A Note on the Quantum of Time

Abstract

Quantum mechanics rests on the assumption that time is a classical variable. As such, classical time is assumed to be measurable with infinite accuracy. However, all real clocks are subject to quantum fluctuations, which leads to the existence of a nonzero uncertainty in the time variable. The existence of a quantum of time modifies the Heisenberg evolution equation for observables. In this letter we propose and analyse a generalisation of Heisenberg's equation for observables evolving in real time (the time variable measured by real clocks), that takes the existence of a quantum of time into account. This generalisation of Heisenberg's equation turns out to be a delaydifferential equation.

A Mechanics for the Ricci Flow

“…After setting ϕ = f we appear to have a contradiction, since we have two different flow equations in (17) for just one field f . That there is in fact no contradiction can be seen as follows.…”

“…Specifically [13], when n = 3, a necessary and sufficient condition for conformality is the vanishing of the Cotton tensor; when n ≥ 4, a necessary and sufficient condition for conformality is the vanishing of the Weyl tensor. In what follows we will assume that the corresponding conformality condition is always satisfied as the initial condition for the Ricci flow equations (17). Then, with respect to the initial metric, M admits isothermal coordinates, that we continue to denote by x i and that we will use systematically in what follows.…”

“…That there is in fact no contradiction can be seen as follows. In (17) we have two different flow equations for two independent fields f and ϕ. Equating the latter two fields implies that the two flow equations must reduce to just one. This can be achieved by substituting one of the two flow equations (17) into the remaining one.…”

Semi-Classical Limit and Minimum Decoherence in the Conditional Probability Interpretation of Quantum Mechanics

“…This in turn implies that the system under study will not evolve as SQM predicts. Rather, a Lindblad type equation [8] describes its evolution [4,9],…”

Ricci Flow, Quantum Mechanics and Gravity

“…In this spirit one should also cite [14,15], where it has been speculated that gravity could possibly have a quantum origin. Further interesting topics at the interface of gravity and quantum mechanics are dealt with in [16][17][18][19][20][21][22]; a classical/quantum duality with gravitational side effects has been analyzed in [23][24][25]. Other issues, in principle outside the realm of quantum gravity and concerning quantum mechanics proper, but in fact intimately related, are interpretational problems such as the measurement problem and the collapse of the wavefunction [26].…”