# Weekly Papers on Quantum Foundations (13)

The Landscape and the Multiverse: What’s the Problem?

Read, James and Le Bihan, Baptiste (2021) The Landscape and the Multiverse: What’s the Problem? [Preprint]

The Sheaf-Theoretic Structure of Definite Causality. (arXiv:2103.13771v1 [quant-ph])

We extend the sheaf-theoretic framework for non-locality by Abramsky and Brandenburger to deal with operational scenarios in the presence of arbitrary definite causal orders.

Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. (arXiv:2012.15238v2 [math-ph] UPDATED)

We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalised super-adiabatic theorem for the automorphism group describing the infinite volume dynamics on the quasi-local algebra of observables. The key assumption is the existence of a sequence of gapped finite volume Hamiltonians which generates the same infinite volume dynamics in the thermodynamic limit. Our adiabatic theorem holds also for certain perturbations of gapped ground states that close the spectral gap (so it is an adiabatic theorem also for resonances and in this sense generalised’), and it provides an adiabatic approximation to all orders in the adiabatic parameter (a property often called super-adiabatic’). In addition to existing results for finite lattices, we also perform a resummation of the adiabatic expansion and allow for observables that are not strictly local. Finally, as an application, we prove the validity of linear and higher order response theory for our class of perturbations also for infinite systems.

While we consider the result and its proof as new and interesting in itself, they also lay the foundation for the proof of an adiabatic theorem for systems with a gap only in the bulk, which will be presented in a follow-up article.

Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. (arXiv:2012.15239v2 [math-ph] UPDATED)

We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding GNS-Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite volume Hamiltonians need not have a spectral gap.

Decoherence, Collapse, and Conservation Laws. (arXiv:2102.11370v2 [quant-ph] UPDATED)

Interactions establish correlations between physical systems. The correlations that persist through subsequent interactions with other physical systems pick out a distinct basis of decoherent branches of the wave function. This preferred basis is seen by many as the key to understanding what happens in quantum measurements. However, there is still no generally accepted explanation of how one particular branch is selected with the right probability. One possible explanation is that the entangling interactions that constitute measurements and generate decoherence induce an actual collapse of the wave function. This hypothesis leads to a stochastic collapse equation that does not require the introduction of any new physical constants. The collapse operator is based on interaction potentials, with a variable timing parameter related to the rate at which individual interactions generate the branching process. The distance-dependent nature of the interactions leads to the approximate localization of systems. The equation is consistent with strict conservation of momentum and orbital angular momentum, and it is also consistent with energy conservation within the accuracy allowed by the limited forms of energy that can be described within nonrelativistic theory.

Universal Constants as Manifestations of Relativity. (arXiv:2103.13854v1 [physics.hist-ph])

Authors: A. A. Sheykin

We study the possible interpretation of the “universal constants” by the classification of J.~M.~L\’evy-Leblond. $\hbar$ and $c$ are the most common example of constants of this type. Using Fock’s principle of the relativity w.r.t. observation means, we show that both $c$ and $\hbar$ can be viewed as manifestations of certain relativity. We also show that there is a possibility to interpret the Boltzmann’s constant in a similar way, and make some comments about the relativistic interpretation of the constant spacetime curvature and gravitational constant $G$.

Standard Quantum Mechanics without observers. (arXiv:2008.04930v3 [quant-ph] UPDATED)

Authors: Ovidiu Cristinel Stoica

The Projection Postulate from Standard Quantum Mechanics relies fundamentally on measurements. But measurements implicitly suggest the existence of anthropocentric notions like measuring devices, which should rather emerge from the theory. This article proposes an alternative formulation of the Standard Quantum Mechanics, in which the Projection Postulate is replaced with a version in which measurements and observations are not assumed as fundamental. More precisely, the Wigner functions representing the quantum states on the phase space are required to be tightly constrained to regions of the classical coarse-graining of the phase space. This ensures that states are quasiclassical at the macro level. Within a coarse-graining region, the time evolution of the Wigner functions representing the quantum system is required to obey the Liouville-von Neumann equation, the phase-space equivalent of the Schr\”odinger equation. The projection is postulated to happen when the system transitions from a coarse-graining region to others, by selecting one of them according to the Born rule, but without reference to a measurements. The connection with the standard formulation of Quantum Mechanics is explained, as well as the problems that the present formulation solves, in particular the Wigner’s friend type of paradoxes. Experimental consequences and open problems of the proposed formulation are discussed.

Physical principles of brain-computer interfaces and their applications for rehabilitation, robotics and control of human brain states

Publication date: Available online 24 March 2021

Source: Physics Reports

Author(s): Alexander E. Hramov, Vladimir A. Maksimenko, Alexander N. Pisarchik

Conformal gravity does not predict flat galaxy rotation curves. (arXiv:2103.13451v1 [gr-qc])

Authors: Michael HobsonAnthony Lasenby

We reconsider the widely held view that the Mannheim–Kazanas (MK) vacuum solution for a static, spherically-symmetric system in conformal gravity (CG) predicts flat rotation curves, such as those observed in galaxies, without the need for dark matter. The conformal equivalence of the MK and Schwarzschild–de-Sitter (SdS) metrics, where the latter does not predict flat rotation curves, raises concerns that the prediction in the MK frame may be a gauge artefact. This ambiguity arises from assuming that, in each frame, test particles have fixed rest mass and follow timelike geodesics, which are not conformally invariant. The mass of such particles must instead be generated dynamically through interaction with a scalar field, the energy-momentum of which means that the spacetime outside a static, spherically-symmetric matter distribution in CG is, in general, not given by the MK vacuum solution. A unique solution does exist, however, for which the scalar field energy-momentum vanishes and the metric retains the MK form. Nonetheless, we show that in both the Einstein and MK frames of this solution, in which the scalar field is constant or radially-dependent, respectively, massive particles follow timelike geodesics of the SdS metric, thereby resolving the apparent frame dependence of physical predictions and unambiguously yielding rotation curves with no flat region. We further find that the general form of the conformal transformation linking the Einstein and MK frames is unique in preserving the structure of any diagonal static, spherically-symmetric metric with a radial coefficient that is (minus) the reciprocal of its temporal one. We also comment briefly on how our analysis resolves the long-standing uncertainty regarding gravitational lensing in the MK metric. (Abridged)

Constraining the Generalized Uncertainty Principle with the light twisted by rotating black holes and M87*. (arXiv:2103.13750v1 [gr-qc])

We test the validity of the Generalized Heisenberg’s Uncertainty principle in the presence of strong gravitational fields nearby rotating black holes; Heisenberg’s principle is supposed to require additional correction terms when gravity is taken into account, leading to a more general formulation also known as the Generalized Uncertainty Principle. Using as probe electromagnetic waves acquiring orbital angular momentum when lensed by a rotating black hole, we find from numerical simulations a relationship between the spectrum of the orbital angular momentum of light and the corrections needed to formulate the Generalized Uncertainty Principle, here characterized by the rescaled parameter $\beta_0$, a function of the Planck’s mass and the bare mass of the black hole. Then, from the analysis of the observed twisted light due to the gravitational field of the compact object observed in M87*, we find new limits for the parameter $\beta_0$. With this method, complementary to black hole shadow circularity analyses, we obtain more precise limits from the experimental data of M87*, confirming the validity of scenarios compatible with General Relativity, within the uncertainties due to the experimental errors present in EHT data and those due to the numerical simulations and analysis.

M-theory and the birth of the Universe. (arXiv:2102.11202v4 [hep-th] UPDATED)

Authors: F.R. Klinkhamer

In this review article, we first discuss a possible regularization of the big bang curvature singularity of the standard Friedmann cosmology, where the curvature singularity is replaced by a spacetime defect. We then consider the hypothesis that a new physics phase gave rise to this particular spacetime defect. Specifically, we set out on an explorative calculation using the IIB matrix model, which has been proposed as a particular formulation of nonperturbative superstring theory (M-theory).

Modelling Ourselves: what the Free Energy Principle reveals about our implicit notions of representation

Pezzulo, Giovanni and Sims, Matthew (2021) Modelling Ourselves: what the Free Energy Principle reveals about our implicit notions of representation. [Preprint]

A Refined Propensity Account for GRW Theory

Lorenzetti, Lorenzo (2021) A Refined Propensity Account for GRW Theory. [Preprint]

Rigour and Thought Experiments: Burgess and Norton

Brown, James Robert (2021) Rigour and Thought Experiments: Burgess and Norton. [Preprint]

“Can machines think?” The missing history of the Turing test

Gonçalves, Bernardo (2021) “Can machines think?” The missing history of the Turing test. [Preprint]

Causal asymmetry from the perspective of a causal agent

Evans, Peter W. and Milburn, Gerard J. and Shrapnel, Sally (2021) Causal asymmetry from the perspective of a causal agent. [Preprint]

The Value of Surprise in Science

French, Steven and Murphy, Alice (2021) The Value of Surprise in Science. [Preprint]

Defending Quantum Objectivity

Okon, Elias (2021) Defending Quantum Objectivity. [Preprint]

Against the Tyranny of ‘Pure States’ in Quantum Theory

de Ronde, Christian and Massri, Cesar (2019) Against the Tyranny of ‘Pure States’ in Quantum Theory. Foundations of Science. ISSN 1233-1821

arXiv:2103.03743 (physics)[Submitted on 18 Jan 2021]

Nonnoetherian Lorentzian manifolds

Charlie Beil

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A nonnoetherian spacetime is a Lorentzian manifold that contains a set of causal curves with no distinct interior points, called ‘pointal curves’. This new geometry recently arose in the study of nonnoetherian coordinate rings in algebraic geometry. We investigate properties of metrics on nonnoetherian spacetimes, and use the Hodge star operator to show that free dust particles have spin 12. We also reproduce the Kochen-Specker ψ-epistemic model of spin using the nonnoetherian metric, and show similarities between our model and spin entanglement for Bell states and four-photon entanglement swapping. Finally, we determine the stress-energy tensor of dust on such spacetimes, and find that it is only nonzero at points where dust is created or annihilated.