Aiming towards a geometric description of quantum theory, we study the coherent states-induced metric on the phase space, which provides a geometric formulation of the Heisenberg uncertainty ...relations (both the position–momentum and the time–energy ones). The metric also distinguishes the original uncertainty relations of Heisenberg from the ones that are obtained from non-commutativity of operators. Conversely, the uncertainty relations can be written in terms of this metric only, hence they can be formulated for any physical system, including ones with non-trivial phase space. Moreover, the metric is a key ingredient of the probability structure of continuous-time histories on phase space. This fact allows a simple new proof the impossibility of the physical manifestation of the quantum Zeno and anti-Zeno paradoxes. Finally, we construct the coherent states for a spinless relativistic particle, as a non-trivial example by which we demonstrate our results.
We show that, when we study the coexistence of general relativity with thermodynamics, some physical properties that are usually thought of as holographic and lying in the domain of quantum gravity ...can actually be accessed even at the classical level. In particular, we demonstrate that the thermodynamics of gravitating systems in equilibrium is fully specified by variables defined on the system's boundary, namely, the boundary's geometry and extrinsic curvature. Hence, information is non-trivially incorporated in boundary variables because of the structure (the symmetries) of the classical gravity theory, without any input from quantum theory (such as black hole entropy).
This is a comment on articles Phys. Rev. Lett. 119, 240401 (2017) arXiv:1707.06050 and Phys. Rev. Lett. 119, 240402 (2017) arXiv:1707.06036. We argue that gravity-induced entanglement by Newtonian ...forces is agnostic to the quantum or classical nature of the gravitational true degrees of freedom.
New J. Phys. 16, 085007 (2014 ) We examine the origin of the Newton-Schr\"odinger equations (NSEs) that play
an important role in alternative quantum theories (AQT), macroscopic quantum
mechanics and ...gravity-induced decoherence. We show that NSEs for individual
particles do not follow from general relativity (GR) plus quantum field theory
(QFT). Contrary to what is commonly assumed, the NSEs are not the weak-field
(WF), non-relativistic (NR) limit of the semi-classical Einstein equation (SCE)
(this nomenclature is preferred over the `M\/oller-Rosenfeld equation') based
on GR+QFT. The wave-function in the NSEs makes sense only as that for a mean
field describing a system of $N$ particles as $N \rightarrow \infty$, not that
of a single or finite many particles. From GR+QFT the gravitational
self-interaction leads to mass renormalization, not to a non-linear term in the
evolution equations of some AQTs. The WF-NR limit of the gravitational
interaction in GR+QFT involves no dynamics. To see the contrast, we give a
derivation of the equation (i) governing the many-body wave function from
GR+QFT and (ii) for the non-relativistic limit of quantum electrodynamics
(QED). They have the same structure, being linear, and very different from
NSEs. Adding to this our earlier consideration that for gravitational
decoherence the master equations based on GR+QFT lead to decoherence in the
energy basis and not in the position basis, despite some AQTs desiring it for
the `collapse of the wave function', we conclude that the origins and
consequences of NSEs are very different, and should be clearly demarcated from
those of the SCE equation, the only legitimate representative of semiclassical
gravity, based on GR+QFT.
In this note we show that Newton-Schr\"odinger Equations (NSEs)
arXiv:1210.0457 and references therein do not follow from general relativity
(GR) and quantum field theory (QFT) by way of two ...considerations: 1) Taking the
nonrelativistic limit of the semiclassical Einstein equation, the central
equation of relativistic semiclassical gravity, a fully covariant theory based
on GR+QFT with self-consistent backreaction of quantum matter on the spacetime
dynamics; 2) Working out a model see C. Anastopoulos and B. L. Hu, Class.
Quant. Grav. 30, 165007 (2013), arXiv:1305.5231 with a matter scalar field
interacting with weak gravity, in procedures analogous to the derivation of the
nonrelativistic limit of quantum electrodynamics. We conclude that the coupling
of classical gravity with quantum matter can only be via mean fields, there are
no $N$-particle NSEs and theories based on Newton-Schr\"odinger equations
assume unknown physics.
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