arXiv subjects

Chris Fields

Publications and source records attributed to Chris Fields.

At least 37 records · Page 2Linked to original sources

arXiv2020

Generalized Holographic Principle, Gauge Invariance and the Emergence of Gravity a la Wilczek

We show that a generalized version of the holographic principle can be derived from the Hamiltonian description of information flow within a quantum system that maintains a separable state. We then show that this generalized holographic principle entails a general principle of gauge invariance. When this is realized in an ambient Lorentzian space-time, gauge invariance under the Poincare group is immediately achieved. We apply this pathway to retrieve the action of gravity. The latter is cast a la Wilczek through a similar formulation derived by MacDowell and Mansouri, which involves the representation theory of the Lie groups SO(3,2) and SO(4,1).

gr-qc↗

arXiv2019

Sharing nonfungible information requires shared nonfungible information

We show that sharing a quantum reference frame requires sharing measurement operators that identify the reference frame in addition to operators that measure its state. Observers restricted to finite resources cannot, in general, operationally determine that they share such operators. Uncertainty about whether system-identification operators are shared induces decoherence.

quant-ph↗

arXiv2019

Decoherence as a sequence of entanglement swaps

Standard semi-classical models of decoherence do not take explicit account of the classical information required to specify the system - environment boundary. I show that this information can be represented as a finite set of reference eigenvalues that must be encoded by any observer, including any apparatus, able to distinguish the system from its environment. When the information required for system identification is accounted for in this way, decoherence can be described as a sequence of entanglement swaps between reference and pointer components of the system and their respective environments. Doing so removes the need for the a priori assumptions of ontic boundaries required by semi-classical models.

quant-ph↗

arXiv2019

Some Consequences of the Thermodynamic Cost of System Identification

The concept of a ``system'' is foundational to physics, but the question of how observers identify systems is seldom addressed. Classical thermodynamics restricts observers to finite, finite-resolution observations with which to identify the systems on which ``pointer state'' measurements are to be made. It is shown that system identification is at best approximate, even in a finite world, and that violations of the Leggett--Garg and Bell/CHSH (Clauser-Horne-Shimony-Holt) inequalities emerge naturally as requirements for successful system identification.

quant-ph↗

arXiv2018

A mosaic of Chu spaces and Channel Theory with applications to Object Identification and Mereological Complexity

Chu Spaces and Channel Theory are well established areas of investigation in the general context of category theory. We review a range of examples and applications of these methods in logic and computer science, including Formal Concept Analysis, distributed systems and ontology development. We then employ these methods to describe human object perception, beginning with the construction of uncategorized object files and proceeding through categorization, individual object identification and the tracking of object identity through time. We investigate the relationship between abstraction and mereological categorization, particularly as these affect object identity tracking. This we accomplish in terms of information flow that is semantically structured in terms of local logics, while at the same time this framework also provides an inferential mechanism towards identification and perception. We show how a mereotopology naturally emerges from the representation of classifications by simplicial complexes, and briefly explore the emergence of geometric relations and interactions between objects.

cs.AI↗

arXiv2016

Building the Observer into the System: Toward a Realistic Description of Human Interaction with the World

Human beings do not observe the world from the outside, but rather are fully embedded in it. The sciences, however, often give the observer both a "god's eye" perspective and substantial a~priori knowledge. Motivated by W. Ross Ashby's statement, "the theory of the Black Box is merely the theory of real objects or systems, when close attention is given to the question, relating object and observer, about what information comes from the object, and how it is obtained" (Introduction to Cybernetics, 1956, p. 110), I develop here an alternate picture of the world as a black box to which the observer is coupled. Within this framework I prove purely-classical analogs of the "no-go" theorems of quantum theory. Focussing on the question of identifying macroscopic objects, such as laboratory apparatus or even other observers, I show that the standard quantum formalism of superposition is required to adequately represent the classical information that an observer can obtain. I relate these results to supporting considerations from evolutionary biology, cognitive and developmental psychology, and artificial intelligence.

quant-ph↗

arXiv2016

Decompositional equivalence: A fundamental symmetry underlying quantum theory

Decompositional equivalence is the principle that there is no preferred decomposition of the universe into subsystems. It is shown here, by using simple thought experiments, that quantum theory follows from decompositional equivalence together with Landauer's principle. This demonstration raises within physics a question previously left to psychology: how do human - or any - observers agree about what constitutes a "system of interest"?

quant-ph↗

arXiv2016

Effective dark energy from decoherence

Within the quantum Darwinist framework introduced by W. H. Zurek ({\em Nat. Phys.}, 5:181-188, 2009), observers obtain pointer-state information about quantum systems by interacting with a local sample of the surrounding environment, e.g. a local sample of the ambient photon field. Because the environment encodes such pointer state information uniformly and hence redundantly throughout its entire volume, the information is equally available to all observers regardless of their location. This framework is applied to the observation of stellar center-of-mass positions, which are assumed to be encoded by the ambient photon field in a way that is uniformly accessible to all possible observers. Assuming Landauer's Principle, constructing such environmental encodings requires $(ln2) kT$ per encoded bit. For the observed 10$^{24}$ stars and a uniform binary encoding of center-of-mass positions into voxels with a linear dimension of 5 km, the free energy required at the current CMB temperature T = 2.7 K is $\sim$ 2.5 $\cdot$ 10$^{-27}$ kg $\cdot$ m$^{-3}$, strikingly close to the observed value of $Ω_Λ ρ_{c}$. Decreasing the voxel size to $(l_{P})^{3}$ results in a free energy requirement 10$^{117}$ times larger.

quant-ph↗

arXiv2014

Hilbert-space factorization is a limited and expensive information-processing resource

By taking the need for quantum reference frames into account, it is shown that Hilbert-space factorization is a dissipative process requiring on the order of kT to reduce by one bit an observer's uncertainty in the provenance of a classically-recorded observational outcome. This cost is neglected in standard treatments of decoherence that assume that observational outcomes are obtained by interacting with a collection of degrees of freedom identified a priori. Treating this cost explicitly leads to a natural measure of the probability of any particular quantum reference frame.

quant-ph↗

arXiv2013

Imposing system-observer symmetry on the von Neumann description of measurement

By imposing system-observer symmetry on the von Neumann description of measurement, it is shown that the quantum measurement problem is structurally equivalent to a familiar reverse-engineering problem: that of describing the behavior of an arbitrary physical device as algorithm instantiation. It is suggested that this problem can at best be given a relational solution.

quant-ph↗

arXiv2013

On the Ollivier-Poulin-Zurek definition of objectivity

The Ollivier-Poulin-Zurek definition of objectivity provides a philosophical basis for the environment as witness formulation of decoherence theory and hence for quantum Darwinism. It is shown that no account of the reference of the key terms in this definition can be given that does not render the definition either empty or circular. It is argued that this is not the fault of the language used, but of the assumption that the laws of physics are independent of Hilbert-space decomposition. All evidence suggests that this latter assumption is true. If it is, decoherence cannot explain the emergence of classicality.

quant-ph↗

arXiv2012

Implementation of classical communication in a quantum world

Observations of quantum systems carried out by finite observers who subsequently communicate their results using classical data structures can be described as "local operations, classical communication" (LOCC) observations. The implementation of LOCC observations by the Hamiltonian dynamics prescribed by minimal quantum mechanics is investigated. It is shown that LOCC observations cannot be described using decoherence considerations alone, but rather require the \textit{a priori} stipulation of a positive operator-valued measure (POVM) about which communicating observers agree. It is also shown that the transfer of classical information from system to observer can be described in terms of system-observer entanglement, raising the possibility that an apparatus implementing an appropriate POVM can reveal the entangled system-observer states that implement LOCC observations.

quant-ph↗

arXiv2012

Consistent quantum mechanics admits no mereotopology

It is standardly assumed in discussions of quantum theory that physical systems can be regarded as having well-defined Hilbert spaces. It is shown here that a Hilbert space can be consistently partitioned only if its components are assumed not to interact. The assumption that physical systems have well-defined Hilbert spaces is, therefore, physically unwarranted.

quant-ph↗

arXiv2012

Bell's Theorem from Moore's Theorem

It is shown that the restrictions of what can be inferred from classically-recorded observational outcomes that are imposed by the no-cloning theorem, the Kochen-Specker theorem and Bell's theorem also follow from restrictions on inferences from observations formulated within classical automata theory. Similarities between the assumptions underlying classical automata theory and those underlying universally-unitary quantum theory are discussed.

quant-ph↗

arXiv2012

A model-theoretic interpretation of environmentally-induced superselection

Environmentally-induced superselection or "einselection" has been proposed as an observer-independent mechanism by which apparently classical systems "emerge" from physical interactions between degrees of freedom described completely quantum-mechanically. It is shown that einselection can only generate classical systems if the "environment" is assumed \textit{a priori} to be classical; einselection therefore does not provide an observer-independent mechanism by which classicality can emerge from quantum dynamics. Einselection is then reformulated in terms of positive operator-valued measures (POVMs) acting on a global quantum state. It is shown that this re-formulation enables a natural interpretation of apparently-classical systems as virtual machines that requires no assumptions beyond those of classical computer science.

quant-ph↗

arXiv2012

Autonomy all the way down: Systems and dynamics in quantum Bayesianism

Quantum Bayesianism ("QBism") has been put forward as an approach to quantum theory that avoids foundational problems by altogether disavowing the objective existence of quantum states. It is shown that QBism suffers its own versions of the familiar foundational problems, and that these QBist versions are illuminating not just for QBism, but for more traditional foundational approaches as well.

quant-ph↗

arXiv2012

If physics is an information science, what is an observer?

Interpretations of quantum theory have traditionally assumed a "Galilean" observer, a bare "point of view" implemented physically by a quantum system. This paper investigates the consequences of replacing such an informationally-impoverished observer with an observer that satisfies the requirements of classical automata theory, i.e. an observer that encodes sufficient prior information to identify the system being observed and recognize its acceptable states. It shows that with reasonable assumptions about the physical dynamics of information channels, the observations recorded by such an observer will display the typical characteristics predicted by quantum theory, without requiring any specific assumptions about the observer's physical implementation.

quant-ph↗

arXiv2011

Classical system boundaries cannot be determined within quantum Darwinism

Multiple observers who interact with environmental encodings of the states of a macroscopic quantum system S as required by quantum Darwinism cannot demonstrate that they are jointly observing S without a joint a priori assumption of a classical boundary separating S from its environment E. Quantum Darwinism cannot, therefore, be regarded as providing a purely quantum-mechanical explanation of the "emergence" of classicality.

quant-ph↗