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Most people associate the word "bra" is an abbreviation of "brassiere".

But in science "bra" is a type of vector which is part of bra-ket notation. I think it sounds a little awkward. What's up with that?

Which one came first?

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    They are different domains. While there may be openings for juvenile humor, no one will actually be confused as to the proper meaning within each domain.
    – Robusto
    Jan 22 at 19:22
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    It appears that both usages appeared in the 1930s. One has to learn to be grown-up about these at first jarring resemblances. Although Rolls-Royce renamed their 'Silver Mist' as 'Mist' means something else in German. Jan 22 at 19:24
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    Actually Bra is a town in the wine area of Piedmonte in Italy. I rather think that came first.
    – David
    Jan 22 at 21:17
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    When I learned Swedish for a year at university, I found it strange that bra is the word for good. It only gradually dawned on me that it corresponds to the Scots word braw. Jan 23 at 8:53
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    Just wait until you have to write a paper with LaTeX and want to know how to format these vectors. Typing "latex bra" into google isn't exactly helpful.
    – pipe
    Jan 23 at 20:41

3 Answers 3

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The bra from physics came from Dirac breaking the word bracket into bra + ket. He introduced these terms in 1939. See Wiktionary.

The clothing bra came from an abbreviation of the word brassiere, which the OED says first appeared in 1936. The other answer and the comments actually have instances of bra that appeared earlier, but these must have been quite rare if the OED couldn't find them.

So the fact that these words are identical may be a complete coincidence. Given the timing, it's also possible that it is a piece of juvenile humor on Dirac's part, but I suspect the clothing bra was generally still called a brassiere in 1939, and that Dirac didn't realize that there would be an unfortunate overlap of terminology.

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    From Life magazine June 7, 1937. I'm not quite sure what to make of it. Jan 23 at 8:10
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    Based on what's known of Dirac, that sort of pun seems entirely out of character for him, and coincidence much more likely. Jan 23 at 13:47
  • I have been told that Dirac was unaware of the other meaning, and considered it at best a mildly-humorous coincidence.
    – KRyan
    Jan 23 at 19:01
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    Related to G-string theory. Jan 23 at 19:09
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    "these must have been quite rare if the OED couldn't find them": or they didn't look very hard. Life magazine isn't exactly very obscure. Regardless, the word may have been rare in print without being rare in spoken language, especially denoting as it does one of a class of garments sometimes called "unmentionables."
    – phoog
    Jan 24 at 13:45
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This answer is meant to supplement the others already given by providing more details on the sources and dates.

The answer to the original question, as others have already said, is that the bra as an abbreviation of brassiere came before Dirac's bra.

Dirac's bra

Dirac's bra comes from breaking up1 the word bracket into bra and ket (this is obvious but is also confirmed by the OED); see e.g. here for details.

1And dropping the middle letter c

Dirac's bra came not much before 1939. In the preface to the third edition of his Principles of Quantum Mechanics, he says (boldfaced emphasis mine),

The book has again been mostly rewritten to bring in various improvements. The chief of these is the use of the notation of bra and ket vectors, which I have developed since 1939.

Note that the second edition was published in 1935 (see here).

(The third edition can be downloaded e.g. here.)

The paper in which the bra-ket notation was introduced is A new notation for quantum mechanics, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 35 , Issue 3 , July 1939 , pp. 416—418 (link).

Bra as short for brassiere

On the other hand, as user66974 pointed out in the comments, etymonline says that bra as a shortening of brassiere appears 'by 1923'. The earliest appearance of it I was able to find on google books is in Life magazine from August 1932, p. 26:

So, with a nest of pillows, began to bolster myself up against the walls of my boudoir clad in a bra and silk shorts secretly purchased for Ned Wayburn, but deciding later against enlisting in his tap dancing class.

(It can be downloaded here.)

Discussion

If we can trust etymonline that bra as short for brassiere already existed by 1923, then the argument for the priority of this sense becomes essentially incontrovertible: 1923 was the year when Dirac only obtained his undergraduate degree from the University of Bristol. He then began graduate study at Cambridge University and only then started seriously thinking about quantum mechanics (in addition to thinking about general relativity). His Ph.D. dissertation was on quantum mechanics, and he completed it in 1926.

Another point to remember is that the Schrödinger equation didn't exist until 1925—1926; after that, one had to show that Heisenberg's and Schrödinger's formulations of quantum theory are equivalent and, more generally, one had to clarify the mathematical structure of quantum theory. This was a task to which many people contributed, but arguably the principal contributors were Dirac himself and, when it comes to full mathematical rigor, von Neuman. (For further discussion, see Casado's A brief history of the mathematical equivalence between the two quantum mechanics.) Dirac's bra-ket notation would not make sense until the mathematical dust had somewhat settled, and that certainly could not predate the introduction of the Schrödinger equation.

Conclusion

So, bra as a short for brassière certainly existed by 1932 (and most likely even by 1923), while Dirac didn't develop his notation until not much before 1939 (and certainly after 1926).

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    And the winner for the 2022 "Most Discussion of Mathematics and Quantum Theory in an English Language & Usage Answer" goes to...
    – FreeMan
    Jan 24 at 16:40
  • With a side dish of Outstanding Lifetime Achievement Award, too!
    – FreeMan
    Jan 24 at 16:40
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It appears that Dirac was in the know:

Dirac, who invented this notation, called the symbol |..> a ket. The symbol <...| is a bra. It was said by my lecturers at Cambridge that when Dirac taught the subject, much of which was his own development, the only time he displayed any personal pride was when he told his little joke: a bra and a ket will be put together to form a braket, <...|...> Charles Francis; Light after Dark II p.109 (2016)

One of Dirac's former students wrote about the lecture based on the book: 'Dirac was scrupulous in not underlining his own formidable contributions to quantum theory. However, one did gain the impression from a slight smile that played around his feature when he introduced bras and kets that this invention (and the harmless joke enshrined in the nomenclature) had given him great satisfaction.' Sigmund Brandt; The Harvest of a Century (2009)


It seems logical that bra as a shortening of brassiere, like mayo for mayonnaise, was in conversational use before it began to appear in print (1940 for mayo), as reflected by these two early examples, one in dialog, the other in an advertisement.

They had unpacked their clothes, and Pauline was burrowing through a pile of lingerie looking for a brassiere . Downstairs everyone was dancing. "If I can't find that darn bra' I'll go without it," threatened Pauline. Eleanor Early; Detour to Happiness (1935)

Completely light and flexible, the two-way stretch all-elastic girdle with a bra attached, shaped like a pinwheel. Harper's Bazaar, vol. 68, part 1 p.124 (1934)

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    This is a very interesting (and entertaining) answer. But, assuming only the information contained in this answer, a devil's advocate could claim that the following timeline is not excluded: 1. Dirac develops his notation (but only publishes it several years later); 2. bra becomes accepted as a short for brassiere; 3. Dirac learns of this development, and, only from then on, starts to snicker anytime he lectures about his bra-ket notation. Jan 23 at 0:16
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    @linguisticturn That's possible--it occurred to me also. We have only these second-hand accounts so far. However, I would present before the jury an illustration showing a bra on the left and a blow up (size DD) of a braket on the right so they could draw their own conclusions.
    – DjinTonic
    Jan 23 at 0:29
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    Note that the "joke" doesn't actually invoke the brassiere at all: It is simply an explanation of the rather obvious pun. Jan 23 at 13:49
  • @chrylis-cautiouslyoptimistic It does convey "aware of the humor."
    – DjinTonic
    Jan 23 at 14:59
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    The humor of "bra-ket is bracket, get it?", not necessarily "brassiere". Jan 25 at 3:24

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