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.
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.
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
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.
ConclusionsIn the Preface to this book, we started with Alice and Bob having very different views of their observations.Alice used an optical telescope and reported nothing unusual about a distant galaxy that she could see.Bob, on the other hand, detected intense radio activity in that galaxy.Our question was: who has the true view of that galaxy?We advised the reader that the answer is not Alice.Neither is it Bob.The answer is not both of them, nor is it neither of them.It is not a trick question either.So what is the answer that this book would supply?Our answer will come presently.While this book has set forth a definite mathematical perspective on empirical physics, it has contained quite a lot of commentary that might be disparaged as metaphysics or philosophy.Such commentary is generally frowned on in science, because it has no empirical content.It is vacuous.In our defense, we point out the obvious: science is not a robotic activity; it is carried out by humans and these are driven by their metaphysical, philosophical, and emotional imperatives.For instance, the hard-core scientific view that quantum theory needs no interpretation but only application is itself a philosophy.It is no more than a conditioned response, based on opinion and subscription to current scientific norms.It is, indeed, a philosophy of how to do quantum mechanics.So we all do it, in one way or another.Our concern in this book is that the way that we do it should be based soundly on scientific principles.The quantized detector approach that we describe and use in this book is our attempt to do just that.There is an excellent paper on all of this that has the provocative title "Quantum Theory Needs No Interpretation," by Fuchs and Peres (2000).It seems on the face of it to dismiss any sort of "interpretation" of quantum mechanics.In fact, close reading of it confirms (to us at least) the agenda that we have set out in this book.Yes, quantum mechanics needs no interpretation, when it is being applied to processes that take place in the information void.
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 ).
In the Preface to this book, we started with Alice and Bob having very different views of their observations. Alice used an optical telescope and reported nothing unusual about a distant galaxy that she could see. Bob, on the other hand, detected intense radio activity in that galaxy. Our question was: who has the true view of that galaxy? We advised the reader that the answer is not Alice . Neither is it Bob . The answer is not both of them , nor is it neither of them . It is not a trick question either. So what is the answer that this book would supply? Our answer will come presently. While this book has set forth a definite mathematical perspective on empirical physics, it has contained quite a lot of commentary that might be disparaged as metaphysics or philosophy. Such commentary is generally frowned on in science, because it has no empirical content. It is vacuous. In our defense, we point out the obvious: science is not a robotic activity; it is carried out by humans and these are driven by their metaphysical, philosophical, and emotional imperatives. For instance, the hard-core scientific view that quantum theory needs no interpretation but only application is itself a philosophy. It is no more than a conditioned response, based on opinion and subscription to current scientific norms. It is, indeed, a philosophy of how to do quantum mechanics. So we all do it, in one way or another. Our concern in this book is that the way that we do it should be based soundly on scientific principles. The quantized detector approach that we describe and use in this book is our attempt to do just that. There is an excellent paper on all of this that has the provocative title “Quantum Theory Needs No Interpretation,” by Fuchs and Peres (2000). It seems on the face of it to dismiss any sort of “interpretation” of quantum mechanics. In fact, close reading of it confirms (to us at least) the agenda that we have set out in this book. Yes, quantum mechanics needs no interpretation, when it is being applied to processes that take place in the information void .
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.