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.
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.
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.
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.
Although quantum states nicely express interference effects, outcomes of experimental trials show no states directly; they indicate properties of probability distributions for outcomes. We prove categorically that probability distributions leave open a choice of quantum states and operators and particles, resolvable only by a move beyond logic, which, inspired or not, can be characterized as a guess. By recognizing guesswork as inescapable in choosing quantum states and particles, we free up the use of particles as theoretical inventions by which to describe experiments with devices, and thereby replace the postulate of state reductions by a theorem. By using the freedom to invent probe particles in modeling light detection, we develop a quantum model of the balancing of a light-induced force, with application to models and detecting devices by which to better distinguish one source of weak light from another. Finally, we uncover a symmetry between entangled states and entangled detectors, a dramatic example of how the judgment about what light state is generated by a source depends on choosing how to model the detector of that light.
Experimenting with metastability in recording devices leads us to wonder about an interface between equations of motion and the stillness of experimental records. Here we delineate an interface between wave functions as language to describe motion and Turing tapes as language to describe experimental records. After extending quantum formalism to make this interface explicit, we report on constraints and freedoms in choosing quantum-mechanical equations to model experiments with devices. We prove that choosing equations of wave functions and operators to achieve a fit between calculated probabilities and experimental records requires reaching beyond both logic and the experimental records. Although informed by experience, a "reach beyond" can fairly be called a guess. Recognizing that particles as features of wave functions depend on guesswork, we introduce their use not as objects of physical investigation but as elements of thought in quantum-mechanical models of devices. We make informed guesses to offer a quantum-mechanical model of a 1-bit recording device in a metastable condition. Probabilities calculated from the model fit an experimental record of an oscillation in a time-varying probability, showing a temperature-independent role for Planck's constant in what heretofore was viewed as a "classical" electronic device.
The design and operation of a quantum-mechanical device as a laboratory instrument puts models written in equations of quantum mechanics in contact with instruments. This contact is recordable in files of a Classical Digital Process-control Computer (CPC) used both to calculate with the equations and to manage the instruments. By noticing that equations and instruments make contact in a CPC, we rewrite equations of quantum mechanics to explicitly include functions of CPC-commands to the instruments. This sets up a proof that a scientist's choice in linking mathematical models to instruments is unresolvable without guesswork to narrow the set of models from which one is to be chosen. As for implications of the proof, scientists inherit choices from the past and frame choices for the future, choices open to guesswork and visible in CPC files. To picture these choices, we adapt colored Petri nets, and the availability of these net fragments makes choice and guesswork part and parcel of physics. Net fragments as a means of expressing guess-demanding choices are applied to portray guesswork needed in testing and calibrating a quantum computer. The sample size required to test a quantum gate in a quantum computer is shown to grow as the inverse square of the error allowed in implementing the gate.