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.
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.
Murray Gell-Mann and James Hartle have made an original proposal for a version of decoherent histories quantum mechanics which is specifically tailored so as not to imply the emergence of multiple quasi-classical worlds. I argue that there is an explanatory gap in the proposal but that there remains an important insight which might be used to tackle what can be seen as an outstanding problem for Hugh Everett III’s “relative state” interpretation of quantum mechanics, if it is understood as giving ontic priority to the wavefunction. The argument employs a recent novel analysis of self-location within any sort of multiverse.
The interpretation of quantum mechanics has been disputed ever since the advent of the theory in the 1920’s. Famous are the discussions over long time between Einstein and Bohr. Einstein refused to accept the so‐called Copenhagen interpretation, where the wave function collapses at a measurement and where the outcome of the measurement is essentially accidental (“God does not play dice”). Alternative interpretations have appeared, but the Copenhagen school has dominated the thoughts throughout the decades. One interesting interpretation was formulated in 1957 by Hugh Everett at Princeton, a student of John Wheeler, which abandons the wave‐function collapse. In this model the universe is governed entirely by the Schrödinger equation, which does not allow for any collapse. In Everett’s model after a measurement the wave function is separated into different branches that do not interact. This model was left unnoticed for long time until Bryce DeWitt took it up in 1970 and termed it “Many‐Worlds Interpretation”, a term that in some sense is misleading. Everett’s model is incomplete, and it was later supplemented by the theory of decoherence, which explains how the different branches decouple as a result of the interaction with the environment. This extended model has in recent years gained increased respect, and some believe that it is the only model made available so far that is fully consistent with quantum mechanics. This interpretation can also shed some light on the development of the universe and, in particular, on the so‐called Anthropic principle, which puts human beings at the center of the development.
The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules of probability theory apply to it when it interacts with a quantum system. Under mild assumptions, we recover the unitary dynamics, collapse and Born rule postulates from quantum theory. Nonetheless, there is no decoherence, because the quantum state remains pure conditioned on the classical trajectory. This results in one world, rather than many-worlds. Our main technical tool is to exploit a change of measure on the space of classical paths, the functional form of which is shown to characterise the quantum dynamics and Born rules of a class of quantum-like theories.
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions about objects in a multiplicity of worlds. In this logical framework, the continuum of worlds is treated in analogy to the continuum of time points; both “time” and “world” are considered as mutually independent modes of existence. The theory combines elements of Bohmian mechanics and of Everett’s many-worlds interpretation; it has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Probability as given by the Born rule emerges as a consequence of insufficient knowledge of observers about which world it is that they live in. The theory describes a continuum of worlds rather than a single world or a discrete set of worlds, so it is similar in spirit to many-worlds interpretations based on Everett’s approach, without being actually reducible to these. In particular, there is no splitting of worlds, which is a typical feature of Everett-type theories. Altogether, the theory explains (1) the subjective occurrence of probabilities, (2) their quantitative value as given by the Born rule, and (3) the apparently random “collapse of the wavefunction” caused by the measurement, while still being an objectively deterministic theory.
The Born rule assigns probabilities to quantum measurement outcomes using only the local quantum amplitudes immediately before measurement. Yet the physical consequences of those outcomes may differ dramatically in their subsequent evolution, producing spacetime histories with very different entropies, information content, computational complexity, entanglement structure, and ultimately even spacetime curvature. These global properties appear to play no role in determining quantum probabilities. This paper argues that, viewed through the relativistic block-universe picture, this separation between local probability and global physical structure raises a natural conceptual question. The Many-Worlds Interpretation (MWI) preserves the complete branching structure of these histories, whereas collapse interpretations retain only a single realized history. The purpose of this paper is not to challenge the Born rule, but to highlight a conceptual asymmetry that may deserve further investigation.
Ultimately, any explanation of quantum measurement must be extendable to relativistic quantum mechanics (RQM), since many precisely confirmed experimental results follow from quantum field theory (QFT), which is based on RQM. Certainly, the traditional "collapse" postulate for quantum measurement is problematic in a relativistic context, at the very least because, as usually formulated, it violates the relativity of simultaneity. The present paper addresses this with a relativistic model of measurement in which the state of the universe is decomposed into decoherent histories of measurements recorded within it. The approach is essentially Everettian, in the sense that it uses the unmodified, unitary quantum formalism of RQM. But it addresses the difficulty with typical "many worlds" interpretations on how to even define probabilities over different possible ``worlds''. To do this, Zurek's concept of envariance is generalized to the context of relativistic spacetime, giving an objective definition of the probability of any one of the quantum histories, consistent with Born's rule. It is then shown that the statistics of any repeated experiment within the universe also tend to follow the Born rule as the number of repetitions increases. The wave functions that we actually use for such experiments are local reductions of very coarse-grained superpositions of universal eigenstates, and their "collapse" can be re-interpreted as simply an update based on additional incremental knowledge gained from a measurement about the "real" eigenstate of our universe.