In models of spontaneous wave-function collapse, why only fermions collapse, not bosons?

Abstract

Objective collapse models are often implemented so that collapse acts only on the fermionic (matter) sector, while bosonic fields do not undergo fundamental collapse. In generalized trace dynamics (GTD), spontaneous localization is expected to arise when the trace Hamiltonian has a significant anti-self-adjoint component. In this note we show, starting from the STM-atom (spacetime-matter atom) trace Lagrangian written in terms of two inequivalent matrix velocities $\dot Q_1$ and $\dot Q_2$, that the purely bosonic subsector admits a self-adjoint Hamiltonian, whereas the fermionic sector carries an intrinsic anti-self-adjoint contribution. The key structural input is that making the trace Lagrangian bosonic requires insertion of two \emph{unequal} odd-grade Grassmann elements $\beta_1\neq \beta_2$. Assuming natural adjoint properties for these elements, we compute the trace Hamiltonian explicitly via trace-derivative canonical momenta (with bosonic and fermionic variations treated separately) and isolate the resulting anti-self-adjoint term. This provides a first-principles mechanism, within GTD, for why only fermionic degrees of freedom act as collapse channels.