Quantum Mechanics from Ergodic Average of Microstates
Abstract
We formulate quantum mechanics as an effective theory of an underlying structure characterized by microstates ${\mathcal M}^j(t)\rangle$, each one defined by the quantum state $\Psi(t)\rangle$ and a complete set of commutative observables $O^j$. At any time $t$, ${\mathcal M}^j(t)\rangle$ corresponds to a state $O^j_k\rangle$, for some $k$ depending on $t$, and jumps after time intervals whose duration, of the order of the Compton time $\tau$, is proportional to the probability $\langle O_k^j\Psi(t)\rangle^2$. This reproduces the Born rule and mimics the waveparticle duality. The theory is based on a partition of time whose flow is characterized by quantum probabilities. Ergodicity arises at ordinary quantum scales with the expectation values corresponding to time averaging over a period $\tau$. The measurement of $O^j$ provides a new partition of time and the outcome is the state $O_k^j\rangle$ to which ${\mathcal M}^j(t)\rangle$ corresponds at that time. The formulation, that shares some features with the path integral, can be tested by experiments involving time intervals of order $\tau$.
 Publication:

arXiv eprints
 Pub Date:
 October 2017
 DOI:
 10.48550/arXiv.1710.08419
 arXiv:
 arXiv:1710.08419
 Bibcode:
 2017arXiv171008419M
 Keywords:

 Quantum Physics;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 4 pages