We consider experimental evidence for the hypothesis that the Planck energy, $E_p \approx 10^{19}GeV$ , sets the scale $ε$ at which wave function collapse causes deviations from linear Schrödinger evolution. With a few plausible assumptions about the collapse process, we first show that the observed CP violation in $K_L$ decay implies a lower bound on $ε$ remarkably close to $E_p$ . If the bound is saturated, the entire CP violation is due to collapse and a prediction made that the branching ratio for CP violation in the B meson decay will be $γ\approx 10^{-5}$ . We then show that the assumptions are consequences of a simple non-linear, stochastic modification of the Schrödinger equation with $ε$ setting the scale of the non-linearity.We consider experimental evidence for the hypothesis that the Planck energy, $E_p \approx 10^{19}GeV$, sets the scale $ε$ at which wave function collapse causes deviations from linear Schrödinger evolution. With a few plausible assumptions about the collapse process, we first show that the observed CP violation in $K_L$ decay implies a lower bound on $ε$ remarkably close to $E_p$. If the bound is saturated, the entire CP violation is due to collapse and a prediction made that the branching ratio for CP violation in the B meson decay will be $γ\approx 10^{-5}$. We then show that the assumptions are consequences of a simple non-linear, stochastic modification of the Schrödinger equation with $ε$ setting the scale of the non-linearity.

arXiv:quant-ph/9710042Oct 16, 19976 citations

Microscopic Origins of Collapse Models: Decoherence from Graviton Bremsstrahlung

Moslem Zarei

Some collapse models proposed that gravitational effects cause the instability of mass distribution superpositions, leading to wave function collapse. In this paper, we utilize the quantum Boltzmann equation (QBE) to analyze the behavior of a fermion in a spatial superposition under graviton emission. We introduce a quantitative measure that links the stability of the superposition to the spatial separation, particle mass, and gravitational coupling. By examining the collision term in the QBE, we derive the decoherence rate and show how it depends on these parameters. Our results provide a detailed framework for understanding gravity induced decoherence, bridging the gap between quantum field theory and collapse models. We also discuss the implications of these findings for experimental tests of gravitationally induced wave function collapse and the broader class of collapse models known as dissipative continuous spontaneous localization (CSL) model.Some collapse models proposed that gravitational effects cause the instability of mass distribution superpositions, leading to wave function collapse. In this paper, we utilize the quantum Boltzmann equation (QBE) to analyze the behavior of a fermion in a spatial superposition under graviton emission. We introduce a quantitative measure that links the stability of the superposition to the spatial separation, particle mass, and gravitational coupling. By examining the collision term in the QBE, we derive the decoherence rate and show how it depends on these parameters. Our results provide a detailed framework for understanding gravity induced decoherence, bridging the gap between quantum field theory and collapse models. We also discuss the implications of these findings for experimental tests of gravitationally induced wave function collapse and the broader class of collapse models known as dissipative continuous spontaneous localization (CSL) model.

quant-pharXiv:2605.12955May 14, 20260 citations

OBSERVATIONS IN QUANTUM MECHANICS AND THE “COLLAPSE OF THE WAVE FUNCTION”

Ronald F. Peierls

World Scientific series in 20th century physicsApr 1, 19973 citations

We consider experimental evidence for the hypothesis that the Planck energy,

E_p \approx 10^{19}GeV

, sets the scale

ε

at which wave function collapse causes deviations from linear Schrödinger evolution. With a few plausible assumptions about the collapse process, we first show that the observed CP violation in

K_L

decay implies a lower bound on

ε

remarkably close to

E_p

. If the bound is saturated, the entire CP violation is due to collapse and a prediction made that the branching ratio for CP violation in the B meson decay will be

γ\approx 10^{-5}

. We then show that the assumptions are consequences of a simple non-linear, stochastic modification of the Schrödinger equation with

ε

setting the scale of the non-linearity.