The Multiverse Interpretation of Quantum Mechanics

TL;DR

The paper contends that the many-worlds interpretation and the cosmological multiverse are one and the same structure, with causal diamonds providing an objective decoherence framework. It shows that standard global pictures of eternal inflation fail to deliver true decoherence and proposes a hat region (Λ = 0) where exact observables and irreversible decoherence can be realized, linking finite-diamond observables to hat observables via hat complementarity. A constructive program then builds a global multiverse from decoherent causal-diamond histories, leveraging a light-cone time duality and a simple 1+1D toy model. The Census Taker in the hat serves as an arena for operationally precise quantum predictions, with postulates ensuring infinite repetition and irreversibility, and hat-complementarity connecting hat and non-hat physics in a coherent global picture.

Abstract

We argue that the many-worlds of quantum mechanics and the many worlds of the multiverse are the same thing, and that the multiverse is necessary to give exact operational meaning to probabilistic predictions from quantum mechanics. Decoherence - the modern version of wave-function collapse - is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the "environment". In fact decoherence is absent in the complete description of any region larger than the future light-cone of a measurement event. However, if one restricts to the causal diamond - the largest region that can be causally probed - then the boundary of the diamond acts as a one-way membrane and thus provides a preferred choice of environment. We argue that the global multiverse is a representation of the many-worlds (all possible decoherent causal diamond histories) in a single geometry. We propose that it must be possible in principle to verify quantum-mechanical predictions exactly. This requires not only the existence of exact observables but two additional postulates: a single observer within the universe can access infinitely many identical experiments; and the outcome of each experiment must be completely definite. In causal diamonds with finite surface area, holographic entropy bounds imply that no exact observables exist, and both postulates fail: experiments cannot be repeated infinitely many times; and decoherence is not completely irreversible, so outcomes are not definite. We argue that our postulates can be satisfied in "hats" (supersymmetric multiverse regions with vanishing cosmological constant). We propose a complementarity principle that relates the approximate observables associated with finite causal diamonds to exact observables in the hat.

Figures (13)

• Figure 1: Decoherence and causality. At the event $M$, a macroscopic apparatus $A$ becomes correlated with a quantum system $S$. Thereafter, environmental degrees of freedom $E$ interact with the apparatus. In practice, an observer viewing the apparatus is ignorant of the exact state of the environment and so must trace over this Hilbert space factor. This results in a mixed state which is diagonal in a particular "pointer" basis picked out by the interaction between $E$ and $A$. The state of the full system $SAE$, however, remains pure. In particular, decoherence does not take place, and no preferred bases arises, in a complete description of any region larger than the future lightcone of $M$.
• Figure 2: The future domain of dependence, $D(\Sigma_0)$, (light or dark shaded) is the spacetime region that can be predicted from data on the timeslice $\Sigma_0$. If the future conformal boundary contains spacelike portions, as in eternal inflation or inside a black hole, then the future light-cones of events in the dark shaded region remain entirely within $D(\Sigma_0)$. Pure quantum states do not decohere in this region, in a complete description of $D(\Sigma_0)$. This is true even for states that involve macroscopic superpositions, such as the locations of pocket universes in eternal inflation (dashed lines), calling into question the self-consistency of the global picture of eternal inflation.
• Figure 3: Environmental degrees of freedom entangled with an observer at $O$ remain within the causal future of the causal past of $O$, $J^+[J^-(O)]$ (cyan/shaded). They are not entangled with distant regions of the multiverse. Tracing over them will not lead to decoherence of a bubble nucleated at $P$, for example, and hence will fail to reproduce the standard global picture of eternal inflation.
• Figure 4: The causal diamond (pink/shaded) spanned by two events $p$ and $q$ is the set of points that lie on causal curves from $p$ to $q$. $p$ is called the origin and $q$ the tip of the causal diamond. In the example shown, $p$ lies on the initial surface and $q$ on the future conformal boundary of the spacetime. The causal diamond is largest spacetime region that can be causally probed by an observer travelling from $p$ to $q$.
• Figure 5: Causal diamond spanned by the world-line (green) of an observer. Environmental degrees of freedom (purple dashed line) that leave the observer's past light-cone (blue) at some finite time can be recovered using mirrors.