# Dimension of the candela unit: What does J stand for?

The J symbol can represent the unit of energy but it's also the symbol for the dimension of the candela (or luminous intensity).

For the energy unit, it clearly comes from the family name of the English physicist James Prescott Joule (1818–1889), but for the luminous intensity dimension, what's the origin? What does it stand for?

I'm also asking because the energy unit has the dimension $$\mathsf{L}^2\cdot\mathsf{M}\cdot\mathsf{T}^{-2}$$ which doesn't contain the dimension of the luminous intensity.

• This is a history-of-physics question. – G. Smith Aug 3 '19 at 17:59
• @G.Smith Should I re-ask it on physics.meta ? Or can I move it there somehow ? – maxagaz Aug 3 '19 at 18:30
• I don't think it's standard notation. Did you read the note there: «The symbols in this column denote dimensions; "L", "T" and "J" are for length, time and luminous intensity respectively, not the symbols for the units litre, tesla and joule.»? – Geremia Aug 3 '19 at 18:38
• @Geremia It is standard notation as you can read here. – maxagaz Aug 3 '19 at 19:01
• The dimension symbol for current is $\textsf I$, presumably because $I$ is also the usual variable used for current in equations. (I have no idea why.) According to the Wikipedia article on luminous intensity, the variable $I_v$ is used to indicate luminous intensity in equations. (“I” for intensity, presumably.) So I speculate that the corresponding dimension symbol is $\textsf J$ because $\textsf I$ was already “taken” as the dimension symbol for current. They just picked the next letter in the alphabet. – G. Smith Aug 3 '19 at 21:06

The symbol for candela is cd according to the NIST's website.

I gather you are mixing the concept of dimensions symbols (M, L, T) with dimensional analysis and energy units. The symbol for the mass dimension is M, it can be in any kg, mg, g etc, Length is L which can be millimeters, yards, kilometers etc. The dimension symbol for temperature is $$\Theta$$. So what should be the dimensional symbol for candela? It is J. Does it have to anything with Joule? No. It is by chance that the symbol matches with Joules. The problem is that English has only 26 letters. Have you heard of the pigeonhole principle?

In mathematics, the pigeonhole principle states that if $$n$$ items are put into $$m$$ containers, with $$n>m$$, then at least one container must contain more than one item. This theorem is exemplified in real life by truisms like "in any group of three gloves there must be at least two left gloves or at least two right gloves"

The same applies on symbols and quantities. From the official website of SI Units, this is the list of symbols to be used for these dimensions: https://www.bipm.org/en/publications/si-brochure/

• Thank you for this answer. I'm not mixing the concepts (or at least, I don't think so ;-)), I was actually more wondering why most symbols for dimension are pretty obvious while only this one is not clear and explained nowhere. I guess the correct answer is actually the one given by @G.Smith : "𝖨 was already “taken” as the dimension symbol for current. They just picked the next letter in the alphabet." – DevonDahon Aug 4 '19 at 15:50
• Dear maxagaz, In science and history, one cannot rely on casual coincidences, e.g. I is the symbol for current, J was chosen as the next symbol for candela. No need to rationalize such choices until and unless it is explicitly written by the SI committee. This makes an assumption someone was sitting and thinking about the symbols sequentially and he/she must have chosen I for current first and then thought what should we choose for candela? For instance, J or sometimes j is used for current density. How can we rationalize this choice? – M. Farooq Aug 4 '19 at 16:11
• I think G. Smith's suggestion should be taken with caution. I and J are closely linked (they were one letter for many centuries), so that may have been the reason rather than the proximity in dictionaries. "I was already taken" is solid, but the reason for choosing J is speculation until someone finds evidence. – Peter Taylor Aug 6 '19 at 7:48

Candela contains the power emitted and the power is energy per sec or Joules/sec. So the J in candela is still Joules.