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So I ask, is there a formula for true random?
If there is no formula which produces true randomness, then is there anything within this universe which is random? If we restarted the Universe all over again, would the universe produce a different result?
Originally posted by LiveEquation
How come no one said anything about my experimental design...if randomness exists, then there should be a random particle that follows no laws...
Originally posted by john_bmth
Why would a random particle that obeys no laws be a requisite for randomness in nature? I see no basis for this.
Originally posted by confreak
reply to post by Havick007
Does chaos theory try explain why some things are hard to predict, for example weather patterns etc? That's what I'm getting as I read Wikipedia.
In that sense chaos theory agrees that there is no such thing as random? Rather either we don't know all the variables, or we just don't have precise enough equipment to calculate the exact variables, hence its sensitive dependency. Am I reading this correctly?
Werner Heisenberg (5 December 1901 – 1 February 1976) was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory. In addition, he made important contributions to nuclear physics, quantum field theory, and particle physics.
In 1925, following pioneering work with Hendrik Kramers, Heisenberg developed matrix mechanics, which replaced the ad-hoc old quantum theory with modern quantum mechanics. The central assumption was that the classical concept of motion does not fit at the quantum level, and that electrons in an atom did not travel on sharply defined orbits. Rather, the motion was smeared out in a strange way: the Fourier transform of time only involving those frequencies that could be seen in quantum jumps.
Heisenberg's paper did not admit any unobservable quantities like the exact position of the electron in an orbit at any time; he only allowed the theorist to talk about the Fourier components of the motion. Since the Fourier components were not defined at the classical frequencies, they could not be used to construct an exact trajectory, so that the formalism could not answer certain overly precise questions about where the electron was or how fast it was going.
The most striking property of Heisenberg's infinite matrices for the position and momentum is that they do not commute. Heisenberg's canonical commutation relation indicates by how much:
[X,P] = X P - P X = i \hbar (see derivations below)
A mathematical statement of the principle is that every quantum state has the property that the root mean square (RMS) deviation of the position from its mean (the standard deviation of the x-distribution):
\sigma_x = \sqrt[\langle(x - \langle x\rangle)^2\rangle] \,
times the RMS deviation of the momentum from its mean (the standard deviation of p):
\sigma_p = \sqrt[\langle(p - \langle p \rangle)^2\rangle] \,
can never be smaller than a fixed fraction of Planck's constant:
\sigma_x \sigma_p \ge \hbar/2.
The uncertainty principle can be restated in terms of other measurement processes, which involves collapse of the wavefunction. When the position is initially localized by preparation, the wavefunction collapses to a narrow bump in an interval Δx > 0, and the momentum wavefunction becomes spread out. The particle's momentum is left uncertain by an amount inversely proportional to the accuracy of the position measurement:
\sigma_p \,\ge\,\pi\hbar/\Delta x.
If the initial preparation in Δx is understood as an observation or disturbance of the particles then this means that the uncertainty principle is related to the observer effect. However, this is not true in the case of the measurement process corresponding to the former inequality but only for the latter inequality.