Principle of least decoherence for Newtonian semiclassical gravity

Abstract

Recent works have proved that semi-classical theories of gravity needed not be fundamentally inconsistent, at least in the Newtonian regime. Using the machinery of continuous measurement theory and feedback, it was shown that one could construct well behaved models of hybrid quantumclassical dynamics at the price of an imposed (non unique) decoherence structure. We introduce a principle of least decoherence (PLD) which allows to naturally single out a unique model from all the available options; up to some unspecified short distance regularization scale. Interestingly, the resulting model is found to coincide with the old -erstwhile only heuristically motivated-proposal of Penrose and one of us for gravity-related spontaneous decoherence and collapse. Finally, this letter suggests that it is in the submillimeter behavior of gravity that new phenomena might be found.Gluing gravity and quantum mechanics in a unified theory has proved to be a discouragingly difficult task. Most efforts have so far been focused on constructing a quantum theory of gravity [1] but the very nature of the gravitational force -classical or quantum-remains unknown. Whereas distinguishing different approaches to quantum gravity might for long remain out of experimental reach, pining down the classical or quantum character of gravity may be doable at low energy. To distinguish a quantum and classical gravitational force, one needs a candidate classical theory. In the Newtonian limit, the standard approach has been to consider the Schrödinger-Newton (SN) equation [2,3], the low energy limit of the fundamentally semi-classical gravity of Møller and Rosenfeld [4,5], as a paradigmatic example. However, the latter is plagued by conceptual complications requiring one to drop, at the very least, the statistical interpretation of quantum states of matter. Interestingly, these foundational problems of SN are not related to relativity but, rather, to the difficulties in constructing consistent hybrid quantum-classical dynamics, a fact that has often been seen as a conclusive proof of the need for quantum gravity [6]. Yet, SN is only one (rather naive) approach: we shall discuss below an alternative while other options [7,8] are available.The conceptual difficulties of hybrid quantum-classical coupling can be solved, without full quantization, provided fluctuations are added to the classical variables [9,10]. The loss of unitarity can then be seen as the necessary price of semi-classical coexistence. For gravity in the Newtonian limit, it means adding a noise term δΦ to the Newtonian potential Φ. These fluctuations are not to be derived from quantum theory (as is e.g. the case in stochastic gravity [11,12]) but are typically posited from heuristic considerations and required to be minimum so long as the hybrid classical-quantum coupling remains consistent. Historically, such considerations [13][14][15] were instrumental in the construction of models of gravityrelated decoherence and collapse [16][17][18][19][20][21][22]. The latter used Gaussian fluct...

Does gravity have to be quantized? Lessons from non-relativistic toy models

“…Should we pick yet anoter kernel? Following [7], we may want to find a principle allowing us to single out one kernel. A natural principle is to ask that the total decoherence induced by the model be minimal.…”

Spontaneous Wave Function Collapse with Frame Dragging and Induced Gravity

“…which is highly singular due to the idealized Markovian model, and its interpretation is non-trivial if possible at all. level proposals like the semiclassical [15,16], the Bohmian [17,18], or the stochastic semiclassical [13,14] couplings.…”

“…The intrinsic -non-dynamical-combination between SC and gravity has been basic for the DP-model from its conception [10,11]. Much later, this has been shown to be the unique combination of SC and semiclassical gravity that eliminates the essential nonlinearity of semiclassical gravity [13,14]. But the derivation of an emergent Newtonian gravity from SC lacked the sufficient inspiration.…”

“…Selected features of the SSE (12) -with definitions (13,14), andĤ = 1 2p 2 /M)-are derived below. 3 Instances of anomalies, fake action-at-a-distance among others, assume an entangled composite system AB of remote parts A and B, and standard collapse in B where B can be a single "massless" spin-half system.…”

Fundamental Irreversibility: Planckian or Schrödinger–Newton?

“…Penrose discussed the fundamental conflict between general relativity and quantization. To resolve it, heuristically at least, he also found the necessity of space-time's fundamental blurriness, guessed it non-relativistically and determined its equivalent with expression (6) up to a factor of 2 (a discrepancy which has recently been resolved by [16]). …”