arXiv subjects

John M. Myers

Publications and source records attributed to John M. Myers.

At least 19 recordsLinked to original sources

arXiv2025

The chanciness of time

Digital network failures stemming from instabilities in measurements of temporal order motivate attention to concurrent events. A century of attempts to resolve the instabilities have never eliminated them. Do concurrent events occur at indeterminate times, or are they better seen as events to which the very concept of temporal order cannot apply? Logical dependencies of messages propagating through digital networks can be represented by marked graphs on which tokens are moved in formal token games. However, available mathematical formulations of these token games invoke "markings" -- global snapshots of the locations of tokens on the graph. The formulation in terms of global snapshots is misleading, because distributed networks are never still: they exhibit concurrent events inexpressible by global snapshots. We reformulate token games used to represent digital networks so as to express concurrency. The trick is to replace global snapshots with "local snapshots." Detached from any central clock, a local snapshot records an action at a node during a play of a token game. Assemblages of local records define acyclic directed graphs that we call history graphs. We show how history graphs represent plays of token games with concurrent motions, and, importantly, how history graphs can represent the history of a network operating while undergoing unpredictable changes.

physics.soc-ph↗

arXiv2024

Synchronizing Rhythms of Logic

Although quantum states nicely explain experiments, the outcomes of experiments are not states. Instead, outcomes correspond to probability distributions. Twenty years ago we proved categorically that probability distributions leave open a choice of quantum states to explain experiments that is resolvable only by a move beyond logic, which, inspired or not, can be characterized as a guess. Guesses link the inner lives of investigators to their explanations of experimental results. Recognizing the inescapability of guesswork in physics leads to avenues of investigation, one of which is presented here. We invert the quest for the logical foundations of physics to reveal a physical basis for logic and calculation, and we represent this basis mathematically, in such a way as to show the shaping and re-shaping of calculations by guesswork. We draw on the interplay between guessing and computation in digital contexts that, perhaps surprisingly, include living organisms. Digital computation and communication depend on a type of synchronization that coordinates transitions among physically distinct conditions represented by "digits." This logical synchronization, known to engineers but neglected in physics, requires guesswork for its maintenance. By abstracting digital hardware, we model the structure of human thinking as logically synchronized computation, punctuated by guesses. We adapt marked graphs to mathematically represent computation and represent guesses by unpredictable changes in these marked graphs. The marked graphs reveal a logical substructure to spatial and temporal navigation, with implications across physics and its biological applications. By limiting our model to the logical aspect of communications and computations we unveil logical structure in relation to guesswork, applicable not just to electronics but also to the functioning of living organisms.

physics.gen-ph↗

arXiv2020

Clocks without "time" in entangled-state experiments

Entangled states of light exhibit measurable correlations between light detections at separated locations. These correlations are exploited in entangled-state quantum key distribution. To do so involves setting up and maintaining a rhythm of communication among clocks at separated locations. Here, we try to disentangle our thinking about clocks as used in actual experiments from theories of time, such as special relativity or general relativity, which already differ between each other. Special relativity intertwines the concept of time with a particular definition of the synchronization of clocks, which precludes synchronizing every clock to every other clock. General relativity imposes additional barriers to synchronization, barriers that invite seeking an alternative depending on any global concept of time. To this end, we focus on how clocks are actually used in some experimental situations. We show how working with clocks without worrying about time makes it possible to generalize some designs for quantum key distribution and also clarifies the need for alternatives to the special-relativistic definition of synchronization.

quant-ph↗

arXiv2019

Synchronization of symbols as the construction of times and places

We demonstrate an unsuspected freedom in physics, by showing an essential unpredictability in the relation between the behavior of clocks on the workbench and explanations of that behavior written in symbols on the blackboard. In theory, time and space are defined by clocks synchronized as specified by relations among clock readings at the transmission and reception of light signals; however spacetime curvature implies obstacles to this synchronization. Recognizing the need to handle bits and other symbols in both theory and experiment, we offer a novel theory of symbol handling, centered on a kind of "logical synchronization," distinct from the synchronization defined by Einstein in special relativity. We present three things: (1) We show a need in physics, stemming from general relativity, for physicists to make choices about what clocks to synchronize with what other clocks. (2) To exploit the capacity to make choices of synchronization, we provide a theory in which to express timing relations between transmitted symbols and the clock readings of the agent that receives them, without relying on any global concept of "time". Dispensing with a global time variable is a marked departure from current practice. (3) The recognition of unpredictability calls for more attention to behavior on the workbench of experiment relative to what can be predicted on the blackboard. As a prime example, we report on the "horse race" situation of an agent measuring the order of arrival of two symbols, to show how order determinations depart from any possible assignment of values of a time variable.

physics.gen-ph↗

arXiv2019

Agency and the physics of numbers

Analogous to Gödel's incompleteness theorems is a theorem in physics to the effect that the set of explanations of given evidence is uncountably infinite. An implication of this theorem is that contact between theory and experiment depends on activity beyond computation and measurement -- physical activity of some agent making a guess. Standing on the need for guesswork, we develop a representation of a symbol-handling agent that both computes and, on occasion, receives a guess from interaction with an oracle. We show: (1) how physics depends on such an agent to bridge a logical gap between theory and experiment; (2) how to represent the capacity of agents to communicate numerals and other symbols, and (3) how that communication is a foundation on which to develop both theory and implementation of spacetime and related competing schemes for the management of motion.

physics.hist-ph↗

arXiv2019

Incompleteness theorem for physics

We show how Gödel's first incompleteness theorem has an analog in quantum theory. Gödel's theorem implies endless opportunities for appending axioms to arithmetic, implicitly showing a role for an agent, namely an agent that asserts an axiom. There is an analog of this theorem in physics, to do with the set of explanations of given evidence. We prove that the set of explanations of given evidence is uncountably infinite, thereby showing how contact between theory and experiment depends on activity beyond computation and measurement -- physical activity characterized as agency.

physics.hist-ph↗

arXiv2016

Gaps between equations and experiments in quantum cryptography

Proofs of the security of quantum key distribution are propositions about models written in the mathematical language of quantum mechanics, and the issue is the linking of such models to actual devices in an experiment on security. To explore this issue, we adapt Wittgenstein's method of language games to view quantum language in its application to experimental activity involving transmitting and receiving devices. We sketch concepts with which to think about models in relation to experiments, without assuming the experiments accord with any model included is a concept of one quantum-mechanical model enveloping another. For any model that agrees with given experimental results and implies the security of a key, there is an enveloping model that agrees with the same results while denying that security. As a result there is a gap between equations and the behavior recorded from devices in an experiment, a gap bridged only by resort to something beyond the reach of logic and measured data, well named by the word guesswork. While this recognition of guesswork encourages eavesdropping, a related recognition of guesswork in the design of feedback loops can help a transmitter and receiver to reduce their vulnerability to eavesdropping.

quant-ph↗

arXiv2016

Symbols of a cosmic order

The world runs on communicated sequences of symbols, e.g. numerals. Examining both engineered and natural communications networks reveals an unsuspected order that depends on contact with an unpredictable entity. This order has three roots. The first is a proof within quantum theory that no evidence can ever determine its explanation, so that an agent choosing an explanation must do so unpredictably. The second root is the showing that clocks that step computers do not "tell time" but serve as self-adjusting symbol-handling agents that regulate "logically synchronized" motion in response to unpredictable disturbances. Such a clock-agent has a certain independence as well as the capacity to communicate via unpredictable symbols with other clock-agents and to adjust its own tick rate in response to that communication. The third root is the noticing of unpredictable symbol exchange in natural systems, including the transmission of symbols found in molecular biology. We introduce a symbol-handling agent as a role played in some cases by a person, for example a physicist who chooses an explanation of given experimental outcomes, and in other cases by some other biological entity, and in still other cases by an inanimate device, such as a computer-based detector used in physical measurements. While we forbear to try to explain the propensity of agents at all levels from cells to civilizations to form and operate networks of logically synchronized symbol-handling agents, we point to this propensity as an overlooked cosmic order, an order structured by the unpredictability ensuing from the proof. Appreciating the cosmic order leads to a conception of agency that replaces volition by unpredictability and re-conceives the notion of objectivity in a way that makes a place for agency in the world as described by physics. Some specific implications for physics are outlined.

physics.hist-ph↗

arXiv2016

Logical synchronization: how evidence and hypotheses steer atomic clocks

A clock steps a computer through a cycle of phases. For the propagation of logical symbols from one computer to another, each computer must mesh its phases with arrivals of symbols from other computers. Even the best atomic clocks drift unforeseeably in frequency and phase; feedback steers them toward aiming points that depend on a chosen wave function and on hypotheses about signal propagation. A wave function, always under-determined by evidence, requires a guess. Guessed wave functions are coded into computers that steer atomic clocks in frequency and position---clocks that step computers through their phases of computations, as well as clocks, some on space vehicles, that supply evidence of the propagation of signals. Recognizing the dependence of the phasing of symbol arrivals on guesses about signal propagation elevates `logical synchronization.' from its practice in computer engineering to a discipline essential to physics. Within this discipline we begin to explore questions invisible under any concept of time that fails to acknowledge the unforeseeable. In particular, variation of spacetime curvature is shown to limit the bit rate of logical communication.

quant-ph↗

arXiv2016

Irreversibility in physics stemming from unpredictable symbol-handling agents

The basic equations of physics involve a time variable t and are invariant under the transformation $t goes to -t$. This invariance at first sight appears to impose time reversibility as a principle of physics, in conflict with thermodynamics. But equations written on the blackboard are not the whole story in physics. In prior work we sharpened a distinction obscured in today's theoretical physics, the distinction between obtaining evidence from experiments on the laboratory bench and explaining that evidence in mathematical symbols on the blackboard. The sharp distinction rests on a proof within the mathematics of quantum theory that no amount of evidence, represented in quantum theory in terms of probabilities, can uniquely determine its explanation in terms of wave functions and linear operators. Building on the proof we show here a role in physics for unpredictable symbol-handling agents acting both at the blackboard and at the workbench, communicating back and forth by means of transmitted symbols. Because of their unpredictability, symbol-handling agents introduce a heretofore overlooked source of irreversibility into physics, even when the equations they write on the blackboard are invariant under t goes to -t$. Widening the scope of descriptions admissible to physics to include the agents and the symbols that link theory to experiments opens up a new source of time-irreversibility in physics.

quant-ph↗

arXiv2015

Unpredictability and the transmission of numbers

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.

quant-ph↗

arXiv2015

Clocking in the face of unpredictability beyond quantum uncertainty

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.

quant-ph↗

arXiv2014

Ambiguity in quantum-theoretical descriptions of experiments

This paper contributes to a burgeoning area of investigation, the ambiguity inherent in mathematics and the implications for physics of this ambiguity. To display the mathematical form of equations of quantum theory used to describe experiments, we make explicit the knobs by which the devices of an experiment are arranged and adjusted. A quantum description comes in two parts: (1) a statement of results of an experiment, expressed by probabilities of detections as functions of knob settings, and (2) an explanation of how we think these results come about, expressed by linear operators, also as functions of knob settings. Because quantum mechanics separates the two parts of any description, it is known that between the statements of results and the explanations lurks a logical gap: given any statement of results one has a choice of explanations. Here we work out some consequences of this openness to choice. We show how quantum theory as mathematical language in which to describe experiments necessarily involves multiple descriptions: multiple explanations of a given result, as well as multiple statements of results and multiple arrangement of knobs. Appreciating these multiplicities resolves what otherwise is a confusion in the concept of invariance. Implications of multiplicity of description for the security of quantum key distribution are noted.

quant-ph↗

arXiv2014

What probabilities tell about quantum systems, with application to entropy and entanglement

As described quantum mechanically, an experimental trial parses into "a preparation" expressed by a density operator and "a measurement" expressed by a set of detection operators, one for each measurable event. A density operator and a detection operator combine via the "trace rule" to generate the probability of a measurable event. As used to describe experiments, both density operators and detection operators depend on parameters expressing experimental choices, so the probabilities they generate also depend on these parameters. The trace rule answers the question: "what parametrized probabilities are generated by a given parametrized density operator and given parametrized detection operator?" Recognizing that the accessibility of operators to experimental tests is only indirect, via probabilities, we ask what probabilities tell about operators, or, put more precisely: "what combinations of a parametrized density operator and parametrized detection operators generate any given set of parametrized probabilities?" We show that any parametrized probability measure can be explained by many inequivalent models expressed by density operators and detection operators. so that a parametrized probability measure, detached from any of the (infinitely many) parametrized operators that generate it, becomes an interesting object in its own right. By detaching a parametrized probability measure from the operators that may have led us to it, we (1) strengthen Holevo's bound on a quantum communication channel and (2) clarify a role for multiple levels of modeling in an example based on quantum key distribution. We then inquire into some parametrized probability measures generated by entangled states and into the topology of the associated parameter spaces; in particular we display some previously overlooked topological features of level sets of these probability measures.

quant-ph↗

arXiv2014

Distinguishing between evidence and its explanations in the steering of atomic clocks

Quantum theory reflects within itself a separation of evidence from explanations. This separation leads to a known proof that: (1) no wave function can be determined uniquely by evidence, and (2) any chosen wave function requires a guess reaching beyond logic to things unforeseeable. Chosen wave functions are encoded into computer-mediated feedback essential to atomic clocks, including clocks that step computers through their phases of computation and clocks in space vehicles that supply evidence of signal propagation explained by hypotheses of spacetimes with metric tensor fields. The propagation of logical symbols from one computer to another requires a shared rhythm---like a bucket brigade. Here we show how hypothesized metric tensors, dependent on guesswork, take part in the logical synchronization by which clocks are steered in rate and position toward aiming points that satisfy phase constraints, thereby linking the physics of signal propagation with the sharing of logical symbols among computers. Recognizing the dependence of the phasing of symbol arrivals on guesses about signal propagation transports logical synchronization from the engineering of digital communications to a discipline essential to physics. Within this discipline we begin to explore questions invisible under any concept of time that fails to acknowledge unforeseeable events. In particular, variation of spacetime curvature is shown to limit the bit rate of logical communication.

quant-ph↗

arXiv2012

High-energy asymptotic behavior of the Bourrely-Soffer-Wu model for elastic scattering

Some time ago, an accurate phenomenological approach, the BSW model, was developed for proton-proton and antiproton-proton elastic scattering cross sections at center-of-mass energies above 10 GeV. This model has been used to give successful theoretical predictions for these processes, at successive collider energies. The BSW model involves a combination of integrals that, while computable numerically at fairly high energies, require some mathematical analysis to reveal the high-energy asymptotic behavior. In this paper we present a high-energy asymptotic representation of the scattering amplitude at moderate momentum transfer, for the leading order in an expansion parameter closely related to the logarithm of the center-of-mass energy. The fact that the expansion parameter goes as the logarithm of the energy means that the asymptotic behavior is accurate only for energies greatly beyond any foreseeable experiment. However, we compare the asymptotic representation against the numerically calculated model for energies in a less extreme region of energy. The asymptotic representation is given by a simple formula which, in particular, exhibits the oscillations of the differential cross section with momentum transfer. We also compare the BSW asymptotic behavior with the Singh-Roy unitarity upper bound for the diffraction peak.

hep-ph↗

arXiv2011

Rhythms of Memory and Bits on Edge: Symbol Recognition as a Physical Phenomenon

Preoccupied with measurement, physics has neglected the need, before anything can be measured, to recognize what it is that is to be measured. The recognition of symbols employs a known physical mechanism. The elemental mechanism-a damped inverted pendulum joined by a driven adjustable pendulum (in effect a clock)-both recognizes a binary distinction and records a single bit. Referred to by engineers as a "clocked flip-flop," this paired-pendulum mechanism pervades scientific investigation. It shapes evidence by imposing discrete phases of allowable leeway in clock readings; and it generates a mathematical form of evidence that neither assumes a geometry nor assumes quantum states, and so separates statements of evidence from further assumptions required to explain that evidence, whether the explanations are made in quantum terms or in terms of general relativity. Cleansed of unnecessary assumptions, these expressions of evidence form a platform on which to consider the working together of general relativity and quantum theory as explanatory language for evidence from clock networks, such as the Global Positioning System. Quantum theory puts Planck's constant into explanations of the required timing leeway, while explanations of leeway also draw on the theory of general relativity, prompting the question: does Planck's constant in the timing leeway put the long known tension between quantum theory and general relativity in a new light?

quant-ph↗

arXiv2008

On statements of experimental results expressed in the mathematical language of quantum theory

We note the separation of a quantum description of an experiment into a statement of results (as probabilities) and an explanation of these results (in terms of linear operators). The inverse problem of choosing an explanation to fit given results is analyzed, leading to the conclusion that any quantum description comes as an element of a family of related descriptions, entailing multiple statements of results and multiple explanations. Facing this multiplicity opens avenues for exploration and consequences that are only beginning to be explored. Among the consequences are these: (1) statements of results impose topologies on control parameters, without resort to any quantum explanation; (2) an endless source of distinct explanations forces an open cycle of exploration and description bringing more and more control parameters into play, and (3) ambiguity of description is essential to the concept of invariance in physics.

quant-ph↗