Tim Palmer

Abstract:

Motivated in part by John Wheeler's assertion that the continuum nature of Hilbert Space conceals the "it-from-bit" information-theoretic character of the quantum wavefunction, a theory of quantum physics (Rational Quantum Mechanics-RaQM) is proposed based on a specific discretization of complex Hilbert Space. The Schrödinger equation is not modified in RaQM, even during measurement. However, the bases in which the quantum state is defined must satisfy certain rational-number constraints. These constraints lead to the notion of finite qubit information capacity [Formula: see text]: For any [Formula: see text] qubit state, there is insufficient information in the [Formula: see text] qubits (linearly growing in [Formula: see text]) to allocate even one bit to each of all [Formula: see text] continuum degrees of freedom (exponentially growing in [Formula: see text]) associated with quantum mechanics/theory (QM, where [Formula: see text]). It is proposed that the discretization of Hilbert Space in RaQM is due to gravity, hence QM is the (singular) continuum limit of RaQM at [Formula: see text]. On this basis, it is estimated that [Formula: see text] lies between about 200 and 400 for current qubit technologies, and will never exceed 1,000. While QM and RaQM are experimentally indistinguishable for small numbers of qubits, RaQM predicts that the exponential advantage of quantum algorithms which, like Shor's, require bases with maximal [Formula: see text]-qubit superposition/entanglement, will have saturated at 1,000 perfect qubits. Hence, insofar as a classical computer will never factor a 2,048-bit RSA integer, RaQM predicts that a quantum computer will not either. This predicted breakdown of QM could be testable in less than 5 y.

Abstract:

Negating the Measurement Independence assumption (MI) is often referred to as the ‘third way’ to account for the experimental violation of Bell’s inequality. However, this route is generally viewed as ludicrously contrived, implying some implausible conspiracy where experimenters are denied the freedom to choose measurement settings as they like. Here, a locally realistic model of quantum physics is developed (Rational Mechanics - RaQM - based on a gravitational discretisation of Hilbert Space) which violates MI without denying free will. Crucially, RaQM distinguishes experimenters’ ability to freely choose measurement settings to some nominal accuracy, from an inability to choose exact settings which were never under their control anyway. In RaQM, Hilbert states are necessarily undefined in bases where squared amplitudes and/or complex phases are irrational numbers. Such ‘irrational’ bases correspond to conceivable but necessarily impossible counterfactual measurements and are shown to play a ubiquitous role in the analysis of both single- and entangled-particle quantum physics. It is concluded that violation of Bell inequalities can be understood with none of the strange processes historically associated with it. Instead, using concepts from (non-classical) p-adic number theory, we relate RaQM to Bohm and Hiley’s concept of a holistic Machian-like Undivided Universe. If this interpretation of Bell’s Theorem is correct, building more and more energetic particle accelerators to probe smaller and smaller scales, in the search for a theory which synthesises quantum and gravitational physics and hence a Theory of Everything, may be a fruitless exercise.

Abstract:

We propose terminology to classify interpretations of quantum mechanics and models that modify or complete quantum mechanics. Our focus is on models which have previously been referred to as superdeterministic (strong or weak), retrocausal (with or without signalling, dynamical or non-dynamical), future-input-dependent, atemporal and all-at-once, not always with the same meaning or context. Sometimes, these models are assumed to be deterministic, sometimes not, the word deterministic has been given different meanings, and different notions of causality have been used when classifying them. This has created much confusion in the literature, and we hope that the terms proposed here will help to clarify the nomenclature. The general model framework that we will propose may also be useful to classify other interpretations and modifications of quantum mechanics. This document grew out of the discussions at the 2022 Bonn Workshop on Superdeterminism and Retrocausality.

Abstract:

The 2021 Pacific Northwest heatwave was so extreme as to challenge conventional statistical and climate-model-based approaches to extreme weather attribution. However, state-of-the-art operational weather prediction systems are demonstrably able to simulate the detailed physics of the heatwave. Here, we leverage these systems to show that human influence on the climate made this event at least 8 [2–50] times more likely. At the current rate of global warming, the likelihood of such an event is doubling every 20 [10–50] years. Given the multi-decade lower-bound return-time implied by the length of the historical record, this rate of change in likelihood is highly relevant for decision makers. Further, forecast-based attribution can synthesise the conditional event-specific storyline and unconditional event-class probabilistic approaches to attribution. If developed as a routine service in forecasting centres, it could provide reliable estimates of human influence on extreme weather risk, which is critical to supporting effective adaptation planning.

Abstract:

The 2021 Pacific Northwest heatwave was so extreme as to challenge conventional statistical and climate-model-based approaches to extreme weather attribution. However, state-of-the-art operational weather prediction systems are demonstrably able to simulate the detailed physics of the heatwave. Here, we leverage these systems to show that human influence on the climate made this event at least 8 [2–50] times more likely. At the current rate of global warming, the likelihood of such an event is doubling every 20 [10–50] years. Given the multi-decade lower-bound return-time implied by the length of the historical record, this rate of change in likelihood is highly relevant for decision makers. Further, forecast-based attribution can synthesise the conditional event-specific storyline and unconditional event-class probabilistic approaches to attribution. If developed as a routine service in forecasting centres, it could provide reliable estimates of human influence on extreme weather risk, which is critical to supporting effective adaptation planning.