Continuing the thread from yesterday…
ON DETERMINISM
In the first post I explained that quantum mechanics teaches us that we cannot know the state of a particle until we measure it. Andre Parsa responded, “each particle does have its own absolute state, a position and velocity etc. [It] is not random, only difficult to measure.”
If Andre is right, then I will concede that the Universe is deterministic. My claim that the future is undetermined relies upon the assumption that particles do not have absolute states. It turns out our disagreement gets right to the heart of quantum mechanics, but to examine it more closely requires bringing the “wave function” into the discussion.
The quantum mechanical wave function depends on both position and time. Manipulated in this way or that, it provides information about its system. For example, if you square the wave function you obtain the probability that a particle exists in the vicinity of position 
Let’s further separate these two philosophical interpretations by asking the question, “What was the state of the particle just before measurement?” Andre would say, “I don’t know, but it definitely had one.” I would say, “There was no state. It was all states and no states. It wasn’t anything at all until we measured it.” Given that we can never measure a particle’s position immediately before we measure it, this problem seems intractable.
But Einstein, Podolsky, and Rosen (the latter two also physicists) couldn’t help but think that as a theory quantum mechanics was incomplete. They introduced a thought experiment known as the EPR Paradox to illustrate. They considered the decay of a neutral Ï€ meson into an electron and positron, the latter two flying off in opposing directions towards opposite sides of the Universe. Through conservation of momentum, when one is measured to be spin-up the other must be spin-down.
Andre would say, “Of course! One actually was spin-up and the other actually was spin-down. When we measured we figured out which was which.” He would then go on to criticize me further by saying, “If you honestly believe that measuring the electron’s spin caused it to be spin-up, then the ‘message’ that the positron must consequently be spin-down would have had to travel across the Universe instantaneously to assure that any measurement of the positron would reveal as much, and as we all know information doesn’t travel faster than the speed of light, so there.”
At this point EPR and A would all smile satisfied smiles while humbly admitting that their version of quantum mechanics wasn’t perfect. There was some unknown quantity, some hidden variable within the quantum mechanical wave function that had yet to reveal itself. If the Universe was truly deterministic then such a variable testifying to the particle’s state must exist. The challenge would be finding it.
And people tried. Many “hidden variable theories” were proposed, but none worked. Then, in 1964, my champion, J. S. Bell, proved that any local hidden variable theory is fundamentally incompatible with quantum mechanics. Einstein once famously quipped that “God doesn’t play dice,” a statement which served as a slap in the face to the Copenhagen interpretation. Had he still been alive at the time of its publication in 1964, Bell’s theorem would have caused him to spit his drink all over the Baccarat table. And in case you’re wondering, there have been many tests of Bell’s Theorem. They have all confirmed its veracity.
This result plays a large part in my belief that the Universe is not deterministic. Assuming quantum mechanics is correct (a fairly safe assumption at this point), there’s no hidden information (as represented by an unknown variable) within the wave function of which we’re unaware. There CAN’T BE. Therefore the measurement (more technically the perturbation) of that aforementioned electron does determine its spin state, and that reality is somehow conveyed to the positron in the form of its opposite spin state.
PR and Andre (Einstein is wiping himself off at the bar) make one last gasp, “But even if we’re wrong, you still can’t explain how information about the electron’s spin can travel instantly across the Universe and effect the positron’s spin. That would violate causality! We may not win, but neither do you.”
Sure, but only if you agree that “information is being sent.” So let’s say the electron is measured as spin-up while simultaneously, a million light years away the positron is measured as spin-down. I claim that no information has been conveyed between those two positions. Why, you ask? Because the experimenter at the positron has no idea whether the electron has been measured yet. All he knows is his positron is spin-down. The only way this “spooky action at a distance” information is revealed is when the two experimenters travel (causally) to each other to compare data.
While we physicists certainly don’t have all the answers when it comes to quantum mechanics, the facts as we know them now more strongly support a random Universe than a deterministic one. Given that particles lack absolute states, it’s impossible to claim they will evolve identically, and therefore the future progress of all particles was not inevitably set in motion after the moments of the Big Bang.
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