# Weekly Papers on Quantum Foundations (34)

Russell on Weyl’s unified field theory. (arXiv:2208.08495v1 [physics.hist-ph])

Authors: C. Romero

In 1918, H. Weyl proposed a unified theory of gravity and electromagnetism based on a generalization of Riemannian geometry. With hindsight we now could say that the theory carried with it some of the most original ideas that inspired the physics of the twentieth century. In a book published in 1927, Bertrand Russell devoted an entire chapter to explain and give a critical appraisal of Weyl’s theory. We briefly revisit the text written by Russell, who gave one of the first philosophical approaches to Weyl’s ideas.

Quantum Mechanics in Phase Space: An introduction. (arXiv:2208.08682v1 [quant-ph])

Collection of lecture notes introducing quantum mechanics in phase space and basic Gaussian quantum mechanics.

Early heart disease prediction using hybrid quantum classification. (arXiv:2208.08882v1 [quant-ph])

The rate of heart morbidity and heart mortality increases significantly which affect the global public health and world economy. Early prediction of heart disease is crucial for reducing heart morbidity and mortality. This paper proposes two quantum machine learning methods i.e. hybrid quantum neural network and hybrid random forest quantum neural network for early detection of heart disease. The methods are applied on the Cleveland and Statlog datasets. The results show that hybrid quantum neural network and hybrid random forest quantum neural network are suitable for high dimensional and low dimensional problems respectively. The hybrid quantum neural network is sensitive to outlier data while hybrid random forest is robust on outlier data. A comparison between different machine learning methods shows that the proposed quantum methods are more appropriate for early heart disease prediction where 96.43% and 97.78% area under curve are obtained for Cleveland and Statlog dataset respectively.

Bell test in a classical pilot-wave system. (arXiv:2208.08940v1 [physics.flu-dyn])

Since its discovery in 2005, the hydrodynamic pilot-wave system has provided a concrete macroscopic realization of wave-particle duality and concomitant classical analogs of many quantum effects. The question naturally arises as to whether this hydrodynamic pilot-wave system might provide a platform for violating Bell’s inequality, and so yield a classical analog of quantum entanglement. We here present the results of a static Bell test performed with a numerical model of the hydrodynamic pilot-wave system, specifically a coupled bipartite tunneling system. We demonstrate that, under certain conditions, the Bell inequality is violated owing to the wave-mediated coupling between the two subsystems. Our system represents a new platform for exploring whether Bell’s Theorem, typically taken to be a no-go theorem for all local hidden variable theories, need be respected by the class of hidden variable theories based on non-Markovian pilot-wave dynamics.

Physical interpretation of non-normalizable harmonic oscillator states and relaxation to pilot-wave equilibrium. (arXiv:2208.08945v1 [quant-ph])

Non-normalizable states are difficult to interpret in orthodox quantum mechanics and usually discarded as mathematical artifacts. We argue that pilot-wave theory gives a straightforward physical interpretation of non-normalizable quantum states, as the theory requires only a normalized density of configurations to generate statistical predictions. In order to better understand such states, we conduct the first study of non-normalizable solutions of the harmonic oscillator from a pilot-wave perspective. We show that, contrary to intuitions from orthodox quantum mechanics, the non-normalizable eigenstates and their superpositions are bound states in the sense that the velocity field $v_y \to 0$ at large $\pm y$. We argue that defining a physically meaningful equilibrium density for such states requires a new notion of equilibrium, named pilot-wave equilibrium, which is a generalisation of the notion of quantum equilibrium. We define a new $H$-function $H_{pw}$, and prove that a density in pilot-wave equilibrium minimises $H_{pw}$, is equivariant, and remains in equilibrium with time. We prove, via an $H$-theorem for $H_{pw}$, that an arbitrary initial density relaxes to pilot-wave equilibrium density at a coarse-grained level, under assumptions similar to those for relaxation to quantum equilibrium. Using the relationship between the two notions of equilibrium and the asymptotic nature of the velocity field, we show how existing numerical simulations on quantum equilibrium can be utilised to study relaxation to pilot-wave equilibrium. Lastly, we outline an experimental proposal to detect continuous-energy eigenstates, discuss applications in quantum field theory and quantum gravity, and discuss implications for pilot-wave theory and quantum foundations in general.

Resource theory of causal connection. (arXiv:2110.03233v2 [quant-ph] UPDATED)

The capacity of distant parties to send signals to one another is a fundamental requirement in many information-processing tasks. Such ability is determined by the causal structure connecting the parties, and more generally, by the intermediate processes carrying signals from one laboratory to another. Here we build a fully fledged resource theory of causal connection for all multi-party communication scenarios, encompassing those where the parties operate in a definite causal order and also where the order is indefinite. We define and characterize the set of free processes and three different sets of free transformations thereof, resulting in three distinct resource theories of causal connection. In the causally ordered setting, we identify the most resourceful processes in the bipartite and tripartite scenarios. In the general setting, instead, our results suggest that there is no global most valuable resource. We establish the signalling robustness as a resource monotone of causal connection and provide tight bounds on it for many pertinent sets of processes. Finally, we introduce a resource theory of causal non-separability, and show that it is — in contrast to the case of causal connection — unique. Together our results offer a flexible and comprehensive framework to quantify and transform general quantum processes, as well as insights into their multi-layered causal connection structures.

Computing spacetime. (arXiv:2205.05705v2 [hep-th] UPDATED)

Inspired by the universality of computation, we advocate for a principle of spacetime complexity, where gravity arises as a consequence of spacetime optimizing the computational cost of its own quantum dynamics. This principle is explicitly realized in the context of the Anti-de Sitter/Conformal Field Theory correspondence, where complexity is naturally understood in terms of state preparation via Euclidean path integrals, and Einstein’s equations emerge from the laws of quantum complexity. We visualize spacetime complexity using Lorentzian threads which, conceptually, represent the operations needed to prepare a quantum state in a tensor network discretizing spacetime. Thus, spacetime itself evolves via optimized computation.

A holographic dark energy from the laws of thermodynamics with R\’enyi entropy. (arXiv:2208.08736v1 [gr-qc])

This article investigates the relationship between the holographic principle and the laws of thermodynamics in explaining the late-time acceleration of the universe. First, we explore the possibilities of generating the standard holographic dark energy (SHDE) from the laws of horizon thermodynamics. Except for entropies that follow an exponent stretched area law, unless we redefine the horizon temperature, we found it challenging to construct a one-to-one correspondence between the dark energies defined by the holographic principle and the laws of thermodynamics. Secondly, in SHDE models, unless we invoke some phenomenological interactions, it is impossible to explain the late-time cosmic acceleration with the Hubble horizon as the IR cutoff. On the other hand, it is possible to induce dark energy as an integration constant using the laws of thermodynamics on the Hubble horizon. These motivated us to explore a feasible way to invoke the holographic principle from the laws of horizon thermodynamics. We show that the additional terms that appear in the modified Friedmann equations on using entropies other than the Bekenstein-Hawking entropy in the first law of thermodynamics can behave like a dynamic holographic dark energy (HDE). We study the features of such an HDE with R\’enyi entropy as the choice without considering any non-standard interactions. Interestingly, the resulting form of dark energy reduces to the standard cosmological constant when R\’enyi entropy reduces to the Bekenstein-Hawking entropy. By examining different parameters, we affirm the validity of our approach to dark energy, which respects both holographic principle and thermodynamics.

GUP-corrected $\Lambda$CDM cosmology. (arXiv:2208.08830v1 [gr-qc])

Authors: Salih Kibaroğlu

In this study, we investigate the effect of the generalized uncertainty principle on the $\Lambda$CDM cosmological model. Using quantum corrected Unruh effect and Verlinde’s entropic gravity idea, we find Planck-scale corrected Friedmann equations with a cosmological constant. These results modify the $\Lambda$CDM cosmology.

Old Ideas for New Physicists:1. (arXiv:2208.08959v1 [hep-th])

Authors: T. Banks

We review and clarify ideas proposed many years ago for understanding cosmology in a holographic framework. The basic strategy is to use Jacobson’s\cite{ted95} identification of Einstein’s equations with the hydrodynamic equations of the “Area = 4 Entropy” law for causal diamonds, to identify a quantum system whose hydrodynamics match those of a given space-time. This can be done exactly for a system with any positive cosmological constant, which saturates the entropy bound for all times. The quantum system is a sequence of (cut-off) $1+1$ dimensional CFTs, with central charge proportional to the entropy in causal diamonds along an FRW geodesic. This matches with a recent\cite{BZ} proposal that the modular Hamiltonian of any causal diamond for non-negative c.c. is the $L_0$ generator of such a CFT. When an early de Sitter era is followed by slow roll expansion of the horizon, disjoint horizon volumes (which are gauge copies in an eternal dS space, but become physical due to slow roll expansion of the horizon area) manifest as a dilute gas of black holes in a post-inflationary era. Entropy fluctuations of individual black holes manifest as CMB fluctuations, and the tensor/scalar ratio is suppressed by an extra factor of the slow roll parameter $\epsilon$. Black hole evaporation provides the Hot Big Bang and baryogenesis. Black hole mergers can easily provide a source of primordial BH dark matter that dominates radiation at a temperature of $1$ eV, but numerical simulations are required to determine whether the model can explain the actual dark matter in our universe.

Can pragmatist quantum realism explain protective measurements?

Gao, Shan (2022) Can pragmatist quantum realism explain protective measurements? [Preprint]

Search for Spontaneous Radiation from Wave Function Collapse in the Majorana Demonstrator

Author(s): I. J. Arnquist et al. (Majorana Collaboration)

The Majorana Demonstrator neutrinoless double-beta decay experiment comprises a 44 kg (30 kg enriched in Ge76) array of p-type, point-contact germanium detectors. With its unprecedented energy resolution and ultralow backgrounds, Majorana also searches for rare event signatures from beyond standard …

[Phys. Rev. Lett. 129, 080401] Published Tue Aug 16, 2022

MOND and meta-empirical theory assessment

Abstract

While $$\Lambda$$ CDM has emerged as the standard model of cosmology, a small group of physicists defends modified newtonian dynamics (MOND) as an alternative view on cosmology. Exponents of MOND have employed a broad, at times explicitly philosophical, conceptual perspective in arguing their case. This paper offers reasons why that MONDian defense has been ineffective. First, we argue that the defense is ineffective according to Popperian or Lakatosian views–ostensibly the preferred philosophical views on theory assessment of proponents of MOND. Second, we argue that the defense of MOND can instead best be reconstructed as an instance of meta-empirical theory assessment. The formal employment of meta-empirical assessment by MONDians is unconvincing, however, because it lacks a sufficient epistemic foundation. Specifically, the MONDian No Alternatives Argument relies on falsifiability or explanation conditions that lack epistemic relevance, while the argument from Unexpected Explanatory Success fails since there is a known alternative to MOND. In the last part of the paper, we draw some lessons for applications of meta-empirical assessment more generally.

Cantor diagonal argument for real numbers

Hudson, Richard (2022) Cantor diagonal argument for real numbers. [Preprint]

Direct observation of relativistic broken plasma waves

Nature Physics, Published online: 15 August 2022; doi:10.1038/s41567-022-01717-6

In a plasma-based accelerator, the amplitude of the plasma wave is constrained by the wavebreaking limit. Experiments reveal features of the plasma waves at the point at which wavebreaking occurs.

Physical Time as Human Time

Kastner, Ruth (2022) Physical Time as Human Time. [Preprint]

Constructive Axiomatics in Spacetime Physics Part III: A Constructive Axiomatic Approach to Quantum Spacetime

Adlam, Emily and Linnemann, Niels and Read, James (2022) Constructive Axiomatics in Spacetime Physics Part III: A Constructive Axiomatic Approach to Quantum Spacetime. [Preprint]