### Speed of Light

April 3, 2023

The speed of light in vacuum, symbolized by c, has an exact value of 299,792,458 meters/second. The reason for the exactness of this value is that in 1983 it became a fixed quantity used to define the meter, rather than the other way around. The meter was previous defined in reference to a physical object kept at the International Bureau of Weights and Measures near Paris. To obtain the meter from the speed of light, you also need a definition for a second. This is defined as the duration of 9,192,631,770 periods of the radiation from a certain electron transition in cesium-133.

Why is the speed of light in a vacuum symbolized as c? The acclaimed science and science fiction author, Isaac Asimov (1920-1992), stated the false idea that this relates to the initial letter of the Latin word, "celeritas," meaning speed. In actuality, it's derived from the use of the letter to symbolize a constant. This can be traced back to 1856 in a paper by German physicists, Wilhelm Weber (1804-1891) and Rudolf Kohlrausch (1809-1858) in which c is used as a constant in a force equation. Before that time, the use of the character v was common, and this convention was used by James Clerk Maxwell (1831-1879) in his 1865 paper, A Dynamical Theory of the Electromagnetic Field,[1] and by Albert Einstein (1879-1955) in his first papers on relativity.

Most physicists use 300,000,000 meters/sec for the speed of light in casual calculation, since it's easy to remember, and it's just 0.07% larger than the actual value. The speed of light is so large that it appears to be infinite. Aristotle (384-322 BC) thought light traveled at infinite speeds. An earlier Greek philosopher, Empedocles (c.494-c.434 BC), originated the emission theory of sight in which light is emitted by the eyes and was reflected back to the observer to enable sight.

While Empedocles believed that the speed of light was finite, Hero of Alexandria (fl. 60 AD) reasoned by the emission theory that the speed of light must be infinite, since we instantly see distant objects, such as stars, when we open our eyes. The emission theory was embraced by Euclid (fl. 300 BC) and Ptolemy (c.100-c.170 AD). As to the actual nature of light, Democritus (c.460-c.370 BC) was quite near to the truth when he wrote that light consisted of small invisible particles moving at a finite speed. Contrary to the emission theory, these photons are emitted from the source. Aristotle thought that light was not a substance, but rather a state of transparency.

Hero of Alexandria, from the Codex of Saint Gregory Nazianzenos, a Greek manuscript of the 9th century.

Hero is known for many things, including Hero's formula giving the area of a triangle from its sides.

As I wrote in an earlier article (Steam Power, January 28, 2011), Hero (more properly, Heron) demonstrated a steam engine, called an Aeolipile, in the 1st century AD.

(Wikimedia Commons image.)

The first experiment designed to measure the speed of light was performed by Galileo in 1638. The experiment was done using signal lanterns separated by a large distance, and 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, which is too short an interval for humans to notice.

A half century after Galileo's experiment, Christiaan Huygens (1629-1695) published his 1690 Traité de la Lumière (Treatise on Light). In this book, Huygens presented a wave theory of light. According to Huygens, light is a stream of spherical waves emitted from a luminous source. The vibrations are along the direction of light travel. These waves propagate in the now infamous luminiferous ether that permeates the universe.

Huygen's contemporary, Isaac Newton (1642-1727), had a different theory of light. Newton believed that light was composed of particles that he named corpuscles; and, as particles, they were influenced by inertia and gravity. One proof of this theory was that light reflects off plane surfaces just as a ball would. Our present idea of light is that it sometimes behaves as a wave, and it sometimes behaves as a particle.

Left, Christiaan Huygens (1629-1695). Right, Isaac Newton (1642-1727). (Left image, a Wikimedia Commons image from the 1920 book, "Practical Physics," by Millikan and Gale. Right image via Wikimedia Commons

The Danish astronomer, Ole Rømer, was the first to give an actual value for the speed of light. In 1676, Rømer used the period of Jupiter's moon, Io, as a clock to find a value of 220,000,000 meters/sec, which is about 75% of the established value. His measurement was based on the idea that light needed to travel farther when Earth was on the opposite side of the Sun from Jupiter, but the orbits of Earth and Jupiter were not that well known in his time, leading to his rather large error. 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.

While the speed of light appears to be constant, might its value have been different in the early universe? The fine structure constant, a dimensionless number calculated from the speed of light and other fundamental constants, is important to the stability of atoms. Observation has shown that its rate of change, if it does change at all, is extremely small, of the order of (-1.6±2.3)x10-17 parts per year.[2] Another astronomical measurement of 120 ultra-compact radio sources gave an estimate of the speed of light when the universe was just 3.80 billion years old. That estimate, 2.995(±0.235)x105 km/s, is consistent with our accepted value of 299,792,458 meters/second.[3]

A recent paper in arXiv by scientists at the Laboratoire National des Champs Magnétiques Intenses (Toulouse, France) examines the history of experiments on the possible affect of magnetic fields on the speed of light.[4] As they write early in their paper, its title, "On the speed of light in a vacuum in the presence of a magnetic field," would have been considered as nonsense just a few centuries ago... "Not only because we talk about light velocity but also because we assume the existence of a vacuum, a thing that has been considered impossible for centuries following the Aristotle teaching."[4]

That light is affected at all by a magnetic field was established by Michael Faraday (1791-1867) in 1845 when he observed what is now called the Faraday effect in which the linear polarization of light rotates in the presence of a magnetic field along its propagation direction in certain materials. This effect is present in many aluminum garnets, a fact that enabled one of my early inventions.[5] Since intense electric fields were more easily obtained in the 19th century, the initial efforts were on determining whether the speed of light is influenced by an electric field. As H. Wild wrote (in German) in 1865,
"Since November 1860, I performed some experiences to test experimentally the consequences of this hypothesis. Since all of them has given a negative result, and that for some of them I have employed somewhat inadequate apparatus, I had avoided to publish them. Since then, discussion with some physicists, friends of mine, have shown me that others have also tested experimentally this hypothesis with as few success as me. I have thought then that it was worth while to report to the public my investigations on this point, that I have been somewhat finishing this autumn, even if it has done nothing more than confirming my previous negative results."[6]

Sir Oliver Lodge (1851-1940) with historical plaque marking his birthplace. Lodge, who became a Doctor of Science in 1877, was awarded the Rumford Medal of the Royal Society in 1898, and he was knighted in 1902. He was a staunch advocate of Maxwell's theory of the luminiferous aether, defending it into the 20th century. He is known for his radio research, and he was able to sell one of his patents to the Marconi Company in 1912. (Left, a Wikimedia Commons portrait of Lodge from the Wellcome Collection, image reference 13104i. Right, a Wikimedia Commons image by Rept0n1x. Click for larger image.)

Radio pioneer, Oliver Lodge (1851-1940) examined the affect of electric and magnetic fields on light in 1897. As he wrote, "without further delay I conclude that neither an electric nor a magnetic transverse field confers viscosity upon the ether, nor enables moving matter to grip and move it rotationally."[7] In most of Lodge's life, light propagation was assumed to be through the ether, and thus his wording. However, the famous Michelson and Morley experiment disproving the ether was published ten years earlier, in 1887; thereby, proving again, that old habits die hard.

Albert Einstein (1879-1955) is quoted in the arXiv paper as saying, "I think that die liebe Gott could not have created the world in such a fashion that a magnetic field would be unable to influence the velocity of light.[4] As we now know, the vacuum state is not really devoid of substance. It's a quantum foam in which virtual particles enter into a brief existence, then vanish. Quantum electrodynamics gives a prediction for the influence of a magnetic field on the speed of light. It changes about a few parts in 1024 in a one tesla applied field.[4] Laboratory magnets can produced about 10 teslas of magnetic field; so, the change would be 10-23, not within the realm of experimental proof.

### References:

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