The Infinity of Quantum Physics Quantum Mechanics the Infinity Photon Electron Couplings creating sets of infinities of Fractal Self-Similarities Atom surround by Photon Electron Coupling. Expanding as a Wave-Particle Function of future possibilities. Wave-Particle Function collapsing into sets of Fractal Self-Similarities expanding as set of infinities creating there own Spacetime. Infinity can always be divided up into ever increasing sets of infinities because of the continuous expansion at the quantum level.
Wave–particle duality Origin of theory[edit] The idea of duality originated in a debate over the nature of light and matter that dates back to the 17th century, when Christiaan Huygens and Isaac Newton proposed competing theories of light: light was thought either to consist of waves (Huygens) or of particles (Newton). Through the work of Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, and many others, current scientific theory holds that all particles also have a wave nature (and vice versa).[2] This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. For macroscopic particles, because of their extremely short wavelengths, wave properties usually cannot be detected.[3] Brief history of wave and particle viewpoints[edit] Thomas Young's sketch of two-slit diffraction of waves, 1803 Particle impacts make visible the interference pattern of waves. A quantum particle is represented by a wave packet.
Heisenberg picture It stands in contrast to the Schrödinger picture in which the operators are constant, instead, and the states evolve in time. The two pictures only differ by a basis change with respect to time-dependency, which corresponds to the difference between active and passive transformations. The Heisenberg picture is the formulation of matrix mechanics in an arbitrary basis, in which the Hamiltonian is not necessarily diagonal. It further serves to define a third, hybrid, picture, the Interaction picture. Mathematical details[edit] In the Heisenberg picture of quantum mechanics the state vectors, |ψ⟩, do not change with time, while observables A satisfy This approach also has a more direct similarity to classical physics: by simply replacing the commutator above by the Poisson bracket, the Heisenberg equation reduces to an equation in Hamiltonian mechanics. Derivation of Heisenberg's equation[edit] where H is the Hamiltonian and ħ is the reduced Planck constant. It now follows that Thus which implies
Quantum mechanics Description of physical properties at the atomic and subatomic scale Quantum mechanics is a fundamental theory in physics that describes the behavior of nature at and below the scale of atoms.[2]: 1.1 It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Quantum mechanics arose gradually from theories to explain observations that could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, and the correspondence between energy and frequency in Albert Einstein's 1905 paper, which explained the photoelectric effect. Overview and fundamental concepts Mathematical formulation . and , where Here .
Complementarity (physics) In physics, complementarity is a fundamental principle of quantum mechanics, closely associated with the Copenhagen interpretation. It holds that objects governed by quantum mechanics, when measured, give results that depend inherently upon the type of measuring device used, and must necessarily be described in classical mechanical terms. Further, a full description of a particular type of phenomenon can only be achieved through measurements made in each of the various possible bases — which are thus complementary. The complementarity principle was formulated by Niels Bohr, the developer of the Bohr model of the atom, and a leading founder of quantum mechanics.[1] Bohr summarized the principle as follows: ...however far the [quantum physical] phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. For example, the particle and wave aspects of physical objects are such complementary phenomena. Physicists F.A.M. Dr.
Interaction picture Equations that include operators acting at different times, which hold in the interaction picture, don't necessarily hold in the Schrödinger or the Heisenberg picture. This is because time-dependent unitary transformations relate operators in one picture to the analogous operators in the others. Definition[edit] Operators and state vectors in the interaction picture are related by a change of basis (unitary transformation) to those same operators and state vectors in the Schrödinger picture. Any possible choice of parts will yield a valid interaction picture; but in order for the interaction picture to be useful in simplifying the analysis of a problem, the parts will typically be chosen so that H0,S is well understood and exactly solvable, while H1,S contains some harder-to-analyze perturbation to this system. by the corresponding time-evolution operator in the definitions below. State vectors[edit] A state vector in the interaction picture is defined as[4] Operators[edit] References[edit]
8 shocking things we learned from Stephen Hawking's book From the idea that our universe is one among many, to the revelation that mathematician Pythagoras didn't actually invent the Pythagorean theorem, here are eight shocking things we learned from reading physicist Stephen Hawking's new book, "The Grand Design," written with fellow physicist Leonard Mlodinow of Caltech. The book, covering major questions about the nature and origin of the universe, was released Sept. 7 by its publisher, Bantam. 1. For example, if all we know is that a particle traveled from point A to point B, then it is not true that the particle took a definite path and we just don't know what it is. Yeah, we're still trying to wrap our brains around this. The authors sum up: "No matter how thorough our observation of the present, the (unobserved) past, like the future, is indefinite and exists only as a spectrum of possibilities." 2. This fun fact: A 1-watt night-light emits a billion billion photons each second. Photons are the little packets that light comes in. 3. 4. 5.
Quantum entanglement Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently – instead, a quantum state may be given for the system as a whole. Such phenomena were the subject of a 1935 paper by Albert Einstein, Boris Podolsky and Nathan Rosen,[1] describing what came to be known as the EPR paradox, and several papers by Erwin Schrödinger shortly thereafter.[2][3] Einstein and others considered such behavior to be impossible, as it violated the local realist view of causality (Einstein referred to it as "spooky action at a distance"),[4] and argued that the accepted formulation of quantum mechanics must therefore be incomplete. History[edit] However, they did not coin the word entanglement, nor did they generalize the special properties of the state they considered. Concept[edit] Meaning of entanglement[edit] Apparent paradox[edit] The hidden variables theory[edit]
Matrix mechanics Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. In some contrast to the wave formulation, it produces spectra of energy operators by purely algebraic, ladder operator, methods.[1] Relying on these methods, Pauli derived the hydrogen atom spectrum in 1926,[2] before the development of wave mechanics. Development of matrix mechanics[edit] In 1925, Werner Heisenberg, Max Born, and Pascual Jordan formulated the matrix mechanics representation of quantum mechanics. Epiphany at Helgoland[edit] In 1925 Werner Heisenberg was working in Göttingen on the problem of calculating the spectral lines of hydrogen. "It was about three o' clock at night when the final result of the calculation lay before me. The Three Fundamental Papers[edit] After Heisenberg returned to Göttingen, he showed Wolfgang Pauli his calculations, commenting at one point:[4] In the paper, Heisenberg formulated quantum theory without sharp electron orbits. W.
Physicists challenge classical world with quantum-mechanical implementation of 'shell game' Inspired by the popular confidence trick known as "shell game," researchers at UC Santa Barbara have demonstrated the ability to hide and shuffle "quantum-mechanical peas" -- microwave single photons -- under and between three microwave resonators, or "quantized shells." In a paper published in the Jan. 30 issue of the journal Nature Physics, UCSB researchers show the first demonstration of the coherent control of a multi-resonator architecture. This topic has been a holy grail among physicists studying photons at the quantum-mechanical level for more than a decade. The UCSB researchers are Matteo Mariantoni, postdoctoral fellow in the Department of Physics; Haohua Wang, postdoctoral fellow in physics; John Martinis, professor of physics; and Andrew Cleland, professor of physics. According to the paper, the "shell man," the researcher, makes use of two superconducting quantum bits (qubits) to move the photons -- particles of light -- between the resonators.
Quantum superposition Quantum superposition is a fundamental principle of quantum mechanics that holds that a physical system—such as an electron—exists partly in all its particular theoretically possible states (or, configuration of its properties) simultaneously; but when measured or observed, it gives a result corresponding to only one of the possible configurations (as described in interpretation of quantum mechanics). and . Here is the Dirac notation for the quantum state that will always give the result 0 when converted to classical logic by a measurement. is the state that will always convert to 1. Concept[edit] The principle of quantum superposition states that if a physical system may be in one of many configurations—arrangements of particles or fields—then the most general state is a combination of all of these possibilities, where the amount in each configuration is specified by a complex number. For example, if there are two configurations labelled by 0 and 1, the most general state would be . . . .
Schrödinger picture In physics, the Schrödinger picture (also called the Schrödinger representation[1]) is a formulation of quantum mechanics in which the state vectors evolve in time, but the operators (observables and others) are constant with respect to time.[2][3] This differs from the Heisenberg picture which keeps the states constant while the observables evolve in time, and from the interaction picture in which both the states and the observables evolve in time. The Schrödinger and Heisenberg pictures are related as active and passive transformations and have the same measurement statistics. In the Schrödinger picture, the state of a system evolves with time. The evolution for a closed quantum system is brought about by a unitary operator, the time evolution operator. For time evolution from a state vector at time to a state vector , the time-evolution operator is commonly written , and one has where the exponent is evaluated via its Taylor series. Background[edit] and returns some other ket , or both.
SCHOPENHAUER'S 38 STRATAGEMS, OR 38 WAYS TO WIN AN ARGUMENT Arthur Schopenhauer (1788-1860), was a brilliant German philosopher. These 38 Stratagems are excerpts from "The Art of Controversy", first translated into English and published in 1896. Carry your opponent's proposition beyond its natural limits; exaggerate it. The more general your opponent's statement becomes, the more objections you can find against it. The more restricted and narrow his or her propositions remain, the easier they are to defend by him or her. (abstracted from the book:Numerical Lists You Never Knew or Once Knew and Probably Forget, by: John Boswell and Dan Starer)