Why is c the symbol for the speed of light?
[Physics FAQ] -<br>[Copyright]
By Philip Gibbs, 1997, 2004.
Why is c the symbol for the speed of light?
"As for c, that is the speed of light in vacuum, and if you ask why c,<br>the answer is that it is the initial letter of celeritas, the Latin word meaning<br>speed." Isaac Asimov in "C for Celeritas (1959)" [1]
A Short Answer
Although c is now the universal symbol for the speed of light, the most common<br>symbol in the nineteenth century was an upper-case V which Maxwell had started<br>using in 1865. That was the notation adopted by Einstein for his first few papers on<br>relativity from 1905. The origins of the letter c being used for the speed of<br>light can be traced back to a paper of 1856 by Weber and Kohlrausch [2]. They<br>defined and measured a quantity denoted by c that they used in an electrodynamics<br>force law equation. It became known as Weber's constant and was later shown to have<br>a theoretical value equal to the speed of light times the square root of two. In<br>1894 Paul Drude modified the usage of Weber's constant so that the letter c became<br>the symbol for the speed of electrodynamic waves [3]. In optics Drude continued to<br>follow Maxwell in using an upper-case V for the speed of light. Progressively<br>the c notation was used for the speed of light in all contexts as it was picked up<br>by Max Planck, Hendrik Lorentz and other influential physicists. By 1907 when<br>Einstein switched from V to c in his papers, it had become the standard<br>symbol for the speed of light in vacuum for electrodynamics, optics, thermodynamics and<br>relativity.
Weber apparently meant c to stand for "constant" in his force law, but there is<br>evidence that physicists such as Lorentz and Einstein were accustomed to a common<br>convention that c could be used as a variable for velocity. This usage can be<br>traced back to the classic Latin texts in which c stood for "celeritas" meaning<br>"speed". The uncommon English word "celerity" is still used when referring to the<br>speed of wave propagation in fluids. The same Latin root is found in more familiar<br>words such as acceleration and even celebrity, a word used when fame comes quickly.
Although the c symbol was adapted from Weber's constant, it was probably thought<br>appropriate for it to represent the velocity of light later on because of this Latin<br>interpretation. So history provides an ambiguous answer to the question "Why is<br>c the symbol for the speed of light?", and it is reasonable to think of c as<br>standing for either "constant" or "celeritas".
The Long Answer
In 1992 Scott Chase wrote on sci.physics that "anyone who read hundreds of books by<br>Isaac Asimov knows that the Latin word for `speed' is `celeritas', hence the symbol `c'<br>for the speed of light". Asimov had written an article entitled "C for Celeritas" in<br>a sci-fi magazine in 1959 and had reprinted it in some of his later books [1]. Scott<br>was the first editor of the Physics FAQ on Usenet and Asimov's explanation was later<br>included in the relativity section as the "probable" answer to the question "Why is<br>c the symbol for the speed of light?". Since then, Asimov's answer has become<br>a factoid repeated in many articles and books. But if you go back and read his essay<br>you discover that Asimov merely stated his case in one sentence, and made no further<br>attempt to justify his theory for the origin of the "c" notation. So is his claim<br>really born out by history, or was c originally introduced as a variable standing<br>for something else? The special theory of relativity is based on the principle that<br>the speed of light is constant; so did c stand for "constant", or did it simply<br>appear by accident in some text where all the other likely variables for speed had already<br>been used up? These questions have been asked repeatedly on usenet, and now after<br>much searching through old papers and books the answers can be revealed.
A lower-case c has been consistently used to denote the speed of light in<br>textbooks on relativity almost without exception since such books started to be<br>written. For example, the notation was used in the earliest books on relativity by<br>Lorentz (1909) [4], Carmichael (1913) [5], Silberstein (1914) [6], Cunningham (1915) [7],<br>and Tolman (1917) [8]. That was not the case just a few years before. In his<br>earliest papers on relativity from 1905 to 1907, Einstein began by using an upper-case<br>V for the speed of light [9]. At that time he was also writing papers about<br>the thermodynamics of radiation, and in those he used up upper-case L [10].<br>All of these papers appeared in volumes of the German periodical Annalen Der<br>Physik. Einstein's notation changed suddenly in 1907 in a paper for the Journal<br>Jahrbuch der Radioaktivit�t und Elektronik [11]. There he used the lower<br>case c, and his most famous equation E = mc2<br>came into being.
It is not difficult to find where the upper case V had come from. Maxwell<br>used it extensively in his publications on electrodynamics from as early as 1865<br>[12]. It was the...