[Paper Review] Some remarks on the mathematical structure of the multiverse

A L McKenzie|arXiv (Cornell University)|Feb 6, 2016

Quantum Mechanics and Applications23 references3 citations

TL;DR

This paper proposes a multiverse model composed of discrete, parallel block universes that diverge according to Everettian branching, preserving unitary quantum evolution while reconciling quantum probability with relativity. By framing the multiverse as a mathematical structure akin to Tegmark's Mathematical Universe Hypothesis, it shows that Gödelian self-referential structures naturally account for quantum uncertainty within individual universes and deterministic evolution across the multiverse.

ABSTRACT

The Copenhagen interpretation of quantum entanglement experiments is at best incomplete, since the intermediate state induced by collapse of the wave function apparently depends upon the inertial rest frame in which the experiment is observed. While the Many Worlds Interpretation of Everett, MWI, avoids the issue of wave function collapse, it, too, is a casualty of the special theory of relativity. This requires all events in the universe, past, present and future, to be unique, as in the block universe picture, which rules out Everett style branching. The benefits of MWI may be retained, however, by postulating a multiverse of discrete, parallel, block universes which are identical to each other up to certain points in the MWI trunk before they diverge according to the MWI branching. The quantum probability of an event then emerges from the number of parallel universes in which the event happens divided by the total number of universes. This means that the total number of such universes is finite. Such a picture is more easily envisaged by thinking of it as a purely mathematical structure, as in the Mathematical Universe Hypothesis proposed by Tegmark. However, while Tegmark wished to avoid contamination from Goedelian self referential knots, not only does such contamination appear to be inevitable, it brings an unexpected benefit. The mathematical hierarchy required by the enigmatic footnote 48a in the paper by Goedel leads to an explanation for a unitary evolution of deterministic quantum rules across the multiverse while accounting for quantum uncertainty within an individual universe. Other aspects of this structure, called here the Plexus, are discussed, including awareness of existence and other questions raised by the hypothesis.

Motivation & Objective

• To resolve the conflict between the Many Worlds Interpretation (MWI) and special relativity, which requires a unique, block universe structure.
• To preserve the benefits of MWI—such as unitary evolution and avoidance of wave function collapse—within a relativistically consistent framework.
• To explain quantum probability as a measure of the relative number of parallel universes in which an event occurs.
• To explore how Gödelian self-referential structures in the multiverse's mathematical foundation can account for quantum uncertainty and deterministic evolution.
• To develop a coherent model of the multiverse as a purely mathematical structure, addressing issues of self-consistency and awareness of existence.

Proposed method

• Postulating a multiverse composed of discrete, parallel block universes that are identical up to branching points, following MWI dynamics.
• Modeling the multiverse as a mathematical structure inspired by Tegmark's Mathematical Universe Hypothesis, treating it as a formal system.
• Integrating Gödel's incompleteness theorems into the multiverse framework to explain the emergence of quantum uncertainty within individual universes.
• Using the mathematical hierarchy from Gödel's footnote 48a to define a structure that supports deterministic quantum evolution across the multiverse.
• Defining quantum probability as the ratio of the number of universes in which an event occurs to the total number of universes, assuming finitely many universes.
• Analyzing the implications of self-referential structures for consciousness and awareness within the multiverse framework.

Experimental results

Research questions

• RQ1 How can the Many Worlds Interpretation be reconciled with the block universe structure demanded by special relativity?
• RQ2 What mathematical structure underlies a multiverse that preserves unitary quantum evolution while allowing for probabilistic outcomes in individual universes?
• RQ3 Can Gödelian self-referential structures in the multiverse's foundation explain quantum uncertainty without violating determinism?
• RQ4 How does the finite number of parallel universes affect the definition and interpretation of quantum probability?
• RQ5 What are the implications of the multiverse's mathematical structure for the emergence of consciousness and awareness?

Key findings

• The multiverse is modeled as a finite set of discrete, parallel block universes that diverge at specific branching points, preserving relativistic consistency.
• Quantum probability emerges from the ratio of favorable to total universes, providing a finite, mathematically grounded interpretation of probability.
• Gödelian self-referential structures within the multiverse's mathematical framework naturally account for quantum uncertainty in individual universes.
• The mathematical hierarchy from Gödel's footnote 48a supports a deterministic, unitary evolution of quantum rules across the multiverse.
• The model avoids wave function collapse and maintains consistency with special relativity by embedding the multiverse in a timeless, block-structure.
• The framework suggests that awareness and existence may be emergent properties of the multiverse's self-referential mathematical architecture.