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

TL;DR

The paper challenges the universal applicability of standard quantum mechanics to the center of mass of macroscopic systems, arguing that wave mechanics may break down near the Planck mass $M_P$ and that a Heisenberg cut to separate quantum from classical behavior is physically warranted. It proposes a quantum spacetime theory (QST) framework in which both QM and classical mechanics emerge, with a ridge near $m \sim M_P$ and Planck-scale spacetime preventing a straightforward Fock-space description for large masses. A minimal, Lorentz-invariant extension of QM is outlined through gravitational self-decoherence (AM2025a) that decoheres Planck-mass systems while leaving lighter masses unaffected; black holes are used to illustrate the coexistence of classical bulk behavior with quantizable perturbations. The work aims to redefine the boundary between quantum and classical domains, guiding experimental efforts with mesoscopic masses and informing the search for new physics at the boundary between these regimes.

Abstract

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.''

Figures (2)

• Figure 1: The figure shows clock ${\@fontswitch\mathcal{C}}_1$ moving from the left to the right along a small rod and measuring the proper time $\tau_1$ of its one-way trip, clock ${\@fontswitch\mathcal{C}}_2$ measuring the return-trip proper time $\tau_2$, and clock ${\@fontswitch\mathcal{C}}_3$ measuring the time interval between the departure of ${\@fontswitch\mathcal{C}}_1$ and returning of ${\@fontswitch\mathcal{C}}_2$.
• Figure 2: The figure depicts a landscape representation for our physical scenario. Both QM and CM would emerge on nearly the same footing from an as yet unknown underlying QST. Even though QM and CM would be emergent theories, it is QM that fixes the Heisenberg cut at $m \sim M_\text{P} \equiv \hbar^{1 / 2}$. The realm of the QST would be at space scales $\ell < L_\text{P}$. Still, a QST ridge at $m \sim M_\text{P}$ would emerge, giving rise to the Heisenberg cut and segregating QM from CM. In this scenario, tabletop experiments aiming to place the c.m. of systems in a spatial superposition should exhibit deviations from QM as their masses approach $M_\text{P}$ due to the QST ridge (red arrows).