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.
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.
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.
While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the trajectories of the correct classical motion must emerge from quantum mechanics, a process referred to as the quantum to classical transition. Extending previous work [Bhattacharya, Habib, and Jacobs, Phys. Rev. Lett. 85, 4852 (2000)], here we elucidate this transition in some detail, showing that once the measurement processes that affect all macroscopic systems are taken into account, quantum mechanics indeed predicts the emergence of classical motion. We derive inequalities that describe the parameter regime in which classical motion is obtained, and provide numerical examples. We also demonstrate two further important properties of the classical limit: first, that multiple observers all agree on the motion of an object, and second, that classical statistical inference may be used to correctly track the classical motion.
Quantum theory encounters a difficulty when attempting to describe recording devices. If the recording is of events in which quantum uncertainty plays a role, such as an experiment on a quantum system, quantum theory is unable to correctly predict the probabilities of both future and past states of the recording. The nature of this difficulty will be laid out at the outset. A resolution then will be presented, in which the Born rule will be lightly amended so as to correctly predict all probabilities. The resolution will have the further benefit of clarifying how quantum theory applies to an array of situations in which the theory can be ambiguous, such as the descriptions of continuous measurements, and of closed systems containing all observers.
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.
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.