Nothing happens in the Universe of the Everett Interpretation

Abstract: Since the scalar product is the only internal structure of a Hilbert space, all vectors of norm 1 are equivalent, in the sense that they form a perfect sphere in the Hilbert space, on which every vector looks the same. The state vector of the universe contains no information that distinguishes it from other state vectors of the same Hilbert space. If the state vector is considered as the only fundamental entity, the world is completely structureless. The illusion of interacting subsystems is due to a "bad" choice of factorization (i.e. decomposition into subsystems) of the Hilbert space. There is always a more appropriate factorization available in which subsystems don't interact and nothing happens at all. This factorization absorbs the time evolution of the state vector in a trivial way. The Many Worlds Interpretation is therefore rather a No World Interpretation. A state vector gets the property of "representing a structure" only with respect to an external observer who measures the state according to a specific factorization and basis.

• The paper critiques the Everett Interpretation by analyzing the factorization problem, arguing that perceived universe structure relies on arbitrary choices of basis.
• The analysis suggests that the universe's structure and emergent classical properties are not inherent in the global wave function but depend on external observation or factorization.
• Ultimately, the paper challenges the completeness and parsimony of the Everett Interpretation, suggesting the need for additional entities or perspectives to reconcile abstract quantum states with observable reality.

An Analysis of the Factorization Problem in the Everett Interpretation

Jan-Markus Schwindt's paper, "Nothing happens in the Universe of the Everett Interpretation," presents a critical inquiry into the Many Worlds Interpretation (MWI) of quantum mechanics, famously associated with Hugh Everett. The central focus of the paper is the factorization problem within the Everett Interpretation (EI), where the fundamental challenge is determining how observers identify subsystems in the quantum universe amid countless potential factorizations of the global Hilbert space.

The paper begins by laying the groundwork of the EI, positing that the global wave function ψ and the Hamiltonian operator H are fundamental components of quantum mechanics, diverging from interpretations that introduce additional elements or processes, such as the collapse of the wave function. Schwindt emphasizes that, within EI, the state vector describes a unitary, deterministic evolution according to the Schrödinger equation. This description leads to an outcome where each possible measurement result corresponds to a separate "world."

One of the critical contentions of the paper is the notion that the observed structure and interactions within the universe rely heavily on arbitrary choices of factorization of the global Hilbert space. This idea is encapsulated in the comparison between what Schwindt terms "Nirvana" and "Samsara" factorizations. A Nirvana frame portrays a universe devoid of interaction, drawing a parallel to Minkowski spacetime, where nothing intrinsically "happens." In contrast, a Samsara frame seems to show dynamic interactions due to an arbitrary choice of basis.

Schwindt argues that while interactions and measurements in quantum mechanics produce entanglement, the perceived branching and evolution of subsystems are dependent on the selected factorization. This raises the basis problem, which comprises the challenge of justifying a unique factorization that corresponds to subsystems consistent with classical observations.

The significance of this inquiry lies in its questioning of one of the core premises of EI—that the universe, as described by a global wave function, does not inherently contain distinguished structures without external observation or measurement. The implication is that, at the most basic level, the state vector conveys no intrinsic structure or information distinguishing one vector from another in the Hilbert space unless observed from an external frame.

Schwindt further critiques alternative approaches to address the factorization dilemma, including the Bohmian mechanics or Pilot Wave Theory, which introduces trajectories of particles in addition to the wave function, thereby providing a concrete framework for factorizing subsystems. These methods offer a defined basis and minimize the arbitrary nature of subsystem decomposition inherent in the EI.

The analysis implicitly challenges the completeness of the EI by suggesting that the universe's structure and emergent classical properties can only be understood in terms of additional assumptions or interpretations beyond the pristine quantum state description. The failure to solve the factorization problem leaves the EI with the unenviable position of being structurally ambiguous unless coupled with external observational data.

Ultimately, Schwindt's examination calls for a resolution or reevaluation of the EI and challenges its claim to parsimony and universality. The discourse on whether quantum mechanics should include additional entities or perspectives to instantiate the classical world remains essential in advancing our understanding of quantum reality and its interpretations. Future work may explore deeper theoretical frameworks or employ new philosophical paradigms to bridge the gap between the abstract state vector and observable reality in quantum mechanics.