arXiv subjects

Antony Valentini

Publications and source records attributed to Antony Valentini.

At least 19 recordsLinked to original sources

arXiv2026

First constraint on Born-rule violations at high-energy colliders

We obtain an experimental constraint on possible Born-rule violations at high-energy colliders. We model Born-rule violations with differential scattering cross sections $d\sigma/d\Omega$ subject to an angular smearing by a narrow Gaussian of width $\varepsilon$ (with respect to $x=\cos\theta$ for scattering angle $\theta$). For large-angle Bhabha ($e^{+}e^{-} \rightarrow e^{+}e^{-}$) scattering, at a centre-of-mass energy $\sqrt{s}=29\, \mathrm{GeV}$, data from the PEP collider at SLAC allow us to set an upper bound of $\varepsilon<0.042$ at $95\%$ confidence. This corresponds to a Gaussian smearing over an angular range of twice the experimental bin width, and hence provides a physically meaningful limit on deviations from the Born rule. Future prospects for improving this limit are discussed.

hep-ph↗

arXiv2025

Towards a test of the Born rule in high-energy collisions

We consider how the Born rule, a fundamental principle of quantum mechanics, can be tested for particles created on the shortest timescales ($\sim10^{-25}\,\mathrm{s}$) currently accessible at high-energy colliders. We focus on targeted tests of the Born rule for spin or polarisation probabilities, which offer a particularly clean experimental signal, and which can be described by a simple hidden-variables model of two-state systems proposed by Bell. These probabilities test a remarkable feature of the quantum formalism, whereby expectation values for incompatible experiments are linearly related. Born-rule violations can be parameterised by nonlinear expectation values for quantum measurements of spin or polarisation, together with anomalies in ensemble averages, which may then be constrained by experiment. Notable experiments considered here include the recent detection of single photons from top-quark decay, and the indirect measurement of tau-lepton polarisation. Repurposing these experiments as tests of the Born rule, however, presents several challenges, which are discussed in this paper.

hep-ph↗

arXiv2024

Pilot-wave theory and the search for new physics

We show how pilot-wave theory points to new physics, beyond quantum mechanics, in three distinct ways. First, generalised cosmological initial conditions, departing from the Born rule, can lead to observable anomalies in the cosmic microwave background and in relic cosmological particles. Second, a breakdown of the Born rule in the deep quantum-gravity regime, with gravitational corrections that render the Born rule semiclassically unstable, can create anomalies in Hawking radiation from evaporating black holes. Third, a regularised equation of motion that remains finite at nodes of the wave function generates corrections to the Born rule at short distances, while a natural time-dependent generalisation implies an instability of quantum equilibrium at short times, effects which may be observable in high-energy collisions.

gr-qc↗

arXiv2024

De Broglie-Bohm Quantum Mechanics

We provide an overview of the de Broglie-Bohm pilot-wave formulation of quantum mechanics, emphasising its applications to field theory, high-energy physics, gravitation, and cosmology.

quant-ph↗

arXiv2024

The trouble with pilot-wave theory: a critical evaluation

Objections to pilot-wave theory frequently come in three mutually-contradictory categories: that the theory is too bizarrely different from ordinary physics, that the theory is not radically different enough, and that the physics of pilot-wave theory is after all just the same as quantum physics. After a brief review of pilot-wave theory, we critically evaluate these objections. We show how the radical nature of pilot-wave theory is often misunderstood or overlooked. We highlight the novelty of its dynamics, and clarify its implications for our understanding of measurement, as well as discussing the status of Lorentz invariance, conservation laws, and the Born rule. We examine Einstein's early work on pilot-wave theory and argue that he turned away from it for reasons which are no longer compelling. We urge that the theory be understood on its own terms, as a generalised nonequilibrium theory empirically distinct from quantum mechanics, with all its potentially revolutionary implications.

quant-ph↗

arXiv2023

Evolution of Quantum Nonequilibrium for Coupled Harmonic Oscillators

In the context of de Broglie-Bohm pilot-wave theory, violations of the Born rule are allowed and can be considered as describing nonequilibrium distributions. We study the effects of interactions on quantum relaxation towards equilibrium for a system of one-dimensional coupled harmonic oscillators. We show by numerical simulations that interactions can delay or even prevent complete relaxation for some initial states. We also discuss how this effect might be relevant for cosmological scenarios and how nonequilibrium could be detected in some models.

quant-ph↗

arXiv2022

Beyond the Born rule in quantum gravity

We have recently developed a new understanding of probability in quantum gravity. In this paper we provide an overview of this new approach and its implications. Adopting the de Broglie-Bohm pilot-wave formulation of quantum physics, we argue that there is no Born rule at the fundamental level of quantum gravity with a non-normalisable Wheeler-DeWitt wave functional $Ψ$. Instead the universe is in a perpetual state of quantum nonequilibrium with a probability density $P\neq\left\vert Ψ\right\vert ^{2}$. Dynamical relaxation to the Born rule can occur only after the early universe has emerged into a semiclassical or Schrödinger approximation, with a time-dependent and normalisable wave functional $ψ$, for non-gravitational systems on a classical spacetime background. In that regime the probability density $ρ$ can relax towards $\left\vert ψ\right\vert ^{2}$ (on a coarse-grained level). Thus the pilot-wave theory of gravitation supports the hypothesis of primordial quantum nonequilibrium, with relaxation to the Born rule taking place soon after the big bang. We also show that quantum-gravitational corrections to the Schrödinger approximation allow quantum nonequilibrium $ρ\neq\left\vert ψ\right\vert ^{2}$ to be created from a prior equilibrium ($ρ=\left\vert ψ\right\vert ^{2}$) state. Such effects are very tiny and difficult to observe in practice.

gr-qc↗

arXiv2021

Quantum gravity and quantum probability

We argue that in quantum gravity there is no Born rule. The quantum-gravity regime, described by a non-normalisable Wheeler-DeWitt wave functional $Ψ$, must be in quantum nonequilibrium with a probability distribution $P\neq\left\vert Ψ\right\vert ^{2}$ (initially and always). A Born rule can emerge only in the semiclassical regime of quantum systems on a classical spacetime background, with normalisable Schrödinger wave functions $ψ$. Conditioning on the underlying quantum-gravitational ensemble yields a nonequilibrium distribution $ρ\neq\left\vert ψ\right\vert ^{2}$ at the beginning of the semiclassical regime, with quantum relaxation $ρ\rightarrow\left\vert ψ\right\vert ^{2}$ taking place only afterwards. Quantum gravity naturally creates an early nonequilibrium universe. We also show how small corrections to the Schrödinger equation yield an intermediate regime in which the Born rule is unstable: an initial distribution $ρ=\left\vert ψ\right\vert ^{2}$ can evolve to a final distribution $ρ\neq\left\vert ψ\right\vert ^{2}$. These results arise naturally in the de Broglie-Bohm pilot-wave formulation of quantum gravity. We show that quantum instability during inflation generates a large-scale deficit $\sim1/k^{3}$ in the primordial power spectrum at wavenumber $k$, though the effect is too small to observe. Similarly we find an unobservably large timescale for quantum instability in a radiation-dominated universe. Quantum instability may be important in black-hole evaporation, with a final burst of Hawking radiation that violates the Born rule. Deviations from the Born rule can also be generated for atomic systems in the gravitational field of the earth, though the effects are unlikely to be observable. The most promising scenario for the detection of Born-rule violations appears to be in radiation from exploding primordial black holes.

gr-qc↗

arXiv2020

Superdeterministic hidden-variables models I: nonequilibrium and signalling

This is the first of two papers which attempt to comprehensively analyse superdeterministic hidden-variables models of Bell correlations. We first give an overview of superdeterminism and discuss various criticisms of it raised in the literature. We argue that the most common criticism, the violation of `free-will', is incorrect. We take up Bell's intuitive criticism that these models are `conspiratorial'. To develop this further, we introduce nonequilibrium extensions of superdeterministic models. We show that the measurement statistics of these extended models depend on the physical system used to determine the measurement settings. This suggests a fine-tuning in order to eliminate this dependence from experimental observation. We also study the signalling properties of these extended models. We show that although they generally violate the formal no-signalling constraints, this violation cannot be equated to an actual signal. We therefore suggest that the so-called no-signalling constraints be more appropriately named the marginal-independence constraints. We discuss the mechanism by which marginal-independence is violated in superdeterministic models. Lastly, we consider a hypothetical scenario where two experimenters use the apparent-signalling of a superdeterministic model to communicate with each other. This scenario suggests another conspiratorial feature peculiar to superdeterminism. These suggestions are quantitatively developed in the second paper.

quant-ph↗

arXiv2020

Superdeterministic hidden-variables models II: conspiracy

We prove that superdeterministic models of quantum mechanics are conspiratorial in a mathematically well-defined sense, by further development of the ideas presented in a previous article $\mathcal{A}$. We consider a Bell scenario where, in each run and at each wing, the experimenter chooses one of $N$ devices to determine the local measurement setting. We prove, without assuming any features of quantum statistics, that superdeterministic models of this scenario must have a finely-tuned distribution of hidden variables. Specifically, fine-tuning is required so that the measurement statistics depend on the measurement settings but not on the details of how the settings are chosen. We quantify this as the overhead fine-tuning $F$ of the model, and show that $F > 0$ (corresponding to `fine-tuned') for any $N >1$. The notion of fine-tuning assumes that arbitrary (`nonequilibrium') hidden-variables distributions are possible in principle. We also show how to quantify superdeterministic conspiracy without using nonequilibrium. This second approach is based on the fact that superdeterministic correlations can mimic actual signalling. We argue that an analogous situation occurs in equilibrium where, for every run, the devices that the hidden variables are correlated with are coincidentally the same as the devices in fact used. This results in extremely large superdeterministic correlations, which we quantify as a drop of an appropriately defined formal entropy. Nonlocal and retrocausal models turn out to be non-conspiratorial according to both approaches.

quant-ph↗

arXiv2020

Anomalous spectral lines and relic quantum nonequilibrium

We describe features that could be observed in the line spectra of relic cosmological particles should quantum nonequilibrium be preserved in their statistics. According to our arguments, these features would represent a significant departure from those of a conventional origin. Among other features, we find a possible spectral broadening that is proportional to the energy resolution of the recording telescope (and so could be much larger than any conventional broadening). Notably, for a range of possible initial conditions we find the possibility of spectral line "narrowing", whereby a telescope could observe a line that is narrower than it is conventionally able to resolve. We discuss implications for the indirect search for dark matter, with particular reference to some recent controversial spectral lines.

quant-ph↗

arXiv2020

Perturbations and quantum relaxation

We investigate whether small perturbations can cause relaxation to quantum equilibrium over very long timescales. We consider in particular a two-dimensional harmonic oscillator, which can serve as a model of a field mode on expanding space. We assume an initial wave function with small perturbations to the ground state. We present evidence that the trajectories are highly confined so as to preclude relaxation to equilibrium even over very long timescales. Cosmological implications are briefly discussed.

quant-ph↗

arXiv2019

Mechanism for nonlocal information flow from black holes

We show that quantum nonequilibrium (or deviations from the Born rule) can propagate nonlocally across space. Such phenomena are allowed in the de Broglie-Bohm pilot-wave formulation of quantum mechanics. We show that an entangled state can act as a channel whereby quantum nonequilibrium can be transferred nonlocally from one region to another without any classical interaction. This suggests a novel mechanism whereby information can escape from behind the classical event horizon of an evaporating black hole.

hep-th↗

arXiv2019

Modeling the large-scale power deficit with smooth and discontinuous primordial spectra

We investigate a set of cosmological models for which the primordial power spectrum has a large-scale power deficit. The standard power-law spectrum is subject to long-wavelength modifications described by some new parameters, resulting in corrections to the anisotropies in the cosmic microwave background. The new parameters are fitted to different data sets: temperature only, temperature and polarization, the low-redshift determination of $H_0$, and baryonic acoustic oscillations. We discuss the statistical significance of the modified spectra, from both frequentist and Bayesian perspectives. Our analysis suggests motivations for considering models that break scalar-tensor consistency, or models with negligible power in the far super-Hubble limit. We present what appears to be substantial evidence for a new scale around 350 Mpc above which the primordial (scalar) power spectrum is sharply reduced by about 20%.

astro-ph.CO↗

arXiv2019

Foundations of statistical mechanics and the status of the Born rule in de Broglie-Bohm pilot-wave theory

We compare and contrast two distinct approaches to understanding the Born rule in de Broglie-Bohm pilot-wave theory, one based on dynamical relaxation over time (advocated by this author and collaborators) and the other based on typicality of initial conditions (advocated by the 'Bohmian mechanics' school). It is argued that the latter approach is inherently circular and physically misguided. The typicality approach has engendered a deep-seated confusion between contingent and law-like features, leading to misleading claims not only about the Born rule but also about the nature of the wave function. By artificially restricting the theory to equilibrium, the typicality approach has led to further misunderstandings concerning the status of the uncertainty principle, the role of quantum measurement theory, and the kinematics of the theory (including the status of Galilean and Lorentz invariance). The restriction to equilibrium has also made an erroneously-constructed stochastic model of particle creation appear more plausible than it actually is. To avoid needless controversy, we advocate a modest 'empirical approach' to the foundations of statistical mechanics. We argue that the existence or otherwise of quantum nonequilibrium in our world is an empirical question to be settled by experiment.

quant-ph↗

arXiv2016

Cosmological history in York time: inflation and perturbations

The constant mean extrinsic curvature on a spacelike slice may constitute a physically preferred time coordinate, `York time'. One line of enquiry to probe this idea is to understand processes in our cosmological history in terms of York time. Following a review of the theoretical motivations, we focus on slow-roll inflation and the freezing and Hubble re-entry of cosmological perturbations. We show how the mathematical account of these processes is distinct from the conventional account in terms of standard cosmological or conformal time. We also consider the cosmological York-timeline more broadly and contrast it with the conventional cosmological timeline.

gr-qc↗

arXiv2016

Robust predictions for the large-scale cosmological power deficit from primordial quantum nonequilibrium

The de Broglie-Bohm pilot-wave formulation of quantum theory allows the existence of physical states that violate the Born probability rule. Recent work has shown that in pilot-wave field theory on expanding space relaxation to the Born rule is suppressed for long-wavelength field modes, resulting in a large-scale power deficit ξ(k) which for a radiation-dominated expansion is found to have an approximate inverse-tangent dependence on k (assuming that the width of the initial distribution is smaller than the width of the initial Born-rule distribution and that the initial quantum states are evenly-weighted superpositions of energy states). In this paper we show that the functional form of ξ(k) is robust under changes in the initial nonequilibrium distribution -- subject to the limitation of a subquantum width -- as well as under the addition of an inflationary era at the end of the radiation-dominated phase. In both cases the predicted deficit ξ(k) remains an inverse-tangent function of k. Furthermore, with the inflationary phase the dependence of the fitting parameters on the number of superposed pre-inflationary energy states is comparable to that found previously. Our results indicate that, for the assumed broad class of initial conditions, an inverse-tangent power deficit is likely to be a fairly general and robust signature of quantum relaxation in the early universe.

gr-qc↗

arXiv2015

Statistical anisotropy and cosmological quantum relaxation

We show that cosmological quantum relaxation predicts an anisotropic primordial power spectrum with a specific dependence on wavenumber k. We explore some of the consequences for precision measurements of the cosmic microwave background (CMB). Quantum relaxation is a feature of the de Broglie-Bohm pilot-wave formulation of quantum theory, which allows the existence of more general physical states that violate the Born probability rule. Recent work has shown that relaxation to the Born rule is suppressed for long-wavelength field modes on expanding space, resulting in a large-scale power deficit with a characteristic inverse-tangent dependence on k. Because the quantum relaxation dynamics is independent of the direction of the wave vector for the relaxing field mode, in the limit of weak anisotropy we are able to derive an expression for the anisotropic power spectrum that is determined by the power deficit function. As a result, the off-diagonal terms in the CMB covariance matrix are also determined by the power deficit. We show that the lowest-order l-(l+1) inter-multipole correlations have a characteristic scaling with multipole moment l. Our derived spectrum also predicts a residual statistical anisotropy at small scales, with an approximate consistency relation between the scaling of the l-(l+1) correlations and the scaling of the angular power spectrum at high l. We also predict a relationship between the l-(l+1) correlations at large and small scales. Cosmological quantum relaxation appears to provide a single physical mechanism that predicts both a large-scale power deficit and a range of statistical anisotropies, together with potentially testable relationships between them.

astro-ph.CO↗