Re: What's so "beautiful" or "elegant" about string theory?

From: Doug Sweetser (sweetser_at_alum.mit.edu)
Date: 11/03/04 

Date: Wed, 3 Nov 2004 16:05:15 +0000 (UTC)

Hello Lubos:

> The document on PBS has been created for regular viewers, so it does
> not cover any math

For the pure fun of it, I am making my own physics videos. This is the
standard practice, don't show the math, or if it does, make it slide
away quickly. In my own productions, the equations I reference are
always on the screen. Why? Because that is what I am talking about,
how a small set of symbols are relevant to how our Universe works. If
one talks about Beethoven, one should also hear his tunes. It
is a fun challenge to come up with graphics good enough that my
girlfirend wants them on the walls of our apartment :-)

> Elementary particles are called elementary because according to the
> most current theory that describes them (and their interactions),
> namely the Standard Model, they have no internal structure. In string
> theory, they would not be quite elementary, but we tolerate the term
> anyway. ;-)

Agreed, my language was imprecise.

 
> Which rules of logic do you precisely misunderstand? We may be able to
> help you. ;-)

Take for example the two slit experiment. We completely understand the
math (it is easy). Feynman gets the math. Yet he said in his New
Zealand he does not understand why it works that way. There have
certainly been quite a few threads in SPR on the topic.

>> but no particles are making tricky calculations very rapidly.
>
> Apologies for I don't quite understand this sentence.

There are limits to how many Feynman diagrams we can include in a
perturbation series expansion, say of an electron being scattered by a
photon. I don't know what the current record is, perhaps 8. That is a
"tricky calculation". I know I cannot do it, getting hung up at 2.
Yet electrons interact with photons all the time, and apparently to the
complete perturbation series expansion.

...
> This is the 1915 type of beauty, but in 2004 we're a bit further.
...
> That's a 1864-style beauty.
(question: I know that Maxwell wrote up his field equations in that
year, but did he also wrote down the Lagrangian then too, or if someone
else gets the credit for that?)
...
> 1969.
...
> 1974.

For me, this is too focused on the humans who have achieved great
insights. To a flaw, I am equation-centric, not physicist-centric.
These equations will last, no matter when they were discovered.
Imagine changing the order of their discovery, and that has no effect
on the beauty of the Lagrangians.

> The only Lagrangian in large 11 dimensions worth your time is the
> Lagrangian of 11-dimensional supergravity - which is more beautiful,
> in a physics counting, than just general relativity - because it has
> not only general covariance, but also local supersymmetry. But in a
> sense, it is just some Lagrangian - a generalization of your GR and
> Maxwell's system, plus some fermions. See e.g. the original paper by
> Cremmer+Julia+Scherk
>
> http://ccdb3fs.kek.jp/cgi-bin/img_index?7805106

OK, I did print this one out with some difficulty (odd page length). So
I can try to write this one out, at least for the record. To quote the
entire abstract:

"We present the action and transformation laws of supergravity in 11
dimensions which is expected to be closely related to the O(8) theory
in 4 dimensions after dimensional reduction."

This must be a classic paper since it dates to 1978. Here is the
Lagrangian:

    L = 1. Bosonic part like GR,
        2. Fermionic terms for the gravitino,
        3. Antisymmetric gauge field strength F(4) contraction,
        4. Gravitino coupling to the F(4),
        5. Chern-Simons term required by super symmetry.

1. = - V/(4 k^2) R(omega)
2. - iV/2 phibar_mu Gamma^mu nu rho D_nu (omega + omegahat)/2 phi_rho
3. - V/48 F_mu nu rho sigma F^mu nu rho sigma
4. + KV/192 (phibar_mu Gamma^mu nu alpha beta gamma sigma phi_nu +
                12 phibar^alpha Gamma^gamma sigma phi^beta)
               (F_alpha beta gamma sigma + Fhat_alpha beta gamma sigma)
5. + 2K/(144)^2 Eta^alpha1 alpha2 alpha3 alpha4 beta1 beta2 beta3
        beta4 mu nu rho
                F_alpha1 alpha2 alpha3 alpha4
                F_beta1 beta2 beta3 beta4 A_mu nu rho

    where
       V^alpha_mu is the vierbein (graviton field?)
       phi^mu is a Majorana spin 3/2
       A_mu nu rho is an antisymmetric gauge tensor
       F_mu nu rho sigma is the field strength tensor
            associated with A_mu nu rho (4 d[_mu A_nu rho sigma])
       D_nu omega phi_mu is the covariant derivative of phi_mu
       (= d_nu phi_mu + 1/4 omega_nu alpha beta Gamma^alpha beta phi_mu)

At this point in my intellectual development, I don't understand this
Lagrange density, although if I wrote it down correctly, it is in a
rare class of "meaningful SUSY Lagrangian in 11 dimensions". As Bob
Dylan once penned in a very different context, "Don't criticize what
you can't understand." So I will comment that the SUSY 11D Lagrange
density looks difficult even for bright folks to fully comprehend.

doug
quaternions.com

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