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	Quantum mechanics - Wikipedia, the free encyclopedia
		Relativistic quantum mechanics (quantum field theory) provides the framework for some of the most accurate physical theories known, though non-relativistic quantum mechanics is also frequently used for reasons of convenience.
		In the mathematically rigorous formulation of quantum mechanics, developed by Paul Dirac and John von Neumann, the possible states of a quantum mechanical system are represented by unit vectors (called "state vectors") residing in a complex separable Hilbert space (variously called the "state space" or the "associated Hilbert space" of the system).
		An alternative formulation of quantum mechanics is Feynman's path integral formulation, in which a quantum-mechanical amplitude is considered as a sum over histories between initial and final states; this is the quantum-mechanical counterpart of action principles in classical mechanics.
	en.wikipedia.org /wiki/Quantum_physics (4111 words)

	Relativistic mass -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-18)
		The rest mass, or invariant mass, is an observer independent quantity, while the relativistic mass, or apparent mass depends on one's (A system of assumptions and standards that sanction behavior and give it meaning) frame of reference.
		In the earlier years of relativity, it was the relativistic mass that was taken to be the "correct" notion of mass, and the invariant mass was referred to as the rest mass.
		The idea of relativistic mass combined with the notion of (Click link for more info and facts about Lorentz contraction) Lorentz contractions leads some people to the incorrect conclusion that an object traveling fast enough will form a (A region of space resulting from the collapse of a star; extremely high gravitational field) fl hole.
	www.absoluteastronomy.com /encyclopedia/r/re/relativistic_mass.htm (1624 words)

	Relativistic Mechanics Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-18)
		Special relativity is mathematically self-consistent, and is also compatible with all modern physical theories, most notably quantum field theory, string theory, and general relativity (in the limiting case of negligible gravitational fields).
		Sometimes people claim that the apparent increase of relativistic mass is not uniform and appears twice as large in the direction of travel as tangentially.
		Physics textbooks sometimes use the relativistic mass as it allows the students to utilize their knowledge of Newtonian physics to gain some intuitive grasp of relativity in their frame of choice (usually their own!).
	www.karr.net /search/encyclopedia/Relativistic_mechanics (3772 words)

	Relativistic Mechanics
		Newtonian mechanics is extremely well tested at speeds which are a small fraction of the speed of light.
		The new theory of mechanics had to reduce to the old one in the "low speed" limit.
		Use the correct relativistic expression for the kinetic energy of a one-kilogram object moving at 5/13 of the speed of light.
	www.people.vcu.edu /~rgowdy/mod/r42/xmp.htm (270 words)

	TIQM: 3.3 The Transactional Model and Relativistic Quantum Mechanics
		This would seem, in effect, to invalidate Born's statistical interpretation of quantum mechanics (CI2), in that the description of the state vector as a mathematical representation of the probability of finding a definite value of a particular observable as a result of a measurement made at a given instant is untenable.
		Another problem which raises some concern about the statistical interpretation of quantum mechanics in the relativistic domain is the observation that the solutions of the field equations cannot always be used to construct a relativistically invariant or positive definite probability density (Bjorken, 1964).
		The scope of the present paper is limited to the interpretation of quantum mechanics in the low-velocity non-relativistic limit, the arena where almost all of the previous discussion on the interpretation of quantum mechanics has been focussed.
	www.npl.washington.edu /npl/int_rep/tiqm/TI_33.html (3611 words)

	LAWRENCE P. HORWITZ
		Relativistic mass distribution of event-anti-event systems and a ``realistic'' equation of state for hot hadronic matter.
		Manifestly covariant relativistic thermodynamics and avoidance of gravitational singularities.
		It is also shown that from this point of view, one has a natural mechanism for the dynamical mixing of the quantum mechanical states as observed by means of time translation invariant operators.
	www.biu.ac.il /PH/horwitz (1170 words)

	Relativistic Quantum Mechanics : With Applications in Condensed Matter and Atomic Physics by Paul Strange [ISBN: ...
		Relativistic quantum theory is the unification of Einstein's theory of relativity and the quantum mechanics of Bohr, Schrödinger and Heisenberg.
		Interestingly, a relativistic version of the microscopic theory of superconductivity in the framework of the Bogolubov-de Gennes equations has been presented in Chapter 13.
		Later chapters aim to give the reader insight into how Relativistic Quantum Mechanics can be used to describe, for example, magneto-optical effects (important in the magentic recording industry) and superconductivity (another 'hot' area of research in physics today).
	www.gettextbooks.com /isbn_0521562716.html (575 words)

	Relativistic Quantum Mechanics and Field Theory: Current Amazon U.S.A. One-Edition Data
		In surveying available books on advanced quantum mechanics and field theory, Franz Gross determined that while established books were outdated, newer titles tended to focus on recent developments and disregard the basics.
		Relativistic Quantum Mechanics and Field Theory fills this striking gap in the field.
		Developing the material at a level accessible even to newcomers to quantum mechanics, the book begins with topics that every physicist should know-quantization of the electromagnetic field, relativistic one body wave equations, and the theoretical explanation of atomic decay.
	www.ferretexpert.info /stuff-0471591130.html (3797 words)

	Quantum Reality
		Quantum Mechanics may well be an approximation to some other grander theory, but interpretations accept the current theory as it is and try to make sense of it.
		If, for example, the standard treatment of Quantum Mechanics indicates that a system should be regarded as being in a superimposition of two states, the interpretation must also regard the system as being in a superimposition of two states.
		Furthermore, it is not acceptable to challenge the validity of Quantum Mechanics to escape the unpleasant consequences of an interpretation.
	www.quantum.bowmain.com /Quantum_Reality.htm (11040 words)

	Quantum Mechanics
		In standard texts on quantum mechanics, the vector is represented by a function known as the wave-function, or ψ-function.
		From a mathematical point of view, what really distinguishes quantum mechanics from its classical predecessors is that states and quantities have a richer structure; they form families with a more interesting network of relations among their members.
		That, in a nutshell, is the Measurement Problem in quantum mechanics; any interpretation of the theory, any detailed story about what the world is like according to quantum mechanics, and in particular those bits of the world in which measurements are going on, has to grapple with it.
	plato.stanford.edu /entries/qm (3833 words)

	Michael G. Fuda
		His original research interest was in the nonrelativistic quantum mechanics of few particle systems, but for the many years now his research has focused on the relativistic quantum mechanics of such systems.
		For the subgroup of continuous transformations the unitary operators can be constructed in terms of ten generators, which can be taken to be the components of the four-momentum operator, the three components of the angular momentum operator, and the three components of the so-called boost operator.
		In particular a relativistic one boson exchange model of the two-nucleon system has been constructed which allows for the exchange of pi, eta, rho, omega, delta, and sigma mesons.
	www.physics.buffalo.edu /professors/fuda.html (960 words)

	Selected Papers on Geometric Algebra in Quantum Mechanics
		These papers analyze the quantum mechanical Dirac theory of the electron with respect to its geometric structure as revealed by reformulation in terms of Spacetime Algebra.
		This amounts to a further "relativistic" constraint on the spinor theory and so may be expected to have physical consequences.
		Implications for the structure and interpretation of relativistic quantum theory are discussed.
	modelingnts.la.asu.edu /html/GAinQM.html (1386 words)

	PhilSci Archive - On Mass Problem in Relativistic Mechanics and Gravitational Physics (Site not responding. Last check: 2007-10-18)
		The proper mass constancy in SRT Mechanics is, in fact, a weak field approximation leading to the Newtonian limit.
		It should be considered a new relativistic test having a falsifying power in a strong-field domain.
		The purpose is to present in a simple form for a wide physical community some results of our study of Relativistic Mechanics, in which a source of a gravitational field is the proper mass.
	philsci-archive.pitt.edu /archive/00000973 (495 words)

	Relativistic Quantum Mechanics, for lack of a better name (Site not responding. Last check: 2007-10-18)
		Now, in classical mechanics that was an old-fashioned equation into which you plug variables.
		After all, in quantum mechanics the wavefunctions are generally complex or imaginary!
		In relativistic quantum mechanics, the only way to properly write down the Hamiltonian is as an equation relating, not real numbers, not complex numbers, but actually 4x4 matrices.
	www.mit.edu /people/bmonreal/amsantimatter/node5.html (868 words)

	Relativistic Momentum
		It is typical in high energy physics, where relativistic quantities are encountered, to make use of the Einstein relationship to relate mass and momentum to energy.
		In relativistic mechanics, the quantity pc is often used in momentum discussions.
		Note that the m with the zero subscript is the rest mass, and that m without a subscript is the effective relativistic mass.
	hyperphysics.phy-astr.gsu.edu /hbase/relativ/relmom.html (242 words)

	Theory of relativity
		It had been suggested that light waves actually did not travel through any medium: the speed of light was thus fixed, and not relative to the movement of the observer.
		This was impossible under Newtonian classical mechanics however, and Einstein provided a new system which allowed for this.
		This leads to redefinitions of such fundamental notions as time, distance, mass, energy and momentum with wide ranging consequences.
	www.sciencedaily.com /encyclopedia/theory_of_relativity (760 words)

	[No title] (Site not responding. Last check: 2007-10-18)
		The aim of these notes is to generalize non-relativistic quantum mechanics for electrons to relativistic quantum mechanics.
		The requirement of relativistic invariance and invariance under space reflexion forces one to use wave functions with 4 components -- so-called 4-spinors.
		It is not possible to construct a relativistically invariant theory for the electron.
	pwnielsen.homepage.dk /lecturen/rqmtoc/rqmtoc.html (209 words)

	An Introduction to Relativistic Electronic Structure Theory in Quantum Chemistry (Site not responding. Last check: 2007-10-18)
		Athens, GA Relativistic effects have been found to play a crucial role in the description of the electronic structure of heavy elements.
		Ab initio quantum mechanical methods which are based upon many-electron extensions of Dirac's relativistic single-particle wave equation have proven to be extremely effective in properly describing the electronic structure of molecules which contain heavy atoms, though these methods are prohibitively expensive for most systems of chemical interest.
		Finally, the major effects of special relativity on atomic electronic structure are explored and quantified, and the consequences of these effects on molecular structure and chemical behavior are discussed.
	zopyros.ccqc.uga.edu /~kellogg/docs/rltvt/rltvt.html (168 words)

	2 (Site not responding. Last check: 2007-10-18)
		Quantum mechanics in fact goes so far as to require this complex time representation, in the form of a procedure for reduction of the state vector which is technically equivalent to mixing (>c, -t) and (, +t) wave trajectories.
		In other words, in Newtonian mechanics the time derivative of the momentum, or the force F, is in the direction of the acceleration; but this will not hold in PM because the quantity m is itself an indeterminate vector associated with a non-zero extension, x.
		It appears that a relativistic ‘field’ theory cannot be discriminated from a sophisticated renormalisation device for keeping numerical ‘constants’ constant in terms of one another, for the very good reason that the theory so marvellously models a renormalisation device which is the structure of Nature itself.
	www.parcellular.fsnet.co.uk /FoundPM2-3.htm (9371 words)

	Relativistic mechanics (from physics) -- Encyclopædia Britannica
		More results on "Relativistic mechanics (from physics)" when you join.
		Atomic physics has proved to be a spectacularly successful application of quantum mechanics, which is one of the cornerstones of modern physics.
		In 1900, German physicist Max Planck explored the concept of flbody radiation and gave birth to the concept of quantum mechanics, or particle physics.
	www.britannica.com /eb/article-32486?tocId=32486 (759 words)

	Directory - Science: Physics: Quantum Mechanics: Relativistic
		Selected Papers on Geometric Algebra in Quantum Mechanics · cached · These papers analyze the quantum mechanical Dirac theory of the electron with respect to its geometric structure as revealed by reformulation in terms of Spacetime Algebra
		The Quantum Theory of Particles · cached · A new approach to relativity, quantum mechanics, and field theory which solves many old puzzles, such as ultraviolet infinities and superluminal spreading of wave packets.
		Relativistic quantum mechanics · cached · An electronic textbook for relativistic quantum mechanics is presented.
	www.incywincy.com /default?p=276657 (121 words)

	Relativistic momentum, mass, and energy (from relativistic mechanics) -- Encyclopædia Britannica
		More results on "Relativistic momentum, mass, and energy (from relativistic mechanics)" when you join.
		Such bodies are said to be relativistic, and when their motion is studied, it is necessary to take into account Einstein's special theory of...
		At the speeds treated in classical mechanics, the effect of speed on the...
	www.britannica.com /eb/article-77443 (927 words)

	Particles, Special Relativity and Quantum Mechanics (Site not responding. Last check: 2007-10-18)
		Special Relativity (SR) tells A that time was slowed down for the relativistic sister, B, so that upon her return to Earth, she knows that B will be younger than she is, which she suspects was the the ulterior motive of the trip from the start.
		The quantum mechanical spin of a particle along each of the three space axes is a set of mutually noncommuting observables.
		In quantum mechanics, the future quantum state of a system can be derived by applying the rules for time evolution to its present quantum state.
	atschool.eduweb.co.uk /rmext04/92andwed/pf_quant.html (8959 words)

	RELATIVISTIC CONTINUUM MECHANICS COURSE
		Relativistic conditions prevail when either temperatures are so high, that the thermal energy is no longer negligible compared to the rest mass energy or when the gravitational field is so strong, that it cannot be described with Newtonian theory.
		In the course the basics of relativistic continuum mechanics for elastic materials will be treated.
		The relativistic Lagrangean for an elastic continuum and the corresponding equations of motion.
	www2.mech.kth.se /~lhs/relcont.html (362 words)

	Wave Mechanics; Prince Louis de Broglie
		A consequence of de Broglie's reasoning is that a phase wave, often referred to as the "pilot" wave, appears to accompany the particle.
		Yet, modern introductions to quantum mechanics often fail to emphasize that this phase wave arises as an inevitable consequence of de Broglie's assumption of the internal periodic phenomenon of the particle and the transformation laws of the special theory of relativity.
		Given de Broglie's assumptions, quantum mechanics, which is to say the study of the behavior and interpretation of the phase wave, is the study of an inherently relativistic phenomenon.
	www.davis-inc.com /physics (869 words)

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