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Proton to Electron Mass Ratio

January 11, 2013

Over the years, there have been quite a few astronomical observations that have sought to determine something of very fundamental importance; namely, are the physical constants actually constant, or do they have values that change with time as our universe expands. Dirac, himself, published a paper on this idea in 1938, stating that
"...there is no definite reason why the constants of atomic theory should not appear in cosmology - in fact, one would expect them to, since one would expect a closer connexion between the atom and the cosmos to show itself with a deeper understanding of Nature."[1]

Something that sounds so cosmological as variable physical constants can actually be checked very close to the Earth. Thomas Van Flandern, who was an astronomer with the United States Naval Observatory, thought that a temporal change in the gravitational constant could be seen in the orbit of the Moon.[2]

Unfortunately, Van Flandern is better known for his wild speculations on various topics, as his Wikipedia entry will show. That notwithstanding, he was still a foremost authority on the orbit of the Moon, and he coauthored a widely used algorithm for calculating the Julian date from the Gregorian date.[3]

Every physicist's favorite dimensionless constant is the fine-structure constant, commonly symbolized as α. 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)

Since the fine structure constant agrees with quantum electrodynamics to eleven decimal places, any suggestion that it's variable requires considerable evidence. You must also ask yourself, has it changed because e, h or c has changed?

In a previous article (Alpha Anisotropy, November 30, 2011), I reviewed evidence that α might not be that constant on a cosmological scale. A team of radio astronomers from Australia and the UK determined that α is either higher or lower than the terrestrial value, depending on the measurement direction.[4-5]

Enrico Fermi with alpha equation

One example of the fine-structure constant changing with time.

In this photograph, Enrico Fermi has written the wrong equation for α. The symbol h-bar is known as the reduced Plank Constant. It's h divided by

Fermi's sly smile might indicate that he did this on purpose; or, this is an early example of a photobomb.

(Smithsonian Institution photograph, via Wikimedia Commons.)

The research team measured the absorption spectrum of the intergalactic medium between Earth and quasars visible in the northern and southern hemispheres. Their data showed a dipole at the 4.2-sigma level. The putative dipole direction is 17.5 ± 0.9 h right ascension, -58 ± 9 deg declination.[4-5]

Another interesting dimensionless number is μ, the proton-to-electron mass ratio, which is presently known to be 1836.15267245. In 1951, when this constant was measured to be 1836.12, Friedrich Lenz of Düsseldorf, Germany, published a one-sentence paper in the Physical Review stating that this number was very nearly 5 (1836.11810845).[6] Nowadays, it's possible to find many such relationships using computers, none of which are worthwhile without a backing theory.

Scientists at the Vrije Universiteit (Amsterdam, The Netherlands) and the Max Planck Institute for Radio Astronomy (Bonn, Germany) decided to check whether μ has changed with time. To accomplish this, they used the 100-meter radio telescope at Effelsberg, Germany, operated by the Max Planck Institute for Radio Astronomy, to examine the absorption spectrum of methanol.[7-8]

They observed absorption lines for methanol in the spectrum of PKS1830-211, a lensed quasar with a lensing galaxy at a redshift of about 0.89.[9] This redshift places the lensing galaxy at a time seven billion years in the past. Four spectral lines were observed around 25 GHz for methanol, two of which would be especially sensitive to μ.[7] They found that at that redshift, Δμ/μ = (0.0 ± 1.0) x 10−7, which is essentially a null result.[8]

Said Karl Menten, Director at the Max Planck Institute for Radio Astronomy,
"If we were really to find deviations in this fundamental constant, we would have a problem with our understanding of the foundations of physics... Most importantly, this would violate Einstein's equivalence principle, the cornerstone of the general theory of relativity."[7]
100 meter Radio Telescope Effelsberg, Germany (Hans-Peter Scholz Ulenspiegel, modified from original)

The 100 meter radio telescope at Effelsberg, Germany.

(Photograph by Hans-Peter Scholz Ulenspiegel, artistically modified, via Wikimedia Commons)


  1. P.A.M. Dirac, "A New Basis for Cosmology, Proc. Roy. Soc. London, vol. A165 (1938), pp. 199-208.
  2. T. C. Van Flandern, “Is the gravitational constant changing?”. Astrophysical Journal, vol. 248 (1981), pp. 813-816.
  3. Henry F. Fliegel and Thomas C. van Flandern, "Letters to the editor: a machine algorithm for processing calendar dates,"Communications of the ACM, vol. 11, no. 10 (October, 1968), p. 657.
  4. 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.
  5. 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.
  6. Friedrich Lenz, "The Ratio of Proton and Electron Masses," Phys. Rev., vol. 82, no. 4 (May, 1951), pp. 554–554
  7. Physical constant passes the alcohol test - Fundamental properties of molecules have not changed during the past seven billion years, Max-Planck-Gesellschaft, München, Press Release, December 13, 2012.
  8. Julija Bagdonaite, Paul Jansen, Christian Henkel, Hendrick L. Bethlem, Karl M. Menten and Wim Ubachs, "A Stringent Limit on a Drifting Proton-to-electron Mass Ratio from Alcohol in the Early Universe," Science Express, December 13, 2012, DOI: 10.1126/science.1224898.
  9. T. Wiklind and F. Combes, "The redshift of the gravitational lens of PKS1830–211 determined from molecular absorption lines," Nature, vol. 379, no. 6561 (January 11, 1996), pp. 139-141.
  10. E. J. Salumbides, M. L. Niu, J. Bagdonaite, N. de Oliveira, D. Joyeux, L. Nahon and W. Ubachs, "The CO A-X System for Constraining Cosmological Drift of the Proton-Electron Mass Ratio," arXiv Preprint Server, August 23, 2012

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