Bell's theorem establishes that a local and spatially separable physical theory with no superdeterminism or retrocausality must be a theory of many local worlds. The local many worlds formalism of quantum mechanics is a transparent separable physical theory in spacetime with a Lorentz covariant causal structure. Unlike the Everett many worlds interpretation, there is no nonseparable universal wavefunction in configuration space, but like Everett, there is only local unitary evolution which conserves probability (fluid) current, and no wavefunction collapse. Each event in spacetime has its own local wavefunction which is built up using only the local wavefunctions and local unitary evolution operators within its past light cone, and which is entirely disconnected from spacelike separated local wavefunctions. We call this the local Schrödinger picture. Local many worlds can also be described in the Heisenberg picture by ascribing Deutsch-Hayden (DH) descriptors to each individual system, each of which evolves under local unitary operations. Both the local wavefunctions and DH descriptors contain records of past interactions, and while the local wavefunctions provide a clear and intuitive physical narrative, the descriptors contain all of the same information in a much more compact form. Unfortunately, the compact form is also somewhat cryptic, which has made the local Heisenberg picture relatively inaccessible. The purpose of this article is to show that the local wavefunctions for any $N$-qubit system can always be constructed directly from the DH descriptors, allowing us to combine the benefits of both pictures.
Bell's theorem establishes that a local and spatially separable physical theory with no superdeterminism or retrocausality must be a theory of many local worlds. The local many worlds formalism of quantum mechanics is a transparent separable physical theory in spacetime with a Lorentz covariant causal structure. Unlike the Everett many worlds interpretation, there is no nonseparable universal wavefunction in configuration space, but like Everett, there is only local unitary evolution which conserves probability (fluid) current, and no wavefunction collapse. Each event in spacetime has its own local wavefunction which is built up using only the local wavefunctions and local unitary evolution operators within its past light cone, and which is entirely disconnected from spacelike separated local wavefunctions. We call this the local Schrödinger picture. Local many worlds can also be described in the Heisenberg picture by ascribing Deutsch-Hayden (DH) descriptors to each individual system, each of which evolves under local unitary operations. Both the local wavefunctions and DH descriptors contain records of past interactions, and while the local wavefunctions provide a clear and intuitive physical narrative, the descriptors contain all of the same information in a much more compact form. Unfortunately, the compact form is also somewhat cryptic, which has made the local Heisenberg picture relatively inaccessible. The purpose of this article is to show that the local wavefunctions for any N-qubit system can always be constructed directly from the DH descriptors, allowing us to combine the benefits of both pictures.
It has been more than 20 years since Deutsch and Hayden proved the locality of quantum theory, using the Heisenberg picture of quantum computational networks. Of course, locality holds even in the face of entanglement and Bell’s theorem. Today, most researchers in quantum foundations are still convinced not only that a local description of quantum systems has not yet been provided, but that it cannot exist. The main goal of this paper is to address this misconception by re-explaining the descriptor formalism in a hopefully accessible and self-contained way. It is a step-by-step guide to how and why descriptors work. Finally, superdense coding is revisited in the light of descriptors.
Local realism has been the subject of much discussion in modern physics, partly because our deepest theories of physics appear to contradict one another in regard to whether reality is local. According to general relativity, it is, as physical quantities (perceptible or not) in two spacelike separated regions cannot affect one another. Yet, in quantum theory, it has traditionally been thought that local realism cannot hold and that such effects do occur. This apparent discrepancy between the two theories is resolved by Everettian quantum theory, as first proven by Deutsch & Hayden (2000). In this paper, I will explain how local realism is respected in quantum theory and review the advances in our understanding of locality since Deutsch & Hayden's work, including the concept of local branching and the more general analysis by Raymond-Robichaud (2021)
A growing body of literature supports Deutsch and Hayden’s (2000) claim that in the Heisenberg picture, quantum entanglement can be characterised locally using objects they call descriptors. I argue that their notion of locality rests, in part, on a qualified version of the principle of separability that I call spatial separability. I show that spatial separability is not sufficient for separability simpliciter, and that the more general version, spatiotemporal separability, reveals that their claim is false. Deutsch and Hayden’s approach also has a novel implication: if descriptors represent actual physical properties, they are non-qualitative properties, which are profoundly different from the qualitative properties we have come to expect from other branches of physics.
One of the major concerns of Schrodinger, Lorentz, Einstein, and many others about the wavefunction is that it is defined on the 3N-dimensional configuration space, rather than on the 3-dimensional physical space. This gives the impression that quantum mechanics cannot have a 3D-space or spacetime ontology, even in the absence of quantum measurements. In particular, this seems to affect interpretations which take the wavefunction as a physical entity, in particular the many worlds and the spontaneous collapse interpretations, and some versions of the pilot wave theory.
Here, a representation of the many-particle states is given, as multi-layered fields defined on the 3-dimensional physical space. This representation is equivalent to the usual representation on the configuration space, but it makes it explicit that it is possible to interpret the wavefunctions as living in the physical space. As long as only unitary evolution is involved, the interactions are local. I intended this representation to capture and formalize the non-explicit and informal intuition of many working quantum physicists, who, by considering the wavefunction sometimes to be defined on the configuration space, and sometimes on the physical space, may seem to researchers in the foundations of quantum theory as adopting an inconsistent view about its ontology. This representation does not aim to solve the measurement problem, and it allows for Schrodinger cats just like the usual one. But it may help various interpretations to solve these problems, through inclusion of the wavefunction as (part of) their primitive ontology.
In an appendix, it is shown how the multi-layered field representation can be extended to quantum field theory.
In 1948, Schwinger developed a local Lorentz-covariant formulation of relativistic quantum electrodynamics in space-time which is fundamentally inconsistent with any delocalized interpretation of quantum mechanics. An interpretation compatible with Schwinger’s theory is presented, which reproduces all of the standard empirical predictions of conventional delocalized quantum theory in configuration space. This is an explicit, unambiguous, and Lorentz-covariant “local hidden variable theory” in space-time, whose existence proves definitively that such theories are possible. This does not conflict with Bell’s theorem because it is a local many-worlds theory. Each physical system is characterized by a wave-field, which is a set of indexed piece-wise single-particle wavefunctions in space-time, each with its own coefficient, along with a memory which contains the separate local Hilbert-space quantum state at each event in space-time. Each single-particle wavefunction of a fundamental system describes the motion of a portion of a conserved fluid in space-time, with the fluid decomposing into many classical point particles, each following a world-line and recording a local memory. Local interactions between two systems take the form of local boundary conditions between the differently indexed pieces of those systems’ wave-fields, with new indexes encoding each orthogonal outcome of the interaction. The general machinery is introduced, including the local mechanisms for entanglement and interference. The experience of collapse, Born rule probability, and environmental decoherence are discussed, and a number of illustrative examples are given.
This paper shows how to treat quantum field theory as a modern, locally Lorentz covariant quantum version of the classical, mechanical universe suggested by Laplace over 200 years ago. The result is a fairly common-sense single-history, single-world alternative to decoherent histories (Gell-Mann and Hartle) and many-worlds interpretations (Everett, DeWitt). From the assumption that there is a single universal Heisenberg state whose N-point functions uniquely describe all physical details of our universe, everything is rigorously deduced in a way showing that the mathematical formalism is capable of yielding its own interpretation. Probabilities arise from the neglect of the environment in approximate models. By giving the collapse of the wave function at a double slit a natural unitary explanation, new light is shed on the quantum measurement problem and the origin of the Born rule.