arXiv subjects

Simon Friederich

Publications and source records attributed to Simon Friederich.

15 recordsLinked to original sources

arXiv2026

Can Quantum Field Theory be Recovered from Time-Symmetric Stochastic Mechanics? Part II: Prospects for a Trajectory Interpretation

In a companion paper we derived a unique time-reversal-invariant stochastic generalization of the Liouville equation and showed that it coincides with the evolution equation for the Husimi $Q$-function in a broad class of bosonic quantum field theories. Here we investigate the prospects for interpreting that evolution equation in terms of underlying stochastic trajectories. Drawing on Drummond's time-symmetric stochastic action formalism, we show that the traceless diffusion Fokker-Planck equation defines a natural measure over stochastic trajectories conditional on mixed-time boundary conditions. However, we identify a significant gap: it has not been established that every $Q$-function can be represented as a weighted average of these conditional probabilities over boundary values. The trajectory interpretation holds for ensembles with fixed boundary conditions but does not straightforwardly extend to arbitrary quantum states. Despite this limitation, we show that Drummond's trajectory dynamics are fundamentally non-Markovian -- a natural consequence of combining stochasticity with time-reversal invariance. This non-Markovianity places the dynamics outside the scope of the ontological models framework and thereby explains why the major no-go theorems for hidden-variable theories do not rule out the approach. These results clarify both the achievements and the remaining challenges in the project of understanding quantum field theory as the statistical mechanics of time-symmetric stochastic processes.

quant-ph↗

arXiv2026

Can Quantum Field Theory be Recovered from Time-Symmetric Stochastic Mechanics? Part I: Generalizing the Liouville Equation

We explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant stochastic generalization of Hamiltonian dynamics. The motivation for this project, started with this paper, is to assign sharp values to all observables and thereby avoid the quantum measurement problem. In classical mechanics, motion is deterministic and corresponds to an evolution of the phase space probability density according to Liouville's equation that is governed by first derivatives of the Hamiltonian in phase space. We derive a generalization of the Liouville equation with natural constraints -- namely, reduction to classical Hamiltonian dynamics as the stochasticity parameter $\hbar\mapsto0$, Fokker-Planck form for the probability density evolution, local Hamiltonian dependence, time-reversal invariance, energy conservation, and minimality -- which turns out to be a Fokker-Planck equation with a generalized diffusion matrix that is symmetric, traceless, and constructed from the Hessian of the Hamiltonian. We then show that the Schr\"odinger equation in the coherent-state phase-space formulation of certain bosonic QFTs has precisely this form, with the Husimi function playing the role of the phase space probability density. The question to what extent this equation can be interpreted in terms of objective stochastic field theories is discussed in a companion paper.

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arXiv2025

Sharp values for all dynamical variables via Anti-Wick quantization

This paper proposes an approach to interpreting quantum expectation values that may help address the quantum measurement problem. Quantum expectation values are usually calculated via Hilbert space inner products and, thereby, differently from expectation values in classical mechanics, which are weighted phase-space integrals. It is shown that, by using Anti-Wick quantization to associate dynamical variables with self-adjoint linear operators, quantum expectation values can be interpreted as genuine weighted averages over phase space, paralleling their classical counterparts. This interpretation arises naturally in the Segal-Bargmann space, where creation and annihilation operators act as simple multiplication and differentiation operators. In this setting, the Husimi Q-function - the coherent-state representation of the quantum state - can be seen as a true probability density in phase space. Unlike Bohmian mechanics, the present approach retains the standard correspondence between dynamical variables and self-adjoint operators while paving the way for a classical-like probabilistic interpretation of quantum statistics.

quant-ph↗

arXiv2025

Time evolution of the Husimi and Glauber-Sudarshan functions in terms of complementary Hamiltonian symbols

We present a compact, systematic formulation of the dynamics of the Husimi Q- and Glauber-Sudarshan P-phase space distribution functions expressed in terms of their \emph{complementary} Hamiltonian symbols: Anti-Wick for Q and Wick for P. The resulting evolution equations have a universal leading structure, the classical Liouvillian drift plus terms with higher-order derivatives of the Hamiltonian. For Hamiltonians no higher than quartic in the moduli of the complex phase space variables $\alpha_i$, the higher-order terms reduce to a second-order Fokker-Planck type term with a \emph{traceless} diffusion matrix, thereby clarifying and recovering recent results for such Hamiltonians within a simple star-product framework. We further derive a transparent Ehrenfest theorem for Wick/Anti-Wick symbols of the operators representing dynamical observables. Using these results, we show that a previously reported nonclassical contribution to the Q-function drift for the anharmonic oscillator is an artifact of the quantization scheme used. Our paper consolidates the formulation of the dynamics of the phase space distribution functions using complementary symbols and provides an efficient route to compute and interpret quantum phase space evolution.

quant-ph↗

arXiv2025

An account of the arrow of time when scale is surplus

Existing accounts of the cosmological arrow of time face a dilemma: generalist approaches that posit time-asymmetric laws lack independent motivation, while particularist approaches that invoke a Past Hypothesis face serious conceptual and explanatory problems. We propose a novel account that dispenses with the need for both time-asymmetric laws and a Past Hypothesis. Instead, it is centred around a symmetry argument that reveals attractors and so-called 'Janus points'. The main idea is that the global spatial scale of the Universe is not empirically accessible, and should therefore be treated as surplus structure. By contrast, the Hubble parameter, which encodes the relative rate of change of scale, is empirically accessible. Once the scale redundancy is eliminated, the empirically meaningful description of cosmic dynamics involves a drag-like variable that transforms in a way that preserves time-reversal invariance. The resulting space of dynamical possibilities possesses universal attractors and Janus points, giving rise to particular states in which observers experience a cosmological arrow of time akin to our own. We illustrate the proposal by applying it to cosmological and gravitational N-body models, showing how it accounts, respectively, for the rapid cooling of the early universe and its relative smoothness.

physics.hist-ph↗

arXiv2025

Reproducing EPR correlations without superluminal signalling: backward conditional probabilities and Statistical Independence

Bell's theorem states that no model that respects Local Causality and Statistical Independence can account for the correlations predicted by quantum mechanics via entangled states. This paper proposes a new approach, using backward-in-time conditional probabilities, which relaxes conventional assumptions of temporal ordering while preserving Statistical Independence as a "fine-tuning condition. It is shown how such models can account for EPR/Bell correlations and, analogously, the GHZ predictions while nevertheless forbidding superluminal signalling.

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arXiv2024

Kochen-Specker non-contextuality through the lens of quantization

The Kochen-Specker theorem shows that it is impossible to assign sharp values to all dynamical variables in quantum mechanics in such a way that the algebraic relations among the values of dynamical variables whose self-adjoint operators commute are the same as those among the operators themselves. We point out that, for quantum theories obtained by quantizing some classical theory, this condition -- Kochen-Specker non-contextuality -- is implausible from the start because quantization usually changes algebraic relations. We explain why this is so, using the formalism of deformation quantization and its conception of star products, and we illustrate the relevance of this point using various examples of dynamical variables quantized via Weyl quantization and coherent state quantization. Our observations suggest that the relevance of the Kochen-Specker theorem to the question of whether one can assign sharp values to all dynamical variables is rather limited

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arXiv2021

Gauge Symmetries, Symmetry Breaking, and Gauge-Invariant Approaches

Gauge symmetries play a central role, both in the mathematical foundations as well as the conceptual construction of modern (particle) physics theories. However, it is yet unclear whether they form a necessary component of theories, or whether they can be eliminated. It is also unclear whether they are merely an auxiliary tool to simplify (and possibly localize) calculations or whether they contain independent information. Therefore their status, both in physics and philosophy of physics, remains to be fully clarified. In this overview we review the current state of affairs on both the philosophy and the physics side. In particular, we focus on the circumstances in which the restriction of gauge theories to gauge invariant information on an observable level is warranted, using the Brout-Englert-Higgs theory as an example of particular current importance. Finally, we determine a set of yet to be answered questions to clarify the status of gauge symmetries.

physics.hist-ph↗

arXiv2021

Introducing the Q-based interpretation of quantum theory

This article outlines a novel interpretation of quantum theory: the Q-based interpretation. The core idea underlying this interpretation, recently suggested for quantum field theories by Drummond and Reid [2020], is to interpret the phase space function Q -- a transform of the better known Wigner function -- as a proper probability distribution, roughly analogous to the probability distribution \rho in classical statistical mechanics. Here I motivate the Q-based interpretation, investigate whether it is empirically adequate, and outline some of its key conceptual features. I argue that the Q-based interpretation is attractive in that it promises having no measurement problem, is conceptually parsimonious and has the potential to apply elegantly to relativistic and field-theoretic contexts.

quant-ph↗

arXiv2017

Resolving the observer reference class problem in cosmology

The assumption that we are typical observers plays a core role in attempts to make multiverse theories empirically testable. A widely shared worry about this assumption is that it suffers from systematic ambiguity concerning the reference class of observers with respect to which typicality is assumed. As a way out, Srednicki and Hartle recommend that we empirically test typicality with respect to different candidate reference classes in analogy to how we test physical theories. Unfortunately, as this paper argues, this idea fails because typicality is not the kind of assumption that can be subjected to empirical tests. As an alternative, a background information constraint on observer reference class choice is suggested according to which the observer reference class should be chosen such that it includes precisely those observers who one could possibly be, given one's assumed background information.

physics.hist-ph↗

arXiv2014

Philosophical perspectives on ad hoc hypotheses and the Higgs mechanism

We examine physicists' charge of ad hocness against the Higgs mechanism in the standard model of elementary particle physics. We argue that even though this charge never rested on a clear-cut and well-entrenched definition of "ad hoc", it is based on conceptual and methodological assumptions and principles that are well-founded elements of the scientific practice of high-energy particle physics. We further evaluate the implications of the recent discovery of a Higgs-like particle at the CERN's Large Hadron Collider for the charge of ad hocness against the Higgs mechanism.

physics.hist-ph↗

arXiv2013

In defence of non-ontic accounts of quantum states

The paper discusses objections against non-hidden variable versions of the epistemic conception of quantum states - the view that quantum states do not describe the properties of quantum systems but reflect, in some way to be specified, the epistemic conditions of agents assigning them. In the first half of the paper, the main motivation for the epistemic conception of quantum states is sketched, and a version of it is outlined, which combines ideas from an earlier study of it [Friederich 2011] with elements of Richard Healey's recent pragmatist interpretation of quantum theory [Healey 2012]. In the second half, various objections against epistemic accounts of quantum states are discussed in detail, which are based on criticisms found in the literature. Possible answers by the version outlined here are compared with answers from the quantum Bayesian point of view, which is at present the most discussed version of the epistemic conception of quantum states.

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arXiv2012

Gauge symmetry breaking in gauge theories---In search of clarification

The paper investigates the spontaneous breaking of gauge symmetries in gauge theories from a philosophical angle, taking into account the fact that the notion of a spontaneously broken local gauge symmetry, though widely employed in textbook expositions of the Higgs mechanism, is not supported by our leading theoretical frameworks of gauge quantum theories. In the context of lattice gauge theory, the statement that local gauge symmetry cannot be spontaneously broken can even be made rigorous in the form of Elitzur's theorem. Nevertheless, gauge symmetry breaking does occur in gauge quantum field theories in the form of the breaking of remnant subgroups of the original local gauge group under which the theories typically remain invariant after gauge fixing. The paper discusses the relation between these instances of symmetry breaking and phase transitions and draws some more general conclusions for the philosophical interpretation of gauge symmetries and their breaking.

physics.hist-ph↗

arXiv2011

Functional renormalization for spontaneous symmetry breaking in the Hubbard model

The phases with spontaneously broken symmetries corresponding to antiferromagnetic and d-wave superconducting order in the two-dimensional t-t'-Hubbard model are investigated by means of the functional renormalization group. The introduction of composite boson fields in the magnetic, charge density and superconducting channels allows an efficient parameterization of the four-fermion vertex and the study of regimes where either the antiferromagnetic or superconducting order parameter, or both, are nonzero. We compute the phase diagram and the temperature dependence of the order parameter below the critical temperature, where antiferromagnetic and superconductiving order show a tendency of mutual exclusion.

cond-mat.str-el↗

arXiv2011

How to spell out the epistemic conception of quantum states

The paper investigates the epistemic conception of quantum states---the view that quantum states are not descriptions of quantum systems but rather reflect the assigning agents' epistemic relations to the systems. This idea, which can be found already in the works of Copenhagen adherents Heisenberg and Peierls, has received increasing attention in recent years because it promises an understanding of quantum theory in which neither the measurement problem nor a conflict between quantum non-locality and relativity theory arises. Here it is argued that the main challenge for proponents of this idea is to make sense of the notion of a state assignment being performed correctly without thereby acknowledging the notion of a true state of a quantum system---a state it is in. An account based on the epistemic conception of states is proposed that fulfills this requirement by interpreting the rules governing state assignment as constitutive rules in the sense of John Searle.

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