[Paper Review] Worlds in the Everett Interpretation

David Wallace|ArXiv.org|Mar 16, 2001

Quantum Mechanics and Applications36 references4 citations

TL;DR

This paper defends the use of 'many worlds' terminology in the Everett interpretation of quantum mechanics without requiring a fundamental, mathematically defined preferred basis. By drawing an analogy with spacetime foliations in relativity, Wallace argues that worlds—like instants in time—are useful, pragmatic concepts for understanding the universal quantum state, even if they are not fundamental in the formalism. The key contribution is a metaphysical framework that reconciles Everettian quantum mechanics with relativity and persistence over time.

ABSTRACT

This is a discussion of how we can understand the world-view given to us by the Everett interpretation of quantum mechanics, and in particular the role played by the concept of `world'. The view presented is that we are entitled to use `many-worlds' terminology even if the theory does not specify the worlds in the formalism; this is defended by means of an extensive analogy with the concept of an `instant' or moment of time in relativity, with the lack of a preferred foliation of spacetime being compared with the lack of a preferred basis in quantum theory. Implications for identity of worlds over time, and for relativistic quantum mechanics, are discussed.

Motivation & Objective

• To resolve the interpretive dilemma in the Everett interpretation: whether to treat 'worlds' as fundamental entities or abandon them as unphysical.
• To argue that the concept of 'worlds' is not metaphysically problematic or arbitrary, but analogous to the concept of 'instant' in relativity.
• To show that the lack of a preferred basis in quantum mechanics parallels the lack of a preferred spacetime foliation in relativity, both being acceptable conceptual tools.
• To defend the coherence of the Everett interpretation by grounding it in structural similarities across physical theories, particularly relativity.
• To provide a framework for understanding world persistence and observer experience in Everettian quantum mechanics without requiring a preferred basis or world-identity criterion.

Proposed method

• Uses an analogy between the concept of a 'moment' in relativity (spacetime foliation) and the concept of a 'world' in Everettian quantum mechanics, both being non-fundamental but conceptually indispensable.
• Applies the idea that physical theories require conceptual scaffolding—like 'worlds' or 'instants'—to make sense of formalism, even if not explicitly present in the mathematics.
• Argues that just as relativity does not require a unique foliation to be meaningful, quantum mechanics does not require a unique basis to support the notion of 'worlds'.
• Employs structuralist reasoning: persistence of worlds is defined not by identity over time but by structural similarity across different temporal regions of the universal state.
• Draws on decoherence and consistent histories as pragmatic tools to identify approximate worlds, without requiring exact mathematical definitions.
• Contrasts the Everettian view with many-minds interpretations and pilot-wave theories, emphasizing that the Everett approach avoids foundational conflicts with relativity.

Experimental results

Research questions

• RQ1 Can the concept of 'worlds' in the Everett interpretation be meaningfully used even if no preferred basis is mathematically specified?
• RQ2 How does the lack of a preferred basis in quantum mechanics compare to the lack of a preferred foliation in relativistic spacetime?
• RQ3 Is it possible to define the persistence of worlds through time without a fundamental world-identity criterion?
• RQ4 How can observers in the Everett interpretation have a coherent experience of a single world if the universal state is unitary and branching?
• RQ5 What is the role of relativity in shaping the interpretation of quantum mechanics, particularly in the context of spacetime structure and world-formation?

Key findings

• The concept of 'worlds' in the Everett interpretation is not metaphysically problematic, even without a fundamental preferred basis, because it functions analogously to 'instants' in relativity.
• Just as spacetime does not require a unique foliation to be physically meaningful, the universal quantum state does not require a unique basis to support the use of 'worlds' in interpretation.
• Worlds are not fundamental entities in the formalism but are useful, pragmatic constructs for understanding the structure of the universal wavefunction.
• Persistence of worlds over time is not defined by identity but by structural similarity across different temporal regions of the state, analogous to how objects persist in relativity.
• The use of 'worlds' does not make the theory incomplete, as the universal state can be reconstructed from such descriptions, even if the choice of worlds is somewhat arbitrary.
• The analogy with relativity supports the view that both 'worlds' and 'instants' are legitimate conceptual tools for understanding physical theories, even if they are not directly present in the formalism.