I'll treat chapter 5 of George Gamow's classic, Thirty Years That Shook Physics in one post.
The previous posts were:
1a. Planck's Quantum
1b. Jumping Photons (Einstein and the Photoelectric Effect)
1c. The Compton Effect (Proof of Energy Packets)
2a. Thomson and Rutherford's Atoms
2b. Bohr's Contributions (How electrons fill the atom)
3a. Pauli Exclusion Principle (no two electrons at any one energy state)
3b. The Pauli Neutrino
4a. De Broglie's Wavy Particles
4b. Schrödinger's Wave Equation
1. The plot thickens. A year before Schrödinger produced his famous wave equation, Werner Heisenberg had produced a different mathematical model that came to the same conclusion. The model he used was matrix mechanics. Without knowing it, he reinvented linear algebra, which had been invented about a hundred years earlier. Although at first it wasn't clear if the two approaches said the same thing, Schrödinger eventually showed that they did.
More significant, however, was Heisenberg's famous equation ΔpΔq=h/4π. Although I do not yet fully grasp the basis of this equation, it seems to be saying that the uncertainty in the momentum of a particle and the uncertainty in the position of a particle having a complementarity such that the more certainty with which the one is defined, the less certainty with which the other is defined. This is the famous Uncertainty Principle.
What has always stuck in my craw about this principle (and in the craw of Einstein, Schrödinger, possibly Dirac) is the positivistic interpretation that Niels Bohr gave to it and that became the religion of the Copenhagen cult. Gamow belonged to this group, so it is no surprise that his explanation of the principle has an underlying positivism.
Positivism is the philosophy that claims that, if something cannot be observed, it is not real. It's fundamental flaw is of course that you cannot observe and verify the claim of previous sentence. Positivism is, at its most basic foundations, based on an unobservable assumption.
"If a tree falls in the forest, and no one is there to hear it, does it make a noise?" The positivists in effect said "no." I think they are loonies. For Bohr, if you can't measure the position or momentum of a particle precisely, because you inevitably change it in measuring it, it doesn't exist.
So when you read Gamow's interpretation of the principle, it is all about how in measuring the momentum of a particle, you end up changing its position. Similarly, if you measure the position of a particle, you change its momentum. Gamow also gives the notorious exchange between Bohr and Einstein at the 1930 Solvay Conference in which Einstein disputed an uncertainty between energy and time ΔEΔt=h/4π. Bohr won all those exchanges.
2. The Copenhagen philosophy, forged by Bohr, is the complementarity principle. Bohr expressed it in this way: "any given application of classical concepts precludes the simultaneous use of other classical concepts which in a different connection are equally necessary for the elucidation of phenomena" (210, Quantum Generations). Einstein's final counter was in 1935 which argued for realism, but it was largely ignored at the time.
I reject positivism as absurd. But Heisenburg's principle ΔpΔq=h/4π stands. The question is thus how to interpret it philosophically. On the one hand is Einstein's tact and eventually that of Schrödinger. Just because you don't know the momentum or position doesn't mean it doesn't have one. Thus the famous Schrödinger's cat Gedankenexperiment.
Say a cat is in a box and there is a chance that radiation has gone off and killed the cat but you don't know if the cat is dead because there is a certain probability it has and a certain probability it hasn't. But, as Schrödinger pointed out, you could actually open the box and see if the cat is alive or dead. Bohr thought this large world example was irrelevant to the quantum world.
Einstein suggested that there might be unknown variables involved that would circumvent these uncertainty relationships. He did not think God, as he wrote Born, played dice. von Neumann actually produced somewhat of a mathematical proof that unknown variables were not involved, but later examination suggests he only showed that some unknown variables of certain kinds are not involved.
I am not in a "position" to have much of an opinion at this time. I reject that the issue is a matter of our observation. If there is indeterminacy then it is an uncertainty intrinsic to reality irrespective of our observation of it. But I will leave it at that for now.
I end with a joke in Amazing Stories. "Werner Heisenburg is pulled over for speeding by a highway patrolman. The police officer walks over to Werner's car, leans over, and asks Heisenburg, 'Do you know how fast you were going?' Heisenberg replies, 'No, but I know where I am'" (82).