Proofs that avoid using any relativistic quantum field theory mechanism have defects. Many such proofs rely on a claim that | ψ ψ ( α α 1 , α α 2 , α α 3 , . . . ) | 2 = | P ^ ^ ψ ψ ( α α 1 , α α 2 , α α 3 , . . . ) | 2 where the operator P ^ ^ permutes the coordinates. However, the value on the left-hand-side represents the probability of particle 1 at r 1 , particle 2 at r 2 , and so on, and is thus quantum mechanically invalid for indistinguishable particles.