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The Speed of Light

August 16, 2013

Everyone hates speed limits. I understand and tolerate the 65 mile-per-hour speed limit on most US interstate highways, since it allows a measure of safety against driver reaction time. What I don't tolerate are those stretches of local road where I'm sure the artificially low speed limit was set merely to generate revenue.

Legislated speed limits can be changed, but there's no getting around the universal speed limit, the speed of light, commonly symbolized as c. Even the proverbial "speeding bullet" in the introduction of the Adventures of Superman television series (one or two thousand miles per hour) pales in comparison with the speed of light, 186,000 miles-per-second (300,000 kilometers-per-second).

The speed of light is so rapid that it appears to be infinite, but one argument by the ancient Greek philosophers for an infinite speed of light seems especially strange today. Euclid and Ptolemy thought that the process of vision involved light emanating from the eyes and reflecting back to the observer. From this idea, Hero of Alexandria reasoned that the speed of light must be infinite, since we instantly see distant objects, such as stars, when we open our eyes. I wrote about Hero in a previous article (Steam Power, January 28, 2011).

Through the time of Kepler (c. 1600), all arguments about the speed of light were merely philosophical. As Bernd Matthias demonstrated in the field of superconductivity,[1] one good experiment is worth a hundred theoretical papers, so Galileo performed an experiment in 1638 to measure the speed of light using signal lanterns separated by a large distance. He concluded that the speed was either very rapid or instantaneous. The round trip transit time of light over a mile's distance is just 10.73 microseconds.

Galileo Galilei and Ole Romer
Galileo Galilei (left), who did the first speed of light experiment in 1638, and Ole Rømer, who used a natural satellite of Jupiter as a clock to estimate the speed of light in 1676. (Source images, left, portrait of Galileo Galilei, 1636, by Justus Sustermans (1597–1681), at the National Maritime Museum, Greenwich, London; and, right, portrait of Ole Rømer, circa 1700, by Jacob Coning (circa 1647–1724), at the Frederiksborg Museum, both via Wikimedia Commons).

The Danish astronomer, Ole Rømer, was the first to actually affix a quantity to the speed of light. He did this by noticing that the period of Jupiter's moon, Io, was shorter when the Earth was approaching Jupiter, and longer when receding from it. Rømer's estimate was 220,000 kilometers/sec, about 75% of the established value. A more accurate astronomical measurement was made in 1729 by English astronomer, James Bradley, who used his discovery of the aberration of light to calculate its speed to within 1.5% of its established value.

Since 1983, we are privileged to know the exact value of the speed of light. This value, 299,792.458 kilometers/sec was fixed by a new definition of the meter. Now, any improvement in the measurement of the speed of light is actually an improvement in the definition of the meter. That being said, everyone still uses the 300,000 kilometers/sec value. As my building contractor father would say when surveying for the foundation of a house, "It's close enough for digging."

Since the speed of light is a fundamental quantity and a part of the equations of so many theories, it's still studied. Earlier this year I reported on the possibility that the speed of light we measure is an average value. It might show variation over very short length scales (Light Speed, April 8, 2013).

There was brief excitement among physicists at the end of 2011, with a report that some neutrinos might travel faster than light. This discovery was made during operation of the OPERA experiment in which a beam of muon neutrinos is sent to a detector 730 km (453 miles) away. A small fraction of these seemed to arrive 60 nanoseconds sooner than expected for light speed, as I reported in a previous article (Tachyons, September 26, 2011). This result was found to be erroneous, the consequence of a loose optical cable.

Large instruments such as the Large Hadron Collider at CERN are not required to do meaningful speed of light measurements, as an international team of physicists from the University of California, Berkeley, and the University of New South Wales, Sydney, Australia have shown.[2-5] The results of their laboratory experiment showed that the maximum speed of electrons traversing from one atomic orbital to another, which should be the speed of light, is the same in all directions to within 17 nanometers per second.[4] This is consistent with a general relativity principle called Lorentz invariance.[5] Their experiment is published in Physical Review Letters.[4]

Left to right, Dmitry Budker, Nathan Leefer and Michael HohenseeThe Budker Group of the Berkeley Physics Department.

Left to right, Dmitry Budker, Nathan Leefer and Michael Hohensee. They are posing with their experimental apparatus.

(UCLA Berkeley photo by Andreas Gerhardus.)

The experiment studied the energy required to change the velocity of electrons in transitions from one atomic orbital to another in dysprosium. Dysprosium has a pair of orbitals very close in energy for which the electrons travel at different speeds, so small changes in the electron kinetic energy can be detected.[5] The electron orbitals of the atoms were partially aligned by the polarization of the exciting laser beams, so the rotation of the Earth was equivalent to sampling the electron velocity in different directions of space.[5] The measurements were an order of magnitude more sensitive than previous studies.[4-5]

The dysprosium atoms functioned as atomic clocks having a relative frequency difference. It was found that in a two year period in which the Earth's distance to the Sun changed, the relative frequency of the clocks was constant. This finding was consistent with the local position invariance of general relativity that the kinetic energy of an object is independent of its location in a gravitational field.[4-5]

Berkeley physics postdoc, Michael Hohensee, summarized his motivation for such experiments by saying,
"As a physicist, I want to know how the world works, and right now our best models of how the world works – the Standard Model of particle physics and Einstein's theory of general relativity – don't fit together at high energies... By finding points of breakage in the models, we can start to improve these theories."[4]

The speed of light isn't the only important constant in physics. I've written about the fine structure constant in a previous article (Fine Structure Constant, September 16, 2010). This constant, which is quite close to the reciprocal of 137 (~1/137.036), expresses the strength of the interaction of charged particles, so it's fundamental to electromagnetism. Its value is in agreement with theory to eleven decimal places.

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)
where α is the dimensionless fine structure constant. So, if α changes, is it because e, h or c changes? Any such changes would be notable.

The research team was able to adapt their experiment to perform the same measurements for the fine structure constant. Their results, accepted for publication in Physical Review Letters and available online at arXiv,[6] show that the fine structure constant does not vary with time or gravitational field.[5-6] Their result for the time change of α was (1/α)(∂α/∂t) = (-5.8±6.9)×10-17 yr-1, consistent with zero.[6]

The experimental results, although impressive, were not optimized. The present order of magnitude improvement over past measurements is expected to reach three orders of magnitude in the future.[2-3,5] If there's some secret hiding in c or α, it might be found in the next few years. This research was funded by the National Science Foundation, the Australian Research Council, and other agencies.[4]


  1. T. H. Geballe And J. K. Hulm, "Bernd Theodor Matthias (June 8, 1918-October 27, 1980)," Biographic Memoirs Volume 70 (1996), National Academies Press, ISBN 978-0-309-05541-3, 448 pages.
  2. M. A. Hohensee, N. Leefer, D. Budker, C. Harabati, V. A. Dzuba and V. V. Flambaum, "Limits on Violations of Lorentz Symmetry and the Einstein Equivalence Principle using Radio-Frequency Spectroscopy of Atomic Dysprosium," Phys. Rev. Lett., vol. 111, no. 5 (August 2, 2013), Document No. 050401 [5 pages].
  3. M. A. Hohensee, N. Leefer, D. Budker, C. Harabati, V. A. Dzuba and V. V. Flambaum, "Limits on violations of Lorentz symmetry and the Einstein equivalence principle using radio-frequency spectroscopy of atomic dysprosium," arXiv Preprint Server, March 17, 2013.
  4. Robert Sanders, "Quest to test Einstein's speed limit," University of California, Berkeley, Press Release, July 29, 2013.
  5. Marcus Woo, "Focus: Testing Relativity Using Earth's Motion," Physics, vol. 6, no. 84 (July 29, 2013), DOI: 10.1103/Physics.6.84.
  6. N. Leefer, C. T. M. Weber, A. Cingöz, J. R. Torgerson and D. Budker, "New limits on variation of the fine-structure constant using atomic dysprosium," arXiv Preprint Server, April 25, 2013.

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