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Testing Relativity

February 15, 2016

Unlike sound, light travels fast enough for humans to think that its speed is infinite. Nearly every child knows the trick of counting the seconds between a lightning flash and its associated thunder to estimate the distance to the strike. Since the speed of sound in air is about 335 meters per second (1100 feet per second), and a mile is 5280 feet, then a five second duration is just slightly more than a mile.

From antiquity to the time when the speed of light was first observed in the late 17th century by Ole Rømer, philosophers argued whether the speed of light was infinite, or just too large to sense. Aristotle, who loomed large in early philosophic circles, was of the opinion that the sensation of light was immediate, not because its speed is infinite, but because it's always present, so it doesn't move at all.

Portion of Aristotle's 'De Anima' in which he claims that light is a presence that has no movement.

Portion of Aristotle's "De Anima" in which he claims that light is a presence that has no movement. (Greek text from "The Little Sailing," by Agelos Perdikouris.)[1])


One popular, but strangely anthropocentric, theory of light is that it's emitted from the eye to enable sight. Empedocles, Euclid, Ptolemy, and Heron of Alexandria espoused this theory. Heron reasoned that the speed of light must be infinite, since the distant stars are seen immediately after opening your eyes. Roger Bacon (c. 1214 - c. 1292), not to be confused with Francis Bacon (1561 - 1626), sided with the Aristotelian and Ptolemaic philosophical arguments for a non-finite speed of light in Part V of his Opus Maius.

Closer to our time, Francis Bacon argued from the geocentric model of the universe that the speed of light must be infinite, since the speed of the distant stars revolving around the Earth on the sphere of the fixed stars, must be very great. As he wrote in Aphorism XLVI in Book II of the Novum Organum,
"Again the immense velocity in the body itself as discerned in its daily motion (which has so astonished certain grave men that they preferred believing that the earth moved) renders this motion of ejaculation of rays therefrom (although wonderful, as I have said, in speed) more easy of belief.[4-5]

Galileo Galilei (1564–1642), a contemporary of Francis Bacon, wrote in his Two New Sciences (1638) the opinion that the speed of light was finite; but, as the first experimental physicist, he proposed an experiment. This experiment, which was performed in 1667 by members of the Accademia del Cimento of Florence, showed that the speed was too great to discern.

Galileo's experiment was a variation of one performed by Dutch scientist, Isaac Beeckman (1588 - 1637). Beeckman placed a mirror a mile's distance so that the flash of light from an explosion could be observed immediately and after two miles further travel. No difference could be seen, which is not surprising, since the travel time of light would have been about ten microseconds.[3]

Johannes Kepler (1571 - 1630) was a believer in an infinite speed of light for the simple reason that empty space would present no obstacle to its motion. René Descartes (1596 - 1650) made the analogy between the transmission of light and pushing on a stick. He reasoned that a light source "pushing" at one end of the stick would cause an instantaneous "motion" at the other end.[3] This analogy is false, since it reduces to a tautology. Mechanical movement will traverse a body at its speed of sound, which, in Descartes' case, would be the speed of light.

Finally, the Danish astronomer, Ole Rømer (1644 - 1710), followed-up on the observations of the eclipses of the moons of Jupiter done by Cassini between 1666 and 1668. Cassini found that the times between eclipses were shorter when Earth and Jupiter were close, and longer when Earth was more distant. Cassini actually attributed the cause to a finite speed of light, and he even estimated how long it takes for light to travel from the Sun to the Earth. His estimate was about 25% too long.

Portrait of the Danish astonomer, Ole Roemer, by Jacob Coning (c. 1647-1724).

A c. 1700 portrait of the Danish astronomer, Ole Rømer (1644 - 1710), by Jacob Coning (c. 1647-1724).

Rømer, was a professor of astronomy at the University of Copenhagen, and also the royal mathematician. As part of his duties, he introduced the first system of weights and measures for Denmark in 1683.

(Frederiksborg Museum image, via Wikimedia Commons.)


Rømer, along with his assistant, Jean Picard, observed eclipses of Jupiter's moons between 1671 and 1677. Although Rømer presented his results to the French Academy of Sciences, the best available summary of his observations is given in Newton's Opticks. Newton reported Rømer's value for the speed of light in terms of the transit time of light from the Sun to the Earth. He gave this as 7-8 minutes. The actual value is 8 minutes 19 seconds over the average distance (one astronomical unit).

First part of Prop. XL of Newton's Opticks

The portion of Prop. XI of Newton's Opticks that mentions Rømer's eclipse observations and the imputed travel time of light through the diameter of Earth's orbit. (Via archive.org.)[6])


A team of astrophysicists from the Chinese Academy of Sciences (Nanjing, China), the Beijing Normal University (Beijing, China), the Nanjing University-Purple Mountain Observatory (Nanjing, China) and Pennsylvania State University have just used the speed of light as a sensitive test of the equivalence principle of general relativity. This principle states that any two photons of different frequencies, emitted simultaneously from the same source and traveling through the same gravitational fields, will arrive at exactly the same time when they reach the Earth.

The simultaneous photons the research team analyzed were from the pulsed radio sources known as Fast Radio Bursts. These infrequent radio pulses are generated at great cosmological distances, another factor that enhances the precision of this relativity test. I wrote about Fast Radio Bursts in a recent article (Cosmic Radio Burst, March 5, 2015).

Fast Radio Bursts are extremely energetic radio emissions compacted into a pulse lasting just a few milliseconds. These occur infrequently, and about ten of these have been detected since their first discovery about fifteen years ago. They appear to occur far beyond our Milky Way Galaxy.

Geometry of the equivalence principle measurement

Geometry of the equivalence principle measurement. Two photons, at frequencies νh and νl travel through the gravitational well at the center of our Milky Way Galaxy before reaching Earth.

(Purple Mountain Observatory, Chinese Academy of Sciences, image, via Penn State University.)


Senior author of the study and professor of astrophysics at Penn State, Peter Mészáros, says that the team's data "supersedes by one to two orders of magnitude the previous best limits on the accuracy of the Einstein Equivalence Principle." The previous measurement was based on radiation from supernova 1987A. Says Mészáros,
"Our analysis using radio frequencies shows that the Einstein Equivalence Principle is obeyed to one part in a hundred million... This result is a significant tribute to Einstein's theory, on the hundredth anniversary of its first formulation."[7-8]
By measuring the delay between photons received at 1.23  GHz and 1.45  GHz, the research team was able to calculate a parameter, called gamma (γ), that appears in the Parameterized post-Newtonian formalism that expresses Einstein's equations. The difference in gamma value at these frequencies was less than, or equal to, 4.36x10-9.[7] This research was supported by NASA and several Chinese organizations.[8]

References:

  1. Aristotle, "De Anima (On the soul)," in The Complete Works of Aristotle: The Revised Oxford Translation, J. Barnes, ed., J.A. Smith, trans., Princeton Univ. Press (1984), vol. 1, pp. 641-692.
  2. Αριστοτελους, "Περι Ψυχης," Greek text via mikrosapoplous.gr.
  3. R. J. MacKay and R. W. Oldford, "Scientific Method, Statistical Method and the Speed of Light," Statistical Science, vol. 15, no. 3 (2000), pp. 254-278.
  4. Novum Organum by Francis Bacon, Spedding, Ellis, and Heath, eds.. James Spedding et al., trans., Book II, Instauratio Magna, 1858.
  5. Latin text via the Latin Library, "Etiam immensa illa velocitas in ipso corpore, quae cernitur in motu diurno (quae etiam viros graves ita obstupefecit ut mallent credere motum terrae), facit motum illum ejaculationis radiorum ab ipsis (licet celeritate, ut diximus, mirabilem) magis credibilem."
  6. Isaac Newton, "Opticks: or, A Treatise of the Reflexions, Refractions, Inflexions and Colours of Light; Also Two Treatises of the Species and Magnitude of Curvilinear Figures," (Samuel Smith and Benjamin Walford: London 1704), first edition, Prop. XI, p. 77, via archive.org.
  7. Jun-Jie Wei, He Gao, Xue-Feng Wu, and Peter Mészáros, "Testing Einstein's Equivalence Principle With Fast Radio Bursts," Phys. Rev. Lett., vol. 115, no. 26 (December 31, 2015), Document no. 261101, DOI: 10.1103/PhysRevLett.115.261101.
  8. Barbara Kennedy, "Mysterious radio signals from space are much better test of Einstein's General Relativity," Penn State University Press Release, December 30, 2015.

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