Glossary

Unless otherwise noted, definitions are from the Webster's "New World" Dictionary.

Acceleration: n.

#1. (Physics) To cause a change in the velocity of a moving body, or the rate of such change. The acceleration due to the Earth's gravity is 980.665 cm. or 32.17 Feet per second, per second.

Chiral: adj.

(as used by the author) Giving the impression of a lack of symmetry; rough and/or asymmetrical, especially within or as part of a system having symmetrical characteristics

Any object that is not superimposible on its mirror image. Your hands are chiral, that is why you need two different leather gloves, one that only fits your right hand, and one that only fits your left hand. If your hands were superimposible, then you would only need one kind of glove and it would fit both hands (Courtesy of Dr. Brent Iverson; University of Texas)

Consciousness: n.

The state of being conscious; awareness of ones own feelings and of what is happening in the environment

Cosmological Constant

(With thanks to NASA)

The mathematical term Einstein added to his concept of General Relativity to maintain a static condition in the universe and prevent collapse or accelerating expansion. Its place in cosmology has been debated for decades. Many modern theorists believe the Cosmological Constant may not be constant. Other scientists believe there is no need for the term. Other scientists consider a small constant, or even a "variable one" to reflect conditions of a universe of a different dimensional configuration than the standard 4-D model. (see next)

Einstein first proposed the cosmological constant, usually symbolized by the Greek letter "lambda", as a mathematical fix to the theory of general relativity. In its simplest form, the theory predicted that the universe must either expand or contract. Einstein thought the universe was static, so he added this new term to stop the expansion. Friedmann, a Russian mathematician, realized that this was an unstable fix and proposed an expanding universe model, now called the Big Bang theory. When Hubble's study of nearby galaxies showed that the universe was expanding, Einstein regretted modifying his elegant theory and viewed the cosmological constant term as his "greatest mistake".

Many cosmologists advocate reviving the cosmological constant term. Modern field theory associates this term with the energy density of the vacuum. For this term to be cosmologically interesting, it would require new physics: the addition of a cosmological constant term has profound implications (author's note: the need for a cosmological constant may indicate a dimensional deficiency in out present models) for particle physics and our understanding of the fundamental forces of nature.

The attraction of the cosmological constant term is that it significantly improves the agreement between theory and observation. If the cosmological constant today comprises most of the energy density of the universe, then the extrapolated age of the universe is much larger. Adding a cosmological constant term to the inflationary model, an extension of the Big Bang theory, leads to a model that appears to be consistent with the observed large-scale distribution of galaxies and clusters, with COBE's measurements of cosmic microwave background fluctuations, and with the observed properties of X-ray clusters.

MAP and the Cosmological Constant

By characterizing the detailed structure of the cosmic microwave background fluctuations, MAP should be able to accurately determine the basic cosmological parameters, including the cosmological constant, to better than 5%.

Cosmology: n.

The branch of philosophy and science that deals with the study of the universe as a whole, and of its form, nature, etc. as a physical system

Dimension: n.

Any measurable extent, as length, width, height, time etc.

Entropy:

Is a measure of the amount of order in a closed system. Since the finite 7-Dimensional Einsteinian Hyperspherical Universe is, mass-wise, a closed system, entropy laws apply (eternal motion along an infinite, roughly periodic single process time dimension is a possible "door" to openness). Orderly closed systems in 4-Dimensions tend toward disorder (increasing entropy). Increasing order in a system is expressed as decreasing entropy. In four dimensions this requires that work be done. The Second Law of Thermodynamics (orderly closed systems tend toward disorder) is a characteristic of four dimensional systems, for these systems lack inverse mapping and have a single time flow direction; a drift toward increasing entropy in such systems is difficult to control . Higher dimensional systems such as the 7-Dimensional Einsteinian Hypersphereical Universe presented on this site have inverse mapping and time "reversal". In such systems, the Second Law of Thermodynamics can be rewritten as: The total order in the universe, like the total amount of energy, is roughly constant. Under certain conditions (the Triad in 11 Dimensions), order in such a system may actually gradually increase...order has dimensional characteristics.

Fictitious force ("Pseudo force")

A "force" that arises from using a non-inertial reference frame.

Force

Physics; The cause, or agent that puts an object at rest into motion or alters the motion of a moving object

Function: n. (Math)

A quantity whose value depends on another quantity or quantities

Fundamental Reference Frame

(With thanks to the United States Bureau of Standards)(A most difficult problem, for inwardly, the universe, throughout is dynamic), however, the present-day solution to the definition of the fundamental reference frame has been found by retreating from the Earth to the edges of the known Universe and adopting a cosmological frame of reference defined by a large number (400 to 600) of ``bright'' quasars and Active Galactic Nuclei (AGNs) whose relative positions on the celestial sphere are estimated by Very Long Baseline Interferometry (VLBI) measurements with an internal precision of the order of 0.1 to 0.2 milli-arc seconds or a few parts in . This suite of cosmological objects define what is referred to as the International Celestial Reference Frame (ICRF). The ICRF has been adopted by both the IUGG and the IAU as constituting the fundamental reference frame for astronomy, astrophysics, geodesy, and geophysics.

General Relativity

An extension of Einstein's special theory of relativity to include gravity and other non-inertial (accelerating) frames of reference. The following, for the reader's convenience, is a slightly modified excellent plain English history and description of the theory by: J O'Connor and E. Robertson:

In 1900 Lorentz conjectured that gravitation could be attributed to actions which propagate with the velocity of light. Poincare, in a paper in July 1905 (submitted days before Einstein's special relativity paper), suggested that all forces should transform according the Lorentz transformations. In this case he notes that Newton's law of gravitation is not valid and proposed gravitational waves which propagated with the velocity of light.

In 1907, two years after proposing the special theory of relativity, Einstein was preparing a review of special relativity when he suddenly wondered how Newtonian gravitation would have to be modified to fit in with special relativity. At this point there occurred to Einstein, described by him as the happiest thought of my life , namely that an observer who is falling from the roof of a house experiences no gravitational field. He proposed the Equivalence Principle as a consequence:

... we shall therefore assume the complete physical equivalence of a gravitational field and the corresponding acceleration of the reference frame. This assumption extends the principle of relativity to the case of uniformly accelerated motion of the reference frame.

After the major step of the equivalence principle in 1907, Einstein published nothing further on gravitation until 1911. Then he realized that the bending of light in a gravitational field, which he knew in 1907 was a consequence of the equivalence principle, could be checked with astronomical observations. He had only thought in 1907 in terms of terrestrial observations where there seemed little chance of experimental verification. Also discussed at this time is the gravitational red shift, light leaving a massive body will be shifted towards the red by the energy loss of escaping the gravitational field.

Einstein published further papers on gravitation in 1912. In these he realized that the Lorentz transformations will not apply in this more general setting. Einstein also realized that the gravitational field equations were bound to be nonlinear and the equivalence principle appeared to only hold locally.

This work by Einstein prompted others to produce gravitational theories. Work by �mNordstr, Abraham and Mie was all a consequence of Einstein's, so far failed, attempts to find a satisfactory theory. However Einstein realized his problems.

If all accelerated systems are equivalent, then Euclidean geometry cannot hold in all of them.

Einstein then remembered that he had studied Gauss's theory of surfaces as a student and suddenly realized that the foundations of geometry have physical significance. He consulted his friend Grossmann who was able to tell Einstein of the important developments of Riemann, Ricci (Ricci-Curbastro) and Levi-Civita. Einstein wrote

... in all my life I have not labored nearly so hard, and I have become imbued with great respect for mathematics, the subtler part of which I had in my simple-mindedness regarded as pure luxury until now.

In 1913 Einstein and Grossmann published a joint paper where the tensor calculus of Ricci and Levi-Civita is employed to make further advances. Grossmann gave Einstein the Riemann-Christoffel tensor which, together with the Ricci tensor which can be derived from it, were to become the major tools in the future theory. Progress was being made in that gravitation was described for the first time by the metric tensor but still the theory was not right. When Planck visited Einstein in 1913 and Einstein told him the present state of his theories Planck said

As an older friend I must advise you against it for in the first place you will not succeed, and even if you succeed no one will believe you.

Planck was wrong, but only just, for when Einstein was to succeed with his theory it was not readily accepted. It was the second half of 1915 that saw Einstein finally put the theory in place. Before that however he had written a paper in October 1914 nearly half of which is a treatise on tensor analysis and differential geometry. This paper led to a correspondence between Einstein and Levi-Civita in which Levi-Civita pointed out technical errors in Einstein's work on tensors. Einstein was delighted to be able to exchange ideas with Levi-Civita whom he found much more sympathetic to his ideas on relativity than his other colleagues.

At the end of June 1915 Einstein spent a week at �ttingenG where he lectured for six 2 hour sessions on his (incorrect) October 1914 version of general relativity. Hilbert and Klein attended his lectures and Einstein commented after leaving �ttingenG

To my great joy, I succeeded in convincing Hilbert and Klein completely.

The final steps to the theory of general relativity were taken by Einstein and Hilbert at almost the same time. Both had recognized flaws in Einstein's October 1914 work and a correspondence between the two men took place in November 1915. How much they learnt from each other is hard to measure but the fact that they both discovered the same final form of the gravitational field equations within days of each other must indicate that their exchange of ideas was helpful.

On the 18th November he made a discovery about which he wrote For a few days I was beside myself with joyous excitement. The problem involved the advance of the perihelion of the planet Mercury. Le Verrier, in 1859, had noted that the perihelion (the point where the planet is closest to the sun) advanced by 38" per century more than could be accounted for from other causes. Many possible solutions were proposed, Venus was 10% heavier than was thought, there was another planet inside Mercury's orbit, the sun was more oblate than observed, Mercury had a moon and, really the only one not ruled out by experiment, that Newton's inverse square law was incorrect.

By 1882 the advance was more accurately known, 43'' per century. From 1911 Einstein had realized the importance of astronomical observations to his theories and he had worked with Freundlich to make measurements of Mercury's orbit required to confirm the general theory of relativity. Freundlich confirmed 43" per century in a paper of 1913. Einstein applied his theory of gravitation and discovered that the advance of 43" per century was exactly accounted for without any need to postulate invisible moons or any other special hypothesis. Of course Einstein's 18 November paper still does not have the correct field equations but this did not affect the particular calculation regarding Mercury. Freundlich attempted other tests of general relativity based on gravitational red shift, but they were inconclusive.

Also in the 18 November paper Einstein discovered that the bending of light was out by a factor of 2 in his 1911 work, giving 1.74". In fact after many failed attempts (due to cloud, war, incompetence etc.) to measure the deflection, two British expeditions in 1919 were to confirm Einstein's prediction.

On 25 November Einstein submitted his paper The field equations of gravitation which give the correct field equations for general relativity. The calculation of bending of light and the advance of Mercury's perihelion remained as he had calculated it one week earlier.

Five days before Einstein submitted his 25 November paper Hilbert had submitted a paper The Foundations of Physics which also contained the correct field equations for gravitation. Hilbert's paper contains some important contributions to relativity not found in Einstein's work. Hilbert applied the variational principle to gravitation and attributed one of the main theorem's concerning identities that arise to Emmy Noether who was in �ttingenG in 1915. No proof of the theorem is given. Hilbert's paper contains the hope that his work will lead to the unification of gravitation and electromagnetism.

In fact Emmy Noether's theorem was published with a proof in 1918 in a paper which she wrote under her own name. This theorem has become a vital tool in theoretical physics. A special case of Emmy Noether's theorem was written down by Weyl in 1917 when he derived from it identities which, it was later realized, had been independently discovered by Ricci in 1889 and by Bianchi (a pupil of Klein) in 1902.

Immediately after Einstein's 1915 paper giving the correct field equations, Karl Schwarzschild found in 1916 a mathematical solution to the equations which corresponds to the gravitational field of a massive compact object. At the time this was purely theoretical work but, of course, work on neutron stars, pulsars and black holes relied entirely on Schwarzschild's solutions and has made this part of the most important work going on in astronomy today.

Einstein had reached the final version of general relativity after a slow road with progress but many errors along the way. In December 1915 he said of himself

That fellow Einstein suits his convenience. Every year he retracts what he wrote the year before.

Most of Einstein's colleagues were at a loss to understand the quick succession of papers, each correcting, modifying and extending what had been done earlier. In December 1915 Ehrenfest wrote to Lorentz referring to the theory of November 25, 1915. Ehrenfest and Lorentz corresponded about the general theory of relativity for two months as they tried to understand it. Eventually Lorentz understood the theory and wrote to Ehrenfest saying I have congratulated Einstein on his brilliant results . Ehrenfest responded

Your remark "I have congratulated Einstein on his brilliant results" has a similar meaning for me as when one Freemason recognizes another by a secret sign.

In March 1916 Einstein completed an article explaining general relativity in terms more easily understood. The article was well received and he then wrote another article on relativity which was widely read and went through over 20 printings.

Today relativity plays a role in many areas, particle accelerators, cosmology, the big bang theory etc. and now has been checked by experiment to a high degree of accuracy.

Geodesic: adj.

Designating the shortest line between two points on a surface, especially a curved surface; of or portioning to the geometry of such lines

Hubble's Constant

(With thanks to NASA)

When astronomer Edwin Hubble began to study the large-scale structure of the Universe in the early part of the century, he noticed something very interesting. Distant galaxies in space appeared to be flying away from the Milky Way, some with very large velocities. Not only were the galaxies receding, but the farther away they were, the faster they appeared to be moving away. Thus the Hubble Constant, Ho, a number which describes the speed of apparent recession as a function of distance, was born.

The Hubble Constant is usually expressed in units of "kilometers per second, per Megaparsec." One parsec is a unit of distance equal to about 3.2 light years, and a Megaparsec is a million times this, or about 3.2 million light years. So what the Hubble Constant says is that for every 3.2 million light years you look out into space, the objects there appear to be receding from you at a rate of Ho kilometers per second. If Ho is 100, then the objects appear to recede at 100 km/second for every 3.2 million light years you look out into space. If Ho is 50, then you have to look about 6.4 million light years out into space for the same 100 km/second recessional velocity.

(Authors' note: The Hubble constant is still being investigated. It is not certain the Hubble "Constant" is really constant, especially at the most distant regions of the universe.)

Hypersphere

Math; A sphere existing in four or more dimensions.

For example, the following equation describes a 4-dimensional hypersphere: x² + y² + z² + w² = r²

Inertia: n.

Physics: The tendency of matter to remain at rest, or if moving to keep moving in the same direction, unless affected by some outside force.

Instantaneous Velocity:

(author) The indicated or computed speed of an object at any given instant; The reading on the speedometer of a car for example.

Intelligence: n.

Perception, discernment; a. The ability to learn or understand from experience; ability to acquire and retain knowledge; mental ability b. The ability to respond quickly and successfully to a new situation; use of the faculty of reason in solving problems, directing conduct, etc. effectively. (Compare with definitions of observation and servomechanism)

Momentum: n.

Physics: The quantity of motion of a moving object equal to the product of its mass and velocity.

Motion: n.

The act or process of moving; passage of a body from one place to another; movement

Observation: n.

4. The act or practice of noting and recording facts and events, as for some scientific study; more basic: noticing something

Observer: n.

A person who notices or observes something

Periodic: adj.

Occurring, appearing or recurring at regular intervals

Quantum Mechanics

(With thanks to the Columbia Electronic Encyclopedia)

The branch of mathematical physics that deals with the emission and absorption of energy by matter and with the motion of material particles. Because it holds that energy and matter exist in tiny, discrete amounts, quantum mechanics is particularly applicable to ELEMENTARY PARTICLES and the interactions between them. According to the older theories of classical physics, energy is treated solely as a continuous phenomenon (i.e., WAVES), and matter is assumed to occupy a very specific region of space and to move in a continuous manner. According to the quantum theory, energy is emitted and absorbed in a small packet, called a quantum (pl. quanta), which in some situations behaves as particles of matter do; particles exhibit certain wavelike properties when in motion and are no longer viewed as localized in a given region but as spread out to some degree. The quantum theory thus proposes a dual nature for both waves and particles, with one aspect predominating in some situations and the other predominating in other situations. Quantum mechanics is needed to explain many properties of matter, such as the temperature dependence of the SPECIFIC HEAT of solids, as well as when very small quantities of matter or energy are involved, as in the interaction of elementary particles and fields, but the theory of RELATIVITY assumes importance in the special situation where very large speeds are involved. Together they form the theoretical basis of modern physics. (The results of classical physics approximate those of quantum mechanics for large scale events and those of relativity when ordinary speeds are involved.) Quantum theory was developed principally over a period of thirty years. The first contribution was the explanation of BLACKBODY radiation in 1900 by Max PLANCK, who proposed that the energies of any harmonic oscillator, such as the atoms of a blackbody radiator, are restricted to certain values, each of which is an integral (whole number) multiple of a basic minimum value. In 1905 Albert EINSTEIN proposed that the radiation itself is also quanti zed, and he used the new theory to explain the PHOTOELECTRIC EFFECT. Niels BOHR used the quantum theory in 1913 to explain both atomic structure and atomic spectra, showing the connection between the energy levels of an atom's electrons and the frequencies of light given off and absorbed by the atom. Quantum mechanics, the final mathematical formulation of the quantum theory, was developed during the 1920s. In 1924 Louis de BROGLIE proposed that particles exhibit wavelike properties. This hypothesis was confirmed experimentally in 1927 by Clinton J. Davisson and Lester H. Germer, who observed DIFFRACTION of a beam of electrons. Two different formulations of quantum mechanics were presented following de Broglie's suggestion. The wave mechanics of Erwin SCHRDINGER (1926) involves the use of a mathematical entity, the wave function, which is related to the probability of finding a particle at a given point in space. The matrix mechanics of Werner HEISENBERG (1925) makes no mention of wave functions or similar concepts but was shown to be mathematically equivalent to �dingerSchr's theory. Quantum mechanics was combined with the theory of relativity in the formulation of P.A.M. DIRAC (1928), which also predicted the existence of ANTIPARTICLES. A particularly important discovery of the quantum theory is the uncertainty principle, enunciated by Heisenberg in 1927, which places an absolute theoretical limit on the accuracy of certain measurements; as a result, the assumption by earlier scientists that the physical state of a system could be measured exactly and used to predict future states had to be abandoned. Other developments of the theory include quantum statistics, presented in one form by Einstein and S.N. Bose (Bose-Einstein statistics, which apply to BOSONS) and in another by Dirac and Enrico FERMI (Fermi-Dirac statistics, which apply to FERMIONS); quantum electronics, which deals with interactions involving quantum energy levels and resonance, as in LASERS; quantum gravitation, the quantum theory of gravitational fields; and quantum field theory. In quantum field theory, interactions between particles result from the exchange of quanta: electromagnetic forces arise from the exchange of PHOTONS, weak nuclear forces (see WEAK INTERACTION) from the exchange of W AND Z PARTICLES, strong nuclear forces (see STRONG INTERACTION) from the exchange of gluons, and GRAVITATION from the exchange of gravitons. See also QUANTUM ELECTRODYNAMICS; QUANTUM CHROMODYNAMICS.

Reference Frame: n.

General: Any point from which the universe is observed.

Servomechanism

An automatic control mechanism in which the output is constantly or intermittently compared with the input through feedback so that the error, or difference between the two quantities can be used to bring about the desired amount of control.

Special Relativity

A theory developed by Albert Einstein stating that the laws of motion are the same for all inertial (non-accelerating) frames of reference and that the speed of light (in a vacuum) is the same for all inertial reference frames. This leads to the equivalence of mass and energy, time dilation, and length contraction.

Einstein's Special Theory of Relativity can be stated briefly as: "The experiments (such as Michaelson-Morley) which seem to show that the speed of light isn't changing, are true." More formally, Einstein postulated that the speed of light is the same in all inertial reference frames. You on the sidewalk, me in my car, and an astronaut going by in a super-rocket will all get very different answers if we measure the speed of a Frisbee; but we will all get exactly the same answer when we measure the speed of a beam of light. The answer we get is roughly 186,000 miles per second.

Making the speed of light a constant regardless of the motion of the source or observer redefines all of reality, time and space in the universe in terms of light and results in a model of the universe which is highly counterintuitive- but never the less, observationally verifiable.

Symmetry: n.

Similarity in form or arrangement on either side of a dividing line or plane; correspondence of opposite parts in size, shape or position; condition of being symmetrical

Thermodynamics, The First Law of:

Energy can be changed from one form to another, but it cannot be created or destroyed. The total amount of energy and matter in the Universe remains constant, merely changing from one form to another. The First Law of Thermodynamics (Conservation) states that energy is always conserved, it cannot be created or destroyed. In essence, energy can be converted from one form into another.

Thermodynamics, The Second Law of:

States that orderly closed systems tend toward disorder. "In all energy exchanges, if no energy enters or leaves the system, the potential energy of the state will always be less than that of the initial state." This is also commonly referred to as entropy. A spring-driven watch will run until the potential energy in the spring is converted, and not again until energy is reapplied to the spring to rewind it. A car that has run out of gas will not run again until you walk 10 miles to a gas station and refuel the car. Once the potential energy locked in carbohydrates is converted into kinetic energy (energy in use or motion), the organism will get no more until energy is input again. In the process of energy transfer, some energy will dissipate as heat. Entropy (for additional information) is a measure of disorder: cells are NOT disordered and so have low entropy. The flow of energy maintains order and life. Entropy "wins" when organisms cease to take in energy and die.

Universe: n.

The totality of all the things that exist; creation; the cosmos

World Line: n.

On a Minkowski space-time any particular point represents a time and position, and this is called a world point. The "history" of any particle can be considered to be a sequence of these world points, and the line joining these various world points is called a world line.

(Author) An absolute measure of the changing relationships of time, space and energy at any given frame of reference in the universe.