vol 3: Development
chapter 3: Physics
page 5: Energy
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Energy
Interpreting the 'standard model'
Over the last century physicists, mathematicians and astronomers have put together a model of the universe which, because it is so successful, is known as the standard model. There remain radical problems, but the model seems the best starting point available for a theological understanding of the universe. Standard model - Wikipedia The correspondences we shall establish are tentative, and may harden or be modified as the project proceeds.
The standard model describes the world in terms of fields which are functions of space and time. The existence of the space-time described by special relativity is assumed. The standard model encounters difficulties at very small scales where general relativity has significant influence on the structure of space-time.
The standard model postulates a set of fields (corresponding to each species of particle) which are to be found throughout space-time. Each field carries the amplitudes for the creation or annihilation of corresponding particles.
A particle exists when a state of the field representing the particle is excited, that is, has energy. It ceases to exist when this energy goes elsewhere. Creation and annihilation thus correspond to obtaining and losing energy. This idea is quite general. I am a particle. I need energy to live. When my energy goes, I go. Quantum field theory describes birth and death at all scales.
Quantum field theory assumes the existence of energy and tells us how this energy is distributed among the various possible structures of the world. We work here on the assumption that the network theory can go deeper, explaining the original of energy. Ultimately, it seems, energy is needed to enable the universe to be consistently both one and many.
Unanswered questions (like why do we have to die?) cause us stress which is resolved when the question is answered. This stress creates the energy driving us to answer the question. The situation is analogous in the political realm, where governments deal with social problems by spending money to solve them. The principle of scale invariance suggests that we can use this experience to gain insight into the creation of energy in the universe.
The initial state
From a physical point of view, space-time is the stage in which the game of existence is played. Intuitively space is something that remains remains the same (like the playing field) while other things move around in it (the players). Space orders the positions of the players while time orders their motions.
Our first step toward creating the present universe is to explain how space-time came to be in the initial singularity. Initial singularity To do this we recast ideas from quantum field theory and general relativity into the language of computation and communication.
Quantum field theory sees quantum mechanics as a model of one dimensional physical systems. Zee From the network point of view we guess that quantum mechanics is the protocol of a one dimensional hardware layer underlying space time. Since quantum mechanics is indifferent to the number of dimensions in which it is operating, we expect to see quantum mechanical aalgorithms embodied throughout space time as it comes into existence.
Let us say that the initial singularity is zero dimensional system with but one state having probability 1 (since it exists). We model the initial singularity as the only point in a zero dimensional Hilbert space. We let the Hamiltonian for the initial singularity be 0, so that (like the classical god) it is pure eternal action without energy.
In logical terms, we imagine the initial singularity as an embodiment of the identity operation, which is equivalent to no operation, nop. We see it as the static root of a dynamical tree which grows within it.
Dynamics
Our next step is to introduce dynamics. Dynamics can only have meaning in a space of two or more states. Things cannot move if they have nowhere to go. We thus guess that space-time and motion come into existence at the same time: in some way they are two sides of one coin.
We associate energy with both space and motion. The energy of motion is kinetic energy; the energy of space is potential energy. It is universally observed that energy is conserved, that is in a closed system the sum of potential and kinetic energy remains constant.
General relativity gives us reason to believe that the total energy of the universe, like the energy of the initial singularity, is zero. All the kinetic energy (which includes mass energy) that we see in the universe may be exactly equivalent to the potential energy of the space that has grown out of the initial singularity.
We experience time as a flowing boundary between past and future. It is a one way flow. The past is determined and cannot be revisited, as much as we would sometimes like to go back and change things. On the other hand, we find that we can move in any direction in three dimensional space.
Let us guess that the logical operation corresponding to time it not. This operation distinguishes the past from the future because the future is not the past.
We are aware of the difference between past and future because we live in the current highly evolved universe. At the level we are currently exploring, however, the not operation is not observable because the past is annihilated to create the future and so it is not possible in principle for them to exist simultaneously and come into contact.
Let us place the invisible dynamics of the not operation into correspondence with the invisible dynamics postulated by quantum mechanics. Quantum mechanics postulates two distinct processes. One is the unitary evolution of the wave function in an isolated system. The other is the collapse of the wave function when an isolated system comes into contact with an observer. The universe as we define it is an isolated system ('nothing outside'), so we expect the not operation to be unitary.
Quantum mechanics represents the general two state system by the expression |q> = a |0> +b |1>where |q> is a vector in two dimensional complex Hilbert space with basis vectors |0> and |1>, and a and b are complex numbers called amplitudes. These amplitudes are normalized so that |a| 2 + |b|2 = 1. In the case of the not operator, the only values that a and b can take are 0 and 1. The not operator annihilates the state |0> to give |1> and vice versa.
Energy
Where does energy come from? We can take a hint from cosmology. General relativity suggests that the total energy of the universe is zero, since its kinetic energy may be the exact negative of its potential energy, the energy stored in its structure. Feynman, So we assume that a real space has potential energy equal and opposite to the kinetic energy of the processes within it. At the current level of complexity, however, the most we can say is that potential energy is not kinetic energy
The not operation toggles between two states, one of which is not the other. Let us interpret this physically to mean that it toggles between potential and kinetic energy like a pendulum. Unlike a pendulum, however, this operation is digital rather than continuous.
We want to arrange things so that the total energy of this oscillator is zero. This desideratum brings to mind Newton's third law - action and reaction are equal and opposite. Newton We couple this with the principle of conservation of energy: the total energy of the universe (which we have chosen for heuristic reasons to equate to 0) does not change with the passage of time.
We can develop this picture further by thinking in terms of sources and messages, the elements of networks. The elementary operation in the symmetric network is the transformation of one permutation into another by the exchange of two elements of the permutation. Let these elements be p and not-p. Exchanged, they are not-p and p.
We may imagine this process as requiring two messages, one the inverse of the other. In our network model, a message is a Turing machine, that is a function or mapping. The two messages envisaged above are two functions which are inverses of one another, one sending p to not-p and the other sending not-p to p. Complex entities (like ourselves) are able to send and receive messages while maintaining their identity. At the level of fundamental particles, however, a particle must annihilate itself to communicate.
From the point of view of wave mechanics, this operation is equivalent to a complete circuit, a phase change of 360 degrees or 2π radians. Here we recall that quantum mechanics identifies phase and action so that we can equate a 2π change of phase with one quantum of action, and identify this in turn with an elementary exchange in the symmetric network.
Space and time
We have complicated the initial singularity from a completely static system to one which is a superposition of two states, one with positive, one with negative energy. It is also a superposition of two messages, one which converts
Although we have two sources and two flows of action, the size of the initial singularity remains zero, since the space time interval between its two states is zero. Our little space has a Minkowski metric (1, -1), space being the inverse of time.
What makes the universe go from one state to two? Our answer is that given Cantor's theorem, it would be formally inconsistent not to. We may see this theorem as the formal model of a complexifying force which we might call the Cantor force. Complexification
We may think of this two state system as the ticker of a clock without the accompanying counter. In an ordinary clock the counter gives a name to each tick by mapping it onto the natural line. This structure will come later when the universe acquires memory. Each cycle of the clock is a quantum of action, and we map this setup onto the natural line considered as a numbered and ordered series of ticks of no particular 'distance' apart. This 'line' can be constructed by a computer (a 'Peano machine') that simply adds 1 to its history at each cycle.
Amplitude and wave function
What we have now is an invisible two state process. We assume that this little oscillator is ubiquitous throughout the universe (like the initial singularity), and that it is the first layer in the network above the initial singularity.
Logically we model this with repeated not operation. We guess that this invisible structure is what quantum mechanics calls amplitudes and represents with complex exponentials. Logically, we will let the rate of this operation for the universe be aleph(0). From a quantum mechanical point of view, this rate is measured by the Hamiltonian of the system, that is the rate of change of phase. Since we have yet to establish any particular direction for time, we may see the phase of our oscillator as rotating in two directions, so that we may say that the energy of the universe is aleph(0) - aleph(0) = 0.
Further reading
Books
| Bell, John S, Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press 1987 Jacket: JB ... is particularly famous for his discovery of a crucial difference between the predictions of conventional quantum mechanics and the implications of local causality ... This work has played a major role in the development of our current understanding of the profound nature of quantum concepts and of the fundamental limitations they impose on the applicability of classical ideas of space, time and locality. Amazon back |
| Blair, Georges A, Energeia and Entelecheia: "Act" in Aristotle, University of Ottawa Press 1992 Twenty-five years ago George Blair suggested that "actuality" was the wrong word to use in translating either of Aristotle's two words for "act" and sparked a controversy that has continued to the present day. Here he presents his evidence in detail, and offers a critical examination of the scholarship on the subject. Amazon back |
| de Witt, Bryce S and Neill Graham (eds) , and Hugh Everett III, J A Wheeler, B S DeWitt, L N Cooper, D van Vechten, N Graham (contributors), The Many-Worlds Interpretation of Quantum Mechanics, Princeton UP 1973 Jacket: 'A novel interpretation of quantum mechanics, first proposed in brief form by Hugh Everett in 1957, forms the nucleus around which this book is developed. The volume contains Dr Everett's short paper from 1957, "'Relative State' Formulation of Quantum Mechanics", and a far longer exposition of his interpretation, entitled "The Theory of the Universal Wave Function", never before published. In addition, other papers by De Witt, Graham and Cooper and van Vechtem provide further dicussion of the same theme. Together they constitute virtually the entire world output of scholarly commentary on the Everett interpretation.' Amazon back |
| Einstein, Albert, and Robert W Lawson (translator) Roger Penrose (Introduction), Robert Geroch (Commentary), David C Cassidy (Historical Essay) , Relativity: The Special and General Theory, Pi Press 2005 Preface: 'The present book is intended, as far as possible, to give an exact insight into the theory of relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics. ... The author has spared himself no pains in his endeavour to present the main ideas in the simplext and most intelligible form, and on the whole, in the sequence and connectionin which they actually originated.' page 3 Amazon back |
| Elkana, Yehuda, The Discovery of the Conservation of Energy, Hutchinson Educational 1974 Jacket: 'This book chronicles historically and in a philosophical context the discovery and gradual develoment of the concept of energy ... Metaphysical beliefs in the principle of 'conservation of something' in nature resulted finally in the statement of the physical laws of the conservaiton of energy in the work of Hermann von Helmholtz.' Amazon back |
| Gamow, George, and Roger Penrose (Designer), Mr Tomkins in Paperback, Cambridge University Press 1993 Amazon customer review: 'This is one of the best introductions to the concepts of relativity and quantum theory I have ever read. Not only does it have an excellent nonmathmatical and easy to understand description of these areas of modern physics, but it has an interesting and funny story to move it along. It also includes a more technical description for those who are up to it (even the technical description is nothing too difficult, and also nonmathmatical, it can be skipped)' Edward Wendt III Amazon back |
| Hobson, M P, and G. P. Efstathiou, A. N. Lasenby, General Relativity: An Introduction for Physicists, Cambridge University Press 2006 Amazon Editorial Reviews Book Description 'After reviewing the basic concept of general relativity, this introduction discusses its mathematical background, including the necessary tools of tensor calculus and differential geometry. These tools are used to develop the topic of special relativity and to discuss electromagnetism in Minkowski spacetime. Gravitation as spacetime curvature is introduced and the field equations of general relativity derived. After applying the theory to a wide range of physical situations, the book concludes with a brief discussion of classical field theory and the derivation of general relativity from a variational principle.' Amazon back |
| Jammer, Max, Concepts of Space: The History of Theories of Space in Physics, Dover 1994 Jacket: 'Although the concept of space is of fundamental importance in both physics and philosophy, until the publication of this book, the idea of space had never been treated in terms of its historical development. ... Following an introductory chapter on the concept of space in antiguity, subsequent chapters consider Judeaeo-Christian ideas about space, the emancipation of the space concept from Aristotelianism, Newton's concept of absolute space and the concept of space from the 18th century to the present. ... It is essential reading for philosphers, physicists and mathematicians, but even the nonprofessional reader will find it accessible, for the author has kept the technical language and mathematical details to a minimum.' Amazon back |
| Mazria, Edward, The Passive Solar Energy Book: A complete guide to passive solar home, greenhouse and building design, Rodale Press 1979 Jacket: Passive solar energy systems collect and transport heat by natural means. In essence the building structure or some element of it is the system. There are no separate collectors, storage units of mechanical equipment. ... The most striking difference between passive and active systems is that one operates on the energy available in its immediate environment and the other imports energy to make the system work." Amazon back |
| Pais, Abraham, 'Subtle is the Lord...': The Science and Life of Albert Einstein, Oxford UP 1982 Jacket: In this ... major work Abraham Pais, himself an eminent physicist who worked alongside Einstein in the post-war years, traces the development of Einstein's entire ouvre. ... Running through the book is a completely non-scientific biography ... including many letters which appear in English for the first time, as well as other information not published before.' 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 |
| Smolin, Lee, The Life of the Cosmos, Oxford University Pres 1997 Jacket: 'Smolin posits that a process of self-organisation like that of biological evolution shapes the universe, as it developes and eventually reproduces through black holes, each of which may result in a big bang and a new universe. Natural selection may guide the appearance of the laws of physics, favouring those universes which best reproduce. ... Smolin is one of the leading cosmologists at work today, and he writes with an expertise and a force of argument that will command attention throughout the world of physics.' Amazon back |
| van Fraasen, Bas C, Laws and Symmetry, Clarendon Press 1989 Jacket: 'Metaphysicians speak of laws of nature in terms of necessity and universality; scientists do so in terms of symmetry and invariance. This book argues that no metaphysical account of laws can succeed. The author analyses and rejects the arguments that there are laws of nature, or that we must believe that there are. He argues that we should discard the idea of law as an inadequate clue to science. After exploring what this means for general epistemology, the book develops the empiricist view of science as a construction of models to represent the phenomena. Concepts of symmetry, transformation and invariance illuminate the structure of such models. A central role is played in science by symmetry arguments, and it is shown how these function also in the philosophical analysis of probability. The advocated approach presupposes no realism about laws or necessities in nature.' Amazon back |
Papers
| Chyba, Christopher E, "Energy for microbial life on Europa", Nature, 403, 6768, 27 January 2000, page 381-2. 'A radiation driven ecosystem on Jupiter's moon is not beyond the bounds of possibility'. back |
| Guegan, J F and S Lek. T Oberdoff, "Energy availability and habitat heterogeneity predict global riverine fish diversity", Nature, 391, , 22 January 1998, page 382. back |
Links
| 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 |
| Bob Hawkes Riemann Geometry 'Georg Friedrich Bernard Riemann (1826-1866) was a student of Gauss, and extended his work on spherical, and other non-flat, geometries, extending them to greater numbers of dimensions. His work therefore laid the critical mathematical foundation for later work by Einstein and others on non-spherical geometries.' back |
| ISES International Solar Energy Society 'SES has been serving the needs of the renewable energy community since its founding in 1954. A UN-accredited NGO present in more than 50 countries, the Society supports its members in the advancement of renewable energy technology, implementation and education all over the world.' back |
| J P Leahy Cosmology 'This page provides a collection of links to cosmology-related topics, most related to my course PC3392: Cosmology. ' back |
| Mathematical formulation of quantum mechanics - Wikipedia Mathematical formulation of quantum mechanics - Wikipedia - the free encyclopedia 'The mathematical formulation of quantum mechanics is the body of mathematical formalisms which permits a rigorous description of quantum mechanics. It is distinguished from mathematical formalisms for theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces and operators on these spaces. Many of these structures were drawn from functional analysis, a research area within pure mathematics that developed in parallel with, and was influenced by, the needs of quantum mechanics. In brief, values of physical observables such as energy and momentum were no longer considered as values of functions on phase space, but as eigenvalues of linear operators.' back |
| Mathpages Reflections on relativity Preface: 'This book examines the evolution of the principle of relativity in its classical, special, and general incarnations, both from a technical and a historical perspective, with the aim of showing how it has repeatedly inspired advances in our understanding of the physical world.' 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 |
| Soshichi Uchii Eddington on 1919 Expeditions 'The eclipse photograph and a comparison photograph were placed film to film in the measuring-machine so that corresponding images fell close together, and the small distances were measured in two rectangular directions. From these the relative displacements of the stars could be ascertained. The results from this plate gave a definite displacement, in good accordance with Einstein's theory and disagreeing with the Newtonian prediction. ... ' Sir Arthur Eddington. back |
| Standard model - Wikipedia Standard model - Wikipedia, the free encyclopedia 'The Standard Model of particle physics is a theory that describes three of the four known fundamental interactions between the elementary particles that make up all matter. It is a quantum field theory developed between 1970 and 1973 which is consistent with both quantum mechanics and special relativity. To date, almost all experimental tests of the three forces described by the Standard Model have agreed with its predictions. However, the Standard Model falls short of being a complete theory of fundamental interactions, primarily because of its lack of inclusion of gravity, the fourth known fundamental interaction, but also because of the large number of numerical parameters (such as masses and coupling constants) that must be put "by hand" into the theory (rather than being derived from first principles) . . . ' back |
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