This is a list of this week’s papers on quantum foundations published in the various journals or uploaded to the preprint servers such as arxiv.org and PhilSci Archive.
on 2015-5-15 4:28am GMT
Authors: Aleksey V. Ilyin
It was repeatedly underlined in literature that quantum mechanics cannot be considered a closed theory if the Born rule is postulated rather than derived from the first principles. In this paper the Born postulate is derived from time-reversibility of solutions of quantum equations of motion. The Born postulate is obtained as a solution of simple functional equation that takes into account the properties of probability and time-reversibility of the equation of motion. The form of the equation of motion is not specified, therefore, the result obtained is applicable to any type of reversible quantum equation of motion. In the second part of this article it is emphasized that, due to topological limitations, time-reversibility of quantum equations does not automatically result in reversibility of real physical processes even when a single particle is involved.
on 2015-5-15 4:28am GMT
Authors: Benjamin Yadin, Vlatko Vedral
We suggest that quantum macroscopicity should be quantified in terms of coherence, and propose a set of conditions that should be satisfied by any measure of macroscopic coherence. We show that this enables a rigorous justification of a previously proposed measure of macroscopicity based on the quantum Fisher information, while another measure does not satisfy important monotonicity criteria.
Cosmological Constant, Quantum Measurement, and the Problem of Time. (arXiv:1505.03805v1 [gr-qc])
on 2015-5-15 4:28am GMT
Authors: Shreya Banerjee, Sayantani Bera, Tejinder P. Singh
Three of the big puzzles of theoretical physics are the following: (i) There is apparently no time evolution in the dynamics of quantum general relativity, because the allowed quantum states must obey the Hamiltonian constraint. (ii) During a quantum measurement, the state of the quantum system randomly collapses from being in a linear superposition of the eigenstates of the measured observable, to just one of the eigenstates, in apparent violation of the predictions of the deterministic, linear Schr\”{o}dinger equation. (iii) The observed value of the cosmological constant is exceedingly small, compared to its natural value, creating a serious fine-tuning problem. In this essay we propose a novel idea to show how the three problems help solve each other.
Energy-Time Uncertainty Relations in Quantum Measurements. (arXiv:1505.03707v1 [quant-ph])
on 2015-5-15 4:28am GMT
Authors: Takayuki Miyadera
Quantum measurement is a physical process. A system and an apparatus interact for a certain time period (measurement time). During this interaction, information of an observable is transferred from the system to the apparatus. In this study, we study the amount of energy fluctuation of the apparatus that is required for this physical process to occur. To do so, the interface between the quantum and classical worlds (“Heisenberg cut”) must be carefully chosen so that the quantum side is large enough to autonomously switch on the interaction. At this setting we prove that a trade-off relation (energy-time uncertainty relation) holds between the energy fluctuation of the apparatus and the measurement time. We use this trade-off relation to discuss the spacetime uncertainty relation questioning the operational meaning of the microscopic structure of spacetime. In addition, we derive another trade-off inequality between the measurement time and the strength of interaction between the system and the apparatus. The larger the information carried by an observable to be measured, the stronger restriction the trade-off relations give.
on 2015-5-15 4:28am GMT
Authors: Hans-Thomas Elze
We consider discrete and integer-valued cellular automata (CA). A particular class of which comprises “Hamiltonian CA” with equations of motion that bear similarities to Hamilton’s equations, while they present discrete updating rules. The dynamics is linear, quite similar to unitary evolution described by the Schroedinger equation. This has been essential in our construction of an invertible map between such CA and continuous quantum mechanical models, which incorporate a fundamental discreteness scale. Based on Shannon’s sampling theory, it leads, for example, to a one-to-one relation between quantum mechanical and CA conservation laws. The important issue of linearity of the theory is examined here by incorporating higher-order nonlinearities into the underlying action. These produce inconsistent nonlocal (in time) effects when trying to describe continuously such nonlinear CA. Therefore, in the present framework, only linear CA and local quantum mechanical dynamics are compatible.
A non-dynamical approach for quantum gravity. (arXiv:1505.03719v1 [gr-qc])
on 2015-5-15 4:25am GMT
Authors: Pierre A. Mandrin
This article examines how a quantum gravity concept can be elaborated without assuming any microscopic dynamics. This means that the laws of physics must be derived without assuming any Lagrangian or Hamiltonian to exist on the quantum level. At this level of reasoning, hardly any model-specific assumption should be admitted. Surprisingly, it is possible to recover general relativity and quantum field theory for 3+1 dimensions.
Dark Energy: Reason for the Existence of a Classical Universe?. (arXiv:1505.03672v1 [gr-qc])
on 2015-5-15 4:25am GMT
Authors: Peng Huang, Yue Huang, Miao Li, Nan Li
Dark energy is investigated from the perspective of quantum cosmology. By treating the existence of a classical universe as a constraint, it is found that the normal ordering ambiguity factor q in Wheeler-DeWitt equation tends to take its value on domain (-1, 3). Furthermore, to ensure the existence of a classical universe, there must be dark energy in the universe. It is in this sense we propose that dark energy is the reason for the existence of a classical universe.
[This Week in Science] Tailoring the quantum dynamics of light
on 2015-5-15 12:00am GMT
Author: Jelena Stajic
Short-time quantum propagator and Bohmian trajectories
ScienceDirect Publication: Physics Letters A
on 2015-5-14 4:47pm GMT
Publication date: 6 December 2013
Source:Physics Letters A, Volume 377, Issue 42
Author(s): Maurice de Gosson , Basil Hiley
We begin by giving correct expressions for the short-time action following the work Makri–Miller. We use these estimates to derive an accurate expression modulo Δ t 2 for the quantum propagator and we show that the quantum potential is negligible modulo Δ t 2 for a point source, thus justifying an unfortunately largely ignored observation of Holland made twenty years ago. We finally prove that this implies that the quantum motion is classical for very short times.
The resource theory of informational nonequilibrium in thermodynamics
on 2015-5-14 4:30am GMT
Publication date: Available online 11 May 2015
Source:Physics Reports
Author(s): Gilad Gour , Markus P. Müller , Varun Narasimhachar , Robert W. Spekkens , Nicole Yunger Halpern
We review recent work on the foundations of thermodynamics in the light of quantum information theory. We adopt a resource-theoretic perspective, wherein thermodynamics is formulated as a theory of what agents can achieve under a particular restriction, namely, that the only state preparations and transformations that they can implement for free are those that are thermal at some fixed temperature. States that are out of thermal equilibrium are the resources. We consider the special case of this theory wherein all systems have trivial Hamiltonians (that is, all of their energy levels are degenerate). In this case, the only free operations are those that add noise to the system (or implement a reversible evolution) and the only nonequilibrium states are states of informational nonequilibrium, that is, states that deviate from the maximally mixed state. The degree of this deviation we call the state’snonuniformity; it is the resource of interest here, the fuel that is consumed, for instance, in an erasure operation. We consider the different types of state conversion: exact and approximate, single-shot and asymptotic, catalytic and noncatalytic. In each case, we present the necessary and sufficient conditions for the conversion to be possible for any pair of states, emphasizing a geometrical representation of the conditions in terms of Lorenz curves. We also review the problem of quantifying the nonuniformity of a state, in particular through the use of generalized entropies, and that of quantifying the gap between the nonuniformity one must expend to achieve a single-shot state preparation or state conversion and the nonuniformity one can extract in the reverse operation. Quantum state conversion problems in this resource theory can be shown to be always reducible to their classical counterparts, so that there are no inherently quantum-mechanical features arising in such problems. This body of work also demonstrates that the standard formulation of the second law of thermodynamics is inadequate as a criterion for deciding whether or not a given state transition is possible.
Microscopy: Quantum control of free electrons
Nature – Issue – nature.com science feeds
on 2015-5-13 12:00am GMT
Microscopy: Quantum control of free electrons
Nature 521, 7551 (2015). doi:10.1038/521166a
Authors: Mathieu Kociak
Optical pulses have previously been used to place the electrons in the beam of an electron microscope into well-defined energy states. These electrons can now be put in a quantum superposition of those states. See Letter p.200
Latest Results for Foundations of Physics
on 2015-5-13 12:00am GMT
on 2015-5-12 2:05am GMT
Authors: Xiao-Dong Yu, Yan-Qing Guo, D. M. Tong
Quantum contextuality is one of the fundamental notions in quantum mechanics. Proofs of Kochen-Specker theorem and noncontextuality inequalities are two means for revealing the contextuality phenomenon in quantum mechanics. It has been found that some proofs of Kochen-Specker theorem, such as those based on rays, can be converted to a state-independent noncontextuality inequality, but it remains open whether it is true in general, i.e., whether any proof of Kochen-Specker theorem can always be converted to a noncontextuality inequality. In this paper, we address this issue. We prove that all kinds of proofs of Kochen-Specker theorem, based on rays or any other observables, can always be converted to state-independent noncontextuality inequalities. Besides, Our constructive proof also provides a general approach for deriving a state-independent noncontextuality inequality from a proof of KS theorem.
Quantum jump mechanics. (arXiv:1505.02393v1 [quant-ph])
on 2015-5-12 2:05am GMT
Authors: A.Yu.Samarin
The change with time of the system consisting of the quantum object and the macroscopic measuring instrument is described on the base of the uniform dynamic law, which is suitable both evolution and reduction processes description. It is the integral wave equation with kernel in the form of a path integral. It is shown, that wave function collapse is the specific transformation which is fundamentally differ from Shr\”odinger’s evolution. Specifically, a formal cause of the collapse is a local time derivative (infinite large) of the potential energy. Such transformation can not be described using mathematical apparatus of conventional quantum mechanics.
On the origin of randomness in quantum mechanics. (arXiv:1505.02464v1 [quant-ph])
on 2015-5-12 2:05am GMT
Authors: Holger F. Hofmann
Quantum statistics originate from the physics of state preparation. It is therefore wrong to think of quantum states as fundamental. In fact, quantum states are merely summaries of dynamical processes that randomize the properties of the system by drawing on the inexhaustible reservoir of quantum fluctuations provided by the physical tools used to control the quantum system. The mathematical form of the “state vector” is actually an expression of the laws of causality which describe the relations between physical properties in terms of the action of transformations. These laws of causality directly associate the macroscopic effects of a physical property in an interaction with the environment with dynamical changes to the system caused by the microscopic properties of that environment.
Gravity effects of the quantum vacuum. Dark energy and dark matter. (arXiv:1505.02295v1 [gr-qc])
on 2015-5-12 2:05am GMT
Authors: Emilio Santos
The stress-energy tensor of the quantum vacuum is studied for the particular case of quantum electrodynamics (QED), that is a fictituous universe where only the electromagnetic and the electron-positron fields exist. The integrals involved are ultraviolet divergent but it is suggested that a natural cut-off may exist. It is shown that, in spite of the fact that the stress-energy tensor of the electromagnetic field alone is traceless (i.e the pressure P equals 1/3 the energy density u), the total QED tensor is proportional to the metric tensor to a good approximation (i. e. P = -u). It is proposed that there is a cosmological constant in Einstein equation that exactly balances the stress-energy of the vacuum. It is shown that vacuum fluctuations give rise to a modified spacetime metric able to explain dark energy. Particular excitations of the vacuum are studied that might explain dark matter.
The principle behind the Uncertainty Principle. (arXiv:1505.02223v1 [quant-ph])
on 2015-5-12 2:05am GMT
Authors: Varun Narasimhachar, Alireza Poostindouz, Gilad Gour
Whilst physicists have long been aware of the existence of a fundamental uncertainty principle in quantum mechanics, an explicit understanding of this principle has remained an enigma, our grasp limited to specific “uncertainty relations”. In this work we overcome these limitations by clarifying the concept of uncertainty, based on minimalistic axioms. Applying this notion to quantum-mechanical measurements, we arrive at a general, overarching framework for characterizing all quantum-mechanical uncertainty relations, which we unify into our proposed Uncertainty Principle. Along the way, we find that the variance is an uncertainty measure only in a restricted sense.
Uncertainty equalities and uncertainty relation in weak measurement. (arXiv:1505.02233v1 [quant-ph])
on 2015-5-12 2:05am GMT
Authors: Qiu-Cheng Song, Cong-Feng Qiao
Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak measurement which captures the limitation on the preparation of pre- and post-selected ensemble and hold for two non-Hermitian operators corresponding to two non-commuting observables.
