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The Einstein–Podolsky–Rosen (EPR) paradox is a thought experiment proposed by physicists Albert Einstein, Boris Podolsky and Nathan Rosen which argues that the description of physical reality provided by quantum mechanics is incomplete. In a 1935 paper titled "Can Quantum-Mechanical Description of Physical Reality be Considered Complete?", they argued for the existence of "elements of reality" that were not part of quantum theory, and speculated that it should be possible to construct a theory containing these hidden variables. Resolutions of the paradox have important implications for the interpretation of quantum mechanics.
Quantum entanglement is the phenomenon that occurs when a duet of particles are generated, interact, or share spatial proximity in such a way that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics.
The de Broglie–Bohm theory, also known as the pilot wave theory, Bohmian mechanics, Bohm's interpretation, and the causal interpretation, is an interpretation of quantum mechanics. It postulates that in addition to the wavefunction, an actual configuration of particles exists, even when unobserved. The evolution over time of the configuration of all particles is defined by a guiding equation. The evolution of the wave function over time is given by the Schrödinger equation. The theory is named after Louis de Broglie (1892–1987) and David Bohm (1917–1992).
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measurement. "Local" here refers to the principle of locality, the idea that a particle can only be influenced by its immediate surroundings, and that interactions mediated by physical fields cannot propagate faster than the speed of light. "Hidden variables" are putative properties of quantum particles that are not included in quantum theory but nevertheless affect the outcome of experiments. In the words of physicist John Stewart Bell, for whom this family of results is named, "If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local."
In physics, a hidden-variable theory is a deterministic physical model which seeks to explain the probabilistic nature of quantum mechanics by introducing additional variables.
In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. A theory that includes the principle of locality is said to be a "local theory". This is an alternative to the concept of instantaneous, or "non-local" action at a distance. Locality evolved out of the field theories of classical physics. The idea is that for a cause at one point to have an effect at another point, something in the space between those points must mediate the action. To exert an influence, something, such as a wave or particle, must travel through the space between the two points, carrying the influence.
In quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result. A fundamental feature of quantum theory is that the predictions it makes are probabilistic. The procedure for finding a probability involves combining a quantum state, which mathematically describes a quantum system, with a mathematical representation of the measurement to be performed on that system. The formula for this calculation is known as the Born rule. For example, a quantum particle like an electron can be described by a quantum state that associates to each point in space a complex number called a probability amplitude. Applying the Born rule to these amplitudes gives the probabilities that the electron will be found in one region or another when an experiment is performed to locate it. This is the best the theory can do; it cannot say for certain where the electron will be found. The same quantum state can also be used to make a prediction of how the electron will be moving, if an experiment is performed to measure its momentum instead of its position. The uncertainty principle implies that, whatever the quantum state, the range of predictions for the electron's position and the range of predictions for its momentum cannot both be narrow. Some quantum states imply a near-certain prediction of the result of a position measurement, but the result of a momentum measurement will be highly unpredictable, and vice versa. Furthermore, the fact that nature violates the statistical conditions known as Bell inequalities indicates that the unpredictability of quantum measurement results cannot be explained away as due to ignorance about "local hidden variables" within quantum systems.
In the interpretation of quantum mechanics, a local hidden-variable theory is a hidden-variable theory that satisfies the principle of locality. These models attempt to account for the probabilistic features of quantum mechanics via the mechanism of underlying, but inaccessible variables, with the additional requirement that distant events be statistically independent.
In theoretical physics, the pilot wave theory, also known as Bohmian mechanics, was the first known example of a hidden-variable theory, presented by Louis de Broglie in 1927. Its more modern version, the de Broglie–Bohm theory, interprets quantum mechanics as a deterministic theory, avoiding troublesome notions such as wave–particle duality, instantaneous wave function collapse, and the paradox of Schrödinger's cat. To solve these problems, the theory is inherently nonlocal.
In theoretical physics, a no-go theorem is a theorem that states that a particular situation is not physically possible. Specifically, the term describes results in quantum mechanics like Bell's theorem and the Kochen–Specker theorem that constrain the permissible types of hidden variable theories which try to explain the apparent randomness of quantum mechanics as a deterministic model featuring hidden states.
The free will theorem of John H. Conway and Simon B. Kochen states that if we have a free will in the sense that our choices are not a function of the past, then, subject to certain assumptions, so must some elementary particles. Conway and Kochen's paper was published in Foundations of Physics in 2006. In 2009, the authors published a stronger version of the theorem in the Notices of the American Mathematical Society. Later, in 2017, Kochen elaborated some details.
The Born rule is a postulate of quantum mechanics that gives the probability that a measurement of a quantum system will yield a given result. In its simplest form, it states that the probability density of finding a system in a given state, when measured, is proportional to the square of the amplitude of the system's wavefunction at that state. It was formulated and published by German physicist Max Born in July, 1926.
In mathematical physics, Gleason's theorem shows that the rule one uses to calculate probabilities in quantum physics, the Born rule, can be derived from the usual mathematical representation of measurements in quantum physics together with the assumption of non-contextuality. Andrew M. Gleason first proved the theorem in 1957, answering a question posed by George W. Mackey, an accomplishment that was historically significant for the role it played in showing that wide classes of hidden-variable theories are inconsistent with quantum physics. Multiple variations have been proven in the years since. Gleason's theorem is of particular importance for the field of quantum logic and its attempt to find a minimal set of mathematical axioms for quantum theory.
In theoretical physics, quantum nonlocality refers to the phenomenon by which the measurement statistics of a multipartite quantum system do not allow an interpretation with local realism. Quantum nonlocality has been experimentally verified under a variety of physical assumptions. Any physical theory that aims at superseding or replacing quantum theory should account for such experiments and therefore cannot fulfill local realism; quantum nonlocality is a property of the universe that is independent of our description of nature.
Objective-collapse theories, also known as models of spontaneous wave function collapse or dynamical reduction models, are proposed solutions to the measurement problem in quantum mechanics. As with other theories called interpretations of quantum mechanics, they are possible explanations of why and how quantum measurements always give definite outcomes, not a superposition of them as predicted by the Schrödinger equation, and more generally how the classical world emerges from quantum theory. The fundamental idea is that the unitary evolution of the wave function describing the state of a quantum system is approximate. It works well for microscopic systems, but progressively loses its validity when the mass / complexity of the system increases.
The Feynman checkerboard, or relativistic chessboard model, was Richard Feynman’s sum-over-paths formulation of the kernel for a free spin-½ particle moving in one spatial dimension. It provides a representation of solutions of the Dirac equation in (1+1)-dimensional spacetime as discrete sums.
Basil J. Hiley, is a British quantum physicist and professor emeritus of the University of London.
Peter R. Holland is an English theoretical physicist, known for his work on foundational problems in quantum physics and in particular his book on the pilot wave theory and the de Broglie-Bohm causal interpretation of quantum mechanics.
Quantum foundations is a discipline of science that seeks to understand the most counter-intuitive aspects of quantum theory, reformulate it and even propose new generalizations thereof. Contrary to other physical theories, such as general relativity, the defining axioms of quantum theory are quite ad hoc, with no obvious physical intuition. While they lead to the right experimental predictions, they do not come with a mental picture of the world where they fit.
Adrian Kent is a British theoretical physicist, Professor of Quantum Physics at the University of Cambridge, member of the Centre for Quantum Information and Foundations, and Distinguished Visiting Research Chair at the Perimeter Institute for Theoretical Physics. His research areas are the foundations of quantum theory, quantum information science and quantum cryptography. He is known as the inventor of relativistic quantum cryptography. In 1999 he published the first unconditionally secure protocols for bit commitment and coin tossing, which were also the first relativistic cryptographic protocols. He is a co-inventor of quantum tagging, or quantum position authentication, providing the first schemes for position-based quantum cryptography. In 2005 he published with Lucien Hardy and Jonathan Barrett the first security proof of quantum key distribution based on the no-signalling principle.
References
- ↑ Halvorson, Hans; Clifton, Rob (November 2002). "No place for particles in relativistic quantum theories?". Ontological Aspects of Quantum Field Theory. pp. 181–213. arXiv: quant-ph/0103041 . doi:10.1142/9789812776440_0010. ISBN 978-981-238-182-8. S2CID 8845639.
- ↑ Finster, Felix; Paganini, Claudio F. (2022-09-16). "Incompatibility of Frequency Splitting and Spatial Localization: A Quantitative Analysis of Hegerfeldt's Theorem". Annales Henri Poincaré. 24 (2): 413–467. arXiv: 2005.10120 . doi: 10.1007/s00023-022-01215-8 . PMID 36817968.
- ↑ Moretti, Valter (2023-06-07). "On the relativistic spatial localization for massive real scalar Klein–Gordon quantum particles". Letters in Mathematical Physics. 66. doi: 10.1007/s11005-023-01689-5 . hdl: 11572/379089 .
- ↑ Barat, N.; Kimball, J. C. (February 2003). "Localization and Causality for a free particle". Physics Letters A. 308 (2–3): 110–115. arXiv: quant-ph/0111060 . Bibcode:2003PhLA..308..110B. doi:10.1016/S0375-9601(02)01806-6. S2CID 119332240.
- ↑ Hobson, Art (2013-03-01). "There are no particles, there are only fields". American Journal of Physics. 81 (3): 211–223. arXiv: 1204.4616 . Bibcode:2013AmJPh..81..211H. doi:10.1119/1.4789885. S2CID 18254182.
- ↑ Hegerfeldt, Gerhard C. (1974-11-15). "Remark on causality and particle localization". Physical Review D. 10 (10): 3320–3321. doi:10.1103/PhysRevD.10.3320. ISSN 0556-2821.
- ↑ Hegerfeldt, Gerhard C. (1998). "Causality, particle localization and positivity of the energy". Irreversibility and Causality Semigroups and Rigged Hilbert Spaces. Lecture Notes in Physics. Vol. 504–504. pp. 238–245. arXiv: quant-ph/9806036 . doi:10.1007/BFb0106784. ISBN 978-3-540-64305-0. S2CID 119463020.
- ↑ Hegerfeldt, G.C. (December 1998). "Instantaneous spreading and Einstein causality in quantum theory". Annalen der Physik. 510 (7–8): 716–725. arXiv: quant-ph/9809030 . doi:10.1002/andp.199851007-817. S2CID 248267636.
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