Timeline for Why is ${\partial^i}{\partial_i\phi}$ = ${\partial^i {\phi}}{\partial_i{\phi}}$?
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13 events
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| Jul 6, 2012 at 20:24 | comment | added | Luboš Motl | Susskind is surely a kind of an intuitive "seer", so to say, and a no-nonsense guy from the working class. Did the errors affect the results? Yes, the Rigid Regge Rods paper was just completely wrong. So v1 was wrong, v2 was completely empty, and v3 was there again and it said the opposite conclusion than v1: string theory ultimately guarantees some locality. The sign error in the potential energy (they forgot that the commutator of two Hermitian operators is antiHermitian whose square is therefore negatively definite, so one has to switch the sign to get positively definie) was irrelevant. | |
| Jul 6, 2012 at 19:08 | comment | added | MadScientist | The part on the "stringy uncertainty principle" is very interesting. I've noticed that the papers written by (what I consider to be) the great physicists are easier to read than the ones written by lesser physicists. They weed out everything other than the essentials. This doesn't look that mathematically difficult considering what it's about. | |
| Jul 6, 2012 at 19:05 | comment | added | MadScientist | Motl, lol. It is reassuring to know that the greats make mistakes too. Is it a minor error or does it invalidate the result? | |
| Jul 6, 2012 at 19:01 | comment | added | Luboš Motl | Let me mention an example. Rigid Regge Rods, see: arxiv.org/abs/hep-th/0005015v1 - Then click the version v2 to see what happened what the paper. The error was in eqn 3.5 essentially due to a wrong treatment of the $i\epsilon$ term in the propagators. If I remember well, it was pointed out by Joe Polchinski rather quickly. I can also show you a wrong sign (of the potential term) in the main important equation, the Hamiltonian of Matrix theory, in the BFSS paper - never fixed - and many others. ;-) | |
| Jul 6, 2012 at 18:56 | comment | added | Luboš Motl | BB1, I would have to see that they used those things but I can imagine Lenny omitting this factor. As long as he always implicitly added the factor while deriving the equations of motion or propagators, he could have survived his 40+-year stellar career rather easily with the opinion that the box phi is enough. And maybe there's one of the field redefinitions. I can show you many rather simple errors of this kind in various papers co-authored by Lenny. He's not the kind of a nitpicking rigorous guys caring about details. | |
| Jul 6, 2012 at 18:49 | vote | accept | MadScientist | ||
| Jul 6, 2012 at 18:48 | comment | added | MadScientist | @Motl, True. It would be an absurd notation. But Victor Stenger does the same thing. And I know I've seen it written that way other places too. Like Susskind's Lectures on youtube maybe. It's very strange. These are all great physicists. | |
| Jul 6, 2012 at 18:45 | comment | added | MadScientist | Is it possible that the $\phi$ doesn't contribute to the action because of the standard boundary condtions? | |
| Jul 6, 2012 at 18:45 | comment | added | Luboš Motl | There's one more issue. If you have a field redefinition of the kind $\phi=\exp(a)$ or $\ln(b)$, then the non-derivative prefactors may change in various ways. ... David is a very smart and amusing guy. ... I don't understand how you could say that this mistake is a "different notation". It's like saying that $12\times 12=14$ in a different notation where I may omit the extra $4$ in the result. | |
| Jul 6, 2012 at 18:43 | comment | added | MadScientist | I'm surprised he forgot something. I thought he was using a weird notation. You're lucky to know him. His lectures were very entertaining. One of the best lecturers I've seen. | |
| Jul 6, 2012 at 18:41 | comment | added | Luboš Motl | OK, so David forgot the factor. Please send my best regards to David, I know him quite well. ... It's a somewhat usual, although not the most frequent, way of writing the Lagrangian in terms of the d'Alembertian (and it makes the derivation of the equations of motion somewhat more straightforward, by milliseconds), but the extra $\phi$ really but really can't be forgotten. | |
| Jul 6, 2012 at 18:39 | comment | added | MadScientist | But David Tong and Victor Stenger both write it without the extra $\phi$. See the link I posted above to David Tong's Lectures. | |
| Jul 6, 2012 at 18:36 | history | answered | Luboš Motl | CC BY-SA 3.0 |