arXiv subjects

Mordecai Waegell

Publications and source records attributed to Mordecai Waegell.

At least 19 recordsLinked to original sources

arXiv2026

On measurement, superdeterminism, free will, and contextuality

Superdeterminism has received recent attention as a possible path toward a locally causal explanation of the entanglement correlations that appear in experimental tests of Bell's theorem. While the term `superdeterminism' was coined by Bell to refer to restrictions on the free will of experimenters, it was not rigorously defined until recently. It has now been defined as a property of any physical theory that produces systematic violations of statistical independence. Here we focus on formalizing the requirements that being nonsuperdeterministic places on a physical theory, and setting a standard that must be met before we can conclude that a given theory is not superdeterministic. We begin by carefully examining how a physical theory determines what outcomes we observe when performing measurements in terms of ontic states and response functions, and how this differs between superdeterministic and nonsuperdeterministic theories, in terms of the behavior of the types of vetted random sampling procedures that we use in experiments. The core result is that individual samples and measurement outcomes must be representative of the observed distributions, which is explained in detail. This also has a bearing on how measurement settings are chosen by agents, whether freely or randomly, and we argue that this standard ultimately defines what freedom/independence actually mean. We then discuss contextuality, and show that in most cases, superdeterminism is contextual. Finally, we discuss how different physical theories, with different notions of ontic states and response functions, can give rise to the same empirical data, and how the same operational contextuality may appear in different forms.

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arXiv2026

Is Bohmian mechanics missing some motion? Why a recent experiment is inconclusive

A recent experiment raises a supposed challenge to Bohmian mechanics, claiming to observe stationary states, which should have zero Bohm velocity, while indirectly measuring a nonzero speed based on how an evanescent wavefunction spreads from one waveguide to another coupled waveguide. There were numerous problems with this experiment and how it was interpreted. First, the experiment is not observing stationary states as claimed, but rather the time-averaged density of wave pulses which reflect off the potential step. Second, the proposed method for measuring a propagation speed is shown to be invalid for true stationary states. Third, the invalid method was misapplied to the time-averaged density, and this is shown to have created the false impression that it yields correct speed values for stationary states. These issues notwithstanding, for a wavefunction $ψ= Re^{iS/\hbar}$, the velocity of interest, $\vec{v}_s = -\frac{\hbar}{m}\frac{\vec{\nabla}R}{R}$, is different from the Bohm velocity $\vec{v}_B=\frac{1}{m}\vec{\nabla}S$, and may be nonzero for stationary states. This quantity has been called the \textit{symmetric} or \textit{osmotic} velocity, and while it emerges naturally as an imaginary component of the velocity in the derivation of the Madelung/Bohm description, it is usually disregarded. So, even though we do not think this experiment makes a compelling case for it, if $\vec{v}_s$ is somehow associated with real physical motion, then this motion is indeed absent from Bohmian mechanics, as the authors contend. We discuss a generalized Madelung fluid model where this velocity is given physical meaning, and show how it roughly agrees with the authors' concept of an evanescent De Broglie speed.

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arXiv2025

Nonlocal action in Everettian Quantum Mechanics

According to a common view, Everettian quantum mechanics (EQM) is a local theory because it avoids nonlocal action at a distance, and this is an important point in EQM's favor. Unlike collapse theories, EQM does not allow an action on one system to change the reduced density matrix (RDM) of a remote entangled system - a clear case of nonlocal action. However, EQM does allow an action on one system to change the global state of the system and its remote entangled partners. We argue that such changes should also count as nonlocal actions, meaning EQM is not local after all. First, we consider an argument to the contrary, which deems such global changes to be mere extrinsic changes, whereas nonlocal action requires intrinsic changes to the remote system. We respond that the intrinsic-extrinsic distinction is problematic and cannot hold the weight of this argument. We then try to clarify when actions that change global states count as nonlocal actions. We argue that it is when the global states are essential explanatory mechanisms of the theory. In EQM, the global state is needed to explain why, in an anti-correlated Bell state, Alice's measuring spin-up ensures that she encounters only the branch where Bob measures spin-down.

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arXiv2025

Agency cannot be a purely quantum phenomenon

What are the physical requirements for agency? We investigate whether a purely quantum system (one evolving unitarily in a coherent regime without decoherence or collapse) can satisfy three minimal conditions for agency: an agent must be able to create a world-model, use it to evaluate the likely consequences of alternative actions, and reliably perform the action that maximizes expected utility. We show that the first two conditions conflict with the no-cloning theorem, which forbids copying unknown quantum states: world-model construction requires copying information from the environment, and deliberation requires copying the world-model to assess multiple actions. Approximate cloning strategies do not permit sufficient fidelity or generality for agency to be viable in purely quantum systems. The third agency condition also fails due to the linearity of quantum dynamics. These results imply four key consequences. First, agency requires significant classical resources, placing clear constraints on its physical basis. Second, they provide insight into how classical agents emerge within a quantum universe. Third, they show that quantum computers cannot straightforwardly simulate agential behavior without significant classical components. Finally, they challenge quantum theories of agency, free will, and consciousness.

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arXiv2025

From statistical dependence to the space of possible superdeterministic theories

Bell's theorem demonstrates that any physical theory that is consistent with the predictions of quantum mechanics, and which satisfies some apparently innocuous assumptions, must violate the principle of local causality. It may therefore be possible to maintain local causality by rejecting one of these other assumptions instead. One possibility that has recently received significant attention involves rejecting the principle of statistical independence (SI). In this paper, we consider the frequency interpretation of SI, which states that $ρ(λ) \approx ρ(λ| Z)$, where $ρ(λ)$ is the relative frequency of an element of an ensemble being in the state $λ$, and $Z$ is a label that separates the ensemble into apparently randomly selected sub-ensembles. SI is violated when the sub-ensemble frequency $ρ(λ| Z)$ fails to be representative of the ensemble frequency $ρ(λ)$. We argue that physical theories that systematically violate SI should all be understood as superdeterministic. This perspective on SI sheds light on a number of issues that are being debated in the superdeterminism literature, especially concerning its scope and philosophical consequences. Regarding scope, we argue that superdeterministic theories fall into three categories, deterministic theories with fine-tuned initial conditions, fluke theories, and nomic exclusion theories. We also argue that retrocausal and invariant set theories need not violate SI, which is contrary to how they are normally presented. Regarding philosophical implications, we argue that superdeterminism is incompatible with free will according to some prominent compatibilist accounts. We also argue that although superdeterminism is conspiratorial, it is not unscientific, but pre-scientific.

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arXiv2024

Separating a particle's mass from its momentum

The Quantum Cheshire Cat experiment showed that when weak measurements are performed on pre- and post-selected system, the counterintuitive result has been obtained that a neutron is measured to be in one place without its spin, and its spin is measured to be in another place without the neutron. A generalization of this effect is presented with a massive particle whose mass is measured to be in one place with no momentum, while the momentum is measured to be in another place without the mass. The new result applies to any massive particle, independent of its spin or charge. A gedanken experiment which illustrates this effect is presented using a nested pair of Mach-Zehnder interferometers, but with some of the mirrors and beam splitters moving relative to the laboratory frame. The titular interpretation of this experiment is extremely controversial, and rests on several assumptions, which are discussed in detail. An alternative interpretation using the counterparticle model of Aharonov et al. is also discussed.

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arXiv2024

Madelung Mechanics and Superoscillations

In single-particle Madelung mechanics, the single-particle quantum state $Ψ(\vec{x},t) = R(\vec{x},t) e^{iS(\vec{x},t)/\hbar}$ is interpreted as comprising an entire conserved fluid of classical point particles, with local density $R(\vec{x},t)^2$ and local momentum $\vec{\nabla}S(\vec{x},t)$ (where $R$ and $S$ are real). The Schrödinger equation gives rise to the continuity equation for the fluid, and the Hamilton-Jacobi equation for particles of the fluid, which includes an additional density-dependent quantum potential energy term $Q(\vec{x},t) = -\frac{\hbar^2}{2m}\frac{\vec{\nabla}R(\vec{x},t)}{R(\vec{x},t)}$, which is all that makes the fluid behavior nonclassical. In particular, the quantum potential can become negative and create a nonclassical boost in the kinetic energy. This boost is related to superoscillations in the wavefunction, where the local frequency of $Ψ$ exceeds its global band limit. Berry showed that for states of definite energy $E$, the regions of superoscillation are exactly the regions where $Q(\vec{x},t)<0$. For energy superposition states with band-limit $E_+$, the situation is slightly more complicated, and the bound is no longer $Q(\vec{x},t)<0$. However, the fluid model provides a definite local energy for each fluid particle which allows us to define a local band limit for superoscillation, and with this definition, all regions of superoscillation are again regions where $Q(\vec{x},t)<0$ for general superpositions. An alternative interpretation of these quantities involving a \textit{reduced quantum potential} is reviewed and advanced, and a parallel discussion of superoscillation in this picture is given. Detailed examples are given which illustrate the role of the quantum potential and superoscillations in a range of scenarios.

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arXiv2024

Generation of Kochen-Specker contextual sets in higher dimensions by dimensional upscaling whose complexity does not scale with dimension and their applications

Recently, handling of contextual sets, in particular Kochen-Specker (KS) sets, in higher dimensions has been given an increasing attention, both theoretically and experimentally. However, methods of their generation are diverse, not generally applicable in every dimension, and of exponential complexity. Therefore, we design a dimensional upscaling method, whose complexity does not scale with dimension. As a proof of principle we generate manageable-sized KS master sets in up to 27 dimensional spaces and show that well over 32 dimensions can be reached. From these master sets we obtain an ample number of smaller KS sets. We discuss three kinds of applications that work with KS sets in higher dimensions. We anticipate other applications of KS sets for quantum information processing that make use of large families of nonisomorphic KS sets.

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arXiv2024

Toward Local Madelung Mechanics in Spacetime

It has recently been shown that relativistic quantum theory leads to a local interpretation of quantum mechanics wherein the universal wavefunction in configuration space is entirely replaced with an ensemble of local fluid equations in spacetime. For want of a fully relativistic quantum fluid treatment, we develop a model using the nonrelativistic Madelung equations, and obtain conditions for them to be local in spacetime. Every particle in the Madelung fluid is equally real, and has a definite position, momentum, kinetic energy, and potential energy. These are obtained by defining quantum momentum and kinetic energy densities for the fluid and separating the momentum into average and symmetric parts, and kinetic energy into classical kinetic and quantum potential parts. The two types of momentum naturally give rise to a single classical kinetic energy density, which contains the expected kinetic energy, even for stationary states, and we define the reduced quantum potential as the remaining part of the quantum kinetic energy density. We treat the quantum potential as a novel mode of internal energy storage within the fluid particles, which explains most of the nonclassical behavior of the Madelung fluid. For example, we show that in tunneling phenomena the quantum potential negates the barrier so that nothing prevents the fluid from flowing through. We show how energy flows and transforms in this model, and that enabling local conservation of energy requires defining a quantum potential energy current that flows through the fluid rather than only flowing with it. The nonrelativistic treatment generally contains singularities in the velocity field, which undermines the goal of local dynamics, but we expect a proper relativistic treatment will bound the fluid particle velocities at $c$.

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arXiv2023

The Generative Programs Framework

Recently there has been significant interest in using causal modelling techniques to understand the structure of physical theories. However, the notion of `causation' is limiting - insisting that a physical theory must involve causal structure already places significant constraints on the form that theory may take. Thus in this paper, we aim to set out a more general structural framework. We argue that any quantitative physical theory can be represented in the form of a generative program, i.e. a list of instructions showing how to generate the empirical data; the information-processing structure associated with this program can be represented by a directed acyclic graph (DAG). We suggest that these graphs can be interpreted as encoding relations of `ontological priority,' and that ontological priority is a suitable generalisation of causation which applies even to theories that don't have a natural causal structure. We discuss some applications of our framework to philosophical questions about realism, operationalism, free will, locality and fine-tuning.

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arXiv2023

Aharonov-Bohm effect with an effective complex-valued vector potential

The interaction between a quantum charge and a dynamic source of a magnetic field is considered in the Aharonov-Bohm scenario. It is shown that, in weak interactions with a post-selection of the source, the effective vector potential is, generally, complex-valued. This leads to new experimental protocols to detect the Aharonov-Bohm phase before the source is fully encircled. While this does not necessarily change the nonlocal status of the Aharonov-Bohm effect, it brings new insights into it. Moreover, we discuss how these results might have consequences for the correspondence principle, making complex vector potentials relevant to the study of classical systems.

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arXiv2022

The Golay codes and Quantum Contextuality

It is shown that the codewords of the binary and ternary Golay codes can be converted into rays in RP(23) and RP(11) that provide proofs of the Kochen-Specker theorem in real state spaces of dimension 24 and 12, respectively. Some implications of these results are discussed.

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arXiv2022

Quantum reality with negative-mass particles

Physical interpretations of the time-symmetric formulation of quantum mechanics, due to Aharonov, Bergmann, and Lebowitz are discussed in terms of weak values. The most direct, yet somewhat naive, interpretation uses the time-symmetric formulation to assign eigenvalues to unmeasured observables of a system, which results in logical paradoxes, and no clear physical picture. A top-down ontological model is introduced that treats the weak values of observables as physically real during the time between pre- and post-selection (PPS), which avoids these paradoxes. The generally delocalized rank-1 projectors of a quantum system describe its fundamental ontological elements, and the highest-rank projectors corresponding to individual localized objects describe an emergent particle model, with unusual particles whose masses and energies may be negative or imaginary. This retrocausal top-down model leads to an intuitive particle-based ontological picture, wherein weak measurements directly probe the properties of these exotic particles, which exist whether or not they are actually measured

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arXiv2021

Local Quantum Theory with Fluids in Space-Time

In 1948, Schwinger developed a local Lorentz covariant formulation of relativistic quantum electrodynamics in space-time which is fundamentally inconsistent with any delocalized interpretation of quantum mechanics. An interpretation compatible with Schwinger's theory is presented, which makes all of the same empirical predictions as conventional delocalized quantum theory in configuration space. This is an explicit, unambiguous, and Lorentz-covariant 'local hidden variable theory' in space-time, whose existence proves definitively that such theories are possible. There is no inconsistency with Bell's theorem because this a local many-worlds theory. Each physical system is characterized by a wave-field, which is a set of indexed piece-wise single-particle wavefunctions in space-time, each with with its own coefficient, along with a memory which contains the separate local Hilbert-space quantum state at each event in space-time. Each single-particle wavefunction of a fundamental system describes the motion of a portion of a conserved fluid in space-time, with the fluid decomposing into many classical point particles, each following a world-line and recording a local memory. Local interactions between two systems take the form of local boundary conditions between the differently indexed pieces of those systems' wave-fields, with new indexes encoding each orthogonal outcome of the interaction. The general machinery is introduced, including the local mechanisms for entanglement and interference. The experience of collapse, Born rule probability, and environmental decoherence are discussed, and a number of illustrative examples are given.

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arXiv2020

Nonlocal interferences induced by the phase of the wavefunction for a particle in a cavity with moving boundaries

We investigate the dynamics of a particle in a confined periodic system---a time-dependent oscillator confined by infinitely high and moving walls---and focus on the evolution of the phase of the wavefunction. It is shown that, for some specific initial states in this potential, the phase of the wavefunction throughout the cavity depends on the walls motion. We further elaborate a thought experiment based on interferences devised to detect this form of single-particle nonlocality from a relative phase. We point out that, within the non-relativistic formalism based on the Schrödinger equation (SE), detecting this form of nonlocality can give rise to signaling. We believe this effect is an artifact, but the standard relativistic corrections to the SE do not appear to fix it. Specific illustrations are given, with analytical results in the adiabatic approximation, and numerical computations to show that contributions from high-energy states (corresponding to superluminal velocities) are negligible.

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arXiv2020

An Interaction-Free Quantum Measurement-Driven Engine

Recently highly-efficient quantum engines were devised by exploiting the stochastic energy changes induced by quantum measurement. Here we show that such an engine can be based on an interaction-free measurement, in which the meter seemingly does not interact with the measured object. We use a modified version of the Elitzur-Vaidman bomb tester, an interferometric setup able to detect the presence of a bomb triggered by a single photon without exploding it. In our case, a quantum bomb subject to a gravitational force is initially in a superposition of being inside and outside one of the interferometer arms. We show that the bomb can be lifted without blowing up. This occurs when a photon traversing the interferometer is detected at a port that is always dark when the bomb is located outside the arm. The required potential energy is provided by the photon (which plays the role of the meter) even though it was not absorbed by the bomb. A natural interpretation is that the photon traveled through the arm which does not contain the bomb -- otherwise the bomb would have exploded -- but it implies the surprising conclusion that the energy exchange occurred at a distance despite a local interaction Hamiltonian. We use the weak value formalism to support this interpretation and find evidence of contextuality. Regardless of interpretation, this interaction-free quantum measurement engine is able to lift the most sensitive bomb without setting it off.

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arXiv2020

Reformulating Bell's Theorem: The Search for a Truly Local Quantum Theory

The apparent nonlocality of quantum theory has been a persistent concern. Einstein et. al. (1935) and Bell (1964) emphasized the apparent nonlocality arising from entanglement correlations. While some interpretations embrace this nonlocality, modern variations of the Everett-inspired many worlds interpretation try to circumvent it. In this paper, we review Bell's "no-go" theorem and explain how it rests on three axioms, local causality, no superdeterminism, and one world. Although Bell is often taken to have shown that local causality is ruled out by the experimentally confirrmed entanglement correlations, we make clear that it is the conjunction of the three axioms that is ruled out by these correlations. We then show that by assuming local causality and no superdeterminism, we can give a direct proof of many worlds. The remainder of the paper searches for a consistent, local, formulation of many worlds. We show that prominent formulations whose ontology is given by the wave function violate local causality, and we critically evaluate claims in the literature to the contrary. We ultimately identify a local many worlds interpretation that replaces the wave function with a separable Lorentz-invariant wave-field. We conclude with discussions of the Born rule, and other interpretations of quantum mechanics.

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arXiv2020

Magnetic forces in the absence of a classical magnetic field

It is shown that, in some cases, the effect of discrete distributions of flux lines in quantum mechanics can be associated with the effect of continuous distributions of magnetic fields with special symmetries. In particular, flux lines with an arbitrary value of magnetic flux can be used to create energetic barriers, which can be used to confine quantum systems in specially designed configurations. This generalizes a previous work where such energy barriers arose from flux lines with half-integer fluxons. Furthermore, it is shown how the Landau levels can be obtained from a two-dimensional grid of flux lines. These results suggest that the classical magnetic force can be seen as emerging entirely from the Aharonov-Bohm effect. Finally, the basic elements of a semi-classical theory that models the emergence of classical magnetic forces from fields with special symmetries are introduced.

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