We argue that in quantum gravity there is no Born rule. The quantum-gravity regime, described by a non-normalisable Wheeler-DeWitt wave functional $Ψ$ , must be in quantum nonequilibrium with a probability distribution $P\neq\left\vert Ψ\right\vert ^{2}$ (initially and always). A Born rule can emerge only in the semiclassical regime of quantum systems on a classical spacetime background, with normalisable Schrödinger wave functions $ψ$ . Conditioning on the underlying quantum-gravitational ensemble yields a nonequilibrium distribution $ρ\neq\left\vert ψ\right\vert ^{2}$ at the beginning of the semiclassical regime, with quantum relaxation $ρ\rightarrow\left\vert ψ\right\vert ^{2}$ taking place only afterwards. Quantum gravity naturally creates an early nonequilibrium universe. We also show how small corrections to the Schrödinger equation yield an intermediate regime in which the Born rule is unstable: an initial distribution $ρ=\left\vert ψ\right\vert ^{2}$ can evolve to a final distribution $ρ\neq\left\vert ψ\right\vert ^{2}$ . These results arise naturally in the de Broglie-Bohm pilot-wave formulation of quantum gravity. We show that quantum instability during inflation generates a large-scale deficit $\sim1/k^{3}$ in the primordial power spectrum at wavenumber $k$ , though the effect is too small to observe. Similarly we find an unobservably large timescale for quantum instability in a radiation-dominated universe. Quantum instability may be important in black-hole evaporation, with a final burst of Hawking radiation that violates the Born rule. Deviations from the Born rule can also be generated for atomic systems in the gravitational field of the earth, though the effects are unlikely to be observable. The most promising scenario for the detection of Born-rule violations appears to be in radiation from exploding primordial black holes.We argue that in quantum gravity there is no Born rule. The quantum-gravity regime, described by a non-normalisable Wheeler-DeWitt wave functional $Ψ$, must be in quantum nonequilibrium with a probability distribution $P\neq\left\vert Ψ\right\vert ^{2}$ (initially and always). A Born rule can emerge only in the semiclassical regime of quantum systems on a classical spacetime background, with normalisable Schrödinger wave functions $ψ$. Conditioning on the underlying quantum-gravitational ensemble yields a nonequilibrium distribution $ρ\neq\left\vert ψ\right\vert ^{2}$ at the beginning of the semiclassical regime, with quantum relaxation $ρ\rightarrow\left\vert ψ\right\vert ^{2}$ taking place only afterwards. Quantum gravity naturally creates an early nonequilibrium universe. We also show how small corrections to the Schrödinger equation yield an intermediate regime in which the Born rule is unstable: an initial distribution $ρ=\left\vert ψ\right\vert ^{2}$ can evolve to a final distribution $ρ\neq\left\vert ψ\right\vert ^{2}$. These results arise naturally in the de Broglie-Bohm pilot-wave formulation of quantum gravity. We show that quantum instability during inflation generates a large-scale deficit $\sim1/k^{3}$ in the primordial power spectrum at wavenumber $k$, though the effect is too small to observe. Similarly we find an unobservably large timescale for quantum instability in a radiation-dominated universe. Quantum instability may be important in black-hole evaporation, with a final burst of Hawking radiation that violates the Born rule. Deviations from the Born rule can also be generated for atomic systems in the gravitational field of the earth, though the effects are unlikely to be observable. The most promising scenario for the detection of Born-rule violations appears to be in radiation from exploding primordial black holes.

arXiv:2104.07966Apr 16, 20212 citations

On the Interpretation of Quantum Gravity

Mario Castagnino, C. D'Negri

Jan 1, 19901 citation

Measurement in Quantum Gravity

H.‐H. von Borzeszkowski, H.‐J. Treder

Springer eBooksJan 1, 19880 citations

Pilot-wave theory and the search for new physics

Antony Valentini

We show how pilot-wave theory points to new physics, beyond quantum mechanics, in three distinct ways. First, generalised cosmological initial conditions, departing from the Born rule, can lead to observable anomalies in the cosmic microwave background and in relic cosmological particles. Second, a breakdown of the Born rule in the deep quantum-gravity regime, with gravitational corrections that render the Born rule semiclassically unstable, can create anomalies in Hawking radiation from evaporating black holes. Third, a regularised equation of motion that remains finite at nodes of the wave function generates corrections to the Born rule at short distances, while a natural time-dependent generalisation implies an instability of quantum equilibrium at short times, effects which may be observable in high-energy collisions.We show how pilot-wave theory points to new physics, beyond quantum mechanics, in three distinct ways. First, generalised cosmological initial conditions, departing from the Born rule, can lead to observable anomalies in the cosmic microwave background and in relic cosmological particles. Second, a breakdown of the Born rule in the deep quantum-gravity regime, with gravitational corrections that render the Born rule semiclassically unstable, can create anomalies in Hawking radiation from evaporating black holes. Third, a regularised equation of motion that remains finite at nodes of the wave function generates corrections to the Born rule at short distances, while a natural time-dependent generalisation implies an instability of quantum equilibrium at short times, effects which may be observable in high-energy collisions.

arXiv:2411.10782Nov 16, 20241 citation

Born rule in Schroedinger-Newton scenarios of semiclassical gravity

Tanguy Fontana, Axelle Coulon, Giovanni Manfredi

We investigate dynamical relaxation to the Born rule in a semiclassical gravity model described by the Schrödinger-Newton equations. Using a Gaussian variational solution for the self-gravitating wave packet, combined with Nelson's stochastic representation of quantum dynamics, we track the evolution of particle ensembles whose initial probability distribution differs from $|Ψ|^2$ . Relaxation to the Born rule ("quantum equilibrium") occurs when the wave packet remains bounded, or grows sufficiently slowly in time; in contrast, for rapidly expanding solutions of the Schrödinger-Newton equations, deviations from the Born rule can persist indefinitely. Numerical simulations confirm this analytical picture. These results show that semiclassical self-gravity can either enable or inhibit relaxation towards the Born rule, providing a minimal model relevant to proposals of primordial quantum non-equilibrium, as suggested by Underwood and Valentini [Phys. Rev. D 92, 063531 (2015)].We investigate dynamical relaxation to the Born rule in a semiclassical gravity model described by the Schrödinger-Newton equations. Using a Gaussian variational solution for the self-gravitating wave packet, combined with Nelson's stochastic representation of quantum dynamics, we track the evolution of particle ensembles whose initial probability distribution differs from $|Ψ|^2$. Relaxation to the Born rule ("quantum equilibrium") occurs when the wave packet remains bounded, or grows sufficiently slowly in time; in contrast, for rapidly expanding solutions of the Schrödinger-Newton equations, deviations from the Born rule can persist indefinitely. Numerical simulations confirm this analytical picture. These results show that semiclassical self-gravity can either enable or inhibit relaxation towards the Born rule, providing a minimal model relevant to proposals of primordial quantum non-equilibrium, as suggested by Underwood and Valentini [Phys. Rev. D 92, 063531 (2015)].

gr-qcCross-listedarXiv:2610.03501Oct 5, 20260 citations

We argue that in quantum gravity there is no Born rule. The quantum-gravity regime, described by a non-normalisable Wheeler-DeWitt wave functional

Ψ

, must be in quantum nonequilibrium with a probability distribution

P\neq\left\vert Ψ\right\vert ^{2}

(initially and always). A Born rule can emerge only in the semiclassical regime of quantum systems on a classical spacetime background, with normalisable Schrödinger wave functions

ψ

. Conditioning on the underlying quantum-gravitational ensemble yields a nonequilibrium distribution

ρ\neq\left\vert ψ\right\vert ^{2}

at the beginning of the semiclassical regime, with quantum relaxation

ρ\rightarrow\left\vert ψ\right\vert ^{2}

taking place only afterwards. Quantum gravity naturally creates an early nonequilibrium universe. We also show how small corrections to the Schrödinger equation yield an intermediate regime in which the Born rule is unstable: an initial distribution

ρ=\left\vert ψ\right\vert ^{2}

can evolve to a final distribution

ρ\neq\left\vert ψ\right\vert ^{2}

. These results arise naturally in the de Broglie-Bohm pilot-wave formulation of quantum gravity. We show that quantum instability during inflation generates a large-scale deficit

\sim1/k^{3}

in the primordial power spectrum at wavenumber

k

, though the effect is too small to observe. Similarly we find an unobservably large timescale for quantum instability in a radiation-dominated universe. Quantum instability may be important in black-hole evaporation, with a final burst of Hawking radiation that violates the Born rule. Deviations from the Born rule can also be generated for atomic systems in the gravitational field of the earth, though the effects are unlikely to be observable. The most promising scenario for the detection of Born-rule violations appears to be in radiation from exploding primordial black holes.

|Ψ|^2

. Relaxation to the Born rule ("quantum equilibrium") occurs when the wave packet remains bounded, or grows sufficiently slowly in time; in contrast, for rapidly expanding solutions of the Schrödinger-Newton equations, deviations from the Born rule can persist indefinitely. Numerical simulations confirm this analytical picture. These results show that semiclassical self-gravity can either enable or inhibit relaxation towards the Born rule, providing a minimal model relevant to proposals of primordial quantum non-equilibrium, as suggested by Underwood and Valentini [Phys. Rev. D 92, 063531 (2015)].