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EPR paradox

EPR paradox
Albert Einstein The EPR paradox is an early and influential critique leveled against the Copenhagen interpretation of quantum mechanics. Albert Einstein and his colleagues Boris Podolsky and Nathan Rosen (known collectively as EPR) designed a thought experiment which revealed that the accepted formulation of quantum mechanics had a consequence which had not previously been noticed, but which looked unreasonable at the time. The scenario described involved the phenomenon that is now known as quantum entanglement. According to quantum mechanics, under some conditions, a pair of quantum systems may be described by a single wave function, which encodes the probabilities of the outcomes of experiments that may be performed on the two systems, whether jointly or individually. The routine explanation of this effect was, at that time, provided by Heisenberg's uncertainty principle. The EPR paper, written in 1935, was intended to illustrate that this explanation is inadequate. EPR paper[edit]

Quantum Physics Revealed As Non-Mysterious This is one of several shortened indices into the Quantum Physics Sequence. Hello! You may have been directed to this page because you said something along the lines of "Quantum physics shows that reality doesn't exist apart from our observation of it," or "Science has disproved the idea of an objective reality," or even just "Quantum physics is one of the great mysteries of modern science; no one understands how it works." There was a time, roughly the first half-century after quantum physics was invented, when this was more or less true. Certainly, when quantum physics was just being discovered, scientists were very confused indeed! The series of posts indexed below will show you - not just tell you - what's really going on down there. Some optional preliminaries you might want to read: Reductionism: We build models of the universe that have many different levels of description. And here's the main sequence:

Interpretations of quantum mechanics An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations. There exist a number of contending schools of thought, differing over whether quantum mechanics can be understood to be deterministic, which elements of quantum mechanics can be considered "real", and other matters. This question is of special interest to philosophers of physics, as physicists continue to show a strong interest in the subject. They usually consider an interpretation of quantum mechanics as an interpretation of the mathematical formalism of quantum mechanics, specifying the physical meaning of the mathematical entities of the theory. History of interpretations[edit] Main quantum mechanics interpreters Nature of interpretation[edit] Two qualities vary among interpretations:

Applications Relationship between string theory and quantum field theory Many first principles in quantum field theory are explained, or get further insight, in string theory: Note: formally, gauge symmetries in string theory are (at least in most cases) a result of the existence of a global symmetry together with the profound gauge symmetry of string theory, which is the symmetry of the worldsheet under a local change of coordinates and scales. 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.

Grand Unified Theory A Grand Unified Theory (GUT) is a model in particle physics in which at high energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single interaction characterized by one larger gauge symmetry and thus one unified coupling constant. During the grand unification epoch, the gauge force separated from the gravitational force. Models that do not unify all interactions using one simple Lie group as the gauge symmetry, but do so using semisimple groups, can exhibit similar properties and are sometimes referred to as Grand Unified Theories as well. Unifying gravity with the other three interactions would provide a theory of everything (TOE), rather than a GUT. Nevertheless, GUTs are often seen as an intermediate step towards a TOE. History[edit] Motivation[edit] Unification of matter particles[edit] Schematic representation of fermions and bosons in SU(5) GUT showing 5+10 split in the multiplets. SU(5)[edit] If

Density matrix Explicitly, suppose a quantum system may be found in state with probability p1, or it may be found in state with probability p2, or it may be found in state with probability p3, and so on. The density operator for this system is[1] By choosing a basis (which need not be orthogonal), one may resolve the density operator into the density matrix, whose elements are[1] For an operator (which describes an observable is given by[1] In words, the expectation value of A for the mixed state is the sum of the expectation values of A for each of the pure states Mixed states arise in situations where the experimenter does not know which particular states are being manipulated. Pure and mixed states[edit] In quantum mechanics, a quantum system is represented by a state vector (or ket) . is called a pure state. and a 50% chance that the state vector is . A mixed state is different from a quantum superposition. Example: Light polarization[edit] An example of pure and mixed states is light polarization. . and . . .

Schwinger–Dyson equation The Schwinger–Dyson equations (SDEs), also known as the Dyson–Schwinger equations, named after Julian Schwinger and Freeman Dyson, are general relations between Green functions in quantum field theories (QFTs). They are also referred to as the Euler–Lagrange equations of quantum field theories, since they are the equations of motion of the corresponding Green's function. They form a set of infinitely many functional differential equations, all coupled to each other, sometimes referred to as the infinite tower of SDEs. In his paper "The S-Matrix in Quantum electrodynamics",[1] Dyson derived relations between different S-matrix elements, or more specific "one-particle Green's functions", in quantum electrodynamics, by summing up infinitely many Feynman diagrams, thus working in a perturbative approach. Schwinger also derived an equation for the two-particle irreducible Green functions,[2] which is nowadays referred to as the inhomogeneous Bethe–Salpeter equation. Derivation[edit] , we have

Macroscopic quantum phenomena Quantum mechanics is most often used to describe matter on the scale of molecules, atoms, or elementary particles. However some phenomena, particularly at low temperatures, show quantum behavior on a macroscopic scale. The best-known examples of macroscopic quantum phenomena are superfluidity and superconductivity; another example is the quantum Hall effect. Since 2000 there has been extensive experimental work on quantum gases, particularly Bose–Einstein Condensates. Between 1996 to 2003 four Nobel prizes were given for work related to macroscopic quantum phenomena.[1] Macroscopic quantum phenomena can be observed in superfluid helium and in superconductors,[2] but also in dilute quantum gases and in laser light. Quantum phenomena are generally classified as macroscopic when the quantum states are occupied by a large number of particles (typically Avogadro's number) or the quantum states involved are macroscopic in size (up to km size in superconducting wires). with Ψ₀ the amplitude and