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The IUP Journal of Physics :
Equality and Identity and (In)distinguishability in Classical and Quantum Mechanics from the Point of View of Newtons Notion of State
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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they are equal to another, if both are equal to a third body or particle (Helmholtz, 1903).Newton’s notion of state was superseded by Laplace’s notion for the sake of comprising the motion in phase space.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Newton’s notion of state was superseded by Laplace’s notion for the sake of comprising the motion in phase space.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;

 
 
 

Equality and Identity and (In)distinguishability in Classical and Quantum Mechanics, classical point mechanics, elementary dynamical’ framework, classical bodies, Newtonian state functions, classical and quantum distribution laws, quantum harmonic oscillator, Pauli’s exclusion principle.