Timeline for Does Dirac's idea of filled negative energy states make sense?
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11 events
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| Jun 3, 2014 at 11:33 | comment | added | Luboš Motl | There's a lot of room for idiosyncrasies here - what is the definition of a semiheuristic idea's being wrong? Some implications that someone could derive from the Dirac sea are wrong, but there are lots of careful Dirac-sea-related comments that are completely right and I am confident that Weinberg would agree. He just chooses to erase it for pedagogic reasons. | |
| Jun 1, 2014 at 16:47 | comment | added | joseph f. johnson | If my memory serves me correctly---I am now in a land with bandwidth but without my books, and the liberry is closed---even a textbook as recent as Greiner repeats the exposition of the Dirac sea, without criticism, but the textbook of Weinberg on QFT excoriates the whole idea. I certainly think more highly of Weinberg's textbook writing abilities than I do of Greiner's....if Greiner is right and Weinberg is wrong, it will only be because Greiner has been copying Dirac.... | |
| Mar 2, 2013 at 2:01 | vote | accept | Terry Bollinger | ||
| Mar 2, 2013 at 2:01 | comment | added | Terry Bollinger | So you answered my question, and well. Alas, more understanding has in this case left me less than sanguine regarding argument structure, that is, the deeper scaffolding that lies behind the math. Correct me if I'm misreading this, but the bottom line appears to be this: Dirac proposed a sea model, the naive vacuum. The naive model violates observed reality infinitely both in energy and charge densities. Mathematical methods were developed to repair this by creating and subtracting almost all of two infinite terms. There is just more of a chocolate confection flavor to this than I expected. | |
| Mar 2, 2013 at 1:27 | comment | added | Terry Bollinger | Luboš, thank you. Your answer and to-the-point follow-up comments provide a lucid and remarkably compact explanation of how the issues I described are handled mathematically. In less than a day your answer topped out in Google queries on "naive vacuum" and "physics vacuum"! I think that distinction alone will help folks like me: Dirac's very compact lecture described only the "naive vacuum," without the infinite subtractions that must then be used to fix the infinite mass and charge densities created by that naive model. And from your description I see now, in part, how it was modernized. | |
| Mar 1, 2013 at 19:16 | comment | added | Luboš Motl | Incidentally, Dirac himself had trouble with renormalization - he never understood it well enough to accept that it's the right way to calculate loop processes - however, he was not too allergic to such subtractions that he would feel uncomfortable with the infinite subtraction needed to switch from the naive vacuum to the physical one. He just wrote that the densities are determined up to constants and those constants are adjusted so that the densities are zero in the physical vacuum. It just doesn't matter that the required subtraction is infinite: it can be done, anyway. | |
| Mar 1, 2013 at 19:13 | comment | added | Luboš Motl | The cosmological constant problem is why these terms - like the energy density you could predict for the physical vacuum if you decided that the naive vacuum has $\rho=0$ - mostly cancel but not quite, so that there's a tiny leftover manifesting itself by the accelerated expansion of the Universe. The energy density difference between the naive and physical vacuum is infinite but as always, most of these infinities are unphysical as they cancel up to finite leftovers in all physically realizable situations. The counterterm for energy density is just a constant. | |
| Mar 1, 2013 at 19:11 | comment | added | Luboš Motl | Using the language of renormalization, the energy density and the charge density of the physical vacuum are two adjustable constants a priori. The charge density has to be zero if the physical vacuum is Lorentz-invariant because the charge density is a time component of a 4-vector $j^0$ and its nonzero value would pick a preferred frame. The energy density of the physical vacuum is known to be just $10^{-123}$ in Planck units. The electron field contributes by a term (related to this one, in a sense) and the question why all the contributions almost exactly cancel is the CC problem. | |
| Mar 1, 2013 at 19:09 | comment | added | Luboš Motl | Dear Terry, the bottomlessness just means that the physical vacuum and the naive vacuum differ by infinitely many electrons. Even the energy densities and charge densities of these "two vacua" differ by an infinite amount. That's not a real problem - only the physical vacuum and its finite excitations are realizable in practice. Nevertheless, you may view these infinities by which the densities differ to be the first signs of infinite subtractions that are needed in QFT calculations - QFT requires much more nontrivial and "harder to subtract" infinities if you compute loop corrections! | |
| Mar 1, 2013 at 13:06 | comment | added | Terry Bollinger | Thanks, I think, Lubos. Since you clearly understand the maths very well, could you explain exactly how you fill a bottomless negative kinetic energy Fermi sea with real electrons without reaching infinite charge and mass? I missed that part. Equations are fine! Surely this one is just a matter of mapping the equation component to the real charges and real mass of all those electrons? (Will recheck this evening.) | |
| Mar 1, 2013 at 12:35 | history | answered | Luboš Motl | CC BY-SA 3.0 |