The C, P and T symmetries of classical electromagnetism are quite clear: C negates the charge, P negates one or all three directions in space, and T reverses the direction of time. It is also clear that none of these symmetries can be realised in practice: C converts electrons, of which there are zillions everywhere, into positrons, which scarcely ever exist in the real world; P converts the real world into the looking-glass world, which as Lewis Carroll reminds us, is a figment of our imagination; and T causes time to go backwards, which, as we know, does not happen.

On the other hand, the combinations of any two of C, P and T are symmetries of classical physics, including electromagnetism: CP means that if you reverse a current, you reverse the poles of the electromagnet that the current creates. CT and PT both mean essentially the same thing, from a slightly different philosophical point of view, but with the same mathematical result. Therefore the combination of all three, CPT, is *not* a symmetry of classical physics. Please take careful note of this, I will test you on it later: CPT is NOT a symmetry of classical physics.

Now let us turn our attention to quantum mechanics. In quantum mechanics, there is a theorem called the CPT theorem, which says that CPT *is* a symmetry of quantum mechanics. Ergo, quantum physics is inconsistent with classical physics. Ergo, it is not possible to derive classical physics as a limiting case of quantum physics. Ergo, the measurement problem has no solution. Ergo, the search for a theory of everything is a pointless waste of time. Ergo, why are we wasting so much money on this problem?

I prefer to argue from a realist position, not from a mathematicist position, and take as an axiom the obvious fact that quantum mechanics *is* consistent with classical physics. If this axiom is false, then the universe could not exist. The universe does exist, ergo this axiom is correct. Ergo, the CPT theorem is false. Ergo, at least one of its assumptions is false. Now let us ask, which one of the CPT theorem’s hidden assumptions is false?

Well, I don’t want to get too technical, but the proof of the CPT theorem involves an “analytic continuation” from a Lorentzian spacetime (required for classical electromagnetism) to a Euclidean spacetime (required for quantum theory). It therefore requires spacetime to be a *complex* 4-space, not a real 4-space. But spacetime, in actual hard physical reality, is real, not complex. This is a clear, and obviously false, hidden assumption.

So, if any physicist cares to argue this with me, I will prove that if the CPT theorem holds, then the universe does not exist. Or, in contrapositive form, I will prove that if the universe exists, then the CPT theorem is false. It then depends whether the physicist is a theorist or an experimentalist: if the former, they will dogmatically assert that the CPT theorem is a correct statement about the universe, and will therefore be forced to deny their own existence and that of the entire universe; if the latter, they will (dogmatically?!) assert that they and the universe do exist, and will then set about designing an experiment to test the CPT theorem to destruction.

October 1, 2022 at 11:55 am |

No doubt you recognise my argument as a variant of the Cartesian “cogito ergo sum”. The mathematicist version here is “non cogito ergo non sum”, which is of course a completely different proposition entirely. In the contrapositive version “sum ergo cogito” it is demonstrably false. More appropriate perhaps would be “sum sed non cogito”, although “sum vel non cogito” is equivalent to the original version of Descartes.

October 1, 2022 at 12:24 pm |

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

October 1, 2022 at 2:15 pm |

I think it was Oscar Wilde who explained, in “The picture of Dorian Gray”, why time doesn’t go backwards. Particle physicists seem to have been brought up instead on the Dr Who model of the universe. Especially the Tardis effect, otherwise known as the “Big Bang” followed by inflation, which makes the universe much bigger on the inside than it is on the outside.

October 1, 2022 at 2:26 pm |

As I have said, electromagnetism is invariant under the CP, CT and PT symmetries. The weak force is invariant under the P, T and PT symmetries. That is with the classical meanings. With the standard quantum mechanical meanings, QED is invariant under CP, T and CPT, while the weak force is invariant under P, CT and CPT. Either way, the strong force is invariant under all of C, P and T, but gravity breaks the PT/CPT symmetry of electroweak theory, so that a unified theory of all the four forces has NO such symmetry at all.

October 3, 2022 at 10:35 pm |

I feel that I haven’t expressed this argument very well, but it is closely related to both the adjacent posts, where I may have expressed things better. It seems that in reality, the C, P and T symmetries are not well-defined in physics. In particular, under the usual conventions (following essentially from the Dirac equation that predicted anti-particles) the T symmetry reverses time, but does not negate energy. This is mathematically inconsistent, because it means that T acts differently on the Lorentz group considered as a symmetry group of spacetime, and on the Lorentz group considered as a symmetry group of 4-momentum.

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.

October 3, 2022 at 10:39 pm |

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.