On Principles VI: Uncertainty Principle

"The uncertainty principle refers to the degree of indeterminateness in the possible present knowledge of the simultaneous values of various quantities with which the quantum theory deals; it does not restrict, for example, the exactness of a position measurement alone or a velocity measurement alone." (Werner Heisenberg, "The Uncertainty Principle", [in James R Newman, "The World of Mathematics" Vol. II], 1956)

"Both the uncertainty principle and the negentropy principle of information make Laplace's scheme [of exact determinism] completely unrealistic. The problem is an artificial one; it belongs to imaginative poetry, not to experimental science." (Léon Brillouin, "Science and Information Theory" 2^nd Ed., 1962)

"No branch of number theory is more saturated with mystery than the study of prime numbers: those exasperating, unruly integers that refuse to be divided evenly by any integers except themselves and 1. Some problems concerning primes are so simple that a child can understand them and yet so deep and far from solved that many mathematicians now suspect they have no solution. Perhaps they are 'undecideable'. Perhaps number theory, like quantum mechanics, has its own uncertainty principle that makes it necessary, in certain areas, to abandon exactness for probabilistic formulations." (Martin Gardner, "The remarkable lore of the prime numbers", Scientific American, 1964)

"In particular, the uncertainty principle has stood for a generation, barring the way to more detailed descriptions of nature; and yet, with the lesson of parity still fresh in our minds, how can anyone be quite so sure of its universal validity when we note that, to this day, it has never been subjected to even one direct experimental test?" (Edwin T Jaynes, "Foundations of Probability Theory and Statistical Mechanics", 1967)

"Because of mathematical indeterminancy and the uncertainty principle, it may be a law of nature that no nervous system is capable of acquiring enough knowledge to significantly predict the future of any other intelligent system in detail. Nor can intelligent minds gain enough self-knowledge to know their own future, capture fate, and in this sense eliminate free will." (Edward O Wilson, "On Human Nature", 1978)

"In physics, there are numerous phenomena that are said to be 'true on all scales', such as the Heisenberg uncertainty relation, to which no exception has been found over vast ranges of the variables involved (such as energy versus time, or momentum versus position). But even when the size ranges are limited, as in galaxy clusters (by the size of the universe) or the magnetic domains in a piece of iron near the transition point to ferromagnetism (by the size of the magnet), the concept true on all scales is an important postulate in analyzing otherwise often obscure observations." (Manfred Schroeder, "Fractals, Chaos, Power Laws Minutes from an Infinite Paradise", 1990)

"A bell curve shows the 'spread' or variance in our knowledge or certainty. The wider the bell the less we know. An infinitely wide bell is a flat line. Then we know nothing. The value of the quantity, position, or speed could lie anywhere on the axis. An infinitely narrow bell is a spike that is infinitely tall. Then we have complete knowledge of the value of the quantity. The uncertainty principle says that as one bell curve gets wider the other gets thinner. As one curve peaks the other spreads. So if the position bell curve becomes a spike and we have total knowledge of position, then the speed bell curve goes flat and we have total uncertainty (infinite variance) of speed." (Bart Kosko, "Fuzzy Thinking: The new science of fuzzy logic", 1993)

"According to quantum theory, the ground state, or lowest energy state, of a pendulum is not just sitting at the lowest energy point, pointing straight down. That would have both a definite position and a definite velocity, zero. This would be a violation of the uncertainty principle, which forbids the precise measurement of both position and velocity at the same time. The uncertainty in the position multiplied by the uncertainty in the momentum must be greater than a certain quantity, known as Planck's constant - a number that is too long to keep writing down, so we use a symbol for it: ħ." (Stephen W Hawking, "The Universe in a Nutshell", 2001)

"The uncertainty principle expresses a seesaw relationship between the fluctuations of certain pairs of variables, such as an electron's position and its speed. Anything that lowers the uncertainty of one must necessarily raise the uncertainty of the other; you can't push both down at the same time. For example, the more tightly you confine an electron, the more wildly it thrashes. By lowering the position end of the seesaw, you force the velocity end to lift up. On the other hand, if you try to constrain the electron's velocity instead, its position becomes fuzzier and fuzzier; the electron can turn up almost anywhere." (Steven Strogatz, "Sync: The Emerging Science of Spontaneous Order", 2003)

"The inherent nature of complexity is to doubt certainty and any pretense to finite and flawless data. Put another way, under uncertainty principles, any attempt by political systems to 'impose order' has an equal chance to instead 'impose disorder'." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)