Of course, trying to tell a particle physicist that the Dirac equation is wrong is about as effective as trying to tell Putin he is wrong. Neither can be done without first making time go backwards.

]]>The reason for introducing this inconsistency is the experimental fact that anti-particles have positive mass and positive energy, combined with the theoretical consequence of the Dirac equation that anti-particles travel backwards in time. Now no-one seems to have drawn the obvious conclusion from this, that the Dirac Equation is inconsistent with the Second Law of Thermodynamics. This isn’t something you can investigate experimentally, but it is definitely a red flag as far as theory is concerned. The vast amount of experimental support for the Dirac equation does not have anything at all to say about its contradiction with the Second Law of Thermodynamics, which has far more experimental support than the Dirac equation.

The only possible conclusion from this is that the Dirac equation is only an approximation, and is only valid in circumstances in which the spacetime scale is so small that the statistical consequences of the Second Law of Thermodynamics cannot be detected. Even then, it can only be approximate, because the Second Law of Thermodynamics must ultimately arise as a consequence of the quantum effects that arise from the Dirac equation via the standard model of particle physics.

So how do we resolve this? It has been known for a long time that the two versions of time-reversal (i.e. with or without energy reversal) can be identified as T and CT in some order. The literature seems to be quite inconsistent as to which is which, however. It really depends on whether you regard spacetime as more fundamental than 4-momentum, or vice versa. To put it another way, the usual convention in classical physics is inconsistent with the usual convention in quantum physics. It doesn’t really matter which convention is adopted, but consistency is essential.

And I can’t emphasise enough that the Dirac Equation is inconsistent with the Second Law of Thermodynamics. There is no experiment that tests the two against each other. The experiments that support the Dirac Equation do not touch the Second Law of Thermodynamics, and the experiments that support the Second Law of Thermodynamics do not touch the Dirac Equation. Therefore we have nothing to fall back on except common sense. Common sense tells us that the Second Law of Thermodynamics is correct, because it recognises that time goes forwards and not backwards, and that the Dirac Equation is incorrect, because it says that there is no difference between time going forward and time going backward.

]]>Perhaps more idiomatic would be “sum neque cogito”, although the possibilities of “cogito neque sum” are intriguing.

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