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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 of a group of particles being generated, interacting, or sharing 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.
In quantum mechanics, counterfactual definiteness (CFD) is the ability to speak "meaningfully" of the definiteness of the results of measurements that have not been performed. The term "counterfactual definiteness" is used in discussions of physics calculations, especially those related to the phenomenon called quantum entanglement and those related to the Bell inequalities. In such discussions "meaningfully" means the ability to treat these unmeasured results on an equal footing with measured results in statistical calculations. It is this aspect of counterfactual definiteness that is of direct relevance to physics and mathematical models of physical systems and not philosophical concerns regarding the meaning of unmeasured results.
Determinism is the philosophical view that all events in the universe, including human decisions and actions, are causally inevitable. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and considerations. Like eternalism, determinism focuses on particular events rather than the future as a concept. The opposite of determinism is indeterminism, or the view that events are not deterministically caused but rather occur due to chance. Determinism is often contrasted with free will, although some philosophers claim that the two are compatible.
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."
Wigner's friend is a thought experiment in theoretical quantum physics, first published by the Hungarian-American physicist Eugene Wigner in 1961, and further developed by David Deutsch in 1985. The scenario involves an indirect observation of a quantum measurement: An observer observes another observer who performs a quantum measurement on a physical system. The two observers then formulate a statement about the physical system's state after the measurement according to the laws of quantum theory. In the Copenhagen interpretation, the resulting statements of the two observers contradict each other. This reflects a seeming incompatibility of two laws in the Copenhagen interpretation: the deterministic and continuous time evolution of the state of a closed system and the nondeterministic, discontinuous collapse of the state of a system upon measurement. Wigner's friend is therefore directly linked to the measurement problem in quantum mechanics with its famous Schrödinger's cat paradox.
In philosophy, the philosophy of physics deals with conceptual and interpretational issues in modern physics, many of which overlap with research done by certain kinds of theoretical physicists. Historically, philosophers of physics have engaged with questions such as the nature of space, time, matter and the laws that govern their interactions, as well as the epistemological and ontological basis of the theories used by practicing physicists. The discipline draws upon insights from various areas of philosophy, including metaphysics, epistemology, and philosophy of science, while also engaging with the latest developments in theoretical and experimental physics.
John Stewart Bell FRS was a physicist from Northern Ireland and the originator of Bell's theorem, an important theorem in quantum physics regarding hidden-variable theories.
Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics. Prior to quantum physics, it was thought that
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.
Incompatibilism is the view that the thesis of determinism is logically incompatible with the classical thesis of free will. The term was coined in the 1960s, most likely by philosopher Keith Lehrer. The term compatibilism was coined to name the view that the classical free will thesis is logically compatible with determinism, i.e. it is possible for an ordinary human to exercise free will, even in a universe where determinism is true. These terms were originally coined for use within a research paradigm that was dominant among academics during the so-called "classical period" from the 1960s to 1980s, or what has been called the "classical analytic paradigm". Within the classical analytic paradigm, the problem of free will and determinism was understood as a compatibility question: "Is it possible for an ordinary human to exercise free will when determinism is true?" Those working in the classical analytic paradigm who answered "no" were incompatibilists in the original, classical-analytic sense of the term, now commonly called classical incompatibilists; they proposed that determinism precludes free will because it precludes the ability to do otherwise. Those who answered "yes" were compatibilists in the original sense of the term, now commonly called classical compatibilists. Given that classical free will theorists agreed that it is at least metaphysically possible for an ordinary human to exercise free will, all classical compatibilists accepted a compossibilist account of free will and all classical incompatibilists accepted a libertarian account of free will.
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.
A Bell test, also known as Bell inequality test or Bell experiment, is a real-world physics experiment designed to test the theory of quantum mechanics in relation to Albert Einstein's concept of local realism. Named for John Stewart Bell, the experiments test whether or not the real world satisfies local realism, which requires the presence of some additional local variables to explain the behavior of particles like photons and electrons. As of 2015, all Bell tests have found that the hypothesis of local hidden variables is inconsistent with the way that physical systems behave.
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 quantum mechanics, the Kochen–Specker (KS) theorem, also known as the Bell–KS theorem, is a "no-go" theorem proved by John S. Bell in 1966 and by Simon B. Kochen and Ernst Specker in 1967. It places certain constraints on the permissible types of hidden-variable theories, which try to explain the predictions of quantum mechanics in a context-independent way. The version of the theorem proved by Kochen and Specker also gave an explicit example for this constraint in terms of a finite number of state vectors.
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 quantum mechanics, superdeterminism is a loophole in Bell's theorem. By postulating that all systems being measured are correlated with the choices of which measurements to make on them, the assumptions of the theorem are no longer fulfilled. A hidden variables theory which is superdeterministic can thus fulfill Bell's notion of local causality and still violate the inequalities derived from Bell's theorem. This makes it possible to construct a local hidden-variable theory that reproduces the predictions of quantum mechanics, for which a few toy models have been proposed. In addition to being deterministic, superdeterministic models also postulate correlations between the state that is measured and the measurement setting.
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.
Quantum Theory: Concepts and Methods is a 1993 quantum physics textbook by Israeli physicist Asher Peres. Well-regarded among the physics community, it is known for unconventional choices of topics to include.
References
- Conway and Kochen, The Strong Free Will Theorem, published in Notices of the AMS. Volume 56, Number 2, February 2009.
- Rehmeyer, Julie (August 15, 2008). "Do Subatomic Particles Have Free Will?". Science News.
- Introduction to the Free Will Theorem, videos of six lectures given by J. H. Conway, Mar. 2009.
- Wüthrich, Christian (September 2011). "Can the World Beshown to be Indeterministic after all?". In Beisbart, Claus; Hartmann, Stephan (eds.). Can the world be shown to be indeterministic after all? (PDF). Probabilities in Physics. Oxford University Press. pp. 365–389. doi:10.1093/acprof:oso/9780199577439.003.0014. ISBN 978-0199577439.