[math-fun] Are magnetars baloney? What is the maximum allowed magnetic field?
If a volume of vacuum contains a magnetic field B greater than m_e c^2 / mu_e = 8.82x10^9 tesla (here mu_e is magnetic moment of electron) then it becomes energetically advantageous for the vacuum to break down spontaneously, creating electron-positron pairs, because the energy mu_e B is enough to pay for the energy m_e c^2. Note due to angular momentum and charge conservation the e+e- pair have opposite spins, and opposite charges, which means they have aligned magnetic moments. I conclude it should be impossible to sustain any magnetic field larger than this, in vacuum, for longer than about 10^(-16) seconds. OK, sounds straightforward enough. BUT, (1) I have not seen this "maximum magnetic field" discussed before. (Although the analogous "maximum electric field" is often discussed, it is sometimes called the "Schwinger limit" http://en.wikipedia.org/wiki/Schwinger_limit and has value of order 1.3*10^18 volts/meter. ) (2) http://www.physics.mcgill.ca/~pulsar/magnetar/main.html claims that the "magnetar" (very magnetic type of neutron star) "SGR 1806-20" has a surface magnetic field of about 23 times my upper bound, namely 2*10^11 tesla. There are also are two other magnetars listed with claimed surface magnetic fields each about 8 times my upper bound. Contradiction. I conclude that either there is some reason I do not understand for why magnetic fields much larger than my upper bound can exist for 10000 years -- or -- the magnetar astronomers are pressurized with excrement. Or both. I have looked into this and essentially all the claimed evidence over the last 25 years for the huge magnetic fields around magnetars is based on Maxwell's equations. Maxwell equations, are, however, simply wrong when the fields are this large. (The Euler-Kockel nonlinear equations are less wrong, but probably still very inadequate.) Therefore, everything, ever, that the magnetar astronomers said about these huge fields, is suspect. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
An electron in a magnetic field undergoes circular motion in the plane perpendicular to the field. In quantum theory, this motion becomes a harmonic oscillator, whose associated energy states are called "Landau levels". The positive ground state Landau Level exceeds the negative energy of magnet moment alignment. Hence spontaneous pair creation in a strong magnetic field should not be expected on account of this process. This paper http://arxiv.org/pdf/0705.4275.pdf solves the Dirac equation for an electron in a magnetic field. The energy levels are given in eq. (17). That spontaneous pair creation in a magnetic field does not occur, in contrast to the situation in an electric field, is not unexpected. Consider the case with both fields present, equal in magnitude, and perpendicular, so that the Lorentz invariants E^2 - B^2 and E.B are both zero. Then the field strength can be scaled up or down by choice of observer, and in particular, can be made arbitrarily small. Since no pair creation will be seen in this latter case, and since the existence of pair creation is an invariant fact, there will be no pair creation for any value of field strength. This is the situation in an electromagnetic plane wave. Any attempt to induce pair creation with a high power laser must necessarily use a focused beam, not only to increase the power density at the focus, but also to create a superposition of plane waves in different directions so as to violate E^2 - B^2 = E.B = 0. -- Gene From: Warren D Smith <warren.wds@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Tuesday, June 2, 2015 10:22 AM Subject: [math-fun] Are magnetars baloney? What is the maximum allowed magnetic field? If a volume of vacuum contains a magnetic field B greater than m_e c^2 / mu_e = 8.82x10^9 tesla (here mu_e is magnetic moment of electron) then it becomes energetically advantageous for the vacuum to break down spontaneously, creating electron-positron pairs, because the energy mu_e B is enough to pay for the energy m_e c^2. Note due to angular momentum and charge conservation the e+e- pair have opposite spins, and opposite charges, which means they have aligned magnetic moments. I conclude it should be impossible to sustain any magnetic field larger than this, in vacuum, for longer than about 10^(-16) seconds. OK, sounds straightforward enough. BUT, (1) I have not seen this "maximum magnetic field" discussed before. (Although the analogous "maximum electric field" is often discussed, it is sometimes called the "Schwinger limit" http://en.wikipedia.org/wiki/Schwinger_limit and has value of order 1.3*10^18 volts/meter. ) (2) http://www.physics.mcgill.ca/~pulsar/magnetar/main.html claims that the "magnetar" (very magnetic type of neutron star) "SGR 1806-20" has a surface magnetic field of about 23 times my upper bound, namely 2*10^11 tesla. There are also are two other magnetars listed with claimed surface magnetic fields each about 8 times my upper bound. Contradiction. I conclude that either there is some reason I do not understand for why magnetic fields much larger than my upper bound can exist for 10000 years -- or -- the magnetar astronomers are pressurized with excrement. Or both. I have looked into this and essentially all the claimed evidence over the last 25 years for the huge magnetic fields around magnetars is based on Maxwell's equations. Maxwell equations, are, however, simply wrong when the fields are this large. (The Euler-Kockel nonlinear equations are less wrong, but probably still very inadequate.) Therefore, everything, ever, that the magnetar astronomers said about these huge fields, is suspect. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step) _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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