Path integrals, spontaneous localisation, and the classical limit. (arXiv:1808.04178v3 [quant-ph] UPDATED)
We recall that in order to obtain the classical limit of quantum mechanics one needs to take the $\hbar\rightarrow 0$ limit. In addition, one also needs an explanation for the absence of macroscopic quantum superposition of position states. One possible explanation for the latter is the Ghirardi-Rimini-Weber (GRW) model of spontaneous localisation. Here we describe how spontaneous localisation modifies the path integral formulation of density matrix evolution in quantum mechanics. (Such a formulation has been derived earlier by Pearle and Soucek; we provide two new derivations of their result). We then show how the von Neumann equation and the Liouville equation for the density matrix arise in the quantum and classical limit, respectively, from the GRW path integral. Thus we provide a rigorous demonstration of the quantum to classical transition.
Effective gravity and effective quantum equations in a system inspired by walking droplets experiments. (arXiv:1706.05640v2 [physics.class-ph] UPDATED)
Authors: Christian Borghesi
In this paper we suggest a macroscopic toy system in which a potential-like energy is generated by a non-uniform pulsation of the medium (i.e. pulsation of transverse standing oscillations that the elastic medium of the system tends to support at each point). This system is inspired by walking droplets experiments with submerged barriers. We first show that a Poincar\’e-Lorentz covariant formalization of the system causes inconsistency and contradiction. The contradiction is solved by using a general covariant formulation and by assuming a relation between the metric associated with the elastic medium and the pulsation of the medium. (Calculations are performed in a Newtonian-like metric, constant in time). We find ($i$) an effective Schr\”odinger equation with external potential, ($ii$) an effective de Broglie-Bohm guidance formula and ($iii$) an energy of the `particle’ which has a direct counterpart in general relativity as well as in quantum mechanics. We analyze the wave and the `particle’ in an effective free fall and with a harmonic potential. This potential-like energy is an effective gravitational potential, rooted in the pulsation of the medium at each point. The latter, also conceivable as a natural clock, makes easy to understand why proper time varies from place to place.
In a joint paper Jeff Bub and Itamar Pitowski argued that the quantum state represents `the credence function of a rational agent […] who is updating probabilities on the basis of events that occur’. In the famous thought experiment designed by Wigner, Wigner’s friend performs a measurement in an isolated laboratory which in turn is measured by Wigner. Here we consider Wigner’s friend as a rational agent and ask what her `credence function’ is. We find experimental situations in which the friend can convince herself that updating the probabilities on the basis of events that happen solely inside her laboratory is not rational and that conditioning needs to be extended to the information that is available outside of her laboratory. Since the latter can be transmitted into her laboratory, we conclude that the friend is entitled to employ Wigner’s perspective on quantum theory when making predictions about the measurements performed on the entire laboratory, in addition to her own perspective, when making predictions about the measurements performed inside the laboratory.
Author(s): Saronath Halder, Manik Banik, Sristy Agrawal, and Somshubhro Bandyopadhyay
Quantum nonlocality is usually associated with entangled states by their violations of Bell-type inequalities. However, even unentangled systems, whose parts may have been prepared separately, can show nonlocal properties. In particular, a set of product states is said to exhibit “quantum nonlocalit…
[Phys. Rev. Lett. 122, 040403] Published Fri Feb 01, 2019
More than a century after the birth of quantum mechanics, physicists and philosophers are still debating what a “measurement” really means.
Can quantum ideas explain chemistry’s greatest icon?
Can quantum ideas explain chemistry’s greatest icon?, Published online: 30 January 2019; doi:10.1038/d41586-019-00286-8
Simplistic assumptions about the periodic table lead us astray, warns Eric Scerri.
The term ‘locality’ is used in different contexts with different meanings. There have been claims that relational quantum mechanics is local, but it is not clear then how it accounts for the effects that go under the usual name of quantum non-locality. The present article shows that the failure of ‘locality’ in the sense of Bell, once interpreted in the relational framework, reduces to the existence of a common cause in an indeterministic context. In particular, there is no need to appeal to a mysterious space-like influence to understand it.
Gao (Synthese, 2017. http://dx.doi.org/10.1007/s11229-017-1476-y) presents a new mentalistic reformulation of the well-known measurement problem affecting the standard formulation of quantum mechanics. According to this author, it is essentially a determinate-experience problem, namely a problem about the compatibility between the linearity of the Schrödinger’s equation, the fundamental law of quantum theory, and definite experiences perceived by conscious observers. In this essay I aim to clarify (i) that the well-known measurement problem is a mathematical consequence of quantum theory’s formalism, and that (ii) its mentalistic variant does not grasp the relevant causes which are responsible for this puzzling issue. The first part of this paper will be concluded claiming that the “physical” formulation of the measurement problem cannot be reduced to its mentalistic version. In the second part of this work it will be shown that, contrary to the case of quantum mechanics, Bohmian mechanics and GRW theories provide clear explanations of the physical processes responsible for the definite localization of macroscopic objects and, consequently, for well-defined perceptions of measurement outcomes by conscious observers. More precisely, the macro-objectification of states of experimental devices is obtained exclusively in virtue of their clear ontologies and dynamical laws without any intervention of human observers. Hence, it will be argued that in these theoretical frameworks the measurement problem and the determinate-experience problem are logically distinct issues.