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arXiv:1810.05307 · Physical Review A

Single-world consistent interpretation of quantum mechanics from fundamental time and length uncertainties

Rodolfo Gambini, Luis Pedro García-Pintos, Jorge A. Pullin

Published Jul 15, 2019• 9 citations
arXivHTMLPDF

Abstract

The production of events in quantum theory, that is, of outcomes to which a probability can be associated, is inconsistent with a unitary evolution for systems in arbitrary initial states. In particular, within unitary quantum mechanics, there exist global protocols that allow verifying that no definite event occurs. Instead, states that start in a coherent superposition over possible outcomes always remain as a superposition. We show that when taking into account fundamental errors in measuring length and time intervals, which have been put forward as a consequence of a conjunction of quantum mechanical and general relativity arguments, there are instances in which such global protocols no longer allow one to distinguish whether or not the state is in a superposition. All predictions become identical as if one of the outcomes occurs, with probability determined by the state. We use this as a criteria to define events, as put forward in the Montevideo interpretation of quantum mechanics. We analyze in detail the occurrence of events in the paradigmatic case of a particle in a superposition of two different locations. We argue that our approach provides a consistent (C) single-world (S) picture of the universe, thus allowing an economical way out of the limitations imposed by a recent theorem by Frauchiger and Renner showing that having a self-consistent single-world description of the universe is incompatible with quantum theory. In fact, the main observation of this paper may be stated as follows: If quantum mechanics is extended to include gravitational effects to a quantum-gravitational (QG) theory, then QG, S, and C are satisfied.

DOI
10.1103/physreva.100.012113

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The production of events in quantum theory, that is, of outcomes to which a probability can be associated, is inconsistent with a unitary evolution for systems in arbitrary initial states. In particular, within unitary quantum mechanics, there exist global protocols that allow verifying that no definite event occurs. Instead, states that start in a coherent superposition over possible outcomes always remain as a superposition. We show that when taking into account fundamental errors in measuring length and time intervals, which have been put forward as a consequence of a conjunction of quantum mechanical and general relativity arguments, there are instances in which such global protocols no longer allow one to distinguish whether or not the state is in a superposition. All predictions become identical as if one of the outcomes occurs, with probability determined by the state. We use this as a criteria to define events, as put forward in the Montevideo interpretation of quantum mechanics. We analyze in detail the occurrence of events in the paradigmatic case of a particle in a superposition of two different locations. We argue that our approach provides a consistent (C) single-world (S) picture of the universe, thus allowing an economical way out of the limitations imposed by a recent theorem by Frauchiger and Renner showing that having a self-consistent single-world description of the universe is incompatible with quantum theory. In fact, the main observation of this paper may be stated as follows: If quantum mechanics is extended to include gravitational effects to a quantum-gravitational (QG) theory, then QG, S, and C are satisfied.
We review the Montevideo Interpretation of quantum mechanics, which is based on the use of real clocks to describe physics, using the framework that was recently introduced by Höhn, Smith, and Lock to treat the problem of time in generally covariant systems. These new methods, which solve several problems in the introduction of a notion of time in such systems, do not change the main results of the Montevideo Interpretation. The use of the new formalism makes the construction more general and valid for any system in a quantum generally covariant theory. We find that, as in the original formulation, a fundamental mechanism of decoherence emerges that allows for supplementing ordinary environmental decoherence and avoiding its criticisms. The recent results on quantum complexity provide additional support to the type of global protocols that are used to prove that within ordinary—unitary—quantum mechanics, no definite event—an outcome to which a probability can be associated—occurs. In lieu of this, states that start in a coherent superposition of possible outcomes always remain as a superposition. We show that, if one takes into account fundamental inescapable uncertainties in measuring length and time intervals due to general relativity and quantum mechanics, the previously mentioned global protocols no longer allow for distinguishing whether the state is in a superposition or not. One is left with a formulation of quantum mechanics purely defined in quantum mechanical terms without any reference to the classical world and with an intrinsic operational definition of quantum events that does not need external observers.
We review the Montevideo Interpretation of quantum mechanics, which is based on the use of real clocks to describe physics, using the framework recently introduced by Hoehn, Smith and Lock to treat the problem of time in generally covariant systems. The use of the new formalism makes the whole construction more accessible to readers without familiarity with totally constrained systems. We find that as in the original formulation, a fundamental mechanism of decoherence emerges that allows to supplement ordinary environmental decoherence and avoid its criticisms. Recent results on quantum complexity provide additional support to the type of global protocols used to prove that within ordinary ---unitary--- quantum mechanics no definite event ---an outcome to which a probability can be associated--- occurs. In lieu of this, states that start in a coherent superposition of possible outcomes always remain as a superposition. We show that, if one takes into account fundamental inescapable uncertainties in measuring length and time intervals due to general relativity and quantum mechanics, the previously mentioned global protocols no longer allow to distinguish whether the state is in a superposition or not. One is left with a formulation of quantum mechanics purely defined in quantum mechanical terms without any reference to the classical world and with an intrinsic operational definition of quantum events that does not need external observers.
A potentially new interpretation of quantum mechanics posits the state of the universe as a consistent set of facts, such that the relationships between objects in the universe are the information storing and instantiating those facts. A fact (or event) occurs exactly when the number or density of future possibilities decreases, and a quantum superposition exists if and only if the facts of the universe are consistent with the superposition. An example is analyzed in which the number of possibilities of N distinguishable classical objects in a discretized phase space is reduced by the introduction of chronological facts consisting of repelling impacts. It is shown how some facts have the effect of rendering impossible certain measurement outcomes of an object, independently of measurement outcomes of other objects, while some facts have the effect of correlating measurement outcomes of one object to those of another. The potential for further analysis through numerical simulation is discussed, particularly whether quantum uncertainty emerges from the specification of sufficient facts. Implications of and objections to the interpretation are briefly discussed, including the extent to which identity of objects must be preserved, the extent to which entanglement among objects must be universal, and whether this interpretation conflicts with special relativity. This interpretation may show that quantum mechanics, Planck’s constant, and the discretization of spacetime are emergent phenomena that successfully and very accurately approximate a more fundamental ontology.
We discuss the no-go theorem of Frauchiger and Renner based on an extended Wigner's friend thought experiment which is supposed to show that any single-world interpretation of quantum mechanics leads to inconsistent predictions if it is applicable on all scales. We show that no such inconsistency occurs if one considers a complete description of the physical situation. We then discuss implications of the thought experiment that have not been clearly addressed in the original paper, including a tension between relativity and nonlocal effects predicted by quantum mechanics. Our discussion applies in particular to Bohmian mechanics.
There has recently been a renewed focus on ‘perspectival’ quantum theories. which simultaneously maintain the existence of single measurement outcomes and the universality of unitary evolution. At the same time, these theories have come under attack with results by Frauchiger and Renner, Baumann and Wolf, and others. This dissertation aims to respond to a number of these attacks by providing a groundwork for these types of theories. To lay this groundwork I focus on encapsulated measurements, which involve an isolated observer and a superobserver (who measures the observer). I first distinguish between invasive and non-invasive measurements. Each leads to a possible inconsistency: In non-invasive measurements, the observer is certain of the superobserver’s measurement outcome while the superobserver’s physics predicts multiple possible outcomes. In invasive measurements the superobserver can be certain of his measurement outcome while the observer predicts non-zero probabilities for all possible outcomes. I argue that in the case of non-invasive measurements, the perspectivalist avoids diffculty by denying that the observer’s result has any impact on the physics experienced by the superobserver. Consistency is then maintained between them by looking to the unitary evolution of the superobserver’s measurement. This response leads to a detailed discussion about the metaphysical commitments of the perspectival approach. Here I argue the perspectivalist must accept one surprising result – there is a significant divorce of fundamental ontological states from physical dynamics. Turning to invasive measurements, I argue that the concern here is entirely misplaced. Arguments that raise worries about invasive measurements assume the observer should describe herself to be in a quantum state of having observed her measurement outcome when predicting the superobserver’s measurement results. I argue that this is incorrect. Rather, I explain that it is impossible for any observer to know her quantum state and so she should never describe herself as being in any quantum state at all, let alone use such a description to make predictions about a superobserver’s measurement. To conclude, I explain how the perspectivalist responds to concerns raised about entanglement and the possibility of action at a distance. Combining this with the results above brings into focus how the perspectivalist may develop a consistent, single-world picture of quantum mechanics.
We argue that the many worlds of quantum mechanics and the many worlds of the multiverse are the same thing, and that the multiverse is necessary to give exact operational meaning to probabilistic predictions from quantum mechanics. Decoherence---the modern version of wave-function collapse---is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the environment. In fact decoherence is absent in the complete description of any region larger than the future light cone of a measurement event. However, if one restricts to the causal diamond---the largest region that can be causally probed---then the boundary of the diamond acts as a one-way membrane and thus provides a preferred choice of environment. We argue that the global multiverse is a representation of the many worlds (all possible decoherent causal diamond histories) in a single geometry. We propose that it must be possible in principle to verify quantum-mechanical predictions exactly. This requires not only the existence of exact observables but two additional postulates: a single observer within the Universe can access infinitely many identical experiments; and the outcome of each experiment must be completely definite. In causal diamonds with a finite surface area, holographic entropy bounds imply that no exact observables exist, and both postulates fail: experiments cannot be repeated infinitely many times; and decoherence is not completely irreversible, so outcomes are not definite. We argue that our postulates can be satisfied in hats (supersymmetric multiverse regions with vanishing cosmological constant). We propose a complementarity principle that relates the approximate observables associated with finite causal diamonds to exact observables in the hat.