Researchers Find Massless Quanta Lack a Classical Particle Limit

A fundamental limit to understanding massless quanta as classical particles has been identified by Riccardo Falcone and Simon Fuchs at the Academy of Sciences. Falcone and Fuchs prove a “no-go” theorem demonstrating that the requirement of covariance, a key principle in physics relating to symmetry, conflicts with the conditions necessary for defining classical behaviour in massless particles. The work develops a new axiomatic framework for examining the relationship between quantum and classical physics, independent of specific physical systems, and sharply clarifies the boundary between the quantum and classical realms by ruling out the existence of classical counterparts to particles like photons or gravitons.

Emergence of particle or field descriptions from second-quantised quantum mechanics

Investigations into the classical limit of quantum theory address two related questions: how a classical description arises from a quantum theory, and which classical theory emerges. In nonrelativistic quantum mechanics, the classical limit for a single particle with Hilbert space L2(R3) is typically assumed to be ordinary Hamiltonian mechanics on the canonical phase space T ∗R3, using position and momentum as classical variables. However, the situation differs in second-quantized quantum mechanics, where fields and particles are unified, allowing descriptions in terms of field operators or particle-number sectors.

Particle and field theories differ classically, with particle theories using positions, momenta, and trajectories, while field theories use field configurations and their conjugate variables. A complete account of the quantum-to-classical transition must explain not only the emergence of classical behaviour, but also whether the emergent description is particle-like or field-like. This issue is central in relativistic quantum theory, where the second-quantized formulation is natural.

The question of how quantum systems become effectively classical has been extensively studied, with environment-induced decoherence offering a dynamical explanation by suppressing interference and stabilising classical records. Coarse-graining provides a complementary perspective, focusing on finite measurement resolution and identifying accessible statistics for an effective classical probabilistic description. Dynamical routes to classicality provide decoherence, while coarse-graining offers a kinematical criterion for identifying classical interpretations of quantum observables.

Both decoherence and coarse-graining are influenced by the target theory, tying them to pointer states in decoherence and to the choice of finite-resolution observables in coarse-graining. In the nonrelativistic single-particle case, these approaches recover the same classical phase-space limit on T ∗R3 by employing canonical coherent states, also known as Schrödinger or Weyl, Heisenberg coherent states. Defined as |x, p⟩= e−i ħx· P e i ħp· X |0, 0⟩, these states have |0, 0⟩ as a Gaussian wave packet centred at the origin, with X and P being the canonical position and momentum operators.

Each state is localized around x in position space and around p in momentum space, and is covariant under phase-space translations. Localized Gaussian wave packets are natural candidates for pointer states in nonrelativistic particle models. In the coarse-graining approach, the phase-space localization and covariance of these states make them a natural kernel for phase-space POVMs, assigning to each cell C an effect ΠC = ∫C d3xd3p |x, p⟩⟨x, p|. For sufficiently coarse cells, the corresponding measurement statistics admit an effective classical probabilistic description on the canonical position-momentum phase space.

Current investigations focus on whether a similar particle-like target exists for relativistic massless particles. While relativistic point particles are standard in classical mechanics, the classical limits of massless quantum degrees of freedom are often field-like, as seen in classical electrodynamics where massless electromagnetic sectors are described by fields. The central question is not whether massless quantum systems can have a classical limit, but whether they can have a classical particle phase-space limit.

A particle-like target is obstructed at the kinematical level, first becoming apparent when attempting to construct relativistic analogues of the nonrelativistic coherent states |x, p⟩. Poincaré covariance requires the seed state |0, p⟩ associated with a null momentum pμ to be invariant under the corresponding little group, forcing its momentum-space wavefunction ψ0,p(k) to depend on k and p only through the invariant combination kμpμ = |k| |p| −k · p. Along the direction k ∥p this invariant is independent of the magnitude |k|, meaning the wavefunction cannot be localized around a definite value of |p|. Consequently, coarse-grained measurements cannot resolve different energy scales along the same null direction, even though these correspond to distinct momentum labels in a classical phase space. This obstruction also affects the decoherence program, as there is no Poincaré-covariant analogue of Weyl, Heisenberg coherent states optimally localized in both position and momentum to serve as natural pointer states for massless particles. This coherent-state construction failure is not a general no-go theorem; a more general coarse-grained POVM, not built from rank-one coherent-state projectors, might define a particle-like classical phase space. Therefore, the problem is formulated directly at the level of phase-space effects, asking whether there exists a POVM on the candidate classical phase space of massless particles, C 7→ΠC, satisfying four main requirements: (i) the assignment C 7→ΠC must be Poincaré covariant; (ii) for any sufficiently coarse partition {Ci}N i=1, the corresponding outcomes should be mutually exclusive and stable under immediate repetition at the coarse-grained level, i.e. , ΠCi ΠCj ≃δij ΠCi; (iii) the momentum marginal must agree, up to coarse-grained accuracy, with the standard momentum spectral measure.

Covariance and classicality preclude massless quantum interpretations

A fundamental limit to understanding massless quanta as classical particles has been demonstrated, establishing a no-go theorem that surpasses previous methods by explicitly addressing incompatibilities with covariance. The requirement of covariance, a cornerstone of physics concerning symmetry, fundamentally conflicts with the conditions needed to define classical behaviour in massless particles, reducing the potential for classical interpretations of massless quanta to zero. This work introduces a new axiomatic framework for examining the quantum-to-classical transition, independent of specific physical systems, and clarifies the boundary between the quantum and classical realms by ruling out classical counterparts to particles like photons or gravitons. Published on arXiv in 2026, the research offers a rigorous mathematical proof of this incompatibility.

Relativistic limitations preclude classical descriptions of zero mass particles

A fundamental limit to how we can understand massless particles behaving classically has been demonstrated. Classical fields, like electromagnetic radiation, can still emerge from quantum descriptions, but a stark incompatibility exists when attempting to define a classical phase space for particles lacking mass. This finding challenges the conventional approach of simply applying established techniques from nonrelativistic quantum mechanics to the relativistic realm, where the behaviour of massless entities diverges significantly.

Understanding where classical physics fails is as valuable as confirming its successes, guiding future theoretical development and refining our grasp of fundamental reality. This rigorous exclusion of classical massless particles does not invalidate broader investigations into the quantum-to-classical transition. The work specifically addressed particles with zero mass; it does not preclude classical descriptions of fields like light or gravity, which emerge from quantum origins.

The work establishes a firm boundary regarding how accurately classical physics can describe massless particles. By developing a new framework for examining the transition from quantum to classical behaviour, it proved that a classical description of massless particles is fundamentally impossible given the requirement of covariance, a principle ensuring physical laws remain consistent regardless of an observer’s motion. This incompatibility does not extend to massless fields, such as those governing light and gravity, which can still emerge from quantum origins.

The research demonstrated a fundamental limit to describing massless particles using classical physics. It proves that defining a classical phase space for particles lacking mass is incompatible with the principle of covariance, which ensures physical laws are consistent for all observers. This finding clarifies the boundary between the quantum and classical worlds, ruling out classical counterparts to particles like photons or gravitons, while still allowing for the emergence of classical fields such as electromagnetic radiation. The authors established this incompatibility through a new axiomatic and kinematical framework for coarse-graining approaches.