Toward relativistic branches of the wavefunction

I prepared the following extended abstract for the Spacetime and Information Workshop as part of my continuing mission to corrupt physicists while they are still young and impressionable. I reproduce it here for your reading pleasure.


Finding a precise definition of branches in the wavefunction of closed many-body systems is crucial to conceptual clarity in the foundations of quantum mechanics. Toward this goal, we propose amplification, which can be quantified, as the key feature characterizing anthropocentric measurement; this immediately and naturally extends to non-anthropocentric amplification, such as the ubiquitous case of classically chaotic degrees of freedom decohering. Amplification can be formalized as the production of redundant records distributed over spatial disjoint regions, a certain form of multi-partite entanglement in the pure quantum state of a large closed system. If this definition can be made rigorous and shown to be unique, it is then possible to ask many compelling questions about how branches form and evolve.

A recent result shows that branch decompositions are highly constrained just by this requirement that they exhibit redundant local records. The set of all redundantly recorded observables induces a preferred decomposition into simultaneous eigenstates unless their records are highly extended and delicately overlapping, as exemplified by the Shor error-correcting code. A maximum length scale for records is enough to guarantee uniqueness. However, this result is grounded in a preferred tensor decomposition into independent microscopic subsystems associated with spatial locality. This structure breaks down in a relativistic setting on scales smaller than the Compton wavelength of the relevant field. Indeed, a key insight from algebraic quantum field theory is that finite-energy states are never exact eigenstates of local operators, and hence never have exact records that are spatially disjoint, although they can approximate this arbitrarily well on large scales. This technical challenge frustrates not just the concept of redundancy-based branches, but in fact the entire theory of decoherence as a way to precisely understand measurement in quantum field theories.

There are at least two possible resolutions: (1) Find a framework for identifying branches in fields using approximate records and/or approximate locality; or (2) find an alternative, more fundamental mathematical characterization of branching in the relativistic setting that reduces to (or otherwise supercedes) redundancy on scales much larger than the Compton wavelength. This investigation is closely related to currently open questions about the distribution and interpretation of entanglement in the vacuum. Speculatively, an objective, mathematically rigorous decomposition of a many-body state into branches may also speed up numerical simulations of nonstationary many-body states, illuminate the thermalization of closed systems, and demote measurement from fundamental primitive in the quantum formalism. It also opens up the possibility of analyzing situations where branches may recombine — and the operational Copenhagen approach must fail — such as in the early universe, exotic materials, the distant future, or thermalizing systems.

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