OK, looks like this has been a comedy of errors by physicists. 1.Naohiro Kanda http://arxiv.org/pdf/1106.0592v1.pdf claims the QED calculation of light by light scattering cross section was done wrong by everybody until now (year 2011) when Kanda finally did it right getting the right answer for the first time, apparently nobody ever checked it during 70 years, no matter how many times it appears in no matter how many textbooks, except once when Karplus+Kroll did it wrong out of a too-strong desire to duplicate the previous wrong result. Unless Kanda is wrong. 2.Various papers gave mutually-contradicting formulas for pair creation rate in constant electric field E: (A) (m/(hbar*c))^4 * c / (4*pi^3) * (E/Ecrit)^2 * SUM(n=1,2,...) n^(-2) * exp(-n*pi*Ecrit/E). where Ecrit = m^2*c^3/(e*hbar)=1.3*10^18 volt/meter was stated as EQ1 by Hagen Kleinert: http://users.physik.fu-berlin.de/~kleinert/kleiner_re396/396.pdf and he says it was derived by Euler+Heisenberg and later by Schwinger. This formula was also stated as EQ13 of Dunne+Schubert: http://arxiv.org/pdf/hep-th/9907190v1.pdf And it looks plausible to me, EXCEPT that I suspect there ought to be an extra factor of alpha because this effect should depend on the 4th power of e, i.e. 2nd power of alpha. (B) A different, and obviously-wrong, formula for this is EQ 15 p786 of N.D. Hari Dass: Strong magnetic fields, in "Quantum Electrodynamics of Strong Fields" edited by W.Greiner 1981. https://books.google.com/books?id=MnQECAAAQBAJ&pg=PA786#v=onepage&q&f=false (C)A third different, also obviously wrong, formula is EQ 6.41 p677 in Schwinger's paper [Phys Rev 82 (1951) 664] where he instead says the pair creation rate per time & volume, is (alpha/pi)^2 * E^2 * SUM(n=1,2,...) n^(-2) * exp(-n*pi*m^2/(eE)) which is clearly dimensionally wrong. But it and the Hari Dass formula both involve the extra factor alpha that I wanted. WHAT DO I THINK? I think intuitively that the correct answer is probably of the form K * (m/(hbar*c))^4 * c^2 * alpha^2 * (E/Ecrit)^2 * SUM(n=1,2,...) n^(-2) * exp(-n*pi*Ecrit/E) where Ecrit = m^2*c^3/(e*hbar)=1.3*10^18 volt/meter and K is some dimensionless numerical constant, but none of the above lit cites agree with my intuition. I have not attempted to redo the calculation, though. But we know for sure that at least 2 of those three physicist-camps were wrong. 3.Pair creation in constant magnetic field. On p785 Hari Dass says "a pure magnetic field is stable against pair creation." Chung Ngoc Leung, Shang-Yung Wang: Phys.Lett.B674 (2009) 344-347 say "there does not exist a maximum magnetic field in QED and the magnetized vacuum is stable for all values of the magnetic field." Bulanov et al: Phys.Rev.Lett.105 (2010) 220407 http://arxiv.org/abs/1007.4306 say "Pair creation is determined by the Poincare invariants (E^2 - B^2) and (E.B) and requires the first invariant be positive." WHAT I THINK: Two possible resolutions: (A) every single one of those bastards is wrong. A sustained magnetic field above m_e * c^2 / mu_e = 8.8*10^9 tesla should be impossible due to pair creation. The Schwinger-esque pair-creation mechanism indeed as Bulanov says really does depend on sqrt(E^2-B^2) not E [it was derived for constant E-field and zero B-field, but the resulting formula, if anybody ever managed to state it correctly, then should be correct using sqrt(E^2-B^2) in place of E, more generally] and indeed should only operate when the argument of the sqrt() is positive; BUT what Bulanov forgot to say is, there is a DIFFERENT pair creation mechanism that also operates, and it is not based on the charge*potential interaction energy, but rather on the moment*field interaction energy. No previous author, apparently, has examined this mechanism. (B) The ground state energy for an electron moving slowly in the z-direction in a huge z-directed magnetic field, is m_e*c^2 PROVIDED its moment is aligned with the field, according to http://www.springer.com/cda/content/document/cda_downloaddocument/9783642362... EQ 2.24 with n=0 and beta=|e*B| and section 2.2. Note this does not depend on B. You only get energy dependence on B if your moment is anti-aligned with the field. If so, then it is NOT energetically favored to create a pair in a B-field, no matter how strong that B-field is. Which hypothesis is right -- A or B? I'm favoring B, because: Imagine this thought-experiment. 1. Start with a superconducting circular loop generating some big magnetic dipole. 2. Create N pairs near the centerpoint of the loop, making N large enough that the total magnetic dipole moment of all the pair members, cancels out the dipole moment of the loop. 3. Pull on the loop and the pairs until the loop is moved far away from all the pairs. 4. Annihilate all the pairs. If we believe hypothesis B then we believe step 2 cost energy 2*N*me*c^2, which is exactly regained in step 4. But we know step 3 cost energy. Oops. Therefore, it seems to me, we are forced to believe instead in hypothesis A. And therefore to believe a strong magnetic field will cause pair creation, and all those bastards were wrong. A big cause of their wrongness was their starting point that the B-field extended infinitely far at constant value. This confused matters and screwed up energy bookkeeping. If use realistic model with a finite dipole field, then saved from that confusion, hopefully. So I seem to have arrived at a state of: big dispute with the physicists, with me on one side, but all of them on the other for the last 85 years. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)