The Static Quantum Multiverse

TL;DR

Nomura develops a quantum-mechanical framework for the multiverse built on a fixed reference frame and a quantum-gravity Hilbert space ${\cal H}_{\rm QG}$, addressing the measure problem of eternal inflation. He argues that, under Hypotheses I (quantum mechanics holds) and II (frame-independent predictions), the multiverse state is static, satisfying $H|\Psi\rangle=0$, with predictions read from a zero-eigenvalue subspace via the extended Born rule. A key result is that selection conditions must include quantum operators—not just the state—to ensure covariance; this leads to a precise, testable structure where physical predictions follow from projection operators and a finite, normalizable set of static states. The framework yields an emergent arrow of time within our branch without requiring a true time evolution of the global state and provides a path to unambiguous predictions once the explicit form of the Hamiltonian acting on ${\cal H}_{\rm QG}$ is known, linking cosmology to holographic horizon dynamics and the string landscape.

Abstract

We consider the multiverse in the intrinsically quantum mechanical framework recently proposed in Refs. [1,2]. By requiring that the principles of quantum mechanics are universally valid and that physical predictions do not depend on the reference frame one chooses to describe the multiverse, we find that the multiverse state must be static---in particular, the multiverse does not have a beginning or end. We argue that, despite its naive appearance, this does not contradict observation, including the fact that we observe that time flows in a definite direction. Selecting the multiverse state is ultimately boiled down to finding normalizable solutions to certain zero-eigenvalue equations, analogous to the case of the hydrogen atom. Unambiguous physical predictions would then follow, according to the rules of quantum mechanics.

Figures (2)

• Figure 1: Suppose you know that there are a half of a chair and of a room in the first half of the scene (the upper picture). In a regular ordered world, you expect the second half of the scene contains the other half of the chair and the room, possibly with some other things (the lower left picture). On the other hand, the number of such states is much smaller than that of states in which the second half contains random, disordered configurations (the lower right picture).
• Figure 2: A schematic depiction of the analogy between the hydrogen atom and the quantum multiverse. In the case of the hydrogen atom, the only relevant states are those that satisfy the Schrödinger equation and are normalizable in the Hilbert space spanned by $\left| r \right>$ (solid line); the non-normalizable modes are irrelevant (dashed line). In the quantum multiverse, the relevant states are those that satisfy Eq. (\ref{['eq:Psi-cond']}) and are normalizable in Hilbert space ${\cal H}_{\rm QG}$ (solid line); the non-normalizable modes, which have diverging coefficients for supersymmetric Minkowski or singularity states, are irrelevant (dashed line).