Category:General Theory Of Relativity

From Eurêka

Contents 1 Quantum Physics 2 Quantum Mechanics 3 Uncertainty Principle 4 Quantum Electrodynamics

Quantum Physics

Note : Human language is not really up to the task of quantum physics, and many physicists are tired of thinking about it. Quantum theory works, they say, whatever the hell it means. Niels Bohr put it like this: “We must be clear that, when it comes to atoms, language can be used only as poetry.” Even Planck himself when he discovered the quanta, confessed he did not know what his result meant and guessed his contemporaries would also be perplexed.

Quantum physics Physics based upon the quantum principle, that energy is emitted not as a continuum but in discrete units, quanta.

1. Quantum laws Often-paradoxical laws that seem to replace absolute knowledge with probability statements.
2. Decoherence Quantum phenomenon that is almost inevitable in macroscopic systems which are all but impossible to isolate from the environment.
3. Quantum information Particles that can exist in many places or states at once.

Quantum transition Study of thermal (black body) radiation which initiated the transition from classical physics to Planck’s quantum theory. Kirchhoff, Stefan, Wien, and Rayleigh studied the distribution of radiation emitted by a black body as a function of frequency and temperature.

1. Willian Wien (1864-1928) German physicist, assistant to Helmholtz, who discovered the energy distribution formula of black body radiation, begun 1892.
   1. Wien’s displacement law Red-hot black body on further heating emits shorter wavelength radiation and becomes white hot as the wavelength of maximum radiation shifts from the long (red) end of the spectrum to the center of the visible spectrum.
   2. Wien’s formula Distribution of energy in a radiation spectrum as a function of wavelength and temperature, that is well obeyed at short wavelengths but is clearly wrong for longer values, 1896.
2. Rayleigh (Baron) John William Strutt Rayleigh (1842-1919) found a formula that would agree with experiments at longer wavelengths but not at lower ones. He was married to the sister of Britain’s prime minister, A. J. Balfour. He won the Nobel Prize for physics for his work on gas densities and argon#

• See also Argon

• See also Rayleigh scattering

• See also Rayleigh waves

1. 1. Rayleigh-Jeans formula Agrees well with experiment for long wavelengths, it fails entirely for shorter wavelengths, represented the best that classical theory could achieve in this area of research.

Quantum theory (Quantum principle) Hypothesis that energy comes in discrete units replacing the classical assumption that energy is emitted continuously, that laid to rest scientific determinism. Postulated by Max Planck, 1900.

1. Quanta (b) (from Greco-Latin, = how much, i.e. quantity) Quantum of action, the fundamental units of energy which has come to be regarded as a fundamental constant of nature, on par with Einstein’s c, the velocity of light. The actual amount of energy in a quantum depends on the frequency of the radiation and is proportional to it. Coined by Max Planck, 1900.
   1. Max Planck Max Karl Ernst Ludwig Planck (1858-1947) German physicist who originated the quantum theory that marked the transition between classical and modern physics. Planck won the Nobel Prize for Physics, 1918.
2. Planck length Quantum of space; radius of ‘dimensionless’ particles in string theory. It was Planck himself who first had an inkling of a smallest possible size by taking three fundamental parameters of the universe, gravitational constant, speed of light and Planck's constant, and combine them in such a way that the units canceled one another to yield a length. At the time of discovery Planck was not sure about its meaning but he felt that it must be something very basic.
   1. Quantum foam Condition identified by physicist John Wheeler who said the Planck length marked the boundary where the random roil of quantum mechanics scrambled space and time so violently that ordinary notions of measurement stopped making sense, “So great would be the fluctuations that there would literally be no left or right, no before, no after,” and “Ordinary ideas of length would disappear. Ordinary ideas of time would evaporate,” 1950s.
3. Planck’s constant Fundamental quantity of action in quantum mechanics. The constant of proportionality between the frequency of an electromagnetic wave and the energy of an equivalent photon

Hierarchy problem Formidable puzzle regarding the characteristic energies encountered in physics. All the interaction strengths of particles depend on the energy at which they are measured but when they are extrapolated, they all become equal to one another at an energy of little more than 1016 GeV, and the force of gravitation has the same strength not much higher, c. 1018 GeV.

Quantum Mechanics

Quantum mechanics Theory governing the physical behavior of the ultrasmall, the physics of the atomic and subatomic world. It is the only physical theory that we know that deals with the world of atoms, atomic nuclei, elementary particles, quarks and leptons, and the fundamental forces of nature. Quantum mechanics must be taken not just as a predictive tool but as an explanation for how the world really works, accepting the universe is far stranger than it already appears.

1. Old quantum mechanics Early version of the laws of quantum mechanics developed by a number of physicists including Erwin Schrödinger, Paul Dirac, Niels Bohr and Albert Einstein in the first two decades of the 20th cent.
2. New quantum mechanics Final version of the laws of quantum mechanics, formulated by German physicist Werner Karl Heisenberg (1901-1976), who had worked with Max Born (1882-1970) in Göttingen and Niels Bohr in Copenhagen, in a paper in Zeitschrift für Physik, 1925.
   1. New method for quantum mechanics De Broglie suggested that particles possess wave-like properties in 1924 and collaboration between Born, E. P. Jordan, Heisenberg and Pauli developed a sequence of important ideas, 1924-5.
   2. Matrix mechanics Method of handling quantum mechanics using matrices creating the first consistent version of new quantum mechanics, constructed by Max Born 1925.

De Broglie French physicist (Prince) Louis-Victor Pierre Raymond (1892-1987) of a Piendmontese family, who discovered the wave nature of particles, published in Annals de Physique#

1. Wave-particle duality Defining foundation of quantum mechanics, that matter and radiation alike, within the reduced dimensions of the quantum world, behave at time like a wave and at other times, just as convincingly like a particle. This is the most perplexing and paradoxical of all the mysteries of quantum physics.

E. P. Jordan German theoretical physicist Ernst Pascual Jordan (1902-?) gained his doctorate at Göttingen who collaborated with Born and then Heisenberg 1926 and later contributed to quantum electrodynamic# Schrödinger Austrian physicist Erwin Schrödinger (1887-1961) who founded wave mechanics in a series of papers 1926. He shared the Nobel Prize for physics with Dirac# He succeeded Planck as professor of theoretical physics in Berlin, but left his post when Hitler assumed power 1933, going to Oxford. Return to Graz, Austria 1936, by fled to Dublin, Ireland at Anschluss 1938 where Irish leader de Valera supported his Institute for Advanced Studies that was created for him. He returned to Vienna 1955.

1. Schrödinger’s theory Any particle has a wave associated with it and the properties of the particle result from a combination of its particle-like and wave-like nature.
2. Schrödinger’s equation Schrödinger used Hamilton’s method of describing particle motion and wrote it in wave form to create a fundamental equation of quantum mechanics describing the behavior of electrons in disordered glasslike material where they can be trapped in some regions yet flow freely in others.

Dirac English theoretical physicist Paul Adrien Maurice Dirac (1902-1984) who made major contributions to new quantum mechanics. He shared the Nobel Prize for physics with Schrödinger#

1. 1. General theoretical structure for quantum mechanics Developed by Dirac 1926.
   2. Relativistic form of quantum mechanics Theory describing the properties of the electron and correcting the failure of Schrödinger’s theory to explain electron spin discovered by Uhlenbeck and Goudsmit in 1925. Developed by Dirac#

Cloud of probability (Superposition) In quantum mechanics, an electron orbiting an atomic nucleus in which all the electron’s possible positions hover together. In some scientists view, the universe itself is a superposition of every possible spin net, all the possible ways it can be curved.

Relativistic quantum mechanics Extension of quantum mechanics into the realm of high speeds, that is relativistic speeds. A theory in which Einstein’s relativity and quantum mechanics have been merged to describe the world of highly energetic elementary particles. One of the important outcomes of this theory was the prediction, and its subsequent confirmation, of the existence of antimatter, the antiparticles.

Quantum geometry New field in mathematics inspired by physicists’ free-flowing ideas and nature, by which they used intuition and analogies to solve some long-standing problems of classical mathematics.

Seiberg-Witten theory Equivalent set of numbers that could be calculated almost 100 times faster than the “Donaldson numbers.” This opened up the quantum-field theories.

Quantum field theory Quantum theory whose basic ingredients are fields, such as the standard model of particle physics.

1. Field Standard model indicates a field for every particle. Little ripples in these fields carry energy and momentum from place to place, and the energy comes in quanta.
   1. Electromagnetic field Quantum is a particle, the photon.
   2. Lepton field Quanta include, the electron which makes up the outer parts of ordinary atoms, similar heavier particles known as muons and tauons, and related electrically neutral particles, neutrinos.
2. Scaler field Field that carries no sense of direction, unlike the electric and magnetic fields and the other fields in the standard model.

Renormalization Term that goes back to when physicists were learning how to use the first quantum field theories to calculate small shifts of atomic energy, only to find they kept on producing infinite quantities, a situation that usually means a theory is badly flawed or is being pushed beyond its limits, 1940s.

1. Constraints Procedure to deal with infinite quantities by absorbing them into a refinition, or renormalization, of just a few physical restraints, such as the charge and mass of the electron.
   1. Scaler particle Minimum version of the Standard Model, with just one scaler particle, has 18 constraints.
2. Principle of renormalizability Principle, together with various symmetry principles of the Standard Model, rules out unobserved processes such as decay of isolated protons and forbids the neutrinos from having masses.
3. Suppressed nonrenormizable interaction Gravitation is a suppressed nonrenormizable interaction and it is from its strength at low energies that it can be inferred that its fundamental energy scale is c. 1018 GeV.

Effective field theory At low energies the interactions are negligible.

Quantum nondemolition Method of measurement that circumvents the standard quantum limit.

1. Stroboscopic measurement Specific kind of quantum nondemolition measurement in which one makes a sequence of very quick measurements of a vibrating bar, each measurement separated by one vibration period.

M theory Single fundamental theory that applies under different approximations, such as the five string theories and a quantum theory in 11 dimensions. No fundamental principle that governs M theory has been found and no one knows how to write down the equations of this theory.

• See also Quantum Computing

Uncertainty Principle

Uncertainty principle (Heisenberg's uncertainty principle; Indeterminancy principle) Principle states that is impossible to specify precisely and simultaneously the position and the velocity of a particle. In other words, our knowledge of the present state of a particle does not permit us to predict with any certainty its future states. From this, German physicist, Werner Karl Heisenberg (1901-76) concluded that quantum mechanics had destroyed the scientific determinism of classical physics and established the final failure of causality. Derived by Werner Heisenberg from quantum mechanics, submitted his paper, “On the Perceptual Content of Quantum Theoretical Kinematics and Mechanics,” to a German journal of physics, March 1927, for which he was awarded the Nobel Prize#

1. God doesn’t play dice Einstein’s statement in rejection of the uncertainty principle, of which he was one of the founders, as he rebelled against the statistical nature of quantum mechanics.

Path integral approach (Sum-over-histories approach) New way to visualize and compute in the quantum world, using an elegant mathematical principle from classical mathematics that added to the bizarreness of quantum mechanics because in it an electron does not follow any single path around an atom but all possible paths at once, even paths that go backward in time, appearing as an anti-particle with identical mass but opposite charge and spin. Most of the paths interfere and cancel one another out, discovered by Richard Phillips Feynman (1918-1988), in 1940s for which he gained the Nobel Prize in Physics in 1965.

1. Feynman diagram Electron-electron scattering can be described as a sum of terms and each term can be written as a Feynman diagram.
2. Feynman propagators Lines which describe the exchange of particles on a Feynman diagram.

Quantum chromodynamics Quantum theory of the strong nuclear force, which it envisions as being conveyed by quanta called gluons.

Quantum Electrodynamics

Quantum electrodynamics (QED) Branch of quantum theory in that a vacuum, far from being empty, teems with transient virtual particles (especially photons) that keep popping weirdly into existence and then disappearing again. A basic theory published by Werner Heisenberg and Wolfgang Pauli, 1930.

1. Charge renormalization Phenomenon that helped to explain some of the earlier difficulties surrounding infinities in QED.
2. Casimir force Short energy bursts in QED carry the forces that hold real particles, and hence the material world, together. Predicted by Dutch physicist, Hendrik Casimir, 1948.
3. Torsion pendulum Part of a device developed by Steve Lamoreaux at Los Alamos NL who first demonstrated the Casimir force, 1997.

Theory of the electrodynamic force Action at the level of the quantum world, the world of atoms, electrons and photons. It arose from the study of how a hydrogen atom behaves in a magnetic field, the pioneers of which were Richard Feynman of the California Institute of Technology at Pasadena, Julian Schwinger at Columbia and Shin’ ichiro Tomonaga in Japan who shared the Nobel Prize for Physics in 1965.

Quantum space Vacuum with the potential to produce virtual particles.

1. Virtual particle In quantum mechanics, a particle that can never be directly detected, but whose existence does have measurable effects.

Quantum leap Disappearance of a subatomic particle, e.g. the electron, at one location and its simultaneous reappearance at another.

Tunneling (Quantum tunneling) Quantum leap through a barrier. It is an exclusively quantum-mechanical effect in which a particle such as an electron seems to penetrate or tunnel through an otherwise impenetrable force barrier, hence its name. Completely inexplicable by the laws of Newtonian physics, such a bizarre event takes place because a particle sometimes behaves as a wave. It is like a ping-pong ball going through a steel door a few feet thick. Discovered by J. Robert Oppenheimer (1904-1967), 1928.

• See also Quantum tunneling transistor

• See also Scanning tunnel microscope

Indeterminacy principle Quantum precept indicating that the position and trajectory of a particle cannot both be known with perfect exactitude. Indeterminacy thus indicates the existence of a basic quantum of knowledge of the particle world. Since information about one quantity can be extracted at the expense of another, it demonstrates that the answers we obtain about natural events result to some extent from the questions we choose to ask about them.

Standard quantum limit Limit due to the uncertainty principle, as how accurately certain quantities can be measured using standard methods. This limit can be circumvented using quantum nondemolition methods.

Special Theory of Relativity (Special Relativity) Einstein’s theory of the electrodynamics of moving systems, which is limited to the description of events as they appear to observers in a state of uniform motion relative to one another. Developed by Albert Einstein (1878-1955) and published 1905. Special relativity is developed from the following axions:

1. Laws of natural phenomena Laws that are the same for all observers.
2. Principle of absoluteness of the speed of light Einstein’s principle that the speed of light is a universal constant, the same for all observers irrespective of their own velocity.
   1. Gauge invariance of the electromagnetic field Implicit symmetry from which Einstein had deduced that the velocity of light is the same for all observers.
3. Principle of Relativity No physical experiment can be devised to detect a uniform state of motion. Or, neither location in space and time, nor uniform motion, affects the description of physical reality.
   1. Time dilation Time intervals appear extended in reference frames moving relative to the observer.
   2. Lorentz contraction Lengths appear foreshortened in reference frames moving relative to the observer.

Albert Einstein (1879-1955) Theoretical physicist with a background in Germany, Switzerland and US, published three papers covering Brownian motion, the photoelectric effect and special relativity 1905. General of relativity was published in 1915, for which he was awarded the Nobel Prize for physics 1921. He was in California when Hitler came to power in 1933, he never returned to Germany.

1. Olympia Academy Einstein and two of his under-employed scholar friends who met in his apartment in Berne and read where they read mathematician, Jules Henri Poincaré’s “Science and Hypothesis” (1902), 1904.

General relativity theory Einstein’s theory of gravitation by a description of space, time and gravity. The theory recognizes the impossibility of determining absolute motion and leads to the concept of a four-dimensional spacetime continuum. Submitted in its final form, 25 November 1916.

1. Brans-Dicke theory Modification of Einstein’s General Relativity theory.
2. Mössbauer effect When an atom absorbs a gamma ray it recoils, and by energy conservation the wavelength of the re-emitted gamma ray is altered, discovered by German physicist, Rudolph Ludwig Mössbauer. Einstein’s general relativity theory was verified by measuring the change in wavelength of a gamma ray due to its moving from one point of gravitational potential to another, 1960.

Einstein v. Hilbert controversy Dispute over the authorship of the general relativity theory between Albert Einstein and David Hilbert. Hilbert’s early proofs lacked “covariance,” the critical ingredient for the theory’s success and although Hilbert’s article bore the submission date of 20 November 1915, it was not published until 31 March 1916, long after Einstein’s paper was public. Hilbert’s final article was covariant, excluding the possibility that Einstein plagiarized Hilbert.

Theory of gravitation Theory that the presence of matter in space causes space to curve in such a manner that the gravitational field is set up. Thus gravitation becomes a property of space itself.

Hyperdimensional Involving more than the customary four dimensions (three of space, plus one of time) of relativistic space-time.

Relative mass Mass of a body is a function of its velocity.

Fitzgerald-Lorentz contraction Hypothesis to explain the Michelson-Morley experiment on the supposition that a body moving with high velocity through the ether would experience a contraction in length in the direction of the motion. This contraction was later shown to be a direct consequence of the theory of relativity.