Hidden variable theory

In physics, hidden-variable theories are held by some physicists who argue that the state of a physical system, as formulated by quantum mechanics, does not give a complete description for the system. An example would be that quantum mechanics is ultimately incomplete, and that a complete theory would provide descriptive categories to account for all observable behavior and thus avoid any indeterminism. In another version, the hidden-variables are inaccessible to us and thus in principle not detectable. The existence of indeterminacy for some measurements is a characteristic of prevalent interpretations of quantum mechanics; moreover, bounds for indeterminacy can be expressed in a quantitative form by the Heisenberg uncertainty principle.Here the whole problem of determinism comes up. From the standpoint of our quantum mechanics there is no quantity which in any individual case causally fixes the consequence of the collision; but also experimentally we have so far no reason to believe that there are some inner properties of the atom which conditions a definite outcome for the collision. Ought we to hope later to discover such properties ... and determine them in individual cases? Or ought we to believe that the agreement of theory and experiment—as to the impossibility of prescribing conditions for a causal evolution—is a pre-established harmony founded on the nonexistence of such conditions? I myself am inclined to give up determinism in the world of atoms. But that is a philosophical question for which physical arguments alone are not decisive.Quantum mechanics is very worthy of regard. But an inner voice tells me that this is not yet the right track. The theory yields much, but it hardly brings us closer to the Old One's secrets. I, in any case, am convinced that He does not play dice.hile we consider ... a quantum mechanical treatment of the electromagnetic field ... as not yet finished, we consider quantum mechanics to be a closed theory, whose fundamental physical and mathematical assumptions are no longer susceptible of any modification....On the question of the 'validity of the law of causality' we have this opinion: as long as one takes into account only experiments that lie in the domain of our currently acquired physical and quantum mechanical experience, the assumption of indeterminism in principle, here taken as fundamental, agrees with experience.Consider a mechanical system consisting of two partial systems A and B which interact with each other only during a limited time. Let the ψ function before their interaction be given. Then the Schrödinger equation will furnish the ψ function after the interaction has taken place. Let us now determine the physical state of the partial system A as completely as possible by measurements. Then quantum mechanics allows us to determine the ψ function of the partial system B from the measurements made, and from the ψ function of the total system. This determination, however, gives a result which depends upon which of the physical quantities (observables) of A have been measured (for instance, coordinates or momenta). Since there can be only one physical state of B after the interaction which cannot reasonably be considered to depend on the particular measurement we perform on the system A separated from B it may be concluded that the ψ function is not unambiguously coordinated to the physical state. This coordination of several ψ functions to the same physical state of system B shows again that the ψ function cannot be interpreted as a (complete) description of a physical state of a single system. Einstein, Podolsky and Rosen contains an ambiguity as regards the meaning of the expression 'without in any way disturbing a system.' ... ven at this stage , there is essentially the question of an influence on the very conditions which define the possible types of predictions regarding the future behavior of the system. Since these conditions constitute an inherent element of the description of any phenomenon to which the term 'physical reality' can be properly attached, we see that the argumentation of the mentioned authors does not justify their conclusion that quantum-mechanical description is essentially incomplete.'As a more appropriate way of expression, one may strongly advocate limitation of the use of the word phenomenon to refer exclusively to observations obtained under specified circumstances, including an account of the whole experiment.'If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity. In physics, hidden-variable theories are held by some physicists who argue that the state of a physical system, as formulated by quantum mechanics, does not give a complete description for the system. An example would be that quantum mechanics is ultimately incomplete, and that a complete theory would provide descriptive categories to account for all observable behavior and thus avoid any indeterminism. In another version, the hidden-variables are inaccessible to us and thus in principle not detectable. The existence of indeterminacy for some measurements is a characteristic of prevalent interpretations of quantum mechanics; moreover, bounds for indeterminacy can be expressed in a quantitative form by the Heisenberg uncertainty principle. Albert Einstein objected to the fundamentally probabilistic nature of quantum mechanics, and famously declared 'I am convinced God does not play dice'. Einstein, Podolsky, and Rosen argued that quantum mechanics is an incomplete description of reality. Later, Bell's theorem, suggested that local hidden variables, a way for finding a complete description of reality, of certain types are impossible, or that they evolve non-locally. A famous non-local theory is the De Broglie–Bohm theory. Under the Copenhagen interpretation, quantum mechanics is non-deterministic, meaning that it generally does not predict the outcome of any measurement with certainty. Instead, it indicates what the probabilities of the outcomes are, with the indeterminism of observable quantities constrained by the uncertainty principle. The question arises whether there might be some deeper reality hidden beneath quantum mechanics, to be described by a more fundamental theory that can always predict the outcome of each measurement with certainty: if the exact properties of every subatomic particle were known the entire system could be modeled exactly using deterministic physics similar to classical physics. In other words, it is conceivable that the standard interpretation of quantum mechanics is an incomplete description of nature. The designation of variables as underlying 'hidden' variables depends on the level of physical description (so, for example, 'if a gas is described in terms of temperature, pressure, and volume, then the velocities of the individual atoms in the gas would be hidden variables'). Physicists supporting De Broglie–Bohm theory maintain that underlying the observed probabilistic nature of the universe is a deterministic objective foundation/property—the hidden variable. Others, however, believe that there is no deeper deterministic reality in quantum mechanics. A lack of a kind of realism (understood here as asserting independent existence and evolution of physical quantities, such as position or momentum, without the process of measurement) is crucial in the Copenhagen interpretation. Realistic interpretations (which were already incorporated, to an extent, into the physics of Feynman), on the other hand, assume that particles have certain trajectories. Under such view, these trajectories will almost always be continuous, which follows both from the finitude of the perceived speed of light ('leaps' should rather be precluded) and, more importantly, from the principle of least action, as deduced in quantum physics by Dirac. But continuous movement, in accordance with the mathematical definition, implies deterministic movement for a range of time arguments; and thus realism is, under modern physics, one more reason for seeking (at least certain limited) determinism and thus a hidden-variable theory (especially that such theory exists: see De Broglie–Bohm interpretation). Although determinism was initially a major motivation for physicists looking for hidden-variable theories, non-deterministic theories trying to explain what the supposed reality underlying the quantum mechanics formalism looks like are also considered hidden-variable theories; for example Edward Nelson's stochastic mechanics. In June 1926, Max Born published a paper, 'Zur Quantenmechanik der Stoßvorgänge' ('Quantum Mechanics of Collision Phenomena') in the scientific journal Zeitschrift für Physik, 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: Born's interpretation of the wave function was criticized by Schrödinger, who had previously attempted to interpret it in real physical terms, but Albert Einstein's response became one of the earliest and most famous assertions that quantum mechanics is incomplete: Niels Bohr reportedly replied to Einstein's later expression of this sentiment by advising him to 'stop telling God what to do.'