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Weekly Papers on Quantum Foundations (26-28)
Published by editor on July 22, 2019
From probabilistic mechanics to quantum theory. (arXiv:1907.08513v1 [quant-ph])
下午3:18 | quant-ph updates on arXiv.org
Authors: Ulf Klein
We show that quantum theory (QT) is a substructure of classical probabilistic physics. The central quantity of the classical theory is Hamilton's function $H(q,p)$, which determines canonical equations, a corresponding flow $\phi_{t}^{H}$, and a Liouville equation for the probability density $\rho(q,p,t)$. We extend this theory in two respects: (1) The same structure is defined for arbitrary observables $A(q,p)$. Thus, we obtain entities $\phi_{\alpha}^{A}$, and $\rho_{A}(q,p,\alpha)$, where $\alpha$ is the independent variable in the canonical equations. (2) We introduce for each $A(q,p)$ an action variable $S_{A}(q,p,\alpha)$. This is a redundant quantity in a classical context but indispensable for the transition to QT. The basic equations of probabilistic mechanics take a "quantum-like" form, which allows for a simple derivation of QT by means of a projection to configuration space reported previously [Quantum Stud.:Math. Found. (2018) 5:219-227]. We obtain the most important relations of QT, namely the form of operators, Schr\"odinger's equation, eigenvalue equations, commutation relations, expectation values, and Born's rule. Implications for the interpretation of QT are discussed, as well as an alternative projection method allowing for a derivation of spin.
Minimal model of quantum measurements and emergence of classical domain. (arXiv:1907.08528v1 [quant-ph])
Authors: Alexei V. Tkachenko
We propose a minimalistic model of quantum measurements within a finite system that undergoes a regular unitary evolution. Based on information theory, the measurement process requires a sacrifice of information entropy. This loss in our model is represented by a single cubit being isolated from the rest of the system. As a result of the partitioning, the classical domain emerges and the measurement occurs. The effect of the measurement on the quantum state of the system can be described by the generalized projection operator, which in general is less restrictive than the traditional wave function collapse.
Could the physical world be emergent instead of fundamental, and why should we ask? (short version). (arXiv:1712.01816v2 [quant-ph] UPDATED)
Authors: Markus P. Mueller
In physics, there is the prevailing intuition that we are part of a unique external world, and that the goal of physics is to understand and describe this world. This assumption of the fundamentality of objective reality is often seen as a major prerequisite of any kind of scientific reasoning. However, here I argue that we should consider relaxing this assumption in a specific way in some contexts. Namely, there is a collection of open questions in and around physics that can arguably be addressed in a substantially more consistent and rigorous way if we consider the possibility that the first-person perspective is ultimately more fundamental than our usual notion of external world. These are questions like: which probabilities should an observer assign to future experiences if she is told that she will be simulated on a computer? How should we think of cosmology's Boltzmann brain problem, and what can we learn from the fact that measurements in quantum theory seem to do more than just reveal preexisting properties? Why are there simple computable laws of physics in the first place? This note summarizes a longer companion paper which constructs a mathematically rigorous theory along those lines, suggesting a simple and unified framework (rooted in algorithmic information theory) to address questions like those above. It is not meant as a "theory of everything" (in fact, it predicts its own limitations), but it shows how a notion of objective external world, looking very much like our own, can provably emerge from a starting point in which the first-person perspective is primary, without apriori assumptions on the existence of "laws" or a "physical world". While the ideas here are perfectly compatible with physics as we know it, they imply some quite surprising predictions and suggest that we may want to substantially revise the way we think about some foundational questions.
Law without law: from observer states to physics via algorithmic information theory. (arXiv:1712.01826v3 [quant-ph] UPDATED)
According to our current conception of physics, any valid physical theory is supposed to describe the objective evolution of a unique external world. However, this condition is challenged by quantum theory, which suggests that physical systems should not always be understood as having objective properties which are simply revealed by measurement. Furthermore, as argued below, several other conceptual puzzles in the foundations of physics and related fields point to limitations of our current perspective and motivate the exploration of an alternative: to start with the first-person (the observer) rather than the third-person perspective (the world). In this work, I propose a rigorous approach of this kind on the basis of algorithmic information theory. It is based on a single postulate: that universal induction determines the chances of what any observer sees next. That is, instead of a world or physical laws, it is the local state of the observer alone that determines those probabilities. Surprisingly, despite its solipsistic foundation, I show that the resulting theory recovers many features of our established physical worldview: it predicts that it appears to observers as if there was an external world that evolves according to simple, computable, probabilistic laws. In contrast to the standard view, objective reality is not assumed on this approach but rather provably emerges as an asymptotic statistical phenomenon. The resulting theory dissolves puzzles like cosmology's Boltzmann brain problem, makes concrete predictions for thought experiments like the computer simulation of agents, and suggests novel phenomena such as "probabilistic zombies" governed by observer-dependent probabilistic chances. It also predicts some basic phenomena of quantum theory (Bell inequality violation and no-signalling) and suggests a novel "algorithmic" perspective on the foundations of quantum mechanics.
Quantum fractionalism: the Born rule as a consequence of the complex Pythagorean theorem. (arXiv:1905.08429v2 [quant-ph] UPDATED)
Authors: André L. G. Mandolesi
Everettian Quantum Mechanics, or the Many Worlds Interpretation, has no Born rule, and lacks a valid explanation for quantum probabilities. We show their values are the factors by which 2-dimensional Lebesgue measures contract under orthogonal projections in complex Hilbert spaces, and that the unit total probability condition corresponds to a Pythagorean theorem for such measures. From this and two simple, yet unorthodox, physical assumptions, we obtain that those factors give, in the set of worlds originating from a quantum measurement, the fractions corresponding to each result. These are associated to probabilities, in both the frequentist and Bayesian views, solving the probability problem of Everett's theory. This allows its preferred basis problem to be solved as well, and may help settle questions about the nature of probability in general.
Locality & Entanglement in Table-Top Testing of the Quantum Nature of Linearized Gravity. (arXiv:1907.01568v3 [quant-ph] UPDATED)
Authors: Ryan J. Marshman, Anupam Mazumdar, Sougato Bose
This paper highlights the importance of the assumption of locality of physical interactions, and the concomitant necessity of the off-shell propagation of quanta between two non-relativistic test masses in probing the quantum nature of linearized gravity in the laboratory. At the outset, we will argue that observing the quantum nature of a system is not limited to evidencing $O\left(\hbar\right)$ corrections to a classical theory: it instead hinges upon verifying tasks that a classical system cannot accomplish, which is the method adopted in the aforementioned tabletop experiments. We explain the background concepts needed from quantum field theory, namely forces arising through the exchange of virtual (off-shell) quanta, as well as the background exploited from quantum information theory, such as Local Operations and Classical Communication (LOCC) and entanglement witnesses. We clarify the key assumption inherent in our evidencing experiment, namely the locality of physical interactions, which is a generic feature of interacting systems of quantum fields around us, and naturally incorporates micro-causality in the description of our experiment. We also present the types of states the matter field must inhabit, putting the experiment on firm relativistic quantum field theoretic grounds. At the end we use a non-local (but not complete action at a distance) theory of gravity to illustrate how our mechanism may still be used to detect the qualitatively quantum nature of a force when the scale of non-locality is finite. We find that the scale of non-locality, including the entanglement entropy production in local/ non-local gravity, may be revealed from the results of our experiment.
Extensivity, entropy current, area law and Unruh effect. (arXiv:1903.05422v3 [hep-th] UPDATED)
下午12:25 | gr-qc updates on arXiv.org
Authors: F. Becattini, D. Rindori (Florence U.)
We present a general method to determine the entropy current of relativistic matter at local thermodynamic equilibrium in quantum statistical mechanics. Provided that the local equilibrium operator is bounded from below and its lowest lying eigenvector is non-degenerate, it is proved that, in general, the logarithm of the partition function is extensive, meaning that it can be expressed as the integral over a 3D space-like hypersurface of a vector current, and that an entropy current exists. We work out a specific calculation for a non-trivial case of global thermodynamic equilibrium, namely a system with constant comoving acceleration, whose limiting temperature is the Unruh temperature. We show that the integral of the entropy current in the right Rindler wedge is the entanglement entropy.
Matter-Geometry entanglement in quantum gravity. (arXiv:1907.03776v2 [gr-qc] UPDATED)
Authors: Viqar Husain, Suprit Singh
We present a study of the evolution of entanglement entropy of matter and geometry in quantum cosmology. For a variety of initial quantum states of the Universe, and with evolution defined with respect to a relational time, we show numerically that (i) entanglement entropy increases rapidly at very early times, and subsequently saturates to a constant non-zero value, and (ii) that the saturation value of this entropy is a linear function of the energy associated to the quantum state: $S_{\text{ent}}^\psi = \gamma \langle \hat{H} \rangle_\psi$. These results suggest a remnant of quantum entanglement in the macroscopic Universe from the era of the Big Bang, independent of the initial state, and a "First Law" associated with matter-gravity entanglement entropy in quantum gravity.
Review of Tim Maudlin's "Philosophy of Physics: Quantum Theory"
上午10:03 | International Journal of Quantum Foundations | International Journal of Quantum Foundations – International Journal of Quantum Foundations
Travis Norsen [Show Biography]
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A Physicist's Road to Emergence: A Revisited Story of "More Is Different"
2019年7月21日 星期日 下午3:08 | Philsci-Archive: No conditions. Results ordered -Date Deposited. (RSS 2.0)
Muñoz Garganté, Nuria (2019) A Physicist's Road to Emergence: A Revisited Story of "More Is Different". In: UNSPECIFIED.
How Dualists Should (Not) Respond to the Objection from Energy Conservation
Cucu, Alin C. and Pitts, J. Brian (2019) How Dualists Should (Not) Respond to the Objection from Energy Conservation. Mind & Matter, 17 (1). pp. 95-121.
How NOT to Build an Infinite Lottery Machine
2019年7月19日 星期五 下午1:46 | Philsci-Archive: No conditions. Results ordered -Date Deposited. (RSS 2.0)
Norton, John D. (2019) How NOT to Build an Infinite Lottery Machine. [Preprint]
Weeding Landauer's Garden
Norton, John D. (2019) Weeding Landauer's Garden. [Preprint]
The Measurement Problem and two Dogmas about Quantum Mechanics
Felline, Laura (2019) The Measurement Problem and two Dogmas about Quantum Mechanics. [Preprint]
A Neo-Kantian Approach to the Standard Model
2019年7月18日 星期四 上午7:05 | Philsci-Archive: No conditions. Results ordered -Date Deposited. (RSS 2.0)
French, Steven (2019) A Neo-Kantian Approach to the Standard Model. [Preprint]
On contextual and ontological aspects of emergence and reduction
2019年7月17日 星期三 下午3:29 | Philsci-Archive: No conditions. Results ordered -Date Deposited. (RSS 2.0)
Céspedes, Esteban (2019) On contextual and ontological aspects of emergence and reduction. [Preprint]
Review – Varieties of Scientific Realism, Ed. Evandro Agazzi, 2017, Springer.
Künstler, Raphaël (2019) Review – Varieties of Scientific Realism, Ed. Evandro Agazzi, 2017, Springer. Lato Sensu, revue de la Société de philosophie des sciences, 6 (1). pp. 20-23. ISSN 2295-8029
2019年7月15日 星期一 上午8:00 | Glenn S. Solomon | Nature Physics – Issue – nature.com science feeds
Nature Physics, Published online: 15 July 2019; doi:10.1038/s41567-019-0566-9
Two-level quantum systems are routinely excited by resonant pump beams. Experiments now show resonant excitation through dichromatic, detuned pumps — providing a coherent control technique that will also aid single-photon emission from solid-state devices.
The Hidden Assumptions of Frauchiger and Renner
2019年7月1日 星期一 上午9:54 | International Journal of Quantum Foundations | International Journal of Quantum Foundations – International Journal of Quantum Foundations
Volume 5, Issue 3, pages 98-109
Anthony Sudbery [Show Biography]
This note is a critical examination of the argument of Frauchiger and Renner, in which they claim to show that three reasonable assumptions about the use of quantum mechanics jointly lead to a contradiction. It is shown that further assumptions are needed to establish the contradiction, and that each of these assumptions is invalid in some version of quantum mechanics.
Comment on Healey's "Quantum Theory and the Limits of Objectivity"
2019年7月1日 星期一 上午8:00 | Latest Results for Foundations of Physics
In this comment we critically review an argument against the existence of objective physical outcomes, recently proposed by Healey [1]. We show that his gedankenexperiment, based on a combination of "Wigner's friend" scenarios and Bell's inequalities, suffers from the main criticism, that the computed correlation functions entering the Bell's inequality are in principle experimentally inaccessible, and hence the author's claim is in principle not testable. We discuss perspectives for fixing that by adapting the proposed protocol and show that this, however, makes Healey's argument virtually equivalent to other previous, similar proposals that he explicitly criticises.
Selective Realism and the Framework/Interaction Distinction: A Taxonomy of Fundamental Physical Theories
Following the proposal of a new kind of selective structural realism that uses as a basis the distinction between framework and interaction theories, this work discusses relevant applications in fundamental physics. An ontology for the different entities and properties of well-known theories is thus consistently built. The case of classical field theories—including general relativity as a classical theory of gravitation—is examined in detail, as well as the implications of the classification scheme for issues of realism in quantum mechanics. These applications also shed light on the different range of applicability of the ontic and epistemic versions of structural realism.
Defining a Relativity-Proof Notion of the Present via Spatio-temporal Indeterminism
2019年6月14日 星期五 上午8:00 | Latest Results for Foundations of Physics
In this paper we describe a novel approach to defining an ontologically fundamental notion of co-presentness that does not go against the tenets of relativity theory. We survey the possible reactions to the problem of the present in relativity theory, introducing a terminological distinction between a static role of the present, which is served by the relation of simultaneity, and a dynamic role of the present, with the corresponding relation of co-presentness. We argue that both of these relations need to be equivalence relations, but they need not coincide. Simultaneity, the sharing of a temporal coordinate, need not have fundamental ontological import, so that a relativizing strategy with respect to simultaneity seems promising. The notion of co-presentness, on the other hand, does have ontological import, and can therefore not be relativized to an observer or to an arbitrarily chosen frame. We argue that a formal representation of indeterminism can provide the structure needed to anchor the relation of co-presentness, and that this addition is in fact congenial to the notion of dynamic time as requiring real (indeterministic) change. The resulting picture is one of an extended dynamic present, implying a formal distinction between static (coordinate) simultaneity and dynamic co-presentness. After working out the basics of our approach in the simpler framework of branching time, we provide our full analysis in the framework of branching space-times, which allows for a formal definition of modal correlations. The spatial extension of the dynamic present can reach as far as the modal correlations do. In the limit, the dynamic present could extend across a maximal space-like hypersurface.
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