Interference and Oscillation in Nambu Quantum Mechanics

Abstract

Nambu Quantum Mechanics, proposed in Phys. Lett. B536, 305 (2002), is a deformation of canonical Quantum Mechanics in which only the time-evolution of the "phases" of energy eigenstates is modified. We discuss the effect this theory will have on oscillation phenomena, and place a bound on the deformation parameters utilizing the data on the atmospheric neutrino mixing angle θ23.

Neutrino Oscillations at JUNO, the Born Rule, and Sorkin's Triple Path Interference

“…We close discussion by recalling that neutrinos can also probe the Leggett-Garg inequalities [19,20], spontaneous collapse models of quantum measurement [21,22], non-standard time-evolution of quantum states [24], and, if Mössbauer neutrinos can be realized, the time-energy uncertainty relation [26]. Further studies will indubitably lead to other ways to utilize neutrinos for foundational QM studies.…”

“…In essence, Nambu QM generalizes the space in which the "phase" (in the sense of the "phase" of a complex number) of a state is allowed to evolve, leading to non-canonical time evolution as well as non-canonical double-path interference. Indeed, we have recently discussed how the vanilla version of the theory can be constrained using atmospheric neutrinos by looking at interference effects [24]. Given the larger freedom that the "phase" is allowed in Nambu QM, we envision generalizations (most probably a non-associative one) in which the triple-path interference and the departure from the Born rule could be precisely modeled.…”

“…[21,22] investigate whether neutrino oscillations can constrain the Continuous Spontaneous Localization model [23] (expected effect is too small to be observed), while Ref. [24] argues that atmospheric neutrino data can constrain Nambu QM extensions [25]. The possibility of utilizing Mössbauer neutrinos to probe the time-energy uncertainty relation has been discussed in Ref.…”

Triple Interference, Non-linear Talbot Effect and Gravitization of the Quantum

“…The fundamental insight is that in the context of gravitizaton of quantum theory, the expression for the probability is generalized from a quadratic expression to a locally (in the space of states, not in spacetime!) quadratic expression, which gravitizes the Born rule (in the manner the local spacetime Minkowski metric is gravitized to a general pseudo-Riemannian metric in general relativity) [17][18][19][20][21]. Furthermore, in order to have such a generalized expression for the Born rule, one needs to generalize the very kinematics of quantum gravity.…”

“…In [1,2] we proposed one such possibility by extending the dynamical aspects of general covariance, that is, the statement that all quantities in our physical theories must be dynamical, to usually fixed quantum mechanical structures. This approach was inspired by our previous work on metastring theory [3][4][5][6][7][8][9][10][11][12][13] and its various ramifications [14][15][16] as well as work on the geometric aspects of quantum foundations 6 [17][18][19][20][21].…”