As explained in alpha, the charge on the electron squared divided by Planck's constant and the speed of light is a pure number describing the strength of electromagnetism at atomic physics energy scales:

α = e2 / (4 π h-bar c)

known as the fine structure constant. It is the basic expansion parameter of QED.

(h-bar is Planck's constant divided by 2 pi. As usual, there are some factors of 2 and pi that come in depending on conventions - whether the units you use are rationalised or not.)

The value of alpha can be found by measuring spectral lines of atoms, which means the particular frequencies at which they absorb or emit light. Roughly speaking, alpha is the ratio between the relativistic corrections and the initial frequency. Its value is about 1/137 - a more accurate value can be found at the National Institute of Standards and Technology.

One fringe idea in physics that has been around for several decades is that fundamental constants such as alpha might vary over time or over space. "Varying constants" sounds like a contradiction, so I will instead use "varying couplings". Such variation would obviously have to be pretty slow for it to go undetected and not radically affect the evolution of stars and galaxies.

Technically, one can only measure couplings which do not have units, such as alpha, since any change in a dimensionful quantity can be absorbed into a change in units so long as dimensionless quantities do not change. In other words there is no way to tell if a metre rule was longer or shorter somewhere else in spacetime, only the ratio between one length and another is meaningful.

Recent interest was sparked in the subject by the result reported by a team from the University of New South Wales, headed by John Webb: they reported a variation in alpha in observations from billions of years ago, relative to today. The most recent numbers released by the group are

delta alpha / alpha = -(5.7 ± 1) × 10-6

for data collected at redshifts 0.2 to 3.7. The method used is interesting: light from distant quasars (QSO's) passes through clouds of interstellar gas, otherwise known as absorbing systems, and the astronomers measure the wavelengths at which the gas absorbs light. The many-multiplet method makes use of several different elements, whose lines may be shifted up or down, for a given variation in alpha, because of the intricacies of atomic physics.

This is a statistically robust result, but is not universally accepted because there is the possibility of undetected systematic errors that would bias the measurements in one direction. However it must be said that the Webb group have done a very thorough job in looking for systematic errors and not found any that would weaken the result.

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