Truly random meaning uncaused and random meaning unpredictable. Is that right? How can a truly random process be governed by anything?
Events can be random individually, but in the aggregate lead to predictable behavior. The motion of individual molecules of a gas can be random, but the pressure exerted by the gas on the container might still obey gas laws. Radioactive decay may be completely random on the nuclear scale, but the decay of a gram of radium can still be predicted accurately using half-life equations.
The probability of an event occurring can be mathematically predictable, but the timing of an event on an individual scale can be utterly unpredictable.
Under a government which imprisons any unjustly, the true place for a just man is also in prison. Thoreau: Civil Disobedience (1846)
History will have to record that the greatest tragedy of this period of social transition was not the strident clamor of the bad people, but the appalling silence of the good people. Martin Luther King
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I'm a bit late to the game on this one, but according to current physical theory, two universes that began identically would not stay identical due to quantum mechanical fluctuations.
Regarding hidden variables (by which I mean the possibility that Quantum events are actually determined by some unknown physics) several results restrict these theories. We know that they would have to be: (a) non-local, communicate faster than light (b) contextual, particles are aware of and contain information on the state of every other particle in the universe (c) have essentially infinite complexity, each particle stores an infinite amount of data
Which I think is just as strange as quantum mechanics.
To add to Son Gokus response, a factor not accounted for in an equation could mess it up. But it's not possible to tell that human activity can mess it up in any other way. I've only seen one argument that purports to do so - and that is easily refuted.
Let us say an atom emits red light if it decays and green light if it remains undecayed. If this atom is next to a photosensitive chemical that contracts under green light and expands under red light, that would be an example of a classical system reacting differently depending on a quantum event.
In fact technically all nearby classical systems react differently to different outcomes of a quantum event. The quantum mechanical decays that power phosphorescence of certain minerals would result in completely different physical states of a cave wall the minerals were embedded in. Wouldn't this be the same as a human going to the right or left depending on the outcome.