Quote from aphexcoil:
One could also argue that there is no such thing as randomness. If all laws of the universe are deterministic, then it is our inability to take into account all variables to explain what otherwise appears chaotic.
However, in the book, "Does God Play Dice with the Universe," the author explains that, no matter how accurately we measure a specific action, movement or process, we are inable to measure it with infinite precision. Anything less than this introduces great unknowns some X time period into the future.
I cannot think of one process in the universe that is truly random. Even in quantum physics, both possibilities occur but then split off into other universes.
The uncertainty principle
http://www.mtnmath.com/whatth/node53.html
Uncertainty in quantum mechanics is not connected to the probabilistic nature of the wave function. It is inherent in any wave function including those in classical physics. The inability to assign exact position and momentum to a particle may only mean that there is no such thing. The inability to make those assignments need not be an obstacle to deterministic predictions. For classical waves frequency and location cannot be simultaneously assigned, but those models are completely deterministic.
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In 1932 the renowned mathematician and physicist von Neumann published a proof that no more complete theory could be consistent with the predictions of quantum mechanics[27][26]. Von Neumann's reputation was so great that the proof stood for thirty years in spite of Bohm's publication in 1952 of a more complete theory that was consistent with quantum mechanics [7]. Bohm thought at the time there were subtle differences in the predictions of the two theories and thus his result did not contradict von Neumann's proof.
In 1966 Bell published a paper revealing a problem with von Neumann's proof[5]. The mathematics was fine but the assumptions von Neumann made about the constraints a more complete theory had to meet were not justified. Bell went on to show that quantum mechanics was not a local theory. Bohm's theory was an explicitly nonlocal theory and Bohm's work was an important influence for Bell. This story continues in Section 6.4.
Locality and quantum mechanics
http://www.mtnmath.com/whatth/node57.html
Locality is the denial of action at a distance It requires that all the information useful in predicting what will happen at a given location and time is contained in a sphere of influence. For an event that will occur in one second the sphere has a radius of 300,000 kilometers, the distance light travels in one second6.1.
Locality is the most powerful simplifying assumption in physics. Without it any event no matter how distant can influence any other event. Prediction would be impossible without locality or some other powerful restriction on what events can affect other events. Otherwise one would need to know the state of the universe to predict anything. Quantum mechanics is a local theory in configuration space but not in physical space.
As mentioned in Section 5.10 Bell refuted von Neumann's proof that no more complete theory could be consistent with quantum mechanics. In proving this Bell was influenced by Bohm's development of a more complete theory that was explicitly nonlocal. This led him to a proof that no local theory with hidden variables could reproduce the statistical predictions of quantum mechanics. Hidden variables were defined by Bell in a general way to include any more complete theory with a mechanism for explaining the conservation laws. He suggested that it should be possible to test some of the nonlocal predictions experimentally[4].
Realistic theories and randomness
http://www.mtnmath.com/whatth/node58.html
Often Bell's result is presented as showing that quantum mechanics is not a realistic theory rather than showing that it is nonlocal. The focus is on the reference to hidden variables in Bell's proof. Eberhard developed a version of Bell's argument that did not involve hidden variables[13]. In turn some physicists objected to Eberhard's proof because he assumed "contrafactual definiteness". That is he assumed one could argue about all possible outcomes of an experiment including those that did not happen.
Arguments like those about hidden variables and contrafactual definiteness are philosophical. They have no clear resolution unlike problems that can be formulated mathematically. Such arguments are rare in the hard sciences. They occur here because of the claim in quantum mechanics that probabilities are fundamental or irreducible.
There is no mathematical model for irreducible probabilities. There is not even a mathematically definition of a random number sequence. There are sequences that are recursively random. Loosely speaking this means that no recursive process can do better than chance at guessing the next element in the sequence. The problem with recursively random sequences is that they are more complex than any recursive sequence. If somehow one could generate such a sequence one could use it to solve recursively unsolvable problems.
This suggests that a truly random sequence cannot exist. Any sequence that we would consider to be truly random must be recursively random. Otherwise there is some computer program that can guess with some degree of accuracy the elements in the sequence. Yet no recursive random sequence can be truly random. This presents a philosophical problem for the claim that quantum mechanics is truly random.
The randomness claimed for quantum mechanics has no foundation in mathematics and it appears to be impossible to construct such a foundation. This does not make it wrong but suggests there are problems in our existing conceptual framework. It also means that physicists when arguing about these issues are debating philosophy with no objective way of deciding the issue.
