Change and Persistence IntroductionOur interest in this chapter is in change, which is another way of discussing persistence, or the apparent endurance over intervals of time of spatially extended structures.Persistence is the phenomenon that underpins all human activity.Given the rule that we may think of as the first law of time, the dictum of Heraclitus that everything changes, persistence is our name for those remarkable processes that appear to circumvent that law and give stability to our lives.We should be interested, for instance, in the fact that when we wake up each morning, we feel that we are the same individuals who went to sleep the previous night.Indeed, without persistence in one form or another, nothing would make sense, including logic, rational thought, and mathematics, for these depend on comparisons of standards and rules that persist in memory with information that we acquire in process time.Persistence is necessary for physics to make sense.It is emphatically not a metaphysical topic but of the greatest relevance to science, including quantum mechanics (QM).Persistence is implicit in Wheeler's dictum that only acts of observation are meaningful in physics, because observers and their apparatus have to endure long enough to make observations.In quantized detector networks (QDN), the persistence of observers and their apparatus long enough to perform experiments should be regarded as axiomatic.The subject of persistence is a deep and complex one, and will probably never be fully understood.Several reasons contribute to this. Observers Themselves are Subject to ChangeContrary to the general implicit belief that the laws of physics transcend the subjective behavior of observers, it is our thesis that this is a vacuous proposition.It cannot be proved; it is just an assertion, albeit a very useful one.A more
Change and Persistence IntroductionOur interest in this chapter is in change, which is another way of discussing persistence, or the apparent endurance over intervals of time of spatially extended structures.Persistence is the phenomenon that underpins all human activity.Given the rule that we may think of as the first law of time, the dictum of Heraclitus that everything changes, persistence is our name for those remarkable processes that appear to circumvent that law and give stability to our lives.We should be interested, for instance, in the fact that when we wake up each morning, we feel that we are the same individuals who went to sleep the previous night.Indeed, without persistence in one form or another, nothing would make sense, including logic, rational thought, and mathematics, for these depend on comparisons of standards and rules that persist in memory with information that we acquire in process time.Persistence is necessary for physics to make sense.It is emphatically not a metaphysical topic but of the greatest relevance to science, including quantum mechanics (QM).Persistence is implicit in Wheeler's dictum that only acts of observation are meaningful in physics, because observers and their apparatus have to endure long enough to make observations.In quantized detector networks (QDN), the persistence of observers and their apparatus long enough to perform experiments should be regarded as axiomatic.The subject of persistence is a deep and complex one, and will probably never be fully understood.Several reasons contribute to this. Observers Themselves are Subject to ChangeContrary to the general implicit belief that the laws of physics transcend the subjective behavior of observers, it is our thesis that this is a vacuous proposition.It cannot be proved; it is just an assertion, albeit a very useful one.A more
Introduction Our interest in this chapter is in change , which is another way of discussing persistence , or the apparent endurance over intervals of time of spatially extended structures. Persistence is the phenomenon that underpins all human activity. Given the rule that we may think of as the first law of time , the dictum of Heraclitus that everything changes , persistence is our name for those remarkable processes that appear to circumvent that law and give stability to our lives. We should be interested, for instance, in the fact that when we wake up each morning, we feel that we are the same individuals who went to sleep the previous night. Indeed, without persistence in one form or another, nothing would make sense, including logic, rational thought, and mathematics, for these depend on comparisons of standards and rules that persist in memory with information that we acquire in process time. Persistence is necessary for physics to make sense. It is emphatically not a metaphysical topic but of the greatest relevance to science, including quantum mechanics (QM). Persistence is implicit in Wheeler's dictum that only acts of observation are meaningful in physics, because observers and their apparatus have to endure long enough to make observations. In quantized detector networks (QDN), the persistence of observers and their apparatus long enough to perform experiments should be regarded as axiomatic. The subject of persistence is a deep and complex one, and will probably never be fully understood. Several reasons contribute to this. Observers Themselves are Subject to Change Contrary to the general implicit belief that the laws of physics transcend the subjective behavior of observers, it is our thesis that this is a vacuous proposition. It cannot be proved; it is just an assertion, albeit a very useful one. A more pragmatic view is the one held throughout this book, that the laws of physics are contextual to observers. Without observers, science means nothing in a literal sense. But according to the first law of time, observers themselves change over time. This includes their memories and the conditioning that they have; these are carried over from one stage to another. If the processes transporting those memories and belief structures change those memories and belief structures, then the laws of physics as understood by the observers at the time change as well.
What is information? A short answer could be: Anything that changes our minds and states of thinking! Information is virtual. It can be carried by speech, an image, scratches on a stone, patterns in a photon field, the connections of neurons in our brains or even by the wavefunction of an electron. Information does not depend on the actual means of transmission nor does its identity change when changing the carrier. Information is physical. It needs to be sustained by a physical substrate and rearranging that substrate to contain the wanted information requires to spend energy or work. Without a physical world, information can not be stored, processed, or transmitted. Our world is permeated with different representations of information. Actually Information about the physical laws governing our Universe can be found everywhere and in everything. Could it then be that the real fundamental elements of this world are tiny bits of information? Could we get it from bit?1 A number of researcher investigate this possibility, and several of their attempts to recover physical laws from the principles governing information are reported about in this special issue on physics of information. The articles by Gregg Jaeger,2 by Ariel Caticha,3 and by John Skilling and Kevin Knuth4 address the reconstruction of quantum mechanics from information theory. Furthermore, Kevin Knuth and James Walsh5 show how to recover space-time from particles sending each others signals in an initially geometry-free setting. A central element of most works on information is the concept of a probability. Probabilities can be defined via various routes. Most familiar might be their definitions by the frequentists school as relative frequencies of events (in the limit of infinite amounts of such). A more general definition of probabilities is the Bayesians' one, which regards probabilities as quantifiers of statements, expressing how much those should be expected to be true. Although this definition looks subjective on the first glance, it rests on a solid mathematical theorem by Richard Cox6 that any extension of binary logic to a continuum of single valued truthfulness quantifier that respects a minimum of requirements must be isomorphic to probability theory. And this definition turns out to embrace the frequentists' definition in case that infinite numbers of comparable events are actually available and can be counted. The majority of authors of this special issues seem to favor the Bayesian perspective, which is probably a result of our own, the guest editors', preference and not necessarily a reflection of the prevailing position of contemporary scientists. The different views on probabilities of frequentists and Bayesians are addressed by the article of Allen Caldwell.7 He builds a bridge between these antagonistic camps by explaining frequentists' constructions in a Bayesian language. In particular, his argumentation why the omnipresent p-value in statistical and experimental literature might often capture a relevant signal of model misfit is reassuring, given that a large fraction of our medical system is based on decisions backed up by p-values. A Bayesian might add that it would be even more reassuring, if a system rigorously build on logic and its continuous extension would be used for decisions affecting live-or-death questions. The laws governing probabilities themselves seem to reflect that of more elementary mathematical structures. Kevin Knuth shows how these emerge from lattice theory, which deals with relations in partially ordered sets like that of collections of possibilities.8 The sum rule of probability theory is a direct consequence of the underlying lattice structure. Interestingly, a number of other theories are resting also on such lattices and therefore exhibit their own versions of sum rules: measures of sets, mutual information, the Euler characteristics of topological spaces, as well as quantum mechanical interactions that are quantified by pairs of numbers, the real and imaginary parts of complex probability amplitudes (see also4). The theory of information has very practical application in physics and elsewhere. Manfred Opper discusses how the solutions of stochastic differential equations can be inferred via variational methods, which have their origin in thermodynamics.9 Torsten Enßlin introduces information field theory (IFT), the information theory for fields, as a means to infer the configuration of a physical field from incomplete and noisy data.10 The mathematical apparatus for this is that of quantum field theory (QFT), just with ordinary probabilities instead of complex probability amplitudes as in the latter. Could it be that the difference between IFT and QFT is just be the same as between classical information theory and quantum mechanics, the transition from real valued to complex valued quantifier for statements? Anyhow, any practical inference machinery, be it for dynamical systems or for fields, requires sophisticated numerical methods. Michael Betancourt reviews Markov Chain Monte Carlo Methods to calculate expectation values over high dimensional probabilities.11 Theo Steininger and coworkers present the NIFTy3 software package for numerical information field theory calculations, which can handle very high dimensional field inference problems.12 Finally, in an article focused on the subtleties of the Monty Hall problem and mostly aiming at information theoretical entertainment, Torsten Enßlin and Margret Westercamp investigate the possibility that human intuition might be more rational than contemporary psychology thinks.13 A number of possible topics for an issue on physics of information are not addressed here. We would have loved to have articles on Landauer's principle, which states that erasing information has to cost energy, on QBism, a Bayesian version of quantum mechanics, on artificial and biological neural networks, as well as any other aspect of the information-soaked biological world. What has a reader of this special issue to be equipped with in order to follow the lines of thoughts? In addition to the usual physicist's education, the minimal additional equipment are the basics of probability theory and the concept of entropy. Most of the other concepts used in the articles rest on those and are introduced there. Let A, B, and C be propositions (or possibilities). The probability P ( A | B ) of A being true assuming that B is true is a number between 0 and 1, with P ( A | B ) = 1 expressing certainty of A under B ( B ⇒ A ) and P ( A | B ) = 0 expressing certainty of not A being the case under B ( B ⇒ ¬ A ).
Questions and Answers What Is Physics?Throughout this book we shall be concerned greatly with questions and answers.The subject that an observer asks a question of will be denoted by a bold symbol such as Ψ.On the other hand, the question that is asked of a subject will be denoted by a barred bold symbol such as Q.Then the answer A that is obtained when that question is asked of that subject will be denoted by A ≡ QΨ.This notation will be used to explain what quantized detector networks (QDN) is all about and in its mathematical implementation.Note that the left-right ordering here is significant: ΨQ will mean something very different.If I, the author, were asked the question Q ≡ What is physics?, my answer QI would be QI = Physics is the process whereby observers first formulate, then ask, and then answer, empirical questions.We need to clarify some points about this answer.By empirical, we mean according to the established principles of science, whereby theorists make propositions or assertions and then establish the truth values of those propositions relative to experiments carried out by unbiased experimentalists.This is done to acquire information about systems under observation (SUOs) in order to add to our knowledge about the relative physical Universe (that part of the Universe empirically accessible to us).We are motivated to do all this for numerous reasons, not the least of which is basic curiosity.This is the view of physics taken in this book.Physics is emphatically not a discipline that philosophers and metaphysicists can meaningfully contribute to, because without empirical testing, any proposition has to be regarded as scientifically vacuous (empirically meaningless).The questions relevant to physicists are posed through experiments and consequently will be referred to as empirical questions.Other sorts of questions will be referred to as theoretical questions.
We have now concluded our summary of the findings of modern physics, and may turn to consider how these findings affect the practical problems of philosophy and of everyday life. But let us first recapitulate the conclusions we have reached in our scientific discussion. Recapitulation Because we are human beings and not mere animals, we try to discover as much as we can about the world in which our lives are cast. We have seen that there is only one method of gaining such knowledge—the method of science, which consists in a direct questioning of nature by observation and experiment. The first thing we learn from such questioning is that the world is rational; its happenings are not determined by caprice but by law. There exists what we have called a ‘pattern of events’, and the primary aim of physical science is the discovery of this pattern. This, as we have seen, will be capable of description only in mathematical terms. The new quantum theory explained in the preceding chapter has provided a mathematical description of the pattern of events which is believed to be complete and perfect. For it enables us—in principle at least—to predict every possible phenomenon of physics, and not one of its predictions has so far proved to be wrong. In a sense, then, we might say that theoretical physics has achieved the main purpose of its being, and that nothing remains but to work out the details.
Introduction Throughout this book we have commented on the need to have a wider vision of physics as more than merely developing and solving equations of motion for states of systems under observation (SUOs). It is our premise that any attempt to discuss time needs to address issues such as the status of observers, apparatus, and suchlike, relative to those states of SUOs. This echoes the following quote from Wheeler: Stronger than the anthropic principle is what I might call the participatory principle. According to it we could not even imagine a universe that did not somewhere and for some stretch of time contain observers because the very building materials of the universe are these acts of observer participancy. You wouldn't have the stuff out of which to build the universe otherwise. This participatory principle takes for its foundation the absolutely central point of the quantum: No elementary phenomenon is a phenomenon until it is an observed (or registered) phenomenon. (Wheeler, 1979) We agree with Wheeler to this extent: there seems little, if any, point in speculating about truly unobservable parts of the Universe. If, however, there is a possibility that physical signals or effects from currently unobserved parts of the Universe might one day reach us, then that would in essence make those parts observable, albeit indirectly, and therefore suitable for theoretical analysis and speculation.
Introduction In this chapter we move beyond the classical register scenario discussed in the previous chapter, extending the discussion to experiments described by timedependent quantum registers of varying rank. We apply our previous discussion of the signal basis representation (SBR), the computational basis representation (CBR), signal operators, signal classes, and the CBR of signal operators to the quantum case. Our discussion of dynamics covers persistence, that is, the stability of apparatus, observers, and laboratory time, and the Born probability rule. We state the principles of quantized detector network (QDN) dynamics and show how they apply to the description of quantum experiments. We discuss the signal theorem and path summations. Persistence Our first step is to clarify what QDN assumes about the evolution of apparatus in time, because this affects the modeling. QDN is designed to reflect the behavior of apparatus in the real world and so it is not assumed in general that a given observer's apparatus is constant in time, even during a given run of an experiment. Although many experiments appear to be carried out with apparatus that persists over any given run of the experiment, and indeed, perhaps over all the runs of that experiment, that is just an incidental factor that reflects no more than an economy in construction. In practice it is invariably easier and more economical to use the same equipment over and over again rather than use it once, throw it away after each run, and build a new version ready for the next run. Lest this be thought of as a trivial point, it is nevertheless an integral and costly feature of many experiments, involving maintenance and upgrading. Indeed, in laboratories such as the Large Hadron Collider, actual run time is a small fraction of total project time. A related, significant issue has to do with the concept of ensemble , discussed in the Appendix. Persistence has everything to do with time scale , specifically, the relative laboratory time over which any piece of equipment can be meaningfully discussed as such. The degree of persistence of apparatus is as contextual as anything else in physics. If a run is relatively brief, say, over in very small fractions of a second, as in high-energy particle scattering experiments, then in such an experiment, the apparatus will behave as if it persists forever.