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is this conclusion based on their finding that it's position is best described as some kind of probability distribution?

if so, that doesn't conclusively prove to me that it's random. for example, a coin's behavior is accurately given by the probability distribution

{(heads, 0.5), (tails, 0.5)} but a coin's behavior is not random. it is just very sensitive to initial conditions. but if the exact same hand position and forces are applied, the outcome will always be the same.

this is also related to the distribution of prime numbers. there is that formula which estimates how many primes are less than n.

randomness in a sequence means that if one tries to compress the sequence into a formulated function, the formula is not significantly smaller than the sequence itself. (i don't know the precise definition but that's the gist of it.)

let's say you're given a sequence (of data representing an electron's position, for example). how does one go about deciding if that sequence can be compressed into a formulated function that is significantly smaller than the sequence itself? even if you can decide that it is possible, how do you find the formula? after that, how do you find the shortest formula?

for example, since there are as many primes as there are natural numbers, there are many functions from N to P (the set of primes) that are bijections. is it possible to firgure out if any of those bijections are representable by formulas that are finite in length? furthermore, is it possible to determine whether or not you've got the shortest formula?

this all seems to be related to an article analog57 sent me and i think the answers are all negative. as far as i know, the state of things is that it can be proven that there are sequences that are random but always impossible to prove a particular sequence is random. in fact, "most" sequences are random, from what i understand. therefore, a sequence of numbers representing data of an electron's position cannot be proven to be random (or not random), if that is the case.

are physicists using a different definition of random than mathematicians (if they indeed think electron behavior is random)?

how was it established that there are no "hidden variables" that make the behavior appear random?