Will we ever quantize the center of mass of macroscopic systems? A case for a Heisenberg cut in quantum mechanics

The concept of quantum particles derives from quantum field theory. Accepting that quantum mechanics is valid all the way implies that not only composite particles (such as protons and neutrons) would be derived from a field theory, but also the center of mass of bodies as heavy as rocks. Despite the fabulous success of quantum mechanics, it is unreasonable to assume the existence of annihilation and creation operators for rocks, and so on. Fortunately, there are strong reasons to doubt that wave mechanics can describe the center of mass of systems at or above the Planck scale, thereby jeopardizing the construction of the corresponding Fock space. As a result, systems with masses exceeding the Planck mass would have their center of mass described through classical mechanics, regardless of being able to harbor macroscopic quantum phenomena as observed in the laboratory. Here, we briefly revisit (i) the arguments for the need for a Heisenberg cut delimitating the boundary between the quantum and classical realms and (ii) the kind of new physics expected at (the uncharted region of) the Heisenberg cut.''

💡 Research Summary

The paper by Aguiar and Matsas tackles the provocative question of whether the center‑of‑mass (c.m.) of macroscopic objects can ever be treated as a genuine quantum degree of freedom. Starting from the observation that quantum particles are defined within quantum field theory (QFT) – where creation and annihilation operators act on a Fock space built from single‑particle wavefunctions – the authors argue that extending this construction to objects as massive as rocks would imply the existence of annihilation/creation operators for rocks, a notion they deem physically untenable.

To support their claim they introduce the concept of “bona‑fide clocks”: idealized time‑keeping devices that must be point‑like, possess a well‑defined world‑line, and obey quantum‑mechanical constraints. By combining the Heisenberg energy‑time uncertainty relation (ΔE·Δt ≥ ħ/2) with the Schwarzschild radius condition from general relativity (R_S = 2M), they show that any clock capable of resolving intervals shorter than the Planck length (L_P ≈ 10⁻³⁵ m) or Planck time (T_P ≈ 10⁻⁴³ s) would necessarily have a mass and size that force it to become a black hole. Consequently, no physical device can measure spacetime below the Planck scale, and therefore no operational definition of spacetime exists there. This “clock‑black‑hole paradox” leads them to assert that the Planck regime (ℓ < L_P, τ < T_P) is beyond the reach of any conventional spacetime theory.

The authors then turn to the structure of QFT itself. The Dirac and Klein‑Gordon equations define the one‑particle Hilbert space through the reduced Compton wavelength λ̄ = ħ/(mc). For masses m ≳ M_P (Planck mass ≈ 10⁻⁵ g) this wavelength becomes λ̄ ≲ L_P, i.e. smaller than the Planck length. They argue that in this regime the standard wave‑mechanical description breaks down, because the underlying spacetime cannot be probed with sufficient resolution. They therefore postulate a “Quantum Spacetime Theory” (QST) that governs physics at ℓ < L_P, and they locate a “ridge” in the mass‑scale diagram at m ≈ M_P that separates a low‑mass quantum domain (m ≪ M_P) from a high‑mass classical domain (m ≫ M_P). This ridge constitutes the Heisenberg cut: a mass‑dependent boundary beyond which the center‑of‑mass ceases to exhibit spatial superposition.

To give the cut concrete dynamical content, the paper presents a simple gravitational self‑decoherence model (see Ref.