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arXiv2014

Blondel et les oscillations auto-entretenues

In 1893, the "physicist-engineer" André Blondel invents the oscilloscope for displaying voltage and current variables. With this powerful means of investigation, he first studies the phenomena of the arc then used for the coastal and urban lighting and then, the singing arc used as a transmitter of radio waves in wireless telegraphy. In 1905, he highlights a new type of non-sinusoidal oscillations in the singing arc. Twenty years later, Balthasar van der Pol will recognize that such oscillations were in fact "relaxation oscillations". To explain this phenomenon, he uses a representation in the phase plane and shows that its evolution takes the form of small cycles. During World War I the triode gradually replaces the singing arc in transmission systems. At the end of the war, using analogy, Blondel transposes to the triode most of the results he had obtained for the singing arc. In April 1919, he publishes a long memoir in which he introduces the terminology "self-sustained oscillations" and proposes to illustrate this concept starting from the example of the Tantalus cup which is then picked up by Van der Pol and Philippe Le Corbeiller. He then provides the definition of a self sustained system which is quite similar to that given later by Aleksandr Andronov and Van der Pol. To study the stability of oscillations sustained by the triode and by the singing arc he uses, this time, a representation in the complex plane and he expresses the amplitude in polar coordinates. He then justifies the maintaining of oscillations by the existence cycles which nearly present all the features of Poincaré's limit cycles. Finally, in November 1919, Blondel performs, a year before Van der Pol, the setting in equation of the triode oscillations. In March 1926, Blondel establishes the differential equation characterizing the oscillations of the singing arc, completely similar to that obtained concomitantly by Van der Pol for the triode. Thus, throughout his career, Blondel, has made fundamental and relatively unknown contributions to the development of the theory of nonlinear oscillations. The purpose of this article is to analyze his main work in this area and to measure their importance or influence by placing them in the perspective of the development of this theory.

physics.hist-ph↗
arXiv2014

Translation of Michael Sadowsky's paper "An elementary proof for the existence of a developable Möbius band and the attribution of the geometric problem to a variational problem"

This article is a translation of Michael Sadowsky's original paper "Ein elementarer Beweis für die Existenz eines abwickelbaren Möbiusschen Bandes und die Zurückführung des geometrischen Problems auf ein Variationsproblem." which appeared in Sitzungsberichte der Preussischen Akademie der Wissenschaften, physikalisch-mathematische Klasse, 17. Juli 1930, Mitteilung vom 26. Juni, 412-415. Published on September 12, 1930.

math.HO↗
arXiv2013

On the Consistency of the Consistent Histories Approach to Quantum Mechanics

The Consistent Histories (CH) formalism aims at a quantum mechanical framework which could be applied even to the universe as a whole. CH stresses the importance of histories for quantum mechanics, as opposed to measurements, and maintains that a satisfactory formulation of quantum mechanics allows one to assign probabilities to alternative histories of a quantum system. It further proposes that each realm, that is, each set of histories to which probabilities can be assigned, provides a valid quantum-mechanical account, but that different realms can be mutually incompatible. Finally, some of its proponents offer an "evolutionary" explanation of our existence in the universe and of our preference for quasiclassical descriptions of nature. The present work questions the validity of claims offered by CH proponents asserting that it solves many interpretational problems in quantum mechanics. In particular, we point out that the interpretation of the framework leaves vague two crucial points, namely, whether realms are fixed or chosen and the link between measurements and histories. Our claim is that by doing so, CH overlooks the main interpretational problems of quantum mechanics. Furthermore, we challenge the evolutionary explanation offered and we critically examine the proposed notion of a realm-dependent reality.

gr-qc↗
arXiv2014

Benefits of Objective Collapse Models for Cosmology and Quantum Gravity

We display a number of advantages of objective collapse theories for the resolution of long-standing problems in cosmology and quantum gravity. In particular, we examine applications of objective reduction models to three important issues: the origin of the seeds of cosmic structure, the problem of time in quantum gravity and the information loss paradox; we show how reduction models contain the necessary tools to provide solutions for these issues. We wrap up with an adventurous proposal, which relates the spontaneous collapse events of objective collapse models to microscopic virtual black holes.

gr-qc↗
arXiv2014

Manifesting the Quantum World

In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. It concerns the process by which what Sellars called the Manifest Image of the world comes into being. This process consists in the progressive differentiation of an intrinsically undifferentiated entity. By entering into reflexive spatial relations, this gives rise to (i) what looks like a multiplicity of relata if the reflexive quality of the relations is not taken into account, and (ii) what looks like a substantial expanse if the spatial quality of the relations is reified. If there is a distinctly quantum domain, it is a non-spatial and non-temporal dimension across which the transition from the unity of this entity to the multiplicity of the world takes place. Instead of being constituents of the physical world, subatomic particles, atoms, and molecules are instrumental in its manifestation. These conclusions are based on the following interpretive principle: whenever calculating probabilities calls for the addition of amplitudes, the distinctions we make between the alternatives lack objective reality. Applied to alternatives involving distinctions between regions of space, this principle implies that the spatiotemporal differentiation of the physical world is incomplete: the existence of a real-valued spatiotemporal background is an unrealistic idealization. This guarantees the existence of observables whose values are real *per se*, as against "real by virtue of being indicated by the values of observables that are real *per se*." Applied to alternatives involving distinctions between things, it implies that, intrinsically, all fundamental particles are numerically identical and thus identifiable with the aforementioned undifferentiated entity.

quant-ph↗
arXiv2018

Are Hidden-Variable Theories for Pilot-Wave Systems Possible ?

Recently it was shown that certain fluid-mechanical 'pilot-wave' systems can strikingly mimic a range of quantum properties, including single particle diffraction and interference, quantization of angular momentum etc. How far does this analogy go? The ultimate test of (apparent) quantumness of such systems is a Bell-test. Here the premises of the Bell inequality are re-investigated for particles accompanied by a pilot-wave, or more generally by a resonant 'background' field. We find that two of these premises, namely outcome independence and measurement independence, may not be generally valid when such a background is present. Under this assumption the Bell inequality is possibly (but not necessarily) violated. A class of hydrodynamic Bell experiments is proposed that could test this claim. Such a Bell test on fluid systems could provide a wealth of new insights on the different loopholes for Bell's theorem. Finally, it is shown that certain properties of background-based theories can be illustrated in Ising spin-lattices.

quant-ph↗
arXiv2018

Measuring the last burst of non-singular black holes

Non-perturbative quantum gravity prevents the formation of curvature singularities and may allow black holes to decay with a lifetime shorter than evaporation time. This, in connection with the existence of primordial black holes, could open a new window for quantum-gravity phenomenology. I discuss the possibility of observing astrophysical emissions from the explosion of old black holes in the radio and in the gamma wavelengths. These emissions can be discriminated from other astrophysical sources because of a peculiar way the emitted wavelength scales with the distance. The spectrum of the diffuse radiation produced by those objects presents a peculiar distortion due to this scaling.

gr-qc↗
arXiv2017

Extracting Geometry from Quantum Spacetime: Obstacles down the road

Any acceptable quantum gravity theory must allow us to recover the classical spacetime in the appropriate limit. Moreover, the spacetime geometrical notions should be intrinsically tied to the behavior of the matter that probes them. We consider some difficulties that would be confronted in attempting such an enterprise. The problems we uncover seem to go beyond the technical level to the point of questioning the overall feasibility of the project. The main issue is related to the fact that, in the quantum theory, it is impossible to assign a trajectory to a physical object, and, on the other hand, according to the basic tenets of the geometrization of gravity, it is precisely the trajectories of free localized objects that define the spacetime geometry. The insights gained in this analysis should be relevant to those interested in the quest for a quantum theory of gravity and might help refocus some of its goals.

gr-qc↗
arXiv2018

Law without law or "just" limit theorems?

About 35 years ago Wheeler introduced the motto `law without law' to highlight the possibility that (at least a part of) Physics may be understood only following {\em regularity principles} and few relevant facts, rather than relying on a treatment in terms of fundamental theories. Such a proposal can be seen as part of a more general attempt (including the maximum entropy approach) summarized by the slogan `it from bit', which privileges the information as the basic ingredient. Apparently it seems that it is possible to obtain, without the use of physical laws, some important results in an easy way, for instance, the probability distribution of the canonical ensemble. In this paper we will present a general discussion on those ideas of Wheeler's that originated the motto `law without law'. In particular we will show how the claimed simplicity is only apparent and it is rather easy to produce wrong results. We will show that it is possible to obtain some of the results treated by Wheeler in the realm of the statistical mechanics, using precise assumptions and nontrivial results of probability theory, mainly concerning ergodicity and limit theorems.

cond-mat.stat-mech↗
arXiv2018

Binding quantum matter and space-time, without romanticism

Understanding the emergence of a tangible 4-dimensional space-time from a quantum theory of gravity promises to be a tremendously difficult task. This article makes the case that this task may not have to be carried. Space-time as we know it may be fundamental to begin with. I recall the common arguments against this possibility and review a class of recently discovered models bypassing the most serious objection. The generic solution of the measurement problem that is tied to semiclassical gravity as well as the difficulty of the alternative make it a reasonable default option in the absence of decisive experimental evidence.

physics.hist-ph↗
arXiv2018

The notion of locality in relational quantum mechanics

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.

quant-ph↗
arXiv2018

Finetuned Cancellations and Improbable Theories

It is argued that the $x-y$ cancellation model (XYCM) is a good proxy for discussions of finetuned cancellations in physical theories. XYCM is then analyzed from a statistical perspective, where it is argued that a finetuned point in the parameter space is not abnormal, with any such point being just as probable as any other point. However, landing inside a standardly defined finetuned region (i.e., the full parameter space of finetuned points) has a much lower probability than landing outside the region, and that probability is invariant under assumed ranges of parameters. This proposition requires asserting also that the finetuned target region is a priori established. Therefore, it is surmised that highly finetuned theories are generally expected to be highly improbable. An actionable implication of this moderate naturalness position is that the search for a non-finetuned explanation to supplant an apparently finetuned theory is likely to be a valid pursuit, but not guaranteed to be. A statistical characterization of this moderate position is presented, as well as those of the extreme pro-naturalness and anti-naturalness positions.

physics.hist-ph↗
arXiv2019

Quantum Reality, Perspectivalism and Covariance

Paul Busch has emphasized on various occasions the importance for physics of going beyond a merely instrumentalist view of quantum mechanics. Even if we cannot be sure that any particular realist interpretation describes the world as it actually is, the investigation of possible realist interpretations helps us to develop new physical ideas and better intuitions about the nature of physical objects at the micro level. In this spirit, Paul Busch himself pioneered the concept of ``unsharp quantum reality'', according to which there is an objective non-classical indeterminacy---a lack of sharpness---in the properties of individual quantum systems. We concur with Busch's motivation for investigating realist interpretations of quantum mechanics and with his willingness to move away from classical intuitions. In this article we try to take some further steps on this road. In particular, we pay attention to a number of \textit{prima facie} implausible and counter-intuitive aspects of realist interpretations of unitary quantum mechanics. We shall argue that from a realist viewpoint, quantum contextuality naturally leads to ``perspectivalism'' with respect to properties of spatially extended quantum systems, and that this perspectivalism is important for making relativistic covariance possible.

quant-ph↗
arXiv2019

Uncertainty from Heisenberg to Today

We explore the different meanings of "quantum uncertainty" contained in Heisenberg's seminal paper from 1927, and also some of the precise definitions that were explored later. We recount the controversy about "Anschaulichkeit", visualizability of the theory, which Heisenberg claims to resolve. Moreover, we consider Heisenberg's programme of operational analysis of concepts, in which he sees himself as following Einstein. Heisenberg's work is marked by the tensions between semiclassical arguments and the emerging modern quantum theory, between intuition and rigour, and between shaky arguments and overarching claims. Nevertheless, the main message can be taken into the new quantum theory, and can be brought into the form of general theorems. They come in two kinds, not distinguished by Heisenberg. These are, on one hand, constraints on preparations, like the usual textbook uncertainty relation, and, on the other, constraints on joint measurability, including trade-offs between accuracy and disturbance.

physics.hist-ph↗
arXiv2019

Intrinsic, extrinsic, and the constitutive a priori

On the basis of what I call physico-formalist philosophy of mathematics, I will develop an amended account of the Kantian--Reichenbachian conception of constitutive a priori. It will be shown that the features (attributes, qualities, properties) attributed to a real object are not possessed by the object as a "thing-in-itself"; they require a physical theory by means of which these features are constituted. It will be seen that the existence of such a physical theory implies that a physical object can possess a property only if other contingently existing physical objects exist; therefore, the intrinsic--extrinsic distinction is flawed.

physics.hist-ph↗
arXiv2019

What Are Observables in Hamiltonian Einstein-Maxwell Theory?

Is change missing in Hamiltonian Einstein-Maxwell theory? Given the most common definition of observables (having weakly vanishing Poisson bracket with each first-class constraint), observables are constants of the motion and nonlocal. Unfortunately this definition also implies that the observables for massive electromagnetism with gauge freedom (Stueckelberg) are inequivalent to those of massive electromagnetism without gauge freedom (Proca). The alternative Pons-Salisbury-Sundermeyer definition of observables, aiming for Hamiltonian-Lagrangian equivalence, uses the gauge generator G, a tuned sum of first-class constraints, rather than each first-class constraint separately, and implies equivalent observables for equivalent massive electromagnetisms. For General Relativity, G generates 4-dimensional Lie derivatives for solutions. The Lie derivative compares different space-time points with the same coordinate value in different coordinate systems, like 1 a.m. summer time vs. 1 a.m. standard time, so a vanishing Lie derivative implies constancy rather than covariance. Requiring equivalent observables for equivalent formulations of massive gravity confirms that $G$ must generate the $4$-dimensional Lie derivative (not $0$) for observables. These separate results indicate that observables are invariant under internal gauge symmetries but covariant under external gauge symmetries, but can this bifurcated definition work for mixed theories such as Einstein-Maxwell theory? Pons, Salisbury and Shepley have studied $G$ for Einstein-Yang-Mills. For Einstein-Maxwell, both $F_{μν}$ and $g_{μν}$ are invariant under electromagnetic gauge transformations and covariant (changing by a Lie derivative) under $4$-dimensional coordinate transformations. Using the bifurcated definition, these quantities count as observables, as one would expect on non-Hamiltonian grounds.

gr-qc↗