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Hidden-variable theory AI simulator
(@Hidden-variable theory_simulator)
Hub AI
Hidden-variable theory AI simulator
(@Hidden-variable theory_simulator)
Hidden-variable theory
In physics, a hidden-variable theory is a deterministic model which seeks to explain the probabilistic nature of quantum mechanics by introducing additional, possibly inaccessible, variables.
The mathematical formulation of quantum mechanics assumes that the state of a system prior to measurement is indeterminate; quantitative bounds on this indeterminacy are expressed by the Heisenberg uncertainty principle. Most hidden-variable theories are attempts to avoid this indeterminacy, but possibly at the expense of requiring that nonlocal interactions be allowed. One notable, nonlocal hidden-variable theory is the de Broglie–Bohm theory.
In their 1935 EPR paper, Albert Einstein, Boris Podolsky, and Nathan Rosen argued that quantum entanglement might imply that quantum mechanics is an incomplete description of reality. John Stewart Bell in 1964, in his eponymous theorem proved that correlations between particles under any local hidden variable theory must obey certain constraints. Subsequently, Bell test experiments have demonstrated broad violation of these constraints, ruling out such theories. Bell's theorem, however, does not rule out the possibility of nonlocal theories or superdeterminism; these therefore cannot be falsified by Bell tests.
Macroscopic physics requires classical mechanics which allows accurate predictions of mechanical motion with reproducible, high precision. Quantum phenomena require quantum mechanics, which allows accurate predictions of statistical averages only. If quantum states had hidden-variables awaiting ingenious new measurement technologies, then arbitrarily high precision results might be possible.
This classical mechanics description would eliminate unsettling characteristics of quantum theory like the uncertainty principle. More fundamentally however, a successful model of quantum phenomena with hidden variables implies quantum entities with intrinsic values independent of measurements. Existing quantum mechanics asserts that state properties can only be known after a measurement. As N. David Mermin puts it:
It is a fundamental quantum doctrine that a measurement does not, in general, reveal a pre-existing value of the measured property. On the contrary, the outcome of a measurement is brought into being by the act of measurement itself...
In other words, whereas a hidden-variable theory would imply intrinsic particle properties, in quantum mechanics an electron has no definite position and velocity to even be revealed.
In June 1926, Max Born published a paper, in which he was the first to clearly enunciate the probabilistic interpretation of the quantum wave function, which had been introduced by Erwin Schrödinger earlier in the year. Born concluded the paper as follows:
Hidden-variable theory
In physics, a hidden-variable theory is a deterministic model which seeks to explain the probabilistic nature of quantum mechanics by introducing additional, possibly inaccessible, variables.
The mathematical formulation of quantum mechanics assumes that the state of a system prior to measurement is indeterminate; quantitative bounds on this indeterminacy are expressed by the Heisenberg uncertainty principle. Most hidden-variable theories are attempts to avoid this indeterminacy, but possibly at the expense of requiring that nonlocal interactions be allowed. One notable, nonlocal hidden-variable theory is the de Broglie–Bohm theory.
In their 1935 EPR paper, Albert Einstein, Boris Podolsky, and Nathan Rosen argued that quantum entanglement might imply that quantum mechanics is an incomplete description of reality. John Stewart Bell in 1964, in his eponymous theorem proved that correlations between particles under any local hidden variable theory must obey certain constraints. Subsequently, Bell test experiments have demonstrated broad violation of these constraints, ruling out such theories. Bell's theorem, however, does not rule out the possibility of nonlocal theories or superdeterminism; these therefore cannot be falsified by Bell tests.
Macroscopic physics requires classical mechanics which allows accurate predictions of mechanical motion with reproducible, high precision. Quantum phenomena require quantum mechanics, which allows accurate predictions of statistical averages only. If quantum states had hidden-variables awaiting ingenious new measurement technologies, then arbitrarily high precision results might be possible.
This classical mechanics description would eliminate unsettling characteristics of quantum theory like the uncertainty principle. More fundamentally however, a successful model of quantum phenomena with hidden variables implies quantum entities with intrinsic values independent of measurements. Existing quantum mechanics asserts that state properties can only be known after a measurement. As N. David Mermin puts it:
It is a fundamental quantum doctrine that a measurement does not, in general, reveal a pre-existing value of the measured property. On the contrary, the outcome of a measurement is brought into being by the act of measurement itself...
In other words, whereas a hidden-variable theory would imply intrinsic particle properties, in quantum mechanics an electron has no definite position and velocity to even be revealed.
In June 1926, Max Born published a paper, in which he was the first to clearly enunciate the probabilistic interpretation of the quantum wave function, which had been introduced by Erwin Schrödinger earlier in the year. Born concluded the paper as follows: