How Gravity Can Explain the Collapse of the Wavefunction on Superphysics

Model Definition

Mon, 01 Jan 0001 00:00:00 +0000

I present a simple argument for why a fundamental theory that unifies matter and gravity gives rise to what seems to be a collapse of the wavefunction. The resulting model is local, parameter-free and makes testable predictions.

Off the Hamiltonian

Mon, 01 Jan 0001 00:00:00 +0000

B. Off the Hamiltonian

We reconcile the product assumption with the canonical quantum gravity evolution by conceding that the time evolution of the product state cannot be a solution to the Schrodinger equation.

Penrose Case

Mon, 01 Jan 0001 00:00:00 +0000

Having formulated the mathematical framework of the new model, I now want to explain what it is good for.

A. The Penrose Case

The case I want to look at first is one in which we generate a particle of mass m and with wavefunction |χ⟩ in a superposition of two places (in the following called branches), ⃗x1 and ⃗x2 that we will call |χ1⟩ and |χ2⟩. That is, the wavefunction of the particle is |χ⟩ = α1|χ1⟩ + α2|χ2⟩.

Born’s Rule

Mon, 01 Jan 0001 00:00:00 +0000

C. Born’s Rule

Superdeterministic theories are hidden variables theories. This means they explain the seeming randomness of quantum mechanics as due to our lack of information about variables λ which do not appear in standard quantum physics. To recover a probabilistic theory, therefore, we must now incorporate the hidden variables.

Interpretation

Mon, 01 Jan 0001 00:00:00 +0000

D. Interpretation

In this framework, a massive object that is in a superposition of two different locations is somewhat like a virtual particle-antiparticle pair in a Feynman diagram. It can exist temporarily but will not appear in outgoing states, just that here the “outgoing” states are detector eigenstates that must be, to good precision, product states of matter and metric.

Tests

Mon, 01 Jan 0001 00:00:00 +0000

There are some relevant differences to the Penrose-Diosi (hereafter PD) model. ´

In the PD model, the deviation from the standard Schrodinger equation comes from a noise-kernel that scales ¨ with the gravitational self-energy of the mass-density.

Discussion

Mon, 01 Jan 0001 00:00:00 +0000

It makes sense to treat gravity differently from the other interactions.

In canonically or perturbatively quantised gravity, the entanglement between matter and its gravitational field can be best understood by what is called a ‘dressing’ in the context of quantum field theory. This is the formal acknowledgement that a particle which carries a charge—say, an electron that carries electric charge—never occurs in nature without the field created by that charge.

Appendix

Mon, 01 Jan 0001 00:00:00 +0000

I summarise Penrose’s argument and the mean field approach to semi-classical gravity.

Consider a particle in a superposition of two locations ⃗x1 and ⃗x2. Each has an energy density, ρ1 and ρ2, centred around its position, but the particles are so far apart that their overlap is negligible. We will assume that each lump of the superposition on its own is to good accuracy classical and denote their Newtonian potentials as Φ1 and Φ2, respectively, where ∇2Φ1/2 = 4πGρ1/2.