Physical Theories, Eternal Inflation, and Quantum Universe

TL;DR

The paper addresses the measure problem in eternal inflation by introducing an observer-centric quantum framework in which the multiverse is described by a single state $|\Psi(t)\rangle$ defined on the observer's past light cones bounded by apparent horizons. Probabilities are derived via projection operators and the Born rule, yielding gauge-invariant, finite predictions without geometric cutoffs, and unifying the eternally inflating multiverse with many-worlds quantum mechanics. The framework recovers a derivable global spacetime picture from the quantum description, posits the ultimate fate as a relaxation to supersymmetric Minkowski vacua, and offers a mechanism to avoid classic paradoxes such as the youngness problem and Boltzmann brains. It also provides practical schemes for predictions and postdictions using bulk density matrices, horizon degrees of freedom, and a quantum-to-classical transition via decoherence, while allowing for a potential fractal mega-multiverse that obviates a true initial condition.

Abstract

We present a framework in which well-defined predictions are obtained in an eternally inflating multiverse, based on the principles of quantum mechanics. We show that the entire multiverse is described purely from the viewpoint of a single "observer," who describes the world as a quantum state defined on his/her past light cones bounded by the (stretched) apparent horizons. We find that quantum mechanics plays an essential role in regulating infinities. The framework is "gauge invariant," i.e. predictions do not depend on how spacetime is parametrized, as it should be in a theory of quantum gravity. Our framework provides a fully unified treatment of quantum measurement processes and the multiverse. We conclude that the eternally inflating multiverse and many worlds in quantum mechanics are the same. Other important implications include: global spacetime can be viewed as a derived concept; the multiverse is a transient phenomenon during the world relaxing into a supersymmetric Minkowski state. We also present a theory of "initial conditions" for the multiverse. By extrapolating our framework to the extreme, we arrive at a picture that the entire multiverse is a fluctuation in the stationary, fractal "mega-multiverse," in which an infinite sequence of multiverse productions occurs. The framework discussed here does not suffer from problems/paradoxes plaguing other measures proposed earlier, such as the youngness paradox, the Boltzmann brain problem, and a peculiar "end" of time.

Figures (13)

• Figure 1: A schematic picture for obtaining samples of past light cones that satisfy specified conditions $A$. The light cones to be selected are depicted by shaded triangles (with the figure showing ${\cal N}_A = 4$). Note that a single geodesic may encounter relevant light cones multiple times in its history.
• Figure 2: The entire multiverse can be described purely from the viewpoint of a single "observer" in terms of a quantum state $\left| \Psi(t) \right>$, which is defined on the observer's past light cones (and on the initial hypersurface $\Sigma$ at early times; later, the light cones are bounded by the apparent horizons). Once the initial condition is given, the state is uniquely determined according to unitary, quantum mechanical evolution.
• Figure 3: A Penrose diagram representing a traveler who falls into an evaporating black hole (solid curve) carrying some information. For the traveler, information appears to be always with him/her (solid arrow), while from a distant observer, the information appears to be sent back from the black hole in Hawking radiation (dashed arrow) An example of "wrong" constant time hypersurfaces is depicted with the dotted line.
• Figure 4: The state $\left| \Psi(t) \right>$ is defined on the past light cones (thin solid lines) bounded either by the initial hypersurface $\Sigma$ (wavy line) or the stretched horizon (thick solid). The tips of these light cones are on the geodesic corresponding to the "observer," and the time parameter $t$ is chosen such that it agrees with the proper time associated with the observer. If the initial condition is given on a past light cone and the stretched horizon bounding it, then the introduction of the space-like hypersurface $\Sigma$ is not necessary.
• Figure 5: A quantum state for the multiverse, $\left| \Psi(t) \right>$, is defined on past light cones ($45^\circ$ lines) bounded by apparent horizons (thick solid lines). The left (right) diagram represents a nucleation of a Minkowski (anti de Sitter) bubble in a meta-stable de Sitter vacuum. The bubble walls are depicted by dashed lines.