052 Another Quantum Story: At the H-Bar

After the pair left, Erwin quickly went over to the cat in the box. He didn’t open the box at first, as he was still wondering about this state of superposition. He knew that this experiment posed a dilemma to the understanding of the atom. Max has raised one of the problems he still could not solve, what actually is the state of the cat in the box? A superposition of states was quite ridiculous; he could not picture what the cat would look like. Born jokingly said that it was a cat with 4.5 lives, instead of the typical 9, but a joke is a joke, and the problem still remains. Then there was the question from Max that he just managed to avoid, what if the box was opened? Commonsense told him that the state of superposition will never be seen, as he would either see a very angry cat or a dead one. What happens to the probability function? Earlier that year, he had wrote an equation that described the movement of the electron in an atom, but the equation, as he had told Albert and Max, could only give the probability of finding the electron at the point. He called it the wave function, while its square was a probability density function. His head was spinning and he knew Max and Albert will be returning with more questions, while he had no answers, so he decided to pay a visit to Copenhagen, with Heisenberg and Born, to discuss this problem. Of course, he remembered to open the box, and much to his relief, he found the cat alive. He gave the cat to the animal rights people who had just finished reading his book and there was much rejoicing. Erwin quickly packed his bags and left on the next train to Copenhagen.

At Copenhagen, he contacted his friends Heisenberg and Born, and they arranged to meet up at the H-Bar. After ordering a few bottles of wine, they settled down and Erwin revealed his problems…

Erwin: Just yesterday, Max and Albert visited me, and I designed an experiment to explain to them how our model of the atom works. I call it the Schrodinger Cat experiment.
Heisenberg: Those skeptics… so how did they take the idea?
Erwin: Well, Albert is still dissatisfied over how we still cannot certainly determine the position of the electron with absolute certainty, though now he understands how the electron works according to this model.
Born: Oh, he’s the deterministic scientist, isn’t he? You can never teach an old dog new tricks. So, what’s he up to now? Back to his General Unified Theory? It’s just another one of his pipe dreams, other than trying to disprove quantum theory.
Erwin: He’d better be, because the genius in him and Max managed to find a flaw in our model.
Heisenberg: Ah, that’s a problem. What is it?
Erwin: Let me start off by explaining the cat experiment…(explains the experiment again), now here’s the problem. Remember the wave function theory I proposed?
Born: Or the matrix mechanics theory we proposed? Yes, they are one and the same thing, anyway. Both methods will give us the probability of finding an electron at a certain point. There’s no problem with that, hundreds of scientists have verified the mathematics with repeated observations in the laboratory. Why, we’ll be getting Nobel Prizes for our work. How wrong can it be?
Erwin: Now, what if we opened the box? Remember, we would only either see a dead cat or a live cat. Before we open the box, the cat only existed as a wave function, but when we open the box, we do not see a cat in the state of superposition but in either one of the states. So, how do we explain this?
Heisenberg: Why don’t we allow for a collapse of the wave function? We know that the wave function is merely an abstract mathematical entity, which means that it is not a physical state of the cat, but merely a means for us to know the probability of the cat being dead or alive (incidentally, for those who are in the know about mathematics, the wave function is (dead> + alive>)/Ö2
Erwin: Great! But once we open the box, the entity becomes useless, because we can use classical means to measure its state, rather than using the abstract quantum method. Of course, this method can be applied to electron in the atom.
Heisenberg: Exactly, of course, we must not forget that even though the electron can be measured using classical means, it is still subject to the uncertainty priciple which I proposed, we cannot know exactly the position and the momentum of the electron at the same time, but nevertheless, its uncertainty in position is less complex than the state of superposition of all states as shown by the wavefunction.
Born: Well then, I propose we call this new synthesis of our theories the Copenhagen Interpretation, since we figured it out here in Copenhagen.
Erwin: Yes, a toast to our discovery...