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Universal Wavefunction
The universal wavefunction or the wavefunction of the universe is the wavefunction or quantum state of the entire universe. It is regarded as the basic physical entity in the many-worlds interpretation of quantum mechanics,Hugh Everett, Relative State Formulation of Quantum Mechanics, ''Reviews of Modern Physics'' vol 29, (1957) pp 454–462. An abridged summary of ''The Theory of the Universal Wavefunction'' and finds applications in quantum cosmology. It evolves deterministically according to a wave equation. The concept of universal wavefunction was introduced by Hugh Everett in his 1956 PhD thesis draft ''The Theory of the Universal Wave Function''. It later received investigation from James Hartle and Stephen HawkingStephen Hawking, Stephen W Hawking, James Hartle, James B Hartle "The Wave Function of the Universe," ''Physical Review D'', vol 28, (1983) pp 2960–2975 who derived the Hartle–Hawking state, Hartle–Hawking solution to the Wheeler–DeWitt equation to explain t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavefunction
In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter), psi, respectively). Wave functions are complex number, complex-valued. For example, a wave function might assign a complex number to each point in a region of space. The Born rule provides the means to turn these complex probability amplitudes into actual probabilities. In one common form, it says that the squared modulus of a wave function that depends upon position is the probability density function, probability density of measurement in quantum mechanics, measuring a particle as being at a given place. The integral of a wavefunction's squared modulus over all the system's degrees of freedom must be equal to 1, a condition called ''normalization''. Since the wave function is complex-valued, only its relative phase and relative magnitud ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial support of Charles Scribner, as a printing press to serve the Princeton community in 1905. Its distinctive building was constructed in 1911 on William Street in Princeton. Its first book was a new 1912 edition of John Witherspoon's ''Lectures on Moral Philosophy.'' History Princeton University Press was founded in 1905 by a recent Princeton graduate, Whitney Darrow, with financial support from another Princetonian, Charles Scribner II. Darrow and Scribner purchased the equipment and assumed the operations of two already existing local publishers, that of the ''Princeton Alumni Weekly'' and the Princeton Press. The new press printed both local newspapers, university documents, '' The Daily Princetonian'', and later added book publishing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eugene Wigner
Eugene Paul Wigner (, ; November 17, 1902 – January 1, 1995) was a Hungarian-American theoretical physicist who also contributed to mathematical physics. He received the Nobel Prize in Physics in 1963 "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles". A graduate of the Technical Hochschule Berlin (now Technische Universität Berlin), Wigner worked as an assistant to Karl Weissenberg and Richard Becker (physicist), Richard Becker at the Max Planck Institute for Physics, Kaiser Wilhelm Institute in Berlin, and David Hilbert at the University of Göttingen. Wigner and Hermann Weyl were responsible for introducing group theory into physics, particularly the theory of symmetry in physics. Along the way he performed ground-breaking work in pure mathematics, in which he authored a number of mathematical theorems. In particular, Wigner's theorem is a cornerstone ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Psychophysical Parallelism
In the philosophy of mind, psychophysical parallelism (or simply parallelism) is the theory that mental and bodily events are perfectly coordinated, without any causal interaction between them. As such, it affirms the correlation of mental and bodily events (since it accepts that when a mental event occurs, a corresponding physical effect occurs as well), but denies a direct cause and effect relation between mind and body. This coordination of mental and bodily events has been postulated to occur either in advance by means of God (as per Gottfried Leibniz's idea of pre-established harmony) or at the time of the event (as in the occasionalism of Nicolas Malebranche) or, finally, according to Baruch Spinoza's ''Ethics'', mind and matter are two of infinite ''attributes'' of the only Substance-God, which go as one without interacting with each other. On this view, mental and bodily phenomena are independent yet inseparable, like two sides of a coin. Overview Psychophysical paralle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Big Bang
The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models based on the Big Bang concept explain a broad range of phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure. The uniformity of the universe, known as the horizon and flatness problems, is explained through cosmic inflation: a phase of accelerated expansion during the earliest stages. A wide range of empirical evidence strongly favors the Big Bang event, which is now essentially universally accepted.: "At the same time that observations tipped the balance definitely in favor of the relativistic big-bang theory, ..." Detailed measurements of the expansion rate of the universe place the Big Bang singularity at an estimated billion years ago, which is considered the age of the universe. Extrapolating this cosmic expansion backward in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wheeler–DeWitt Equation
The Wheeler–DeWitt equation for theoretical physics and applied mathematics, is a field equation attributed to John Archibald Wheeler and Bryce DeWitt. The equation attempts to mathematically combine the ideas of quantum mechanics and general relativity, a step towards a theory of quantum gravity. In this approach, time plays a role different from what it does in non-relativistic quantum mechanics, leading to the so-called " problem of time". More specifically, the equation describes the quantum version of the Hamiltonian constraint using metric variables. Its commutation relations with the diffeomorphism constraints generate the Bergman–Komar "group" (which ''is'' the diffeomorphism group on-shell). Motivation and background In canonical gravity, spacetime is foliated into spacelike submanifolds. The three-metric (i.e., metric on the hypersurface) is \gamma_ and given by g_\,\mathrmx^\,\mathrmx^\nu = (-N^2 + \beta_k\beta^k)\,\mathrmt^2 + 2\beta_k\,\mathrmx^k\,\ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hartle–Hawking State
The Hartle–Hawking state, also known as the no-boundary wave function is a proposal in theoretical physics concerning the state of the universe prior to the Planck epoch. It is named after James Hartle and Stephen Hawking. History According to the Hartle–Hawking proposal, the universe has no origin as we would understand it: before the Big Bang, which happened about 13.8 billion years ago, the universe was a singularity in both space and time. Hartle and Hawking suggest that if we could travel backwards in time towards the beginning of the universe, we would note that quite near what might have been the beginning, time gives way to space so that there is only space and no time. Technical explanation More precisely, the Hartle-Hawking state is a hypothetical vector in the Hilbert space of a theory of quantum gravity that describes the wave function of the universe. It is a functional of the metric tensor defined at a (''D'' − 1)-dimensional compact ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stephen Hawking
Stephen William Hawking (8January 194214March 2018) was an English theoretical physics, theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge. Between 1979 and 2009, he was the Lucasian Professor of Mathematics at Cambridge, widely viewed as one of the most prestigious academic posts in the world. Hawking was born in Oxford into a family of physicians. In October 1959, at the age of 17, he began his university education at University College, Oxford, where he received a First Class Honours, first-class Honours degree, BA degree in physics. In October 1962, he began his graduate work at Trinity Hall, Cambridge, where, in March 1966, he obtained his PhD in applied mathematics and theoretical physics, specialising in general relativity and cosmology. In 1963, at age 21, Hawking was diagnosed with an early-onset slow-progressing form of motor neurone disease that gradually, over decades, pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Hartle
James Burkett Hartle (August 17, 1939 – May 17, 2023) was an American theoretical physicist. He joined the faculty of the University of California, Santa Barbara in 1966, and was a member of the external faculty of the Santa Fe Institute. Hartle is known for his work in general relativity, astrophysics, and interpretation of quantum mechanics. Early life Hartle was born on August 17, 1939, in Baltimore to Anna Elizabeth Burkett and Charles James Hartle. He began as an engineering major upon entering Princeton, but switched to physics due to the influence of John Wheeler. Hartle completed his AB at Princeton University in 1960 and his Ph.D. in particle physics under Murray Gell-Mann in 1964. Work In collaboration with Gell-Mann and others, Hartle developed an alternative to the standard Copenhagen interpretation, more general and appropriate to quantum cosmology, based on consistent histories. With Dieter Brill in 1964, he discovered the Brill–Hartle geon, an approxi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Cosmology
Quantum cosmology is the attempt in theoretical physics to develop a quantum theory of the universe. This approach attempts to answer open questions of classical physical cosmology, particularly those related to the first phases of the universe. Classical cosmology is based on Albert Einstein's general theory of relativity (GTR or simply GR) which describes the evolution of the universe very well, as long as you do not approach the Big Bang. It is the gravitational singularity and the Planck time where relativity theory fails to provide what must be demanded of a final theory of space and time. Therefore, a theory is needed that integrates relativity theory and quantum theory. Such an approach is attempted for instance with loop quantum cosmology, loop quantum gravity, string theory and causal set theory. In quantum cosmology, the universe is treated as a wave function instead of classical spacetime. See also * String cosmology * Brane cosmology * Loop quantum cosm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum State
In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a prediction for the system represented by the state. Knowledge of the quantum state, and the rules for the system's evolution in time, exhausts all that can be known about a quantum system. Quantum states may be defined differently for different kinds of systems or problems. Two broad categories are * wave functions describing quantum systems using position or momentum variables and * the more abstract vector quantum states. Historical, educational, and application-focused problems typically feature wave functions; modern professional physics uses the abstract vector states. In both categories, quantum states divide into pure versus mixed states, or into coherent states and incoherent states. Categories with special properties include stationary states for tim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academic Press
Academic Press (AP) is an academic book publisher founded in 1941. It launched a British division in the 1950s. Academic Press was acquired by Harcourt, Brace & World in 1969. Reed Elsevier said in 2000 it would buy Harcourt, a deal completed the next year, after a regulatory review. Thus, Academic Press is now an imprint of Elsevier. Academic Press publishes reference books, serials and online products in the subject areas of: * Communications engineering * Economics * Environmental science * Finance * Food science and nutrition * Geophysics * Life sciences * Mathematics and statistics * Neuroscience * Physical sciences * Psychology Psychology is the scientific study of mind and behavior. Its subject matter includes the behavior of humans and nonhumans, both consciousness, conscious and Unconscious mind, unconscious phenomena, and mental processes such as thoughts, feel ... Well-known products include the '' Methods in Enzymology'' series and encyclopedias such ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
