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3

I see this as a partial trace on the $\psi$ space, that is : Let $H$ be the hamiltonian applying on the $(\psi, \chi)$ space, and $H_{eff}$ the reduced hamiltonian applying on the $\chi$ space. Take some density matrix $\rho$ applying on the $\psi$ space. Then : $H_{eff} = Tr_\psi(\rho H)$ Here one is taking $\rho = \int d^3p f(E_p) |\psi(p,s)\rangle ... 1 This looks to me like essentially a mean-field approximation. One is replacing$\psi$with its expectation, so one is treating$\psi$classically and$\chi$quantumly. The back-action of$\chi$on$\psi$is ignored. 1 That is only true if you take a rough look at the number of neutrinos. Actually, a small difference is found when comparing the number of neutrinos during the night (going through the earth) and the day (without having to cross the earth). This difference is mainly due to the high sensitivity of the detectors on electron neutrinos. When interacting with ... 0 As an ex-theoretical chemist, not claiming any expertise in this field: Even though mass-energy of near light-speed neutrinos, individually, might still be very-very small, there are likely to be many-many more of them (~10^9?) than electrons (used in another answer, above, to make a comparison). Can we therefore make a back-of-the-envelope estimate of the ... 5 So let's say these electrons go really really fast like 0.999999997 times the speed of light. We know the upper bound on the neutrino mass is less than 1 eV (the kinetic energy of taking one electron through a one volt potential difference) from experiments. So if we plug in to find the total energy of the neutrino we find.$$E_{relativistic} = \gamma ... 1 The OPERA experiment reported: the speed of neutrinos is consistent with the speed of light within the margin of error The margin of error was around$3 \times 10^{-6}c$, so their result restricted the speed of the neutrinos to be at least$0.999997c$and less than$1.000003c$. For comparison, the speed of the protons in the LHC is$0.999999991 c\$, so ...

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They do not actually travel at the speed of light. Instead, they travel at speeds extremely close to the speed of light.

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the would-be superluminal neutrino speed [...] The relevant comparison is between the arrival of neutrinos at a suitable detector, e.g. regarding neutrinos which had been travelling from CERN to LNGS; and the (first possible) detection of the corresponding "signal front", e.g. regarding signals due to any one neutrino bunch having been released at ...

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