Twelve Days of Physics

This morning I received an email from someone called “Grrrl Einstein” today which read:

I am creating a Physics Calendar for the Holiday season, and I am including twelve entities. So far I have:

  1. Newton’s Laws
  2. The Dirac equation/Schrodinger equation
  3. The Clifford Algebra defining the Dirac gamma matrices
  4. E=mc2/Einstein’s equations/postulates and/or some solution of them, such as the Schwarzschild solution
  5. The principle of least action
  6. Maxwell’s equations
  7. E=hv
  8. The Yang-Mills Lagrangian
  9. The Schwinger-Dyson equations or something else related to functional methods
  10. Stokes’ Theorem
  11. Entropy

What would be a good String Theory equation to round it out? Any things I should include/exclude?

She also says:

We’re also thinking of cool/funny/insightful pictures we could shoot to represent the equations. The pic on my myspace page will probably be the E=mc2 pic.

This sounds like a fun thing to ponder, so she let me put the questions to you, in case you’d like to help out. She plans to upload the calendar to “one of the calendar sites” when done. No, I don’t know what one of those is either, but then this is only the third time I’ve looked at a myspace site, so there you go.

So let’s hear those suggestions for topics, illustrations, etc….

My own immediate thoughts? Instinctively, given the lack of slots, and the volume of fantastic big established physics ideas out there already, I’d not have any string theory equations per se… I’d definitely have Einstein’s Equations (General Relativity) up there somewhere, separately from E=mc2. I’d swop out Stokes’ Theorem for something representing path integrals a la Feynman….But I’d need to think that through a bit more. Hmmm….. this is interesting….

Thoughts?

-cvj

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16 Responses to Twelve Days of Physics

  1. David says:

    The Navier-Stokes equations and the laws of thermodynamics have a large range of applicability. I agree that the Einstein field equations should be on the list too. The Clifford algebra seems unnecessary if the Dirac equation’s there already.

  2. stefan says:

    This Physics Calendar idea reminds me of a very beautiful, small book I have seen shortly, The Equations, by Sander Bais. It presents, on one page each, all kinds of equations in physics, and tries to explain the science described by these equations.

    For string theory, it features the Nambu-Goto action, if I remember correctly…

  3. TheGraduate says:

    I would second Navier-Stokes.

  4. Helge says:

    Just some more suggestions:
    Korteweg-de-Vries as the equation giving rise to solitons, and where solitons were first discovered … (maybe a bit of personal bias here).

    What about some equation describing the motion of a planet around the sun? Kepler’s laws?

    Helge

  5. Paul says:

    I think there should be a propagator in there somewhere, so maybe some form of the Ward identity would be nice, with a few pictures all summing to zero!

    But for string theory one might like to have the spectrum of string states, or perhaps T-duality. Maybe one could be more general and have a BV master equation, but it wouldn’t look too interesting. Perhaps the density of states formula? Or even the formula relating angular momentum to energy squared featuring the Regge slope? Even some AdS/CFT duality pictures might be good for a calendar, potentially I mean.

    Personally I prefer comic calendars, last year my friend brought me a cow calendar: every month had a cow in some exotic location giving warped life-advice always involving a cow, such as, “be nice to your cow and your cow will be nice to you”.

  6. Bee says:

    Hi Stefan,

    I was about to write exactly the same thing 🙂

    Hi Clifford,

    What equation belongs to 11) ‘Entropy’? S= k log \Omega ?

    Or otherwise, how about including something from Thermodynamics of Black holes: T = 1/M, or S ~ A etc.

    And I’d insist on Maxwell’s equations with differential forms, it brings out much better the beauty of it all…

    Best,

    B.

  7. Clifford says:

    Bee. Hi! For entropy, I would have either that equation, or a statement of the Second Law. Actually, in her email to me, Grrrl Einstein did have in brackets (covariant form) next to Maxwell’e Equations, so I imagine that is what she meant. I probably should not have deleted that.

    Stefan: As for Nambu-Goto.. that’s a good idea, but it does not really bring out the best… But thn I don’t knwo what does. (Thanks for the book suggestion by the way).

    Paul:- The Regge slope is good… that’s very stringy and also has experimental roots.

    Helge:- Long time since I’ve heard from you! Hi! KdV – Close to my heart too!

    David and TheGraduate:- Navier-Stokes is good too….. also nice to have an image for… lots of nice fluid flows in the background.

    I think I know what is top of my list to go next:- Th Planck black body spectrum… it encompasses so namy aspects of physics, bridges the classical and the quantum, and is also written in the sky via cosmology and astrophysics. It is such a triumph, it should be as popular as the I heart NY t-shirt.

    -cvj

  8. Moshe says:

    Hey Clifford, that may not fit, but maybe the sigma model action of the string in background fields, followed by the statement that \beta =0 implies Einstein equation. Still one of the defining charecteristics of the theory, and one of the things that makes students ooh and aah (or at least it should…)

  9. damtp_dweller says:

    I definitely think that Einstein’s equations for GR with matter need to be included in that list. As to a possible string theory `day,’ surely the Virasoro algebra with central extension has to be a strong candidate?

    For what it’s worth, assuming that this is for a true `calendar’ my version of that list would have to include topics that can be displayed succinctly. I’d have

    1. F = ma
    2. The Schroedinger equation
    3. M = \sqrt{ Area(S)/16\pi G^2 } (The Penrose inequality)
    4. R_{ab} – \frac{1}{2}g_{ab}R \prop T_{ab}
    5. The principle of least action
    6. Maxwell’s equations
    7. E=hv
    8. [L_m,L_n] = (m-n)L_{m+n} + A(m)d_{m+n} (Centrally extended Virasoro algebra)
    9. The laws of black hole mechanics
    10. Stokes’ Theorem
    11. Entropy
    12. The Navier-Stokes equations

  10. Jonathan says:

    How about the AdS/CFT recipe:

    Generating function of field theory operators=String theory partition function with appropriate boundary values for fields.

    This being the defining equations of AdS/CFT which itself is one of the most exciting outcomes of string theory so far seems appropriate to me.

    All the best,

    J.

  11. TheGraduate says:

    Hi Dr. Johnson,

    I found this over the week-end:

    http://lsiit.u-strasbg.fr/sites/img/rendu_fluide.jpg

    I thought it was great. It’s probably something like what you were talking about with Navier-Stokes.

  12. Clifford says:

    Excellent!

    Thanks….

    -cvj

  13. boreds says:

    Perhaps it should be made into an advent calendar, so that we can fit more stuff in.

    Little doors would open to reveal the exciting equations!

  14. Cynthia says:

    Hi Clifford!

    I’ll edge onto the speculative limb – so to speak – and speculate that #12 equals The Maldacena Conjecture on AdS/CFT. Surprisingly though it may sound, strings are at my heart these days…

    By the way, is Asymptotia sort of like your beach retreat hovering along the shoreline of the Virtual Sea?;)

    Best wishes,
    Cynthia

  15. Rob Knop says:

    Various lists get fairly esoteric, but are also fairly particle physics focused….

    Things which must be represented, if you want to “span” Physics :

    * Newton’s laws (couple gravity in)
    * principle of least action
    * Maxell’s equations
    * entropy
    * kT (I mean, is anything more useful for napkin calculations?)
    * uncertainty principle
    * Shroedinger equation
    * e=mc^2 (as a stand-in for all of SR)
    * Einstein field equation

    Those are just basics. Any of those (except for maybe the last one), and you’ve cut out a big piece of the underpinnings of any undergraduate physics education.

    After that, before getting into esoteric stuff that indicates you’ve specialized into any particular subfield, I’d get fluid stuff (continuity &/or euler &/or Navier-Stokes), something potentialish (del-phi, or scalar/vector potentials of E&M, or perhaps the QM SHO), and perhaps a general category of symmetry->conservation laws.

    Yeah, no strings anywhere there. There’s also no band gap or fermi genergy, no FRW metric and friedmann equation, no isospin or shell model or Standard Model, no Einstein A/B, no equation of radiative transfer, no stern gerlach or bell’s inequality, no cooper pairs, no phase diagrams, no young’s modulus, no alfven waves, and so forth….

    -Rob

    P.S. : there’s a whole separate approach one could take:

    1. extremely long problem sets
    2. fear of the Physics GRE
    3. Trial By Jackson
    4. eight years of grad school
    5. moving every two years jumping between post-docs
    6. inability to get a faculty job
    7. inability to get tenure
    8. constant writing of proposals
    9. constant reviewing of huge stacks of proposals
    10. colleagues who think your subfield is worthless
    11. colleagues in subfields you think is worthless
    12. cancellation of your project

    but that might be too cynical….

  16. Uncle Enzo says:

    How about if we include only things which have to do with the real world as we know it? Hey, this is science, right? So no string theory, please.

    Forza Italia! World Cup Champions! Forza!