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Alpha Anisotropy

November 30, 2011

There's a joke that commonly circulates among new statistics students. Here's one variant.
Two bow hunters were out hunting turkey when they spot one in the bush. One hunter raises his bow and shoots an arrow that lands two feet to the left of the bird. Then the second hunter takes his shot, and the arrow lands two feet to the right of the bird. The first hunter exclaims, "We got him!"

Radio astronomers from Australia and the UK have published measurements that show a difference in the fine structure constant (commonly called α) in the early universe. They've found, also, that the constant is either higher or lower than the terrestrial value, depending on the measurement direction; that is, there's a cosmological anisotropy in the value of the fine structure constant. Based on their analysis of possible error sources, they decided not to exercise hunter's statistics to conclude that there's really no change at all.

The fine structure constant agrees with theory to eleven decimal places. Any suggestion that it's variable requires considerable evidence, since the fine structure constant is related to some rather fundamental things; namely, the elementary charge e, Planck's constant h, the speed of light c and the mathematical constant π,
α = (2 π e2)/(h c)

α, a dimensionless number which is quite close to the reciprocal of 137 (~1/137.036), expresses the strength of the interaction of charged particles, and it's fundamental to electromagnetism. So, if α has changed, is it because e, h or c changed?

I wrote about the preliminary results of this same research team in a previous article (Fine Structure Constant, September 16, 2010). At that time, there was evidence for a smaller value of α at high redshift.[1-5] The difference they found, as they probed to a time nine billion years ago, was just 0.0006%. The research team measured the spectra of quasars visible in the northern and southern hemispheres. The quasar light, itself, was not analyzed; rather, the spectra captured the absorption lines in the intervening intergalactic medium that permeate the universe. Measurements in the northern hemisphere were performed using the Keck telescope (Mauna Kea, Hawaii).

Southern hemisphere observations were performed using the European Southern Observatory Very Large Telescope (VLT) at Cerro Paranal, Chile. At that time, the data also indicated a possible anisotropy. There was a smaller value of α when looking north; and a larger value of α when looking south.

To refine their data and get better statistics, the research team added additional data from the Very Large Telescope for quasars in a different direction. More than 300 quasars have been measured. The new composite data set is the one that confirms the anisotropy.[6-8] The raw data can be seen in the figure.[7]

Fine Structure Constant data plotted on celestial coordinates

Deviation from the established value of the fine structure constant for quasar measurement, as plotted in celestial coordinates. Squares are VLT points, circles are Keck points, and triangles are quasars observed at both Keck and VLT. The symbol size indicates the magnitude of the deviation. The blue dashed line is the equatorial plane, and the gray area is the galactic plane with a bulge at its center. The direction of the anisotropy pole is indicated. (Fig. 5 of Ref. 7, via the arXiv Preprint Server).

This finding has a very good statistical case. The combined data for Keck and the VLT shows a dipole at the 4.2-sigma level. The putative dipole direction is 17.5 ± 0.9 h right ascension, -58 ± 9 deg declination. When taken separately, the Keck and VLT data show a dipole themselves, and the dipole is evident at low and high redshifts. A search for systematic error showed none that would emulate this result.

Critics, of course, are not hard to find. Chad Orzel, a physicist at Union College (Schenectady, New York), is concerned that the Keck data puts the deviation of α mostly in one direction, while the VLT data goes the other way.[8] This seems to indicate that the effect is coming from some difference between the two telescopes. The team has submitted a longer paper with more details to the Monthly Notices of the Royal Astronomical Society to allow other scientists a better way to assess possible errors.[8]

Sean Carroll of Caltech has commented on a possible ramification were the result proved to be true. Having the fine structure constant vary from place to place would cost energy, energy that perhaps relates to dark energy.[8] The alpha measurement team writes in its paper that such an effect could violate the equivalence principle, which asserts the equality between inertial mass and gravitational mass.[6-7]

This isn't the first time that there's been speculation that the constant could have changed over cosmological times. However, any change would need to be small, or life would not exist in our universe. The Anthropic Principle can be applied to the value of the fine structure constant. If the value of α was much different from its measured value, stellar fusion would not produce any carbon, and you wouldn't be around to read this article. Come to think of it, I wouldn't have written this article.


  1. The Fine-Structure Constant and the Nature of the Universe, The Economist, August 31, 2010.
  2. Ron Cowen, "Changing one of nature's constants," Science News, September 3, 2010.
  3. J. K. Webb, J. A. King, M. T. Murphy, V. V. Flambaum, R. F. Carswell and M. B. Bainbridge, "Evidence For Spatial Variation of the Fine Structure Constant," arXiv, August 23, 2010.
  4. Jonathan B. Whitmore, Michael T. Murphy, Kim Griest, "Wavelength Calibration of the VLT-UVES Spectrograph," arXiv, April 20, 2010.
  5. Giuseppe Dattoli, "The fine structure constant and numerical alchemy," arXiv Preprint Server, September 9, 2010.
  6. J. K. Webb, J. A. King, M. T. Murphy, V. V. Flambaum, R. F. Carswell and M. B. Bainbridge, "Indications of a Spatial Variation of the Fine Structure Constant," Physical Review Letters, vol. 107, no. 19 (November 4, 2011), Document No. 191101.
  7. J. K. Webb, J. A. King, M. T. Murphy, V. V. Flambaum, R. F. Carswell and M. B. Bainbridge, "Indications of a spatial variation of the fine structure constant," arXiv Preprint Server, November 1, 2011.
  8. Buzz Blog, Another Law of Physics Broken? November 2, 2011.
  9. Peter J. Mohr, Barry N. Taylor and David B. Newell, "CODATA Recommended Values of the Fundamental Physical Constants: 2006," arXiv Preprint Server, December 29, 2007.

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Linked Keywords: Statistics; bowhunting; turkey; arrow; foot; radio astronomer; Australia; United Kingdom; UK; fine structure constant; universe; cosmology; anisotropy; observational error; quantum electrodynamics; elementary charge; Planck's constant; speed of light; dimensionless number; charged particle; electromagnetism; redshift; astronomical spectroscopy; spectra; quasar; absorption line; intergalactic medium; northern hemisphere; Keck telescope; Mauna Kea, Hawaii; Southern hemisphere; European Southern Observatory; Very Large Telescope; Cerro Paranal, Chile; celestial coordinates; equatorial plane; galactic plane; arXiv Preprint Server; 4.2-sigma; right ascension; declination; dipole; Chad Orzel; physicist; Union College (Schenectady, New York); Monthly Notices of the Royal Astronomical Society; Sean Carroll; California Institute of Technology; Caltech; energy; dark energy; quivalence principle; inertial mass; gravitational mass; Anthropic Principle; stellar fusion; carbon.