Editing Probability (section)

==Relation to randomness and probability in quantum mechanics==
{{Main|Randomness}}
{{See also|Quantum fluctuation#Interpretations}}
In a [[determinism|deterministic]] universe, based on [[Newtonian mechanics|Newtonian]] concepts, there would be no probability if all conditions were known ([[Laplace's demon]]) (but there are situations in which [[chaos theory|sensitivity to initial conditions]] exceeds our ability to measure them, i.e. know them).  In the case of a [[roulette]] wheel, if the force of the hand and the period of that force are known, the number on which the ball will stop would be a certainty (though as a practical matter, this would likely be true only of a roulette wheel that had not been exactly levelled – as Thomas A. Bass' [[eudaemons|Newtonian Casino]] revealed).  This also assumes knowledge of inertia and friction of the wheel, weight, smoothness, and roundness of the ball, variations in hand speed during the turning, and so forth. A probabilistic description can thus be more useful than Newtonian mechanics for analyzing the pattern of outcomes of repeated rolls of a roulette wheel. Physicists face the same situation in the [[kinetic theory of gases]], where the system, while deterministic ''in principle'', is so complex (with the number of molecules typically the order of magnitude of the [[Avogadro constant]] {{val|6.02|e=23}}) that only a statistical description of its properties is feasible.<ref>Riedi, P.C. (1976). Kinetic Theory of Gases-I. In: Thermal Physics. Palgrave, London. https://doi.org/10.1007/978-1-349-15669-6_8</ref>

[[Probability theory]] is required to describe quantum phenomena.<ref>{{cite arXiv|last = Burgin|first= Mark|year =2010|title = Interpretations of Negative Probabilities|page= 1|class= physics.data-an|eprint=1008.1287v1}}</ref> A revolutionary discovery of early 20th century [[physics]] was the random character of all physical processes that occur at sub-atomic scales and are governed by the laws of [[quantum mechanics]]. The objective [[wave function]] evolves deterministically but, according to the [[Copenhagen interpretation]], it deals with probabilities of observing, the outcome being explained by a [[wave function collapse]] when an observation is made. However, the loss of [[determinism]] for the sake of [[instrumentalism]] did not meet with universal approval. [[Albert Einstein]] famously [[:de:Albert Einstein#Quellenangaben und Anmerkungen|remarked]] in a letter to [[Max Born]]: "I am convinced that God does not play dice".<ref>''Jedenfalls bin ich überzeugt, daß der Alte nicht würfelt.'' Letter to Max Born, 4 December 1926, in: [https://books.google.com/books?id=LQIsAQAAIAAJ&q=achtung-gebietend Einstein/Born Briefwechsel 1916–1955].</ref> Like Einstein, [[Erwin Schrödinger]], who [[Schrödinger equation#Historical background and development|discovered]] the wave function, believed quantum mechanics is a [[statistical]] approximation of an underlying deterministic [[reality]].<ref>{{cite book |last=Moore |first=W.J. |year=1992 |title=Schrödinger: Life and Thought |publisher=[[Cambridge University Press]] |page=479 |isbn= 978-0-521-43767-7}}</ref> In some modern interpretations of the statistical mechanics of measurement, [[quantum decoherence]] is invoked to account for the appearance of subjectively probabilistic experimental outcomes.