Planck length challenges non-relativistic quantum mechanics of large masses

Abstract

With the simplest proof ever, we justify the significance of quantum-gravity in non-relativistic quantum mechanics together with the related theories and experiments. Since the de Broglie wave length is inverse proportional to the mass, it would descend towards and below the Planck scale 10^{-33} cm for large masses even at slow non-relativistic motion. The tricky relationship between gravity and quantum mechanics ---well-known in the relativistic case--- shows up in non-relativistic motion of massive objects. Hence the gravity-related modification of their Schrödinger equation is m a n d a t o r y. We also recall the option of an autonomous Newtonian quantum-gravity, a theory parametrized by hbar and G. On cancellation of c from the Newtonian limit of Planck scale metric fluctuations is given a new hint.

5pp,based on invited talk at nineth International Workshop DICE2018 (Castello Pasquini/Castiglioncello/Tuscany, Sept. 17-21, 2018)

References in corpus (3)

• Gravitational Decoherence
• Principle of least decoherence for Newtonian semi-classical gravity
• Fundamental Irreversibility: Planckian or Schrödinger-Newton?

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• Series solution of the time-dependent Schrödinger-Newton equations in the presence of dark energy via the Adomian Decomposition Method
• Attraction Induced by Mutual Quantum Measurements of Velocity