Jared, Jordan:
I think quantum mechanics would only pose a problem for Objectivism if the rules change arbitrarily over time. Say one day you wake up and an electron exhibited only particle behavior and the next day it exhibited only wave behavior. The Objectivist metaphysics is grounded in Identity, not Causality. Jordan's formulation is unfortunate. In most cases physicists don't say an electron 35% exists. They say it exists as a quantum mechanical wave function and the position and momentum cannot be specified exactly until the wave function collapses, in which case we know the position exactly, but we know nothing about its momentum.
There are cases in subatomic physics where you have a collision between subatomic particles where energy is created and any number of combinations of particles could reform as long as certain conservation laws are obeyed. I would say this is a property of the energy created that is statistical, but I fail to see where this poses a problem for Objectivism.Also, there are cases where virtual particles (a particle and antiparticle) spontaneously appear out of spacetime. I would say this is a statistical property of spacetime and as long as the probability of these events remains constant under the same circumstances and conservation laws are obeyed globally, there is no problem.
I think the greatest problem caused by quantum mechanics in the Objectivist philosophy is for agent causation (i.e. Aristotelian entity action causality). However, remember the premise we accept when we call something an entity. We assume divisibility from the spacetime surrounding it. Agent causation is the most effective bookkeeping technique for keeping track of causality, but it too has its boundary conditions.
One last comment. It is unfortunate that there is so much misunderstanding around quantum mechanics. It is not a property of the fact that we "interact with the experiment" and it is not a "measurement problem". The Copenhagen interpretation of quantum mechanics has been proven experimentally in all kinds of experiments and many semiconductor and electronic devices are based on it. Also, the first motivation for Bohr discovering it in the first place was the atom was fundamentally unstable in a Maxwellian universe (the electrons would slowly emit energy until they collapsed into the atom's nucleus). I have included the simplest example I can think of, conceptually, below verifying the Copenhagen interpretation.
In nuclear fusion research, there is a method of catalyzing the fusion of two hydrogen nuclei called muon catalyzed fusion. The muon is a negatively charged elementary particle with a mass that is 207 times heavier than an electron. In order to catalyze the fusion a chemical bond is created between two hydrogen nuclei using a muon. Since the muon is so much heavier than an ordinary electron, the two hydrogen nuclei are brought much closer together than with an electron. The strong nuclear force then binds the two hydrogen nuclei together.
But here’s where it gets interesting! If the two hydrogen nuclei were really point particles with a definite position and momentum, they would not fuse. They would be too far apart for the strong nuclear force to act. In actuality, what happens is that the quantum mechanical wave functions of the two hydrogen nuclei overlap and at the two extreme ends and come close enough to fuse.
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