arXiv:2606.14632

No classical particle limit for massless quanta

Riccardo Falcone, Simon Fuchs

quant-phhep-thSubmitted Jun 12, 2026• Announced Jun 15, 2026• 0 citations

Abstract

We investigate whether relativistic massless classical particles may emerge as the classical limit of massless quanta. To address this question independently of any specific dynamics, environment, or pointer basis, we develop an axiomatic and purely kinematical framework for the coarse-graining approach. In this formulation, a candidate classical phase space is taken as the outcome space of a POVM subject only to minimal classicality and covariance under the relevant spacetime symmetry group. Applying this framework to the Poincaré group, we prove a no-go theorem for massless particles: the covariance requirement is incompatible with the operational conditions for classicality. The theorem leaves open field-like limits of massless quanta, for example the emergence of electromagnetic or gravitational fields, while ruling out classical massless particles, such as classical photons or gravitons.

Related papers

Phase Invariance as a Unifying Principle for Quantum Theory and Relativity

Suhaib Zayed Awad Alkarim alnur

We introduce physical phase invariance as a minimal, observer-independent principle capable of unifying quantum theory and relativity. By identifying the physical phase with the classical action measured in units of Planck’s constant, the framework assigns phase a direct operational meaning. Spacetime structure, Lorentz invariance, and quantum probabilistic behavior emerge as effective descriptions of underlying phase dynamics rather than fundamental postulates. Time is defined relationally through phase evolution, and classical motion arises from stationary phase conditions. A simple dynamical equation for the phase field is proposed, while quantum probabilities are shown to result from statistical coarse-graining over unresolved phase degrees of freedom. This approach provides a coherent conceptual foundation linking quantum mechanics, special relativity, and gravitation.

Jan 22, 20260 citations

Minimal Proper Time and Deterministic Microstates: Emergent Quantum Fields and Relativistic Spacetime

Alessio Maiezza

We develop a top-down counterpart of the minimal proper-time formulation of quantum field theory previously introduced as an effective bottom-up framework. Starting from a deterministic pre-geometric substrate of causally ordered events, we show how coarse-graining over microscopic histories leads, at low energies, to an effective Nambu-like quantum dynamics. The elementary deterministic update is identified with the minimal proper-time step, while the growth of coarse-grained equivalence classes controls both the ultraviolet dissipative correction and the scale dependence of the effective quantization strength, encoded in a running Planck constant. In this way, the proper-time cutoff kernel of the bottom-up formulation acquires a microscopic interpretation as the inverse growth of unresolved deterministic histories. In the infrared limit, the dissipative term vanishes and standard unitary quantum field theory is recovered. The same coarse-grained structure also provides a natural setting for an emergent relativistic spacetime geometry, compatible in the macroscopic limit with Einstein gravity. The resulting picture suggests a common deterministic origin for minimal-scale structure, quantum behavior, and relativistic spacetime.

hep-thCross-listedarXiv:2607.03605Jul 7, 2026

Quantum Kinematics from Renormalization Symmetry: A Convexity-Free Reconstruction in a Timeless Framework (v3)

Sudhakar Rajnikant

(This work presents an initial conceptual formulation of the renormalization-based approach to quantum theory within the TQF framework. A subsequent version 2 develops formulation of the Quantum reconstruction based on a linear state space, providing derivation of quantum-mechanical kinematics—including the emergence of the Hilbert space structure and the Born rule—from resolution independence. Readers primarily interested in the formal derivation are encouraged to consult the later versions, while the present work may be viewed as outlining the guiding ideas and initial physical intuition behind the quantum reconstruction.) The mathematical structure of quantum mechanics is traditionally introduced axiomatically, with the linearity of the state space, the Hilbert space structure, and the Born rule postulated independently. In this work, we investigate whether these features can instead emerge from a fundamental symmetry principle: the absence of a preferred scale, implemented as invariance ofphysical observables under coarse-graining transformations. We formulate a framework in which physical states are represented as functionals over configuration space and are subject to a family of coarse-graining transformations forming a renormalization group (RG) semigroup. Physical observables are required to be invariant under these transformations, while dynamical operators are allowed to transform covariantly withinthe induced RG flow. Under general consistency conditions—including associativity, symmetry, continuity, and invariance under refinement—we show that the admissible composition law of states admits an additive representation up to an invertible reparametrization, leading to a linear structure of the state space in reparametrized variables. Imposing consistency of weight assignments under coarse-graining further constrains the norm, selecting a quadratic form and inducing an inner product structure. As a result, the space of states acquires the structure of a complex Hilbert space without being postulated a priori. Within this framework, probability emerges as a measure induced by the state functional. By analyzing the transformation of weight assignments under coarse-graining, we identify an effective renormalization group flow in the space of admissible probability rules and show that the quadratic rule arises as a distinguished and heuristically stable fixed point. This provides adynamical origin for the Born rule. We further analyze the semiclassical regime, in which coarse-graining suppresses interference between configuration sectors, leading to decoherence and the emergence of effective classical behavior. In this limit, classical dynamics and an effective notion of time arise from the phase of the state functional, and an approximate Schr¨odinger equation is recovered for fluctuations. These results suggest that the core structural features of quantum mechanics can be understood as universal fixed-point properties of an underlying renormalization symmetry acting on the space of states. This perspective provides a conceptual bridge between quantum mechanics and scale-invariant quantum field theories, including the Timeless Quantum Field framework.

Mar 16, 20260 citations

Classical particle limit of non-relativistic quantum mechanics

Roberto Zucchini

We study the Classical Particle Limit of Non-Relativistic Quantum Mechanics. We show that the unitary group describing the evolution of the quantum fluctuation around any classical phase orbit has a classical limit as ħ→0 in the strong operator topology for a very large class of time independent scalar and vector potentials, which in practice covers all physically interesting cases. We also show that the mean values of the quantum mechanical position and velocity operators on suitable states, obtained by time evolution of the product of a Weyl operator centred around the large coordinates and momenta ħ −1/2 ξ and ħ −1/2 π and a fixed ħ-independent wave function, converge to the solution of the classical equations with initial data ξ, π as ħ→0 for a broad class of repulsive interactions On demontre que le groupe unitaire qui decrit l'evolution des fluctuations quantiques autour d'une orbite classique quelconque a une limite classique quand ħ→0 dans la topologie forte des operateurs, pour une vaste classe de potentiels qui couvre en pratique tous les cas physiquement interessants. On demontre que les valeurs moyennes des operateurs quantiques position et vitesse, dans des etats convenables obtenus par l'evolution temporelle du produit d'un operateur de Weyl centre autour de grandes coordonnees et de grandes impulsions ħ −1/2 ξ, ħ -1/2 π et d'une fonction d'onde independante de ħ, tendent vers la solution des equations classiques avec donnees initiales ξ, π quand ħ→0 pour une grande classe d'interactions repulsives

Annales De L Institut Henri Poincare-physique TheoriqueJan 1, 19840 citations

An axiomatic framework for classical particle mechanics without space-time

Adonai S. Sant’Anna

We present an axiomatic framework for non-relativistic classical particle mechanics, inspired on Tati's ideas about a non-space-time description for physics. The main advantage of our picture is that it allows us to describe causality without any reference to elapsed time intervals.

arXiv:physics/9904068Apr 30, 19991 citation

Observers in quantum field theory cannot be fundamental excitations

Daniel Fook Hao Tan

Quantum field theory unifies quantum mechanics with special relativity, so any physical system playing the observer role in a QFT setting must simultaneously satisfy the SR-observer condition (a Poincaré-covariant worldline-tetrad bundle at the representation level) and the QM-observer condition (persistent macroscopic pointer structure supporting record formation). We take the intersection of these two conditions as the necessary content of "QFT observer" and apply it to the fundamental quantum field excitations of the Standard Model. Massless helicity states (photon; gluon perturbatively; hypothetical asymptotic graviton) fail the SR-observer condition because every four-momentum in the spectral support is null and no construction on the massless helicity representation supplies a mode-level rest-frame bundle. Newton-Wigner localisation is excluded on the massless helicity-±1 representation under the standard Wightman hypotheses, non-Wightman photon-position constructions each relax at least one requirement of the bundle, the Fokker-Pryce centroid is singular in the massless limit, and Ehrenfest expectation-value trajectories on non-Wightman photon-position operators fail the mode-level rest-frame requirement even when their tangent is timelike. Massive fundamental bosons (Higgs, W, Z) satisfy the SR-observer condition on their spectral support but fail the QM-observer condition because their decay widths preclude persistent macroscopic structure over any operationally relevant interval (Higgs τ ~ 10⁻²² s; W and Z τ ~ 10⁻²⁵ s, versus a macroscopic detector coarse-graining scale σ ≥ 10⁻¹² s) and the Standard Model contains no stable bound composites of pure fundamental bosons. The elimination leaves fermionic composites as the only surviving class of candidate QFT observer within the Standard Model. The positive characterisation of that class, including the specific field-theoretic content playing the observer role and the application to decoherence branch-selection, is deferred to a companion paper.

Jul 29, 20260 citations