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Cambridge University Press eBooks

Physical Unknowables

Karl Svozil

Published Jun 6, 2011• 5 citations
Publisher

Abstract

As we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don't know we don't know. –United States Secretary of Defense Donald H. Rumsfeld at a Department of Defense news briefing on February 12, 2002 Ei mihi, qui nescio saltem quid nesciam! (Alas for me, that I do not at least know the extent of my own ignorance!) –Aurelius Augustinus, 354–430, “Confessiones” (Book XI, chapter 25) Rise and Fall of Determinism In what follows, a variety of physical unknowables will be discussed. Provable lack of physical omniscience, omnipredictability and omnipotence is derived by reduction to problems that are known to be recursively unsolvable. “Chaotic” symbolic dynamical systems are unstable with respect to variations of initial states. Quantum unknowables include the random occurrence of single events, complementarity, and value indefiniteness. From antiquity onward, various waves of (in)determinism have influenced human thought. Regardless of whether they were shaped by some Zeitgeist , or whether, as Goethe's Faust puts it, “what you the Spirit of the Ages call, is nothing but the spirit of you all, wherein the Ages are reflected,” their proponents have sometimes vigorously defended their stance in irrational, unscientific, and ideologic ways.

DOI
10.1017/cbo9780511974236.013

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Physical unknowables

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A variety of physical unknowables are discussed. Provable lack of physical omniscience, omnipredictability and omnipotence is derived by reduction to problems which are known to be recursively unsolvable. "Chaotic" symbolic dynamical systems are unstable with respect to variations of initial states. Quantum unknowables include the random occurrence of single events, complementarity and value indefiniteness.

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What is ‘real’: A brief comparison

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Steven French’s review of Bernard d’Espagnat’s 500-page tome On Physics and Philosophy (Physics Today, Physics Today 0031-9228 60 6 2007 66 https://doi.org/10.1063/1.2754610. June 2007, page 66 ) got my attention, with its repeated discussion of something d’Espagnat calls “the Real.” I must confess I have not seen d’Espagnat’s book, but the more I read about this Real in French’s review, the more I thought I’d heard of it somewhere before. In the true scientific spirit of bringing to the attention of a researcher the results of prior research bearing on his work, I have interspersed citations from the Summa Theologica by Thomas Aquinas (1225–74) between passages from French’s review of d’Espagnat’s book.French states that the Real “nevertheless exerts an influence on the phenomena.”Aquinas wrote, “As there can be nothing which is not created by God, so there can be nothing which is not subject to His government” (part 1, question 103, article 5).French writes, “The grand laws of physics are ‘highly distorted reflections … of the great structures of “the Real”’ (page 455)…. The Real, although impossible to conceive, is nonseparable; from it, both consciousness and empirical reality ‘co-emerge.’”Aquinas wrote, “From the knowledge of sensible things the whole power of God cannot be known; nor therefore can His essence be seen. But because they are His effects and depend on their cause, we can be led from them so far as to know of God whether He exists, and to know of Him what must necessarily belong to Him, as the first cause of all things, exceeding all things caused by Him” (part 1, question 12, article 12).Aquinas maintained that there cannot ultimately be any disagreement between faith and reason because both come from an infinitely faithful and infinitely reasonable God. It is amusing that an apparently secular philosopher such as d’Espagnat, writing for a modern audience of physicists and philosophers and basing his thought on the latest results of quantum mechanics, has nevertheless arrived at conclusions in harmony with the greatest philosopher of the Middle Ages.© 2008 American Institute of Physics.

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In discussing the fundamental sources of unpredictability, I shall concentrate on those indeterminacies that are definitely required by theory. Let me therefore begin \nby eliminating from consideration supposed indeterminacies stemming from doubts that some people may entertain about basic principles or from certain kinds of ignorance that I believe to be temporary and likely to be remedied in the relatively near future. I assume the following: \n1. Quantum mechanics is correct. The formulation and interpretation of quantum mechanics are still undergoing some necessary evolution, especially in order to accommodate quantum cosmology in a comfortable way, but the basic character of quantum mechanics has always been the same and we may suppose it will remain unchanged. \n2. The elementary particles and their interactions obey a definite dynamical law, discoverable by inquiring complex adaptive systems such as the human scientific enterprise. Although the process of discovery involves a sequence of \napproximate schemata, there is an endpoint to the process after a finite amount of research. (Of course, it can never be possible to prove that the resulting unified theory is perfect; one can only verify it in the usual way by comparing predictions to available observations.) Humans may already have found this unified quantum field theory in the form of superstring theory, which has, to begin with, no arbitrary parameters. (Of course, spontaneous symmetry \nbreaking may give rise to some parameters and even to a choice of solutions, with probabilities for the various alternatives. I will deal with that possibility further on.) This second assumption is equivalent to stating that there is no necessary fundamental unpredictability stemming from ignorance of the universal dynamical law. \n3. The density matrix (in the Schrödinger picture) of the universe near the beginning of its expansion is also knowable. It must in any case be comparatively simple and very far from equilibrium. The second law of thermodynamics and the other associated arrows of time are explained by these properties of the initial density matrix along with the fact that the universe is still very young—the interval of ten billion years is extremely short compared with the relaxation time from the special initial condition.

Annals of the New York Academy of Sciences•Jun 1, 1999•3 citations
As we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don't know we don't know. –United States Secretary of Defense Donald H. Rumsfeld at a Department of Defense news briefing on February 12, 2002 Ei mihi, qui nescio saltem quid nesciam! (Alas for me, that I do not at least know the extent of my own ignorance!) –Aurelius Augustinus, 354–430, “Confessiones” (Book XI, chapter 25) Rise and Fall of Determinism In what follows, a variety of physical unknowables will be discussed. Provable lack of physical omniscience, omnipredictability and omnipotence is derived by reduction to problems that are known to be recursively unsolvable. “Chaotic” symbolic dynamical systems are unstable with respect to variations of initial states. Quantum unknowables include the random occurrence of single events, complementarity, and value indefiniteness. From antiquity onward, various waves of (in)determinism have influenced human thought. Regardless of whether they were shaped by some Zeitgeist , or whether, as Goethe's Faust puts it, “what you the Spirit of the Ages call, is nothing but the spirit of you all, wherein the Ages are reflected,” their proponents have sometimes vigorously defended their stance in irrational, unscientific, and ideologic ways.
Part I Embedded observers, reflexive perception and representation: Intrinsic and extrinsic observation mode -- Embedded observers and self-expression -- Reflexive measurement -- Intrinsic self-representation -- Part II Provable unknowns: On what is entirely hopeless -- Forecasting and unpredictability -- Induction by rule inference -- Other types of recursion theoretic unknowables -- What if there are no laws? Emergence of laws -- Part III Quantum unknowns: "Shut up and calculate" -- Evolution by permutation -- Quantum mechanics in a nutshell -- Quantum oracles -- Vacuum fluctuations -- Radioactive decay -- Part IV Exotic unknowns: Classical continua and infinities -- Classical (in)determinism -- Deterministic chaos -- Partition logics, finite automata and generalized urn models -- Part V Transcendence: Miracles -- Dualistic interfaces -- Part VI Executive summary: Executive summary -- Appendix A: Formal (in)computability and randomness -- B: Two particle correlations and expectations
Steven French’s review of Bernard d’Espagnat’s 500-page tome On Physics and Philosophy (Physics Today, Physics Today 0031-9228 60 6 2007 66 https://doi.org/10.1063/1.2754610. June 2007, page 66 ) got my attention, with its repeated discussion of something d’Espagnat calls “the Real.” I must confess I have not seen d’Espagnat’s book, but the more I read about this Real in French’s review, the more I thought I’d heard of it somewhere before. In the true scientific spirit of bringing to the attention of a researcher the results of prior research bearing on his work, I have interspersed citations from the Summa Theologica by Thomas Aquinas (1225–74) between passages from French’s review of d’Espagnat’s book.French states that the Real “nevertheless exerts an influence on the phenomena.”Aquinas wrote, “As there can be nothing which is not created by God, so there can be nothing which is not subject to His government” (part 1, question 103, article 5).French writes, “The grand laws of physics are ‘highly distorted reflections … of the great structures of “the Real”’ (page 455)…. The Real, although impossible to conceive, is nonseparable; from it, both consciousness and empirical reality ‘co-emerge.’”Aquinas wrote, “From the knowledge of sensible things the whole power of God cannot be known; nor therefore can His essence be seen. But because they are His effects and depend on their cause, we can be led from them so far as to know of God whether He exists, and to know of Him what must necessarily belong to Him, as the first cause of all things, exceeding all things caused by Him” (part 1, question 12, article 12).Aquinas maintained that there cannot ultimately be any disagreement between faith and reason because both come from an infinitely faithful and infinitely reasonable God. It is amusing that an apparently secular philosopher such as d’Espagnat, writing for a modern audience of physicists and philosophers and basing his thought on the latest results of quantum mechanics, has nevertheless arrived at conclusions in harmony with the greatest philosopher of the Middle Ages.© 2008 American Institute of Physics.
Why should special states occur as initial conditions in every physical situation in which they are needed? Half this book has been devoted to making the points that initial conditions may not be as controllable as they seem; that there may be constraints on microscopic initial conditions; that this would not have been noticed; that such constraints can arise from two-time or future conditioning; that in our universe such future conditioning may well be present, although, as remarked, cryptic . In this chapter I will take up more detailed questions: what future conditions could give rise to the need for our ‘special’ states, and why should those particular future conditions be imposed. Before going into this there is a point that needs to be made. Everything in the present chapter could be wrong and the thesis of Chapter 6 nevertheless correct. It is one thing to avoid grotesque states (and solve the quantum measurement problem) by means of special states and it is another provide a rationale for their occurrence. I say this not only to highlight the conceptual dependencies of the theses in this book, but also because there is a good deal of hand waving in the coming chapter and I don't want it to reflect unfavorably on the basic proposal. As pointed out earlier, the usual thermodynamic arrow of time can be phrased as follows: initial states are arbitrary, final states special.
In discussing the fundamental sources of unpredictability, I shall concentrate on those indeterminacies that are definitely required by theory. Let me therefore begin \nby eliminating from consideration supposed indeterminacies stemming from doubts that some people may entertain about basic principles or from certain kinds of ignorance that I believe to be temporary and likely to be remedied in the relatively near future. I assume the following: \n1. Quantum mechanics is correct. The formulation and interpretation of quantum mechanics are still undergoing some necessary evolution, especially in order to accommodate quantum cosmology in a comfortable way, but the basic character of quantum mechanics has always been the same and we may suppose it will remain unchanged. \n2. The elementary particles and their interactions obey a definite dynamical law, discoverable by inquiring complex adaptive systems such as the human scientific enterprise. Although the process of discovery involves a sequence of \napproximate schemata, there is an endpoint to the process after a finite amount of research. (Of course, it can never be possible to prove that the resulting unified theory is perfect; one can only verify it in the usual way by comparing predictions to available observations.) Humans may already have found this unified quantum field theory in the form of superstring theory, which has, to begin with, no arbitrary parameters. (Of course, spontaneous symmetry \nbreaking may give rise to some parameters and even to a choice of solutions, with probabilities for the various alternatives. I will deal with that possibility further on.) This second assumption is equivalent to stating that there is no necessary fundamental unpredictability stemming from ignorance of the universal dynamical law. \n3. The density matrix (in the Schrödinger picture) of the universe near the beginning of its expansion is also knowable. It must in any case be comparatively simple and very far from equilibrium. The second law of thermodynamics and the other associated arrows of time are explained by these properties of the initial density matrix along with the fact that the universe is still very young—the interval of ten billion years is extremely short compared with the relaxation time from the special initial condition.