The Quantum Branching Universe (QBU)

A formal approach to identifying events and timelines in quantum mechanics

Quantum Branching Universe (QBU)

A Quantum Branching Universe (QBU) is a structured representation of all physically possible quantum timelines, organized as a directed acyclic graph (DAG). In this DAG:

• Nodes represent quantum events or measurements.

• Edges represent branching due to quantum outcomes.

• Paths through the DAG represent distinct timelines.

Formally:

\(\text{QBU} \equiv (V, E)\)

where:

• V is the set of all quantum events.

• E is the set of directed edges indicating temporal and causal ordering.

An ancestor event Ea precedes another event Eb if all timelines passing through Eb necessarily pass through Ea.

Pattern Identifiers (PIs)

Pattern Identifiers (PIs) are precise, reproducible patterns or states used to identify and select subsets of timelines within the QBU.

PIs are categorized into two distinct types:

• Strong PIs: Patterns where all matching timelines necessarily share a common ancestor event. These provide strict causal clarity.

  • Examples: Genotypes, neural connectomes, specific quantum states.

• Weak PIs: Patterns that do not require a common ancestor, applicable for cultural or historical identification.

  • Examples: Names, cultural labels, general historical events.

Operational Definitions:

Match Operation:

\(Match(PI, W) \rightarrow \{True, False\}\)

Select Operation:

\(SelectWorlds(PI) = \{W \in QBU \mid Match(PI, W)\}\)

Ancestor/Descendant Operation:

\(AncestorDescendant(PI_a, PI_b) = \begin{cases} True, & \text{if for all timelines containing } PI_b, \text{there exists an ancestor timeline containing } PI_a \\ False, & \text{otherwise} \end{cases}\)

Core Intuitions and Constraints:

• Timelines identified by a Strong PI necessarily share at least one common ancestor event.

• Timelines identified by a Weak PI do not guarantee a common ancestor and thus have limited causal interpretability.

• Logical invariants such as Pi (π) are universally true but trivially differentiate timelines; therefore, they are not operationally useful as primary identifiers.

Relationship to Block Universe:

The Quantum Branching Universe (QBU) extends the classical Block Universe concept, which views time as a static, four-dimensional spacetime structure where past, present, and future coexist without genuine branching. In contrast, the QBU describes an immense static structure composed of an astronomically vast—potentially infinite—number of distinct block universes, each representing a unique, deterministic timeline. Branching within the QBU does not denote dynamic progression through time; rather, it characterizes structural relationships among these timelines at quantum points of divergence. This expansive framework enables rigorous exploration of causality, counterfactual reasoning, and choice by explicitly modeling alternative outcomes as equally real, coexisting timelines.

References and Influences:

• Many-Worlds Interpretation (MWI) of Quantum Mechanics [Everett, 1957]

• Block Universe and Relativity [Putnam, 1967]

• Causality and Counterfactuals in Quantum Theory [Pearl, 2000; Deutsch, 1999]

• Formal Structures in Quantum Mechanics and Quantum Computation [Nielsen & Chuang, 2010]

• Quantum Causality [Adlam, 2021]

This framework supports rigorous exploration of causality, agency, and choice in the the Physics of Agency.