vol III: Development
chapter 3: Physics
page 1: Action and time
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Action and Time
Discrete or continuous?
Following our method, we begin to construct a map between our model and the observed world. We begin with the world of physics because it is relatively simple and well documented. Physicists have yet to arrive at a consistent physical theory of the whole universe, but remain confident that it can be done. Physics - Wikipedia
One of the longest running debates in the history of physics surrounds the question 'is the universe continuous or discrete?' Atomists, whose literary record goes back to Democritus, opt for discrete. Sylvia Berryman Others. like Aristotle. opt for continuity. Aristotle - Physics Even then, we might say that the agreed answer was 'both', for the Atomists' atoms moved in a continuous space.
The situation is pretty much the same now. Physicists see a continuous space inhabited by a fields whose excitations appear to us as particles. Weinberg, Zee
But there is a distinction to be made here. When we observe the universe, we see only discrete events. Max Planck, Planck's Law - Wikipedia Modern experimental physicists set up elaborate structures to 'prepare' the fields in a certain way, and then count the particulate events that result. CERN
We do not observe the continuous space or the continuous fields. These are products of our mathematical imagination looking for a logically satisfying explanation for the behaviour of the particles that we do observe.
As we move back in time toward the initial singularity, the modern theory suggests that the smooth space - observed particle picture breaks down at the Planck scale. Quantum mechanics and relativity suggest that at this scale particles are so energetic that their Schwarzchild radius is comparable to their de Broglie wavelength. Peacock page 257.
One needs to know quite a lot of physics to make sense of this statement. Here we follow two parallel courses, explaining the physicists' view of what is going on behind the scenes and then translating this into terms of our transfinite network model. Model
The observed universe is quantized
Everything we observe, that is every message we receive from our environment, is encoded in discrete particles. So we fall in love by exchanging photons, phonons, and various pheromones. These physical events are processed by our sensory, nervous and hormonal systems to yield the sort of feelings represented by the words 'I'm in love', 'Lets have sex', and so on. This is an example of a layered network of communication.
We will deal with the processing of observations later. Psychology Here we are concerned with the physical layer in which particles are exchanged. All these exchanges are discrete, and the unit of exchange is the quantum of action, Planck introduced the quantum of action 1900 to remove an infinity from the classical continuous calculation of the interaction between matter and radiation. The quantum of action sets the scale of physics. It is a measure of the smallest possible event.
The quantum of action seems to logically precede the distinction between space and time. Quantum mechanics maps action to space and time with the two equations
and
where h is Planck's constant, E is energy, f is frequency, p is momentum and l is wavelength. These equations mean that energy measures the time rate of action ('temporal resolution') and momentum is the spatial rate of action ('spatial resolution') in the universe
The quantum of action corresponds to the smallest observed message
Our first correspondence between physics and the transfinite network is between the quantum of action and the execution of a Turing machine, that is a computation or the exchange of a message.
Energy then corresponds to the frequency of network communication and momentum to the spatial detail that constitutes the message being transmitted.
Clocks tick. The minimum tick in the universe is measured by a quantum of action. Elapsed time (duration) is a count of ticks. Aristotle captured time formally when he wrote: time is the number of motion ordered by before and after, Aristotle Physics IV : xi, 219b2 Time is modelled naturally by the ordered set of natural numbers, each number corresponding to the exchange of a message.
Large processes can be constructed from strings, trees or networks of smaller processes. This idea is a formal product of physics, but it is of more general application.
We often measure jobs and pay for them according to time, attributing a certain hourly rate to workers based on skills and markets. Each job requires, for its completion, a certain amount of action. The time for the job is therefore the total action required divided by the frequency of action, that is in effect, the energy or rate of work of the workers.
(revised 22 October 2008)
Further reading
Books
| Aristotle, and (translated by P H Wickstead and F M Cornford), Physics books I-IV, Harvard University Press, William Heinemann 1980 Introduction: 'The title "Physics" is misleading. .. "Lectures on Nature" the alternative title found in editions of the Greek text, is more enlightening. ... The realm of Nature, for Aristotle, includes all things that move and change ... . Thus the ultimate "matter" which, according to Aristotle, underlies all the elementary substances must be studied, in its changes at least, by the Natural Philosopher. And so must the eternal heavenly spheres of the Aristotelean philosophy, insofar as they themselves move of are the cause of motion in the sublunary world.' Amazon back |
| Dirac, P A M, The Principles of Quantum Mechanics (4th ed), Oxford UP/Clarendon 1983 Jacket: '[this] is the standard work in the fundamental principles of quantum mechaincs, indispensible both to the advanced student and the mature research worker, who will always find it a fresh source of knowledge and stimulation.' (Nature) Amazon back |
| Goethe, Johann Wolfgang von, and Stuart Atkins (editor), Faust I and II (The Collected Works, volume 2), University of Princeton Press 1994 Jacket: Goethe's most complex and profound work, Faust was the work of the great poet's entire lifetime. Written over a period of sixty years, it can be read as a document of Goethe's moral and artistic development. As a drama drawn from an immense variety of cultural and historical material, set in a wealth of poetic and theatrical traditions, it can be read as a story of western humanity striving restlessly and ruthlessly for progress.' Amazon back |
| Kuhn, Thomas S, The Structure of Scientific Revolutions, U of Chicago Press 1996 Introduction: 'a new theory, however special its range of application, is seldom just an increment to what is already known. Its assimilation requires the reconstruction of prior theory and the re-evaluation of prior fact, an intrinsically revolutionary process that is seldom completed by a single man, and never overnight.' [p 7] Amazon back |
| Peacock, John A, Cosmological Physics, Cambridge University Press 1999 Nature Book Review: 'The intermingling of observational detail and fundamental theory has made cosmology an exceptionally rich, exciting and controversial science. Students in the field -- whether observers or particle theorists -- are expected to be acquainted with matters ranging from the Supernova Ia distance scale, Big Bang nucleosynthesis theory, scale-free quantum fluctuations during inflation, the galaxy two-point correlation function, particle theory candidates for the dark matter, and the star formation history of the Universe. Several general science books, conference proceedings and specialized monographs have addressed these issues. Peacock's Cosmological Physics ambitiously fills the void for introducing students with a strong undergraduate background in physics to the entire world of current physical cosmology. The majestic sweep of his discussion of this vast terrain is awesome, and is bound to capture the imagination of most students.' Ray Carlberg, Nature 399:322 Amazon back |
| von Neumann, John, and Robert T Beyer (translator), Mathematical Foundations of Quantum Mechanics, Princeton University Press 1983 Jacket: '... a revolutionary book that caused a sea change in theoretical physics. ... JvN begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which vN regards as the definitive form of quantum mechanics. ... Regarded as a tour de force at the time of its publication, this book is still indispensible for those interested in the fundamental issues of quantum mechanics.' Amazon back |
| Weinberg, Steven, The Quantum Theory of Fields Volume I: Foundations, Cambridge University Press 1995 Jacket: 'After a brief historical outline, the book begins anew with the principles about which we are most certain, relativity and quantum mechanics, and then the properties of particles that follow from these principles. Quantum field theory then emerges from this as a natural consequence. The classic calculations of quantum electrodynamics are presented in a thoroughly modern way, showing the use of path integrals and dimensional regularization. The account of renormalization theory reflects the changes in our view of quantum field theory since the advent of effective field theories. The book's scope extends beyond quantum elelctrodynamics to elementary partricle physics and nuclear physics. It contains much original material, and is peppered with examples and insights drawn from the author's experience as a leader of elementary particle research. Problems are included at the end of each chapter. ' Amazon back |
| Zee, Anthony, Quantum Field Theory in a Nutshell, Princeton University Press 2003 Amazon book description: 'An esteemed researcher and acclaimed popular author takes up the challenge of providing a clear, relatively brief, and fully up-to-date introduction to one of the most vital but notoriously difficult subjects in theoretical physics. A quantum field theory text for the twenty-first century, this book makes the essential tool of modern theoretical physics available to any student who has completed a course on quantum mechanics and is eager to go on. Quantum field theory was invented to deal simultaneously with special relativity and quantum mechanics, the two greatest discoveries of early twentieth-century physics, but it has become increasingly important to many areas of physics. These days, physicists turn to quantum field theory to describe a multitude of phenomena. Stressing critical ideas and insights, Zee uses numerous examples to lead students to a true conceptual understanding of quantum field theory--what it means and what it can do. He covers an unusually diverse range of topics, including various contemporary developments,while guiding readers through thoughtfully designed problems. In contrast to previous texts, Zee incorporates gravity from the outset and discusses the innovative use of quantum field theory in modern condensed matter theory. Without a solid understanding of quantum field theory, no student can claim to have mastered contemporary theoretical physics. Offering a remarkably accessible conceptual introduction, this text will be widely welcomed and used. Amazon back |
Links
| Aquinas 113 Summa I, 18, 3: Is life properly attributed to God? Life is in the highest degree properly in God. In proof of which it must be considered that since a thing is said to live in so far as it operates of itself and not as moved by another, the more perfectly this power is found in anything, the more perfect is the life of that thing. ... back |
| Aquinas 13 Summa: I 2 3: Does god exist? I answer that, The existence of God can be proved in five ways. The first and more manifest way is the argument from motion. ... The second way is from the nature of the efficient cause. ... The third way is taken from possibility and necessity ... The fourth way is taken from the gradation to be found in things. ...The fifth way is taken from the governance of the world. back |
| Aquinas 14 Summa: I 3 1: Is God a body? 'I answer that, It is absolutely true that God is not a body; and this can be shown in three ways. First, because no body is in motion unless it be put in motion, as is evident from induction. Now it has been already proved (2, 3), that God is the First Mover, and is Himself unmoved. Therefore it is clear that God is not a body. ...' back |
| Aristotle - Physics The Internet Classic Archive | Physics y Aritotle Written 350 B.C.E Translated by R. P. Hardie and R. K. Gaye back |
| CERN LHC Homepage 'explain it in 60 seconds The Large Hadron Collider is currently being installed in a 27-kilometer ring buried deep below the countryside on the outskirts of Geneva, Switzerland. When its operation begins in 2007, the LHC will be the world's most powerful particle accelerator. High-energy protons in two counter-rotating beams will be smashed together in a search for signatures of supersymmetry, dark matter and the origins of mass. The beams are made up of bunches containing billions of protons. Traveling at a whisker below the speed of light they will be injected, accelerated, and kept circulating for hours, guided by thousands of powerful superconducting magnets. For most of the ring, the beams travel in two separate vacuum pipes, but at four points they collide in the hearts of the main experiments, known by their acronyms: ALICE, ATLAS, CMS, and LHCb. The experiments' detectors will watch carefully as the energy of colliding protons transforms fleetingly into a plethora of exotic particles. The detectors could see up to 600 million collision events per second, with the experiments scouring the data for signs of extremely rare events such as the creation of the much-sought Higgs boson.' back |
| Elisabeth Pacherie Action theory 'This site aims at providing resources for people interested in action theory in philosophy and cognitive science.' back |
| Eric M Eisel "In the Beginning was the Word...": The Question of the Origin of Language in Goethe's Faust Goethe, Faust (contemplating translation of John's Gospel): 'Tis written: "In the beginning was the Word!" Here now I'm balked! Who'll put me in accord? It is impossible, the Word so high to prize, I must translate it otherwise If I am rightly by the Spirit taught. 'Tis written: In the beginning was the Thought! Consider well that line, the first you see, That your pen may not write too hastily! Is it then Thought that works, creative, hour by hour? Thus should it stand: In the beginning was the Power! Yet even while I write this word, I falter, For something warns me, this too I shall alter. The Spirit's helping me! I see now what I need And write assured: In the beginning was the Deed!' back |
| Max Planck On the Law of Distribution of Energy in the Normal Spectrum 'The recent spectral measurements made by O. Lummer and E. Pringsheim, and even more notable those by H. Rubens and F. Kurlbaum, which together confirmed an earlier result obtained by H. Beckmann, show that the law of energy distribution in the normal spectrum, first derived by W. Wien from molecular-kinetic considerations and later by me from the theory of electromagnetic radiation, is not valid generally. In any case the theory requires a correction, and I shall attempt in the following to accomplish this on the basis of the theory of electromagnetic radiation which I developed.' back |
| NIST Introduction to the constants for non-experts 'Throughout all of the formulations of the basic theories of physics and their application to the real world, there appear again and again certain fundamental invariant quantities. These quantities, called the fundamental physical constants, and which have specific and universally used symbols, are of such importance that they must be known to as high an accuracy as is possible. They include the velocity of light in vacuum (c); the charge of the electron, the absolute value of which is the fundamental unit of electric charge (e); the mass of the electron (me); Planck's constant (h); and the fine-structure constant, symbolized by the Greek letter alpha. . . . ' back |
| Physics - Wikipedia Physics - Wikipedia, the free encyclopedia 'Physics (Greek: "knowledge of nature") is the branch of science concerned with discovering and characterizing universal laws that govern such things as matter, energy, space, and time. Discoveries in physics resonate throughout the natural sciences, and physics has been described as the "fundamental science" because other fields such as chemistry and biology investigate systems whose properties depend on the laws of physics.[1] back |
| Planck's Law - Wikipedia Planck's Law - Wikipedia, the free encyclopedia 'In physics, Planck's law describes the spectral radiance of electromagnetic radiation at all wavelengths from a black body at temperature T. As a function of frequency nu, back |
| Sylvia Berryman Democritus (Stanford Encyclopedia of Phlosophy 'Democritus, known in antiquity as the 'laughing philosopher' because of his emphasis on the value of 'cheerfulness,' was one of the two founders of ancient atomist theory. He elaborated a system originated by his teacher Leucippus into a materialist account of the natural world. The atomists held that there are smallest indivisible bodies from which everything else is composed, and that these move about in an infinite void space.' back |
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