Ensemble interpretation The ensemble interpretation, or statistical interpretation of quantum mechanics, is an interpretation that can be viewed as a minimalist interpretation; it is a quantum mechanical interpretation that claims to make the fewest assumptions associated with the standard mathematical formalization. At its heart, it takes to the fullest extent the statistical interpretation of Max Born for which he won the Nobel Prize in Physics.[1] The interpretation states that the wave function does not apply to an individual system – or for example, a single particle – but is an abstract mathematical, statistical quantity that only applies to an ensemble of similarly prepared systems or particles. Probably the most notable supporter of such an interpretation was Albert Einstein: To date, probably the most prominent advocate of the ensemble interpretation is Leslie E. Ballentine, Professor at Simon Fraser University, and writer of the graduate-level textbook "Quantum Mechanics, A Modern Development".[3]
Consistent histories In quantum mechanics, the consistent histories approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology.[1] This interpretation of quantum mechanics is based on a consistency criterion that then allows probabilities to be assigned to various alternative histories of a system such that the probabilities for each history obey the rules of classical probability while being consistent with the Schrödinger equation. In contrast to some interpretations of quantum mechanics, particularly the Copenhagen interpretation, the framework does not include "wavefunction collapse" as a relevant description of any physical process, and emphasizes that measurement theory is not a fundamental ingredient of quantum mechanics. Histories[edit] A homogeneous history (here labels different histories) is a sequence of Propositions specified at different moments of time is true at time
Hidden variable theory Albert Einstein, the most famous proponent of hidden variables, objected to the fundamentally probabilistic nature of quantum mechanics,[1] and famously declared "I am convinced God does not play dice".[2] Einstein, Podolsky, and Rosen argued that "elements of reality" (hidden variables) must be added to quantum mechanics to explain entanglement without action at a distance.[3][4] Later, Bell's theorem would suggest (in the opinion of most physicists and contrary to Einstein's assertion) that local hidden variables of certain types are impossible. The most famous nonlocal theory is de Broglie-Bohm theory. Motivation[edit] Under the orthodox Copenhagen interpretation, quantum mechanics is nondeterministic, 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. "God does not play dice"[edit] .
Many-worlds interpretation The quantum-mechanical "Schrödinger's cat" paradox according to the many-worlds interpretation. In this interpretation, every event is a branch point; the cat is both alive and dead, even before the box is opened, but the "alive" and "dead" cats are in different branches of the universe, both of which are equally real, but which do not interact with each other.[1] The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction and denies the actuality of wavefunction collapse. The original relative state formulation is due to Hugh Everett in 1957.[3][4] Later, this formulation was popularized and renamed many-worlds by Bryce Seligman DeWitt in the 1960s and 1970s.[1][5][6][7] The decoherence approaches to interpreting quantum theory have been further explored and developed,[8][9][10] becoming quite popular. Before many-worlds, reality had always been viewed as a single unfolding history. Outline[edit] Wojciech H.
De Broglie–Bohm theory The de Broglie–Bohm theory, also known as the pilot-wave theory, Bohmian mechanics, the Bohm or Bohm's interpretation, and the causal interpretation, is an interpretation of quantum theory. In addition to a wavefunction on the space of all possible configurations, it also includes an actual configuration, even when unobserved. The evolution over time of the configuration (that is, of the positions of all particles or the configuration of all fields) is defined by the wave function via a guiding equation. The evolution of the wave function over time is given by Schrödinger's equation. The theory is named after Louis de Broglie (1892–1987) and David Bohm (1917–1992). The de Broglie–Bohm theory is explicitly nonlocal: the velocity of any one particle depends on the value of the guiding equation, which depends on the whole configuration of the universe. The theory is deterministic. Overview[edit] De Broglie–Bohm theory is based on the following postulates: Where is the momentum operator. . .
Objective collapse theory Objective collapse theories are an approach to the interpretational problems of quantum mechanics. They are realistic, indeterministic and reject hidden variables. The approach is similar to the Copenhagen interpretation, but more firmly objective. The most well-known examples of such theories are: Compared to other approaches[edit] Collapse theories stand in opposition to many-worlds interpretation theories, in that they hold that a process of wavefunction collapse curtails the branching of the wavefunction and removes unobserved behaviour. Variations[edit] Objective collapse theories regard the present formalism of quantum mechanics as incomplete, in some sense. Collapse is found "within" the evolution of the wavefunction, often by modifying the equations to introduce small amounts of non-linearity. Objections[edit] The fact that these theories seek to extend the formalism is considered as violation of the principle of parsimony by some. GRW collapse theories have unique problems.
Quantum logic Quantum logic can be formulated either as a modified version of propositional logic or as a noncommutative and non-associative many-valued (MV) logic.[1][2][3][4][5] Quantum logic has some properties which clearly distinguish it from classical logic, most notably, the failure of the distributive law of propositional logic: p and (q or r) = (p and q) or (p and r), where the symbols p, q and r are propositional variables. p = "the particle has momentum in the interval [0, +1/6]" q = "the particle is in the interval [−1, 1]" r = "the particle is in the interval [1, 3]" (using some system of units where the reduced Planck's constant is 1) then we might observe that: p and (q or r) = true in other words, that the particle's momentum is between 0 and +1/6, and its position is between −1 and +3. (p and q) or (p and r) = false Thus the distributive law fails. Introduction[edit] is commutative and associative.There is a maximal element 1, and for any b..The orthomodular law: If then . Theorem. Theorem.
Relational quantum mechanics This article is intended for those already familiar with quantum mechanics and its attendant interpretational difficulties. Readers who are new to the subject may first want to read the introduction to quantum mechanics. Relational quantum mechanics (RQM) is an interpretation of quantum mechanics which treats the state of a quantum system as being observer-dependent, that is, the state is the relation between the observer and the system. This interpretation was first delineated by Carlo Rovelli in a 1994 preprint, and has since been expanded upon by a number of theorists. It is inspired by the key idea behind Special Relativity, that the details of an observation depend on the reference frame of the observer, and uses some ideas from Wheeler on quantum information.[1] The physical content of the theory is not to do with objects themselves, but the relations between them. History and development[edit] The problem of the observer observed[edit] , measuring the state of the quantum system . .
Stochastic interpretation The stochastic interpretation is an interpretation of quantum mechanics. The modern application of stochastics to quantum mechanics involves the assumption of spacetime stochasticity, the idea that the small-scale structure of spacetime is undergoing both metric and topological fluctuations (John Archibald Wheeler's "quantum foam"), and that the averaged result of these fluctuations recreates a more conventional-looking metric at larger scales that can be described using classical physics, along with an element of nonlocality that can be described using quantum mechanics. A stochastic interpretation of quantum mechanics due to persistent vacuum fluctuations is suggested by Roumen Tsekov. The main idea is that vacuum (or spacetime) fluctuations are the reason for quantum mechanics and not a result of it how it is usually considered. See also[edit] References[edit] Edward Nelson (1966).
Transactional interpretation More recently, he has also argued TIQM to be consistent with the Afshar experiment, while claiming that the Copenhagen interpretation and the many-worlds interpretation are not.[3] The existence of both advanced and retarded waves as admissible solutions to Maxwell's equations was explored in the Wheeler–Feynman absorber theory. Cramer revived their idea of two waves for his transactional interpretation of quantum theory. While the ordinary Schrödinger equation does not admit advanced solutions, its relativistic version does, and these advanced solutions are the ones used by TIQM. Cramer uses TIQM in teaching quantum mechanics at the University of Washington in Seattle. Advances over previous interpretations[edit] The transactional interpretation has similarities with the two-state vector formalism (TSVF)[5] which has its origin in work by Yakir Aharonov, Peter Bergmann and Joel Lebowitz of 1964.[6][7] Recent developments[edit] Debate[edit] TIQM faces a number of common criticisms. 1. 2. 3.