to describe the strength of the electromagnetic force which governs how charged particles interact and how molecules form. Since the, the constant  three way defined as:

$\alpha = \frac{k_\mathrm{e} e^2}{\hbar c} = \frac{1}{(4 \pi \varepsilon_0)} \frac{e^2}{\hbar c} = \frac{e^2 c \mu_0}{2 h}$

where:

worked its way into a number of important quantum mechanical equations. The generally accepted value is usually given in first year modern physics texts as 1/ 137 but in higher level textbooks (and to greater place accuracy) as:   α = 7.29735257×10−3. While the value of α can be estimated from the values of the constants appearing in any of its definitions, the theory of quantum electrodynamics (QED) provides a way to measure α directly using the quantum Hall effect or the anomalous magnetic moment of the electron.

But hold strain! Despite the portrayal of  α as a bona fide constant it may not be a true constant at all. According to some recent theories about the origin of dark energy, see e.g. http://brane-space.blogspot.com/2008/10/dark-energy-evidence-for-new-law-of.html

- Specifically the repulsive field that seems to pervade the cosmos  -  alpha's  value might vary depending on how much matter is nearby. To test this possibility a team at Imperial College, London measured alpha on Earth and in interstellar space where the density of matter is far lower.

The latter measurement was difficult but by no means impossible given we know the molecule CH is abundant in interstellar gas clouds scattered throughout the Milky Way. Hence, spectroscopic analysis allowed the measurement of the frequency of light needed to change the electron's energy in a particular way. So once the frequency  (f = c/  l) in deep space could be found than alpha could be as well.

In the case of the Earthbound value, the team produced the normally unstable CH molecule in the lab at ultra-cold temperatures. They then placed the CH molecules in a cavity and bombarded them with microwave pulses to force some of the molecules' electrons to jump to a higher energy state. Measurements were then taken of the frequency of light emitted as the electrons returned to the lower energy state.

The end results showed that alpha cannot vary by more than 1.4 parts in 10 million between the Earth and interstellar space. This is the most stringent constraint yet found on alpha's dependence on local matter density, but obviously it isn't proof that alpha is the same everywhere. (What about near the center of the large galactic black hole?)

Still, for the time being it's a remarkable result and until controverting measurements appear most of us will happily take alpha to be the constant we always thought it was.