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Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields

Gravitation and quantum mechanics of macroscopic objects

F. Károlyházy

Published Mar 1, 1966• 530 citations
Publisher
DOI
10.1007/bf02717926

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Oxford University Press eBooks•Mar 5, 2020•0 citations
We should try to establish the Schr ö dinger equation for gravitational potential energy and use it to describe macroscopic objects. Replacing the electromagnetic potential energy in the Hamiltonian operator with gravitational potential energy can achieve the goal. The successful application of the Schr ö dinger equation for gravitational potential energy can change many existing concepts in quantum mechanics and shake the conceptual system of quantum mechanics. This can promote the development of quantum mechanics and other fields of physics.
From the fact of observation of squeezed light follows the possibility of a nonperturbing or nondemolition measurement (observation) of a single microscopic object in a widely distributed quantum-mechanical state. Macroscopic bodies—objects of classical mechanics—are usually found in states with narrow wave packets, although quantum mechanics does not forbid them to be in states with wide wave packets. The absence of macroscopic bodies in such states requires explanation. In this article it is shown that in virtue of a special, geometrical nature of the gravitational field the absence in nature of macroscopic bodies in widely distributed states can be due to the focusing action of the self-gravitational field of a macroscopic body on its wave packet. Thus, the gravitational field can play an important role in the relaxation of the classical limit of quantum mechanics.
The quantum measurement process connects the quantum world and the classical world. The phrase ‘quantum measurement’ can have two meanings: measurement of a weak classical force, with the impact of quatum fluctuations on the measurement sensitivity, and the quantum mechanics of macroscopic objects: to try to prepare, manipulate and characterize the quantum state of a macroscopic quantum object through quantum measurement. Quantum noise leads to the Standard Quantum Limit (SQL), which provides the magnitude in which we must consider both measurement precision and measurement-induced back-action. The beginning of the chapter will be devoted to this thread of thought. The free-mass SQL actually provides a benchmark for the ‘quantum-ness’ of the system. We will show that a sub-SQL device can be used to prepare nearly pure quantum states and mechanical entanglement, as well as non-Gaussian quantum states that have no classical counterparts.