Evert Willem Beth's The foundations of mathematics: A study in the philosophy of PDF

By Evert Willem Beth

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Extra info for The foundations of mathematics: A study in the philosophy of science

Sample text

The paradox is now resolved by examining the 'rhmr",ss needle in the mirror world (E). Because of the mirror reflecl,ion, electrons in that compass needle are spinning anti clockwise when viewed above, as the artist had indicated in Figure F. Thus, in the mirror world, the pail1led while would actually be the north end. un"tl'" markings into taking the north end as the south end! In other words, the last sentence of the preceding paragraph, the word "south" should be replaced by "north," The physicist in the min'or sees the north end of the comneedle swinging to his rigiu.

S j ~-. 35 SYMMETRY AND DESiGN ••••••• :::. ,: community, a favorite tells of Pauli, after his death, asking God to reveal His design (a standard fantasy among physicists). " In 1933, Pauli suggested that a hitherto unknown particle, which interacts neither strongly nor electromagnetically and thus would escape detection, carries away thelruSSing energy, like a black-clad thief disappearing into th6Jijgiit:l~ mysterious particle, later to be given the Italian name "neutrino," was the first particle predicted to exist before it was actually discovered.

To an observer mov-, ing eastward faster than the particle, the particle would appear to be moving westward. Since handedness describes how the spin direction is aligned with the direction of motion, that observer would disagree with us on the handedness of the particle. In contrast, a massless particle, such as the neutrino, always moves at the speed of light-the maximum speed possible, according to Einstein's theory of relativity. Since no observer can move faster than a massless particle, its handedness is an intrinsic property.

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