CPT: The ‘Intuitive’ Approach

Khriplovich and Lamoreaux (1997, §2) suggest a very interesting argument that CPT provides the correct notion of “complete reversal” in physics.

The background assumption is that “complete reversal” should have effect of reversing the sign of 4-vectors in spacetime. David Malament, for example, has suggested that time reversal in classical electrodynamics should have this effect on timelike vectors. The proposal here is that “complete” motion reversal to have this effect on all vectors (timelike, spacelike, and null).

Clearly, time reversal T on its own is not enough for this — it doesn’t reverse spacelike vectors. Parity reversal P isn’t either — it doesn’t reverse timelike vectors.

What about PT? After all, flipping about two axes is equivalent to a rotation. Shouldn’t that be enough to reverse all four vectors? As it turns out, it’s not enough, at least when it comes to 4-current ja. Since both P and T fix charge density and reverse current, we have:

PT ja = PT (p, j) = P (p, -j) = (p, j).

To reverse current, we need an operator C that sends particles to antiparticles, and thus sending ja to -ja. Thus, to get “total” motion reversal in a world with current, we need the CPT operator.

What I like about this thinking is that it depends crucially on the kind of matter fields in play. It’s only in the presence of 4-currents that PT is not enough to completely reverse motion. But similarly, the discovery of additional exotic matter fields might someday imply that CPT is not enough to reverse motion, either.

Update: Wolfgang reports news about evidence for CPT-violation in a recent Fermilab experiment.

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8 thoughts on “CPT: The ‘Intuitive’ Approach

  1. wolfgang

    I always wonder what is so special about the electromagnetic interaction that its charge shows up in such a fundamental operation like CPT.
    (Why not change the coloring of quarks?)

  2. Bryan

    Actually I think the E&M charge isn’t special. All charges get reversed by C, including color. That’s why the operation is equivalent to exchanging particles with antiparticles.

  3. Bryan

    The quantum numbers that do seem special to me are mass and spin. Both are the charges corresponding to a conserved current. But neither are reversed by C. Why?

    Interestingly, these are exactly the quantum numbers arising from the irreducible representations of the homogeneous Poincaré group. Does that have anything to do with it? I’m not sure…

  4. wolfgang

    >> All charges get reversed by C
    you are right.

    mass is the only special ‘charge’, but mass is obviously a special case…