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arXiv:1504.04345

Clocking in the face of unpredictability beyond quantum uncertainty

F. Hadi Madjid, John M. Myers

Published Apr 16, 2015• 1 citation
arXivHTMLPDF

Abstract

In earlier papers we showed unpredictability beyond quantum uncertainty in atomic clocks, ensuing from a proven gap between given evidence and explanations of that evidence. Here we reconceive a clock, not as an isolated entity, but as enmeshed in a self-adjusting communications network adapted to one or another particular investigation, in contact with an unpredictable environment. From the practical uses of clocks, we abstract a clock enlivened with the computational capacity of a Turing machine, modified to transmit and to receive numerical communications. Such "live clocks" phase the steps of their computations to mesh with the arrival of transmitted numbers. We lift this phasing, known in digital communications, to a principle of \emph{logical synchronization}, distinct from the synchronization defined by Einstein in special relativity. Logical synchronization elevates digital communication to a topic in physics, including applications to biology. One explores how feedback loops in clocking affect numerical signaling among entities functioning in the face of unpredictable influences, making the influences themselves into subjects of investigation. The formulation of communications networks in terms of live clocks extends information theory by expressing the need to actively maintain communications channels, and potentially, to create or drop them. We show how networks of live clocks are presupposed by the concept of coordinates in a spacetime. A network serves as an organizing principle, even when the concept of the rigid body that anchors a special-relativistic coordinate system is inapplicable, as is the case, for example, in a generic curved spacetime.

DOI
10.48550/arxiv.1504.04345

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In earlier papers we showed unpredictability beyond quantum uncertainty in atomic clocks, ensuing from a proven gap between given evidence and explanations of that evidence. Here we reconceive a clock, not as an isolated entity, but as enmeshed in a self-adjusting communications network adapted to one or another particular investigation, in contact with an unpredictable environment. From the practical uses of clocks, we abstract a clock enlivened with the computational capacity of a Turing machine, modified to transmit and to receive numerical communications. Such "live clocks" phase the steps of their computations to mesh with the arrival of transmitted numbers. We lift this phasing, known in digital communications, to a principle of \emph{logical synchronization}, distinct from the synchronization defined by Einstein in special relativity. Logical synchronization elevates digital communication to a topic in physics, including applications to biology. One explores how feedback loops in clocking affect numerical signaling among entities functioning in the face of unpredictable influences, making the influences themselves into subjects of investigation. The formulation of communications networks in terms of live clocks extends information theory by expressing the need to actively maintain communications channels, and potentially, to create or drop them. We show how networks of live clocks are presupposed by the concept of coordinates in a spacetime. A network serves as an organizing principle, even when the concept of the rigid body that anchors a special-relativistic coordinate system is inapplicable, as is the case, for example, in a generic curved spacetime.
In earlier papers we showed unpredictability beyond quantum uncertainty in atomic clocks, ensuing from a proven gap between given evidence and explanations of that evidence. Here we reconceive a clock, not as an isolated entity, but as enmeshed in a self-adjusting communications network adapted to one or another particular investigation, in contact with an unpredictable environment. From the practical uses of clocks, we abstract a clock enlivened with the computational capacity of a Turing machine, modified to transmit and to receive numerical communications. Such “live clocks” phase the steps of their computations to mesh with the arrival of transmitted numbers. We lift this phasing, known in digital communications, to a principle of logical synchronization, distinct from the synchronization defined by Einstein in special relativity. Logical synchronization elevates digital communication to a topic in physics, including applications to biology. One explores how feedback loops in clocking affect numerical signaling among entities functioning in the face of unpredictable influences, making the influences themselves into subjects of investigation. The formulation of communications networks in terms of live clocks extends information theory by expressing the need to actively maintain communications channels, and potentially, to create or drop them. We show how networks of live clocks are presupposed by the concept of coordinates in a spacetime. A network serves as an organizing principle, even when the concept of the rigid body that anchors a special-relativistic coordinate system is inapplicable, as is the case, for example, in a generic curved spacetime.
Curiously overlooked in physics is its dependence on the transmission of numbers. For example the transmission of numerical clock readings is implicit in the concept of a coordinate system. The transmission of numbers and other logical distinctions is often achieved over a computer-mediated communications network in the face of an unpredictable environment. By unpredictable we mean something stronger than the spread of probabilities over given possible outcomes, namely an opening to unforeseeable possibilities. Unpredictability, until now overlooked in theoretical physics, makes the transmission of numbers interesting. Based on recent proofs within quantum theory that provide a theoretical foundation to unpredictability, here we show how regularities in physics rest on a background of channels over which numbers are transmitted. As is known to engineers of digital communications, numerical transmissions depend on coordination reminiscent of the cycle of throwing and catching by players tossing a ball back and forth. In digital communications, the players are computers, and the required coordination involves unpredictably adjusting "live clocks" that step these computers through phases of a cycle. We show how this phasing, which we call `logical synchronization,' constrains number-carrying networks, and, if a spacetime manifold in invoked, put "stripes" on spacetime. Via its logically synchronized channels, a network of live clocks serves as a reference against which to locate events. Such a network in any case underpins a coordinate frame, and in some cases the direct use of a network can be tailored to investigate an unpredictable environment. Examples include explorations of gravitational variations near Earth.
Atomic clocks exchanging signals serve as a background against which to measure the motion of objects on or near the Earth. The background of clocks and signals requires feedback involving computation, both internal to each clock and for regulating relations between clocks. Feedback within a clock responds to a flow of measured outcomes which, by quantum theory, are unpredictable. The steering of atomic clocks in response to unpredictable occurrences of outcomes depends on a wave function, and the choice of this wave function requires an assumption underivable in any logic consistent with quantum theory—another form of unpredictability. Currently backgrounds for motion, for example used in the Global Positioning System, consist of one or another (physical) reference frame as a realization of a (mathematical) reference system that consists of a spacetime coordinate chart with a specified metric tensor field—a structure that expresses neither the unpredictability inherent in atomic clocks nor the feedback by which one deals with this unpredictability. Without requiring the assumption of a metric tensor or even a spacetime, here we introduce a novel type of reference system consisting of the records and criteria resident in real-time computers that mediate feedback, a reference system that, by expressing feedback, structures the unpredictables in a background of motion. The criteria for clock adjustment are discussed. Trade-offs involved in these criteria call for adjusting a background in response to the motion of the objects tracked.
The unexpected plays an important but little-understood role in physics. We are working to understand how the unexpected functions in theory and in experiment. This work leads to novel theoretical and instrumental structures of “two-clock physics”, with implications for the scientific method. The path to these structures that express the unexpected draws on three roots: 1. Physicists write strings of symbols. Quantum theory implies that physicists act as agents who make guesses, expressed as strings of symbols, in the face of unpredictability far more drastic than quantum uncertainty. Assimilating unpredictability as pervasive in theory and experiment opens new avenues to investigation. 2. No two clocks tick alike. We formulate a concept network of transmission of symbols among agents, without assuming any spacetime or any global time variable, but requiring that agents adjust local clock rates. This structure offers alternatives to time and distance adapted to a variety of cases and is an important element of what we call two-clock physics. 3. Sometimes a flipped coin lands on edge. Agents must rely on guesses to steer clock rates to achieve a logical synchronization that avoids confusion of one symbol with another.
In the context of quantum theory, recently we distinguished mathematics for expressing evidence from mathematics for explaining evidence. Here this distinction is made in spacetime physics. We offer a system of mathematical thought-or as termed in geodesy a reference system-for evidence, separated out from additional assumptions of a geometry in terms of which to explain that evidence. The offered reference system for evidence, free of any assumption of a particular explanatory geometry, whether Euclidean or general relativistic, amounts to a (theoretical) "assemblage of histories accumulated in the memories of parties to a synchronous communications network." The assemblage of histories gives voice to the known experimental finding, sometimes forgotten by theorists, that any memory device for recording logical symbols must be insensitive to variations in signals in which those symbols are carried. Out of acknowledging this insensitivity comes an appreciation of rhythms essential to the communication of digital symbols and of the need for analog measurements to maintain these rhythms. The separate reference system for evidence reconciles what otherwise is a conflict between the demand in quantum mechanics for repeatable experiments and the lack in spacetime metrics appropriate to the Global Positioning System of any exact symmetry, a lack that rules out an isometry between two spacetime regions for two occurrences of an experiment.
Quantum dynamics on curved spacetime has never been directly probed beyond the Newtonian limit. Although we can describe such dynamics theoretically, experiments would provide empirical evidence that quantum theory holds even in this extreme limit. The practical challenge is the minute spacetime curvature difference over the length scale of the typical extent of quantum effects. Here, we propose a quantum network of alkaline earth (like) atomic processors for constructing a distributed quantum state that is sensitive to the differential proper time between its constituent atomic processor nodes, implementing a quantum observable that is affected by post-Newtonian curved spacetime. Conceptually, we propose to delocalize one clock between three locations by encoding the presence or absence of a clock into the state of the local atoms. By separating three atomic nodes over approximately kilometer-scale elevation differences and distributing one clock between them via a W state, we demonstrate that the curvature of spacetime is manifest in the interference of the three different proper times that give rise to three distinct beat notes in our nonlocal observable. We further demonstrate that N -atom entanglement within each node enhances the interrogation bandwidth by a factor of N . We discuss how our proposed system can probe new facets of fundamental physics, such as the linearity, unitarity, and probabilistic nature of quantum theory on curved spacetime. Our protocol combines several recent advances with neutral atom and trapped ions to realize a novel quantum probe of gravity uniquely enabled by quantum networks.