Monday, February 08, 2010

Why, oh why, is the Psi called Psi?

I'm currently reading Sean Carroll's book "From Eternity to Here" and stumbled over this remark
In Newtonian mechanics, the space of states is called "phase space" for reasons that are pretty mysterious.

A mystery that hadn't occurred to me before, probably because the German word "Zustandsraum" means literally "state space," so no mystery there. Stefan and I were guessing Gibbs, who introduced the word, might have generalized the terminology from the harmonic oscillator where the location in phase space does indeed tell you the phase of the oscillation. (You find a nice applet depicting the phase-space diagram of the damped and undamped oscillator here).

In any case, this caused me to ponder what other words with funny origin physicists like to use. (Both funny ha-ha, and funny peculiar.) Why, for example, is the recombination in the early universe called recombination if there was no prior combination? Not that I was the first to ask that question. Sean offered the explanation that the word is borrowed from nuclear physics. But then why don't nuclear physicists call the fragmentation refragmentation?

There are more interesting nomenclatures though than presence or absence of prefixes.

A particularly well known oddity is the name "quarks" introduced by Gell-Mann, who couldn't decide how to spell the sound ducks make:
In 1963, when I assigned the name "quark" to the fundamental constituents of the nucleon, I had the sound first, without the spelling, which could have been "kwork". Then, in one of my occasional perusals of Finnegans Wake, by James Joyce, I came across the word "quark" in the phrase "Three quarks for Muster Mark". Since "quark" (meaning, for one thing, the cry of the gull) was clearly intended to rhyme with "Mark", as well as "bark" and other such words, I had to find an excuse to pronounce it as "kwork".
~M. Gell-Mann, The Quark and the Jaguar, via Wikipedia

Had Gell-Mann read a German dictionary instead of Joyce, he'd have noticed "Quark" is the German word for a milk product (often mistakenly translated as "cottage cheese" which is something entirely different). Besides this, "Quark" is a frequently used colloquial expression for nonsense.

But at least we know how that word came along. A mystery remained to me why the English adaption of the German word "Eigenvektor" came out to be "eigenvector." The German word "eigen" simply means "innate," and could easily have been translated.

A better example fo imaginative nomenclature is the Psi-particle (now known as J/Psi) whose cloud-chamber pictures frequently have the shape of a Psi (see picture above).

Then there is the "Penguin diagram", which owes its name to a lost bet and some illegal substances, and the "tadpole diagram" which once run risk of turning into a "spermion." Probably a good thing the tadpoles kept their name - just imagine what issues the anti-abortionists would have had with spermion cancellation.

In General Relativity, we have the conjecture of "cosmic censorship" to prevent us from seeing "naked singularities," and "wormholes" are already a classic. Cosmologists have further blessed us with MACHOs and WIMPs, acronyms for MAssive Compact Halo Object and Weakly Interacting Massive Particles respectively. Loop Quantum Gravity features a LOST theorem, after the last names of its authors. The large gap between the energy scale of currently known physics and the scale where grand unification is thought to occur is also known as "desert." We have a seesaw mechanism, play with Mexican hat potentials, have ghosts and talk about stop particles. There's a swiss cheese universe and neutron stars have pasta-antipasta layers with a spaghetti-phase. The most stupid nomenclature I so far have come up with is a "pullover". Yes, I know, not terribly original, but then I didn't expect a Nobelprize for it ;-)

Did I miss something? Leave it in the comments!


  1. Nice post...
    The question why the psi (J/psi) is called such kind of remains, as the nice decay picture comes from psi' -> pi+pi- J/psi and subsequent J/psi decay to e+e-. The picture by the way is from a wire chamber, not a bubble chamber.
    The really interesting story however is the of the origin of the J - which is linked to a particular Chinese character (in more than one sense of the word character).

  2. J/Psi nomenclature had somewhat evolved and is known on our university as gipsy particle :-)

  3. Nik: Err, yes, that's of course true, the picture I showed is not from a bubble chamber. I just thought that's where the first images came from. Anyway, thanks for the correction. And yes, the wikipedia entry says something about the story with the Chinese character, but I'm afraid my Chinese is a little insufficient to tell how plausible this is. Best,


  4. Maadher: Right! How could I have forgotten about that? :-)

  5. Somewhat beautiful and at the same time somewhat strange nomenclature:

    The virial theorem and the principle of virtual work.

  6. Hi Bee,

    My favourite physics nonsense terms actually make more sense now that you say the word quark in German means milk product, as at least I can imagine them having flavour and colour:-) As for the quarks if had George Zweig had his way they would have been called Aces and perhaps then finding our universe the way that it is would be referred to as the “The Stacked Deck Hypothesis” ;-)



  7. Hi Phil,

    Yes, indeed, that's the kind of joke German students can't resist making either. I am actually wondering why nobody has yet tried to market colored quark. Anyway, this just reminds me of a picture I made some while ago, playing around with povray :-) Best,


  8. Hi Bee,

    Yes nice, yet shouldn’t you have used different cheeses rather than apples to represent both colour and flavour. Who knows maybe we are coming up with a good teaching aid here, well at least a German one :-)



  9. Just thought you'd be interested?

    The idea of the Chronology Protection Agencyappears to be drawn playfully from the Time Patrol or Time Police concept present in works of science fiction such as Isaac Asimov's novel The End of Eternity

    Ummm....something about ducks on a pond?:)


  10. The No-Ghost theorem. Who ya gonna call? We ain't afraid of no ghosts!

    I'm not up on String Theory to the degree I'd like to be in order to debate it, but No-Ghost was significant enough to get its proposer, Peter Goddard, chosen as Director of The Institute for Advanced Study in Princeton.

  11. Hi Bee,

    Psi always reminds me of Trident’s sceptre and as there is a famous statue of the Roman equivalent Poseidon jn Copenhagen this might also had in some way been a subliminal influence on the choice.



  12. Dear Bee,

    actually, about the origing of the notion "phase space", I have found an earlier usage by James Clerk Maxwell. He denoteds the pair of variables (q, p) a "phase" in his 1879 paper "On Boltzmann's theorem on the average distribution of energy in a system of material points", Transactions of the Cambridge Philosophical Society 12 547–570.

    The text is not online, but here is a quote from a draft of his of the paper (from the The Scientific Letters and Papers of James Clerk Maxwell, Volume 3):

    Any particular state of the system, specified by its configuration and velocity, may be called a phase, and the series of phases through which the system passes during its actual motion is called the path of the system.

    So, he seems to have "phases" of motion in mind when using the term, as in periodic motion.



  13. "Black holes have no hair" (perhaps implying Ipanema beach is an event horizon).

  14. But the question remains, where did Joyce get the word quark from? He did live in Zurich during WWI, a place and a time where dairies may well have sold Quark.

    One of the confusing things with Swedish is that momentum is called rörelsemängd (lit. Bewegungsgrösse), whereas moment means torque.

  15. Hi Bee,

    Is there any concern in the physics community about the role that choices of terminology and nomenclature play in promoting either correct understanding or misunderstanding in the public's understanding of physics concepts ?

    So, for example, the word "duality" is well associated for a long time with the wave or particle interpretation (Complementarity) and the sense of the word duality in this context is that it reflects the qualitative oppositeness of waves as (distributed) and particles as (concentrated) so in this sense duality is a word akin to 'polarity'.

    However, in recent years, the word "duality" or "dual to" is being used in literature and discourse to variously replace: correspondence, equivalence, interchageability and maps to, etc.

    These progressively being replaced terms have little to do with polarity or qualitative oppositeness.

    Linguistic expressions are very catchy and the internet 'reverb' effect is making it worse.

    Is there any discussion about this among your peers insofar as the effect that choices of terminology have on the public's correct understanding of physics concepts ?

    Will we soon hear people speaking of the duality of matter and energy ( E=Mc^2 ) for example ?

    Is Linguistic Entropy ( or nomEntropy ) not something to be wary of ? Was it (is it) not considered desirable that nomenclature reflect the physical situation as much as possible, when possible ? Do you have any thoughts about this ?


  16. I have always thought that the mystery of the "phase space" terminology was due to the fact that I was a biochemist. I thought physicists are well aware of the reason why it is called so; and lived a life being convinced it was so and not otherwise.

    Thanks to the Backreaction blog, I know now I was not the idiot of the story.

    Die groBe Offenbarung des Tages :)

  17. What about winos and sinos super-partners of the Supersymmetrical Standard Model (those of R-parity -1)? Typing "winos" as an entry in Google, I only get sites dealing with Windows Operating System.

    Were winos inspired by Microsoft?

    If so, then their monopoly has no limit at all.

  18. "Monogamy [of entanglement]"

    "Entanglement Swapping"

    "Ghost Imaging"

    "Quantum Carpets"

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  21. LastAncientGreek: In my impression, most physicists don't care very much about the public understanding of their terminology. And in any case, that's a thought that comes very often after the fact. Best,


  22. I also received this interesting comment by email reg the question where the "quark" came from. It seems to be a letter to the editor, but I can't find it online.

    ************* Appeared in Physics World ************************


    In the September 2002 issue of Physics World on page 9, Murray
    Gell-Mann mused upon what Joyce may have meant with "Three quarks for
    Muster Mark" in Finnegans Wake. After all, this is the place where
    Gell-Mann took the name quark from. I have no own interpretation, but
    in Dublin where I had stays since the early eighties repeatedly at the
    DIAS and at UCD, an Irish(?) colleague(?) told me the following story:
    In Dublin there was an exhibition of German agricultural products. One
    of the exhibits was a sample of `quark' labelled `Musterquark' or
    `Quarkmuster'. `Quark' is German and means something like the American
    cottage cheese. Sample in German is `Muster'. It is known that Joyce,
    so the story, had visited this exhibition since he signed in the
    guest book. And that is where quark and muster came from. I am told
    that Joyce had traveled in Germany and knew German well. End of the
    story. I cannot recall who told me that, but this story has verifiable

    Friedrich W. Hehl, University of Cologne, Germany

  23. Hi Bee,

    So it seems that your suspicions were right regarding quarks as Joyce expressed are German milk products. After looking into it further it appears quark is actually ‘curd’, which is what’s separated from ‘whey’ where the curd is later processed further to become cheese. Cheese curd is also made and sold without further processing in Canada mainly by small rural factories. With this being the case it appears that gluons should have been called ‘whey’ or rather ‘Molke’ , which would make more sense as at high energies and temperatures (early universe) we had what was discovered to be a soup of the two. So now nature has been revealed to be a Cheesemaker or more properly a Käser :-)



  24. Speaking of cheese, the German word "Käse" is another commonly used expression for something that's meaningless. Eg, if the plot of a movie (abstract of a paper?) doesn't make sense, you'd say it was "totaler Käse." If you keep reading my blog, you'll finally speak German fluently ;-) Best,


  25. Hi Bee,

    I don’t know about improving my German speaking, yet with this it gives me more of a reason to refer to nature from here forward as the ‘Big Cheese’ or should I say 'großen Käse';-)



  26. Hi Bee,

    Well I guess in German that has nature to be a father rather than a mother. I have no problem with this however as being a Bohmian I accept there must be a dual ontological explanation for reality :-) Sorry I jusr couldn’t resist.



  27. "die Natur" (female noun). Which proves that Nature is not a cheese ;-)

  28. Hi Bee,

    Maybe so, yet I’ve never been able to bring myself to be as Bohr convinced as nature being resultant of only of one thing, as that would have it required to be a hermaphrodite and then always believed it takes two to have anything of complexity come to be realized, even a universe. So why then not both a mother and father nature :-)



  29. The SQUID (Superconducting Quantum Interference Device), a circuit built from two Josephson junctions in parallel and used to measure small magnetic fields. What an awful name. Much better name for it: the London Bridge!

  30. Okay so basically your stuck on terminology?. What about Alice in Wonderland?

    I thought it would be nice to extend this to "team mascots?":)

    Oh and of course to support your "penguin story" about how the image came into being.

    The origin of penguins
    Told by John Ellis:

    “Mary K. [Gaillard], Dimitri [Nanopoulos], and I first got interested in what are now called penguin diagrams while we were studying CP violation in the Standard Model in 1976… The penguin name came in 1977, as follows.

    In the spring of 1977, Mike Chanowitz, Mary K. and I wrote a paper on GUTs [Grand Unified Theories] predicting the b quark mass before it was found. When it was found a few weeks later, Mary K., Dimitri, Serge Rudaz and I immediately started working on its phenomenology.

    That summer, there was a student at CERN, Melissa Franklin, who is now an experimentalist at Harvard. One evening, she, I, and Serge went to a pub, and she and I started a game of darts. We made a bet that if I lost I had to put the word penguin into my next paper. She actually left the darts game before the end, and was replaced by Serge, who beat me. Nevertheless, I felt obligated to carry out the conditions of the bet.

    For some time, it was not clear to me how to get the word into this b quark paper that we were writing at the time…. Later…I had a sudden flash that the famous diagrams look like penguins. So we put the name into our paper, and the rest, as they say, is history.”

    John Ellis in Mikhail Shifman’s “ITEP Lectures in Particle Physics and Field Theory”, hep-ph/9510397

    See also Babar and Heart songs


  31. Hello Bee,
    one of my teachers used to comment
    on lengthy essays:

    Getretener Quark
    wird breit, nicht stark!

    I tried to translate, but
    I did not succeed in anything
    which keeps the rhyme.
    PS on that "curd".
    What is used to make a cheese-cake
    in US, Canada or Britain?
    In Germany "Quark" (northern use)
    "weißer Käse" (southwest) and
    "Topfen" (Austria) is a basic
    dairy product used in a lot
    of dishes (e. g. "cheese cake")

  32. billk,

    Maybe the unfortunates to economic scams?

    I do not think Michael Persinger would have liked that.

    So Richard Dawkins didn't experience the god spot, does not mean research about the magnetic field induced application to brain experience would not be an ineffective way to produce "mass agreement":)Would it?

    See, Richard Dawkins did not experience God but he was willing to submit to the experiment:)Nothing about buying a bridge fits into this picture.


  33. Georg,

    In Canada we call it "Cottage Cheese," although "cheese cake" is good too.


  34. Hi Georg,

    Well, your teacher certainly had some sense of humor :-) The Americans use most often cream cheese and whipping cream for the the cake, which is why it a) tastes different and b) is quite heavy. Best,


  35. Sorry Bee, I overreached by dipping into semantics problems. You want cute words/origins, so here is one I hear sometimes at J-Lab: it is "chicane", a device sometimes put into accelerators to detour streams of particles. It is roughly analogous to the "chicane" of automotive use, and BTW Wikipedia needs to include the accelerator physics usage: "A chicane is an artificial feature creating extra turns in a roadway, used in motor racing and on city streets to slow cars."

    I wouldn't cast aspersions by calling use of the device "chicanery"*, but there is a semantic connection. A chicane is about "turns", and "chicanery" implies trickery through various ins and outs of sophistry and misdirection. Even though the word is from French chicaner (to trick) I doubt that's a coincidence.

    (* Not even for, heh, a certain overwrought gripe of mine - which is properly confined to my own blog unless topical elsewhere; see my self-removed comments about "interference" reposted here if anyone is still curious and to address properly.
    PS: "Promethazine VC" - it's been a tough week.)

  36. I have to point out that I have seen "characteristic values" and "characteristic vectors" in old mathematics text books in place of eigenvalues and eigenvectors, though it is rare. Luckily it does not seem to have caught on.

  37. Hi Neil,
    Hah. I didn't even know chicane is a word. I only know it as a band name. (Chicane - Saltwater). Best,


  38. A great compilation of terms and origins. Taken together, it's a fun read!

  39. Hi Stefan:

    Re: I have found an earlier usage by James Clerk Maxwell. He denoteds the pair of variables (q, p) a "phase" in his 1879 paper "On Boltzmann's theorem on the average distribution of energy in a system of material points", Transactions of the Cambridge Philosophical Society 12 547–570.

    Have you considered submitting this to the Oxford English Dictionary?

    The local library's copy of the OED had nothing about the origin of "phase space".


  40. Sorry, correct URL

    Contribute to the OED

    Throughout its history, the Oxford English Dictionary has been enriched by evidence contributed by readers. One hundred and twenty years ago, James Murray, original editor of the OED, launched an ‘Appeal to the English-Speaking and English-Reading Public of Great Britain, America and the British Colonies’ for words for the Dictionary. This appeal was relaunched in 1999 by the current editor, John Simpson, with the aim of gathering evidence of new words and meanings, as well as information that can help our understanding of the language, such as earlier evidence for words recorded in the OED, or later evidence for words thought to have died out.
    OED appeals and submissions

    To suggest a new word, or contribute new evidence for a word already in the OED, please contact us as follows:
    Oxford English Dictionary
    Oxford University Press
    Great Clarendon Street
    Oxford, OX2 6DP
    Tel: +44 (0)1865 353660
    Fax: +44 (0)1865 353811

  41. Arun: Good suggestion! And why not add it also to the Wikipedia entry? Best,


  42. Hi Arun,

    oh, thanks, that's an interesting suggestion! I didn't know that one can contribute to the OED that easily.

    Actually, I have thought about this again, and my guess is that the notion of "phase space" (or the German or French equivalent) may have appeared first in some work of Hamilton, Jacobi, or Liouville, thus in the 1840s or 1850s? Liouville's theorem literally calls for the notion of "phase space"...

    Unfortunately, papers of these people are hard to find, and not online to my knowledge - and I have no idea whatsoever when and where Liouville published his theorem, or even if it is indeed by him, taking into account Stigler's law ;-)

    Cheers, Stefan

  43. I think you should expand your discussion to ask why various physical quantities are designated by various seemingly irrelevant letters. Answering such questions leads one down strange and interesting roads!

    For example:

    Why is current called "I"? Apparently it goes back to Faraday - it comes from the word "ion". And Faraday was the one who introduced the word "ion". This word was invented by his friend William Whewell in 1834. "Ion" comes from a Greek word meaning "to go", so it made sense to use "I" for current. Whewell also invented the words anion, cation, anode, cathode, and electrode!

    Next: why is momentum called "p"? I know the answer...

  44. From Wiki Answers (which I hope is wrong otherwise getting answers is too easy, which may give rise to the age of the amateur, or something):

    "The answer that I've heard is that they ran out of letters to describe all of variables of various physical processes... for example, "m" is more commonly understood to be "mass". "p" is often ascribed to "pressure" though, so even "p" isn't a good letter for momentum."

  45. These nomenclatures aren't all the same in different languages. For example a force is in German sometimes written as K, not F.

  46. Really? Interesting Bee, and thanks for that. In Tini Veltman's book i saw the last few line's of Einstein's 1905 Special relativity paper, and he definitely used different letters. "L" I think, for something.

    Back to John Baez's question:

    From Wikipedia, entry: Momentum:

    Mōmentum was not merely the motion, which was mōtus, but was the power residing in a moving object, captured by today's mathematical definitions. A mōtus, "movement", was a stage in any sort of change,[1] while velocitas, "swiftness", captured only speed. The concept of momentum in classical mechanics was originated by a number of great thinkers and experimentalists. The first of these was Ibn Sina (Avicenna) circa 1000, during the Islamic Renaissance who referred to impetus as proportional to weight times velocity.[2] René Descartes later referred to momentum as mass times velocity and as the fundamental force of motion. This allowed Descartes to maintain that mass and velocity are fundamental and conserved, everywhere and all the time.[3] Galileo, later, in his Two New Sciences, used the Italian word "impeto."

    So, hmm. Italian then? "I" was in use, "m" stood for mass. Use the 3rd letter?

  47. There is also a different definition in the world of business, in Finance, regarding price, though I don't think that is why linear momemtum is "p", but possibly. Again from Wiki:

    Momentum and rate of change (ROC) are simple technical analysis indicators showing the difference between today's closing price and the close N days ago. Momentum is the absolute difference.

  48. In quantum mechanics, one frequently uses k instead of p, sometimes also q. Frankly, I think in most cases symbols were just chosen arbitrarily without any good reason and one of them just was used most often and become commonly accepted. Why is the metric g? Why is g sometimes a coupling constant too? Why are vector fields A, and scalar fields psi? Why are potentials V? Why is z a complex number but x isn't? Why do Latin indices run from 1 to 3 and Greek ones from 0 to 3? And why do some people find perverse pleasure in using them exactly the opposite way? Why is L, depending on context, a luminosity, a Lagrangian or an angular momentum? Why are groups capitalized and algebras not? Why do Americans use letter format instead of ISO normed paper, and why, annoyingly enough did I forget that my ac/dc adapter wouldn't cope with 220 Volts? Best,


  49. You forgot your adapter thing because you're brilliant and can think 5 thoughts simultaneously, like most of us, but you're also a busy Bee, and when Bees get busy, it stands to reason that one of the five reasons will be the least important (at the time) fifth reason, and busy-ness means that when in a rush, the fifth thing is usually the thing to be forgotten. In a nutshell: you're not perfect, just like everyone else. Those other questions were excellent, btw, thanks.

    Another question: Why do the English drive on the left side of the road? It's not right, but does that make it wrong?

  50. Steven, the left-side tradition came from a horseman, usually right-handed, wanting convenience in sword-fighting a challenger if need be. Travelers didn't want to be vulnerable. The curiosity then becomes: why did Americans pick the right side of the road? Politics?

    BTW, the case of a letter is significant to meaning: p for momentum and often P for pressure. In early relativity use L was length of an object, but now more often means angular momentum (esp. orbital, v. "S" for rotational angular momentum on own axis.)

    One confusing change in practice about SRT: they used to distinguish proper mass with m_0, and "relativistic mass" was m = gamma*m_0. I thought that appropriate, but recent revisionism treats "mass" as invariant and started use of "m" for what used to be called proper mass! I see some point to that, but consider: if we had a box with masses whirling around inside, the "effective mass" would be the sum of relativistic masses. (That is, effective linear inertia of e.g. a relativistic flywheel - like accelerating it all parallel to axis - is the sum relativistic mass.) It would be hard to keep track of all the proper masses.

    One thing annoying to me is lack AFAICT of clear standard for space-time dimensions. I see d and D used nearly interchangeably for various combinations of large and compact space-time dimensions and sometimes just space (but "N" has remained mostly standard for large space dimensions.) I care since I'm working on some explanations of why space would have only four large S-T dimensions, without needing string theory (see my link.)

  51. Steven: I had also heard the story about the sword-fight, but find it hard to believe. It sounds to me like one of these a posterio attempts to make sense out of reality. I wonder if there's any evidence for that, or whether it's just one of these stories that are repeated so often till everybody believes them.

    For what I know, there initially (as one can guess) was no law and no rules which side of the road to drive on. Because that requires a lot of attention and takes energy, people began to locally settle on rules. These might have differed from one town to the next. Gradually, the areas in which one side dominated increased, and with increasing traffic finally laws were issued to minimize accidents etc. (This isn't so unlike to spins aligning to get into a preferred energy state in Weiss' areas.) I believe the Swedes initially also drove on the left. And Great Britain is, well, an island. They didn't have much need to align with the mainland. They then tried to export their driving rules to the rest of the empire. South Africans still drive left. Canada had a phase of confusion (where laws differed from one state to the next) but eventually settled on right. And so on.

    I only know that because it was one of the examples in this paper Learning to be thoughtless, that I wrote about some while back. It's a very simplistic agent based model showing that "thoughtlessness" leads systems to settle in a homogenous state, but which state is pretty much irrelevant, it's a very noisy process. A lot of social norms and standards, including notation, are like that. (You can find a lot more examples: why do we read left to right, and others right to left or up to down?) You just settle on one to avoid wasting "thought," not necessarily because it's a particularly great choice. And if you later think it was a dumb choice for one reason or the other, it's very hard to change, take for example the expression "Theory of Everything" to mean unification of the four known interactions - not exactly a great nomenclature, but we're kinda stuck with it now. Best,


  52. Bee wrote:

    Frankly, I think in most cases symbols were just chosen arbitrarily without any good reason and one of them just was used most often and become commonly accepted.

    Sure! But still...

    Why is the metric g? Why is g sometimes a coupling constant too? Why are vector fields A, and scalar fields psi? Why are potentials V?

    There are answers to all these questions! And researching them is a pleasant pastime. It's not that the answers are important. But, one learns interesting stuff in the process. And it's a fun challenge.

    Since nobody seems to have tackled the question of why momentum is called "p", here's what I know about that one. I don't know why the wavefunction is called "psi", or the metric is called "g", and I'ld love to find out.

    From week224:

    Speaking of Hamilton, Theron Stanford recently sent me an answer to one of life's persistent questions: why is momentum denoted by the letter p?

    Since momentum and position play fundamental roles in Hamiltonian mechanics, and they're denoted by p and q, one wonders: could this notation be related to Hamilton's alcoholism in later life? After all, some claim the saying
    "mind your p's and q's" began as a friendly Irish warning not to imbibe too many pints and quarts! So, maybe he used these letters in his work on
    physics as a secret plea for help.

    Umm... probably not. Just kidding. But in the absence of hard facts, speculation runs rampant. So, I'm glad Stanford provided some of the former,
    to squelch the latter.

    He sent me this email:

    While Googling various subjects, I came across the following from your Quantum Gravity Seminar notes from 2001:

    Again Oz was overcome with curiosity, so mimicking Toby's voice, he asked, "Why do we call the momentum p?"

    The Wiz glared at Toby. "Because m is already taken -- it stands for mass! Seriously, I don't know why people call position q and momentum p. All I know is that if you use any other letters, people can tell you're not a physicist. So I urge you to follow tradition on this point."

    Well, I have an answer. Hamilton, the first physicist to actually understand the importance of the concept of momentum, chose pi to stand for momentum (actually, it's not the usual pi, but what TeX calls varpi, a lower-case omega with a top, kinda like the top of a lower-case tau). Jacobi changed this to p in one of his seminal papers on the subject; he also used q in the same paper to stand for position. In the 1800s (I want to say 1850s, though it might have been a decade or two later) Cayley presented a paper to the Royal Academy in which he says (and I paraphrase), "Well, it seems that p and q are pretty well established now, so that's what I'm going to use."

    So, now the question is why Hamilton chose the letter "varpi" for momentum. This variant of pi was fairly common in the mathematical literature of the day, so there may be no special explanation. For
    some further detective work, see:

    Hamilton: two mysteries solved

    Also see equation 12 in this paper for one of the first uses of "varpi" to mean momentum:

    William Rowan Hamilton, Second essay on a general method in dynamics, ed. David R. Wilkins.

    He doesn't say why he chose this letter - it may have been completely random!

  53. Bee: hard to prove such a conjecture, but the theory about left-side traffic has a distinguished advocate. From , we find:
    Some historians, such as C. Northcote Parkinson, believed that ancient travellers on horseback generally rode on the left side of the road. As more people are right-handed, a horseman would thus be able to hold the reins with his left hand and keep his right hand free—to offer in friendship to passing riders or to defend himself with a sword, if necessary.[15]
    See also that [15] "Straight Dope" link.

  54. Jacobi, eh? Darn it, John, I thought came form the French: "puissance", for force or strength. Or this (from the internet):

    * From: "James G. Pengra"
    * Date: Thu, 11 Dec 1997 17:03:21 -0800

    >In a April issue of Am J Phys a few years back, Dan Gillespie wrote a short
    >note revealing the historical origins of the symbol 'p' for momentum. I
    >read it to my general physics classes every time. Jim Marsh
    >>I have been asked to ask the list, what is the origin of the symbol "p" for

    Is that the one where 'p' comes from pimento, as in an olive. At a
    cocktail party Newton, it is reported, was trying to pull the pimento out
    of his olive and thought of the change in the pimentum. Thus we have 'p'
    for momentum. It was a very cute and memorable explanation for using 'p'
    for momentum, especially so since we seem to have no other.

    --Jim Pengra, Walla Walla, Washinton 99362

  55. Hi John,

    thanks a lot for your comments, and revealing the secret of the "p" and "q" - I've spent yesterday night trying to find a clue, but with no results.

    Actually, Hamilton's original paper is available online for free (at least until Feb 28, later from Gallica) at the Royal Society's website ("Second Essay on a General Method in Dynamics", Phil. Trans. R. Soc. Lond. 125 (1835) 95-144), so we can check out the original typesetting...

    Unfortunately, I couldn't find the Cayley paper in the "Philosphical Transactions" where he comments on the use of "p" and "q". Instead, this afternoon I stumbled upon a paper by S. Ross in the Notes and Records of the Royal Society which tells the story of Faraday and Whewell, "Faraday Consults the Scholars: The Origins of the Terms of Electrochemistry", Notes Rec. R. Soc. Lond. 16 (1961) 187-220...

    But I was successful in locating a Jacobi reference: "Neues Theorem der Analytischen Mechanik", in Crelle Journal für die reine und angewandte Mathematik, 30 (1838) 117-120. On page 120, Jacobi introduces the "p" as partial derivatives of "T" by "q", where T is, as in Goldstein, kinetic energy, here still called "lebendige Kraft" (vis viva). And in the Jacobi Collected Papers, there is posthumous text (didn't find a date) where he makes explicit reference to Hamilton and uses the "p", "q" notation.

    Concerning origin of notations in general, I also believe that in most cases where the symbol is not obviously related to a noun, as m for mass, the choice is by chance: Someone used a symbol first, and when the paper or text is influential and the notation not completely opaque, it sticks.

    For "g" in the metric, my guess would have been that it was used first by Riemann in his 1854 Habilitationsschrift - unfortunately, while denoting the line element as "ds" as we still do it (maybe "s", the path length, comes from the German word "strecke"?), Riemann doesn't use a symbol for "g" at all, he just talks about a set of n(n-1)/2 coefficients.

    On the other hand, the "Psi" for the wave function pops up quite abruptly on the first page of Schrödingers "Quantisierung als Eigenwertproblem (Erste Mitteilung)" in
    Annalen der Physik 384 (1926) 361-376 (here is a PDF of the full paper): "We now introduce for S [the Jacobi action] a new unknown Psi such that Psi would appear as a product of a unique [I have never heard the German term "eingriffig" before...] function of the separate coordinates. I. e. we posit S = K log Psi." That seems to be an example of a symbol that has stuck. But why Psi? Maybe the Lady of Arosa knows, but she didn't tell us ;-)...

    Cheers, Stefan

  56. Hi Steven,

    thanks for the "p" story, that's fun!

    For the record, Dan Gillespie's answer was in Am. J. Phys 63 (1995) 297 (it's essentially the one quoted in the usenet post), and this was in response to a question by N. David Mermin (Am. J. Phys. 62 (1994) 871).

    Interestingly, Mermin suggest, as you do, that the "p" may derive from "puissance"!

    Concerning your earlier comment on Einstein's relativity paper, I guess Veltman's book shows the last equations of the short "Energieinhalt" (aka E = mc²) paper (Annalen der Physik 323 (1905) 639)? It is available online as PDF.

    The notation in the paper is indeed strange to us. Speed of light is "V", and total energy is "L", hence E = mc² would read L = mV² in the orginal paper, though this equations doesn't even show up directly...

    Cheers, Stefan

  57. You're welcome Stefan, and thank you very much for those wonderful links, and to John Baez for his simple but wonderful question.

    Well now, Baez got me thinking of all manner of notation sources I never questioned before, so I Googled up the ubiquitous Integral sign and right at the top at Google in response to the question "Where does the Integral sign come from?" was the following wonderful page by Stephen Wolfram:

    Mathematical Notation: Past and Future (History)

    That whole page is fascinating, but I call attention to the differences between the ways Newton and Leibniz regarding notation in general (Newton wasn't a big fan, Leibniz loved it). This may also tie into your 350 Years of the Royal Society page for those who wish to dig into Newton's actual works.

    That page, and the one that follows it, taught me 2 things:

    1) As Mathematics is THE tool of Physics, notation is THE tool of Mathematics.
    2) Notation is truly in its infancy and has quite a ways to go in order to streamline Mathematics, which will in turn streamline Physics, the positive consequences of which are self-evident.

    I have so much more to add, but those two pages make wonderful thought-provoking reading, so I will go. Go to eat some Spanish olives, and wonder why the olives at the bottom seem to have lost their pimentos. Was it asymptotic olivation, gravity g, Gravitational constant G, Pressure P, or pimentum p ? :-)

    There is, apparently, much research to be done. But when has it ever not been so?


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