vol III Development:

Chapter 4: Physics

page 4: Energy and time

Ancient physics

Aristotle modelled the world using the duality translated into Latin as potentia and actus, and into English as potency and act. Aristotle's words are dynamis (δυναμις) and entelecheia (εντελεχεια) or (more commonly) energeia (ενεργεια). Potentiality and actuality - Wikipedia

Aristotle thought that dynamis and energeia were asymmetric. Potential is what might be and act is what actually exists. Aristotle held that the only way for a potential to become actual is through the agency of another actuality. This asymmetry led him to propose the existence of an unmoved mover as the ultimate source of motion. Unmoved mover - Wikipedia

'Energy' has come into the English language as the motivator of action. Classical mechanics defines energy as the capacity to do work.Work is done when a force moves a point through a distance: work = energy = force × distance. Work involves motion, and so it is related to kinetic energy. Energy - Wikipedia, Work (physics) - Wikipedia

A significant moment in the history of mechanics was the discovery that energy is conserved. The amount of energy in a closed system is constant, although it may change form. Conservation of energy - Wikipedia, Elkana: The Discovery of the Conservation of Energy

This discovery was made possible when researchers realized that energy existed in two forms, visible kinetic energy and somewhat invisible potential energy. Conservation of energy is found to hold in a closed system if we take both potential and kinetic energy into account. Potential energy - Wikipedia

A pendulum, for instance, converts the potential energy of the bob at the top of its swing to the kinetic energy of the bob at the bottom of its swing then back to potential energy as it rises on the other side of its swing. If there was no loss of energy through friction, we imagine that a pendulum would swing forever, showing that potential and kinetic energy are exactly equivalent. Simple harmonic motion - Wikipedia

The overall invariance of energy is one of the fundamental fixed points in the Universe. It serves as a broad control on what is and is not possible in physics. It is a fixed point established by the algebraic sum of potential and kinetic energy where potential energy is given a negative sign.

Potential energy is stored in fixed points, like the orbitals of an atom or a water in a dam high in the mountains. The release of potential energy is prevented by some inhibiting force. Once this inhibition is removed, the potential energy will manifest itself as kinetic energy. Opening a valve may let water flow through a turbine to convert it potential energy into electrical energy.

In a classical pendulum, the accumulation and release of potential energy is a continuous process whose turning points are the top and the bottom of the pendulum swing.

Where does energy come from? We can take a hint from cosmology. General relativity suggests that the total energy of the Universe may be zero, since its kinetic energy may be the exact negative of its potential energy, the energy stored in its expanding structure. So we assume that a fixed point has potential energy equal and opposite to the kinetic energy of the processes in which it resides. Feynman

Hawking and Ellis showed that from a mathematical point of view, the general theory of relativity predicts the existence of singularities in space time where the space-time structure as we know it does not exist. Cosmologists believe that the Universe began as an 'initial singularity'. Our first step toward creating the present Universe is to explain how space-time came to be in this initial singularity. To do this we recast ideas from quantum theory and relativity into the language of computation and communication. Initial singularity - Wikipedia

Time

Quantum mechanics establishes a correlation between energy and frequency (ie inverse time) through the formula E = hf = h/t, where E represents energy, h Planck's quantum of action, f frequency and t ( = 1/f) time. Planck-Einstein relation - Wikipedia

Classical dimensional analysis gives us the same answer, consistent with experience. Action has the dimensions of energy × time. Each act in digging a hole removes a shovelful of material out of the hole. The energy applied to this process determines the rate of shovelling, which in turn tells us how long it will take to dig the hole.

Quantum mechanics also establishes that there is no absolute scale of energy. Instead what matters are energy differences, that is frequency differences. We explain much of the structure of the Universe as harmonic relationships between the frequencies corresponding to different energies. These harmonic relationships correspond very well to the fixed points of energy that we observe in the spectra atoms, for instance. The next page on quantum mechanics explains how this works. page 7: Quantum mechanics

Nor does quantum mechanics distinguish between potential and kinetic energy. Both enter its equations on an equal footing, and all that counts is frequency differences and the fixed points or nodes that are revealed when these frequencies are superposed. Quantum superposition - Wikipedia

This symmetry in quantum mechanics suggests that it is blind to space and time as such and reveals to us only the nodes of the cosmic harmony, which we represent by the eigenvectors and corresponding eigenvalues of quantum transformations. Energy in itself is also blind to the distinction between space and time, and so we see basic quantum mechanics as the study of harmony in an infinite dimensional complex 'frequency space' or 'energy space' which exists without reference to the three dimensional space in which we move. Eigenvalues and eigenvectors - Wikipedia

In the network model, quantum mechanics represents the energy layer, the first bifurcation of the action of initial singularity, yielding two orthogonal fixed points in the Universe which we can represent by the real and imaginary axes of the complex plane and the circle group. Circle group - Wikipedia

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. We see only the fixed points, p and not-p and not the dynamics between them. We assume that the Universe is quantized to the core, and the appearance of energy as a binary ticker or clock is the first appearance of duality of stationary points in pure action.

In the network model, all processes go through the physical layer. We take energy to be the next physical layer after the initial singularity. This idea may help to understand the conservation of energy, since the energy we find in all processes is the appearance in each process of some fraction of the primordial energy of the Universe.

We want to arrange things so that the total energy of the Universe is zero. This desideratum brings to mind Newton's third law — action and reaction are equal and opposite. We couple this with the principle of conservation of energy: the total energy of the Universe remains constant because every action is accompanied by an equal and opposite reaction. In other words, every communication in the Universe is a bidirectional event. Newton's third law so understood is implemented digitally, and so remains perfect thoughout all time. Newtons Laws of Motion - Wikipedia

Energy in a network

We can develop this picture further by thinking in terms of sources and messages, the elements of networks. The elementary operation in a network is the encoding, transmission and decoding of a message. We imagine that the simplest message that can be sent is an empty message, merely a quantum of action without meaning. The frequency of transmission of such messages in a network channel is the energy of the channel. When we apply quantum mechanics, we get two sets of answers: the first is the frequency of messaging on a particular channel; the second is the frequency of the actual symbols that represent the messages.

The Word of God

Words can mean whatever we want them to. The interesting structure arises when we start to put words together to make sentences. Here we understand energy and time to be the result of the first bifurcation in the initial singularity, leading to the existence of a p and a not-p which we have named (in no particular order) kinetic and potential energy. A duality is simply a duality, whatever names we choose. We understand that kinetic and potential energy come into existence simultaneously simply because one is not the other, like the binary digits 0 and 1.

This is not a new idea. Its first clear historical expression was developed by Christian theologians over a long period beginning about two thousand years ago and is known as the 'procession of the Word'. As Aquinas explains:

'I answer that, "Word", said of God in its proper sense, is used personally, and is the proper name of the person of the Son. For it signifies an emanation of the intellect: and the person Who proceeds in God, by way of emanation of the intellect, is called the Son; and this procession is called generation, . . . Hence it follows that the Son alone is properly called Word in God.

Since we identify the initial singularity and the classical God, we can see the procession of the Word as formally identical to the origin of energy from pure action. All that differs is the nomenclature. What is constant is the duality. At the simplest level in the Universe, we may imagine that the communication between kinetic and potential energy is analogous to the communication between Father and Son. Aquinas 190: Whether the "Word" is the Son's proper name?

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.

Conservation of energy = symmetry in time

In ancient Greece, Plato pioneered the formalist approach to reality. Perhaps he was motivated by Parmenides belief that we can only have reliable knowledge of eternal things, those that do not change. From a modern point of view this limits certainty to static situations. We have since learnt that we can have certain knowledge of changing phenomena as long as we sample them often enough.

Cinematographers take advantage of this fact to create the illusion of continuous motion by changing their images faster than the human visual system can keep up. Nevertheless there are many features of the Universe that do not change, they are symmetrical or conserved.

The conservation of energy means that no matter when we observe a closed system, the amount of energy in it remains unchanged. Modern physics sees this this conservation law as a consequence of Noether's theorem. Conservation of energy - Wikipedia, Noether's theorem - Wikipedia, Neuenschwander

In general, conservation of some quantity means that it does not change with time. Its future value can be predicted from its present value. This is most clearly demonstrated with the quantum mechanical formalism which shows that the passage of time has no effect on the energy of a system. This happens because the passage of time, represented by a unitary operator, has no effect on a state of fixed energy. Richard Feynman: Lectures on Physics III 17: Symmetry and conservation, equation (17.25)

(revised 16 May 2016)

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Further reading

Books

Click on the "Amazon" link below each book entry to see details of a book (and possibly buy it!)

Davis, Martin, Computability and Unsolvability, Dover 1982 Preface: 'This book is an introduction to the theory of computability and non-computability ususally referred to as the theory of recursive functions. The subject is concerned with the existence of purely mechanical procedures for solving problems. . . . The existence of absolutely unsolvable problems and the Goedel incompleteness theorem are among the results in the theory of computability that have philosophical significance.'  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

Feynman, Richard, Feynman Lectures on Gravitation, Westview Press 2002 Amazon Editorial Reviews Book Description 'The Feynman Lectures on Gravitation are based on notes prepared during a course on gravitational physics that Richard Feynman taught at Caltech during the 1962-63 academic year. For several years prior to these lectures, Feynman thought long and hard about the fundamental problems in gravitational physics, yet he published very little. These lectures represent a useful record of his viewpoints and some of his insights into gravity and its application to cosmology, superstars, wormholes, and gravitational waves at that particular time. The lectures also contain a number of fascinating digressions and asides on the foundations of physics and other issues. Characteristically, Feynman took an untraditional non-geometric approach to gravitation and general relativity based on the underlying quantum aspects of gravity. Hence, these lectures contain a unique pedagogical account of the development of Einstein's general theory of relativity as the inevitable result of the demand for a self-consistent theory of a massless spin-2 field (the graviton) coupled to the energy-momentum tensor of matter. This approach also demonstrates the intimate and fundamental connection between gauge invariance and the principle of equivalence.'  Amazon   back

Kuhn, Thomas S, Black-Body Theory and the Quantum Discontinuity 1894-1912, University of Chicago Press 1987 Jacket: '[This book] traces the emergence of discontinuous physics during the early years of this century. Breaking with historiographic tradition, Kuhn maintains that, though clearly due to Max Planck, the concept of discontinuous energy change does not originate in his work. Instead it was introduced by physicists trying to understand the success of his brilliant new theory of black-body radiation.'  Amazon   back

Lonergan, Bernard J F, and Michael G Shields (translator), Robert M Doran & H Daniel Monsour (editors), The Triune God: Systematics, University of Toronto press 2007 Translated from De Deo Trino: Pars systematica (1964) by Michael G Shields. Amazon Product Description 'Buried for more than forty years in a Latin text written for seminarian students at the Gregorian University in Rome, Bernard Lonergan's 1964 masterpiece of systematic-theological writing, De Deo trino: Pars systematica, is only now being published in an edition that includes the original Latin along with an exact and literal translation. De Deo trino, or The Triune God, is the third great installment on one particular strand in trinitarian theology, namely, the tradition that appeals to a psychological analogy for understanding trinitarian processions and relations. The analogy dates back to St Augustine but was significantly developed by St Thomas Aquinas. Lonergan advances it to a new level of sophistication by rooting it in his own highly nuanced cognitional theory and in his early position on decision and love. Suggestions for a further development of the analogy appear in Lonergan's late work, but these cannot be understood and implemented without working through this volume. This is truly one of the great masterpieces in the history of systematic theology, perhaps even the greatest of all time.'  Amazon   back

Neuenschwander, Dwight E, Emmy Noether's Wonderful Theorem, Johns Hopkins University Press 2011 Jacket: A beautiful piece of mathematics, Noether's therem touches on every aspect of physics. Emmy Noether proved her theorem in 1915 and published it in 1918. This profound concept demonstrates the connection between conservation laws and symmetries. For instance, the theorem shows that a system invariant under translations of time, space or rotation will obey the laws of conservation of energy, linear momentum or angular momentum respectively. This exciting result offers a rich unifying principle for all of physics.'  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

Tanenbaum, Andrew S, Computer Networks, Prentice Hall International 1996 Preface: 'The key to designing a computer network was first enunciated by Julius Caesar: Divide and Conquer. The idea is to design a network as a sequence of layers, or abstract machines, each one based upon the previous one. . . . This book uses a model in which networks are divided into seven layers. The structure of the book follows the structure of the model to a considerable extent.'   Amazon   back

Yourgrau, Wolfgang, and Stanley Mandelstam, Variational Principles in Dynamics and Quantum Theory, Dover 1979 Variational principles serve as filters for parititioning the set of dynamic possibilities of a system into a high probability and a low probability set. The method derives from De Maupertuis (1698-1759) who formulated the principle of least action, which states that physical laws include a rule of economy, the principle of least action. This principle states that in a mathematically described dynamic system will move so as to minimise action. Yourgrau and andelstam explains the application of this principle to a variety of physical systems.   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

Action (physics) - Wikipedia, Action (physics) - Wikipedia, the free encyclopedia, 'In physics, action is an attribute of the dynamics of a physical system. It is a mathematical functional which takes the trajectory, also called path or history, of the system as its argument and has a real number as its result. Action has the dimension of energy × time, and its unit is joule-seconds in the International System of Units (SI). Generally, the action takes different values for different paths. Classical mechanics postulates that the path actually followed by a physical system is that for which the action is minimized, or, more strictly, is stationary. The classical equations of motion of a system can be derived from this principle of least action. The stationary action formulation of classical mechanics extends to quantum mechanics in the Feynman path integral formulation, where a physical system follows simultaneously all possible paths with amplitudes determined by the action.' back

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: Whether God exists?, 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

Aquinas 161, Whether any procession in God can be called generation?, 'I answer that, The procession of the Word in God is called generation. . . . the procession of the Word in God is generation; for He proceeds by way of intelligible action, which is a vital operation:--from a conjoined principle (as above described):--by way of similitude, inasmuch as the concept of the intellect is a likeness of the object conceived:--and exists in the same nature, because in God the act of understanding and His existence are the same, as shown above (14, 4). Hence the procession of the Word in God is called generation; and the Word Himself proceeding is called the Son.' back

Aquinas 162, Whether any other procession exists in God besides that of the Word?, 'I answer that, There are two processions in God; the procession of the Word, and another. In evidence whereof we must observe that procession exists in God, only according to an action which does not tend to anything external, but remains in the agent itself. Such an action in an intellectual nature is that of the intellect, and of the will. The procession of the Word is by way of an intelligible operation. The operation of the will within ourselves involves also another procession, that of love, whereby the object loved is in the lover; as, by the conception of the word, the object spoken of or understood is in the intelligent agent. Hence, besides the procession of the Word in God, there exists in Him another procession called the procession of love.' back

Aquinas 190, Summa I, 34, 2: Whether "Word" is the Son's proper name?, 'I answer that, "Word," said of God in its proper sense, is used personally, and is the proper name of the person of the Son. For it signifies an emanation of the intellect: and the person Who proceeds in God, by way of emanation of the intellect, is called the Son; and this procession is called generation, . . .. Hence it follows that the Son alone is properly called Word in God. back

Aquinas 47, Summa I, 10, 3: Does it belong to god to be eternal?, 'I answer that, Eternity truly and properly so called is in God alone, because eternity follows on immutability; as appears from the first article. But God alone is altogether immutable, as was shown above (9, 1). Accordingly, however, as some receive immutability from Him, they share in His eternity. ... ' back

Black hole - Wikipedia, Black hole - Wikipedia, the free encyclopedia, 'A black hole is a region of space in which the gravitational field is so powerful that nothing can escape after having fallen past the event horizon. The name comes from the fact that even electromagnetic radiation (e.g. light) is unable to escape, rendering the interior invisible. However, black holes can be detected if they interact with matter outside the event horizon, for example by drawing in gas from an orbiting star. The gas spirals inward, heating up to very high temperatures and emitting large amounts of radiation in the process. . . . ' back

Circle group - Wikipedia, Circle group - Wikipedia, the free encyclopedia, 'In mathematics, the circle group, denoted by T, is the multiplicative group of all complex numbers with absolute value 1, i.e., the unit circle in the complex plane or simply the unit complex numbers. back

Conservation of energy - Wikipedia, Conservation of energy - Wikipedia, the free encyclopedia, 'In physics, the law of conservation of energy states that the total energy of an isolated system cannot change—it is said to be conserved over time. Energy can be neither created nor destroyed, but can change form, for instance chemical energy can be converted to kinetic energy in the explosion of a stick of dynamite. back

Eigenvalues and eigenvectors - Wikipedia, Eigenvalues and eigenvectors - Wikipedia, the free encyclopedia, 'An eigenvector of a square matrix A is a non-zero vector vthat, when the matrix multiplies yields a constant multiple of v, the latter multiplier being commonly denoted by λ. That is: Av = λv' back

Energy - Wikipedia, Energy - Wikipedia, the free encyclopedia, 'In physics and other sciences, energy ,. . . is a scalar physical quantity that is a property of objects and systems which is conserved by nature. Energy is often defined as the capacity to do work. Several different forms of energy, such as kinetic, potential, thermal, electromagnetic, chemical, nuclear, and mass have been defined to explain all known natural phenomena. Energy is converted from one form to another, but it is never created or destroyed. This principle, the conservation of energy, was first postulated in the early 19th century, and applies to any isolated system. According to Noether's theorem, the conservation of energy is a consequence of the fact that the laws of physics do not change over time.' back

Energy - Wikipedia, Energy - Wikipedia, the free encyclopedia, 'In physics, energy (Greek: ἐνέργεια energeia "activity, operation") is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems. Since work is defined as a force acting through a distance (a length of space), energy is always equivalent to the ability to exert pulls or pushes against the basic forces of nature, along a path of a certain length.' back

Euclid's Elements - Wikipedia, Euclid's Elements - Wikipedia, the free encyclopedia, 'Euclid's Elements (Greek: Στοιχεῖα Stoicheia) is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria c. 300 BC. It is a collection of definitions, postulates (axioms), propositions (theorems and constructions), and mathematical proofs of the propositions. The thirteen books cover Euclidean geometry and the ancient Greek version of elementary number theory. The work also includes an algebraic system that has become known as geometric algebra, which is powerful enough to solve many algebraic problems, including the problem of finding the square root.' back

Gödel's incompleteness theorems - Wikipedia, Gödel's incompleteness theorems - Wikipedia, 'Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all of mathematics is impossible, giving a negative answer to Hilbert's second problem. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (e.g., a computer program, but it could be any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, a corollary of the first, shows that such a system cannot demonstrate its own consistency.' back

Hamilton's principle - Wikipedia, Hamilton's principle - Wikipedia, the free encyclopedia, 'IIn physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action (see that article for historical formulations). It states that the dynamics of a physical system is determined by a variational problem for a functional based on a single function, the Lagrangian, which contains all physical information concerning the system and the forces acting on it. The variational problem is equivalent to and allows for the derivation of the differential equations of motion of the physical system. Although formulated originally for classical mechanics, Hamilton's principle also applies to classical fields such as the electromagnetic and gravitational fields, and has even been extended to quantum mechanics, quantum field theory and criticality theories.' back

Initial singularity - Wikipedia, Initial singularity - Wikipedia, the free encyclopedia, 'The initial singularity was the gravitational singularity of infinite density thought to have contained all of the mass and spacetime of the Universe before quantum fluctuations caused it to rapidly expand in the Big Bang and subsequent inflation, creating the present-day Universe.' back

Inverter (logic gate) - Wikipedia, Inverter (logic gate) - Wikipedia, the free encyclopedia, 'In digital logic, an inverter or NOT gate is a logic gate which implements logical negation. . . . The digital inverter is considered the base building block for all digital electronics. Memory (1 bit register) is built as a latch by feeding the output of two serial inverters together. Multiplexers, decoders, state machines, and other sophisticated digital devices all rely on the basic inverter.' 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

Max Planck, On the Law of Distribution of Energy in the Normal Spectrum, Annalen der Physik, vol. 4, p. 553 ff (1901) '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.' back

Newtons Laws of Motion - Wikipedia, Newton's Laws of Motion - Wikipedia, the free encyclopedia, 'Newton's laws of motion are three physical laws that together laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to said forces. . . . The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687' back

Nic Huggett, Stanford Encyclopedia of Philosophy: Absolute and Relational Theories of Space and Motion, 'Since antiquity, natural philosophers have struggled to comprehend the nature of three tightly interconnected concepts: space, time, and motion. A proper understanding of motion, in particular, has been seen to be crucial for deciding questions about the natures of space and time, and their interconnections. Since the time of Newton and Leibniz, philosophers' struggles to comprehend these concepts have often appeared to take the form of a dispute between absolute conceptions of space, time and motion, and relational conceptions. This article guides the reader through some of the history of these philosophical struggles.' back

Noether's theorem - Wikipedia, Noether's theorem - Wikipedia, the free encyclopedia, 'Noether's (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proved by German mathematician Emmy Noether in 1915 and published in 1918. The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the system's behavior can be determined by the principle of least action.' back

Planck postulate - Wikipedia, Planck postulate - Wikipedia, the free encyclopedia, 'The Planck Postulate (or Planck's Postulate), one of the fundamental principles of quantum mechanics, is the postulate that the energy of oscillators in a black body is quantized, and is given by E = nhν, where is an integer 1, 2, 3, ..., is Planck's constant, and (the Greek letter nu, not the Latin letter v) is the frequency of the oscillator. The Planck Postulate was introduced by Max Planck in his derivation of his law of black body radiation in 1900. This assumption allowed Planck to derive a formula for the entire spectrum of the radiation emitted by a black body. Planck was unable to justify this assumption based on classical physics; he considered quantization as being purely a mathematical trick, rather than (as we now know) a fundamental change in our understanding of the world. In 1905 in one of his three most important papers, Albert Einstein adapted the Planck postulate to explain the photoelectric effect, but Einstein proposed that the energy of photons themselves was quantized, and that quantization was not merely a feature of microscopic oscillators. Planck's postulate was further applied to understanding the Compton effect, and was applied by Niels Bohr to explain the emission spectrum of the hydrogen atom and derive the correct value of the Rydberg constant. back

Planck scale - Wikipedia, Planck scale - Wikipedia, the free encyclopedia, In particle physics and physical cosmology, the Planck scale is an energy scale around GeV (corresponding to the Planck mass) at which quantum effects of gravity become strong. At this scale, the description of sub-atomic particle interactions in terms of quantum field theory breaks down (due to the non-renormalizability of gravity). That is; although physicists have a fairly good understanding of the other fundamental interactions or forces on the quantum level, gravity is problematic, and cannot be integrated with quantum mechanics (at high energies) using the usual framework of quantum field theory. . . . ' back

Planck-Einstein relation - Wikipedia, Planck-Einstein relation - Wikipedia, the free encyclopedia, 'The Planck–Einstein relation. . . refers to a formula integral to quantum mechanics, which states that the energy of a photon (E) is proportional to its frequency (ν). E = hν. The constant of proportionality, h, is known as the Planck constant.' back

Potential energy - Wikipedia, Potential energy - Wikipedia, the free encyclopedia, 'In physics, potential energy is the energy of an object or a system due to the position of the body or the arrangement of the particles of the system. The SI unit for measuring work and energy is the joule (symbol J). The term potential energy was coined by the 19th century Scottish engineer and physicist William Rankine although it has links to Greek philosopher Aristotle's concept of potentiality. Potential energy is associated with a set of forces that act on a body in a way that depends only on the body's position in space.' back

Potentiality and actuality - Wikipedia, Potentiality and actuality - Wikipedia, the free encyclopedia, 'In philosophy, Potentiality and Actualit are principles of a dichotomy which Aristotle used to analyze motion, causality, ethics, and physiology in his Physics, Metaphysics, Ethics and De Anima (which is about the human psyche). The concept of potentiality, in this context, generally refers to any "possibility" that a thing can be said to have. Aristotle did not consider all possibilities the same, and emphasized the importance of those that become real of their own accord when conditions are right and nothing stops them.[3] Actuality, in contrast to potentiality, is the motion, change or activity that represents an exercise or fulfillment of a possibility, when a possibility becomes real in the fullest sense. back

Quantum superposition - Wikipedia, Quantum superposition - Wikipedia, the free encyclopedia, 'Quantum superposition is the application of the superposition principle to quantum mechanics. The superposition principle is the addition of the amplitudes of waves from interference. In quantum mechanics it is the sum of wavefunction amplitudes, or state vectors. It occurs when an object simultaneously "possesses" two or more possible values for an observable quantity (e.g. the position or energy of a particle)' back

Richard Feynman, Lectures on Physics III,17: Symmetry and Conservation Laws, 'The most beautiful thing of quantum mechanics is that the conservation theorems can, in a sense, be derived from something else, whereas in classical mechanics they are practically the starting points of the laws. . . . In quantum mechanics, however, the conservation laws are very deeply related to the principle of superposition of amplitudes, and to the symmetry of physical systems under various changes. This is the subject of the present chapter. Although we will apply these ideas mostly to the conservation of angular momentum, the essential point is that the theorems about the conservation of all kinds of quantities are—in the quantum mechanics—related to the symmetries of the system.' back

Second law of thermodynamics - Wikipedia, Second law of thermodynamics - Wikipedia - The free encyclopedia, 'The second law of thermodynamics states that in a natural thermodynamic process, there is an increase in the sum of the entropies of the participating systems. The second law is an empirical finding that has been accepted as an axiom of thermodynamic theory. back

Simple harmonic motion - Wikipedia, Simple harmonic motion - Wikipedia, the free encyclopedia, 'In mechanics and physics, simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement. It can serve as a mathematical model of a variety of motions, such as the oscillation of a spring. In addition, other phenomena can be approximated by simple harmonic motion, including the motion of a simple pendulum as well as molecular vibration. Simple harmonic motion is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law. The motion is sinusoidal in time and demonstrates a single resonant frequency. In order for simple harmonic motion to take place, the net force of the object at the end of the pendulum must be proportional to the displacement.' 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

University of Southampton, Gravitational Collapse, 'The modern theory of black holes begins with the 1939 paper by Oppenheimer and Snyder entitled `On continued gravitational contraction'. Their paper showed that if a stars collapsing core had sufficient mass, then even the neutron pressure would be insufficient to prevent further collapse to a black hole. This paper has strong claims to being one of the most prophetic ever written in this field of research. Today, 60 years later, this paper needs little revision - even the terminology is undated!' back

Unmoved mover - Wikipedia, Unmoved mover - Wikipedia, the free encyclopedia, 'The unmoved mover (ού κινούμενον κινεῖ oú kinoúmenon kineῖ) is a philosophical concept described by Aristotle as a primary cause or "mover" of all the motion in the universe. As is implicit in the name, the "unmoved mover" is not moved by any prior action. In Book 12 (Greek "Λ") of his Metaphysics, Aristotle describes the unmoved mover as being perfectly beautiful, indivisible, and contemplating only the perfect contemplation: itself contemplating. He equates this concept also with the Active Intellect. This Aristotelian concept had its roots in cosmological speculations of the earliest Greek "Pre-Socratic" philosophers and became highly influential and widely drawn upon in medieval philosophy and theology. St. Thomas Aquinas, for example, elaborated on the Unmoved Mover in the quinque viae.' back

Work (physics) - Wikipedia, Work (physics) - Wikipedia, the free encyclopedia, 'In physics, (mechanical) work is a scalar quantity that can be described as the product of a force times the distance through which it acts, and it is called the work of the force. Only the component of a force in the direction of the movement of its point of application does work. The term work was first coined in 1826 by the French mathematician Gaspard-Gustave Coriolis.' back

Zero-point energy - Wikipedia, Zero-point energy - Wikipedia, the free encyclopedia, 'In physics, the zero-point energy is the lowest possible energy that a quantum mechanical physical system may possess and is the energy of the ground state of the system. The concept was first proposed by Albert Einstein and Otto Stern in 1913. The term "zero-point energy" is a translation of the German Nullpunktsenergie. All quantum mechanical systems have a zero point energy. The term arises commonly in reference to the ground state of the quantum harmonic oscillator and its null oscillations. In quantum field theory, it is a synonym for the vacuum energy, an amount of energy associated with the vacuum of empty space. In cosmology, the vacuum energy is taken to be the origin of the cosmological constant. Experimentally, the zero-point energy of the vacuum leads directly to the Casimir effect, and is directly observable in nanoscale devices.' back