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Classical mechanics is the safest (if not the ‘only’
safe) ground we physicists can move on.
For this, we will analyze the implications of the fact that
Newton’s notion of state differs
considerably from the contemporary one, for the notions
‘equality’, ‘identity’ and
‘(in)distinguishability’ play a paramount role
in statistics and in quantum mechanics. Newton’s
notion allows for considering them within classical point
mechanics, what frees the discussion
from anthropomorphic elements. Some of Bach’s (1997)
fundamental results will be obtained
within an ‘elementary dynamical’ framework.
Two classical bodies or quantum particles are equal in
given proper ties, if: (i) their
measurement by means of the same measurement method yields
the same value; and
(ii) the arithmetic law applies that they are equal to another,
if both are equal to a third
body or particle (Helmholtz, 1903).Newton’s notion of state was superseded by Laplace’s
notion for the sake of comprising the
motion in phase space. This treatment of equality, identity
and (in)distinguishability shows
that Newton’s notion of state should not be abandoned,
but be exploited in addition
to Laplace’s.
Newton’s notion of state was superseded by Laplace’s notion for the sake of comprising the
motion in phase space. This treatment of equality, identity and (in)distinguishability shows
that Newton’s notion of state should not be abandoned, but be exploited in addition
to Laplace’s. Classical bodies and quantum particles can be treated on equal footing as far as possible;
Non-probabilistic classification of (bodies/particles in) states;
as Newtonian state variable allows for ‘axiomatic’ approaches to gauge invariance
(electrodynamics) and permutation symmetry yielding not only fermions and bosons,
but also anyons);
Distribution functions can be related to energetic spectra and occupation; hence,
they are independent of (in)distinguishability; |
