t'Hooft claims that all elementary particles must be point particles that they cannot be extended deformable objects.

The identity of all particles of the same type is in the quantum statistics of the permutation group. For example the Pauli exclusion principle for electrons that N-electron wave functions are totally antisymmetric in all quantum numbers - a column in the Young diagram notation for irreducible representations of the permutation group. This is in 3+1 spacetime. Anyons in 2+1 spacetime with fractional quantum statistics and fractional angular momenta and charges are modifications that do not change my objection to t'Hooft's above qualitative "informal language" argument.

My point is especially clear in Bohm's pilot wave-hidden variable interpretation. It is less clear in other interpretations.

The identity of elementary particles is a property of the BIT pilot wave or "quantum potential" Q for particles and "super potential" for fields. The actual hidden variable i.e. Newton's "hard massy ball" perhaps an actual string, or brane, or tiny black hole or tiny wormhole in Salam's strong short-range gravity, need not be a rigid extended object at all. It can support all sorts of modes of vibration like a classical object and still not affect the permutation symmetry of identical particles. Therefore, I say that t'Hooft has made an error in his above qualitative heuristic informal argument.

Truly elementary particles can be extended deformable objects consistent with c as the maximal material signal speed. That will not affect their quantum statistics - certainly not in the Bohm pilot wave interpretation where the hidden variables need not be point particles in space.

## Sunday, May 06, 2007

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