Thursday, December 8, 2011

Quantum Leap or Superposition?

Earlier this year a guy named Andrew asked an interesting question on  Are these two quantum systems distinguishable?
The idea was this: suppose you had a machine that could randomly generate atoms in either the ground state or the first excited state. Then someone tried to sell you a cheap knock-off of this machine, except it generated atoms in a random superposition of these two states. Question: could you actually tell which machine you bought, the cheap knock-off or the Real McCoy?
It turns out that some of the people who frequent this site are pretty good at handling things like density matrices, and according to them these two machines were actually indistinguishable! The different output states described by these two machines ultimately reduce to the same density matrix, so expermentally you can’t tell them apart.

I actually proposed a way to build this machine: you take a vial of hot plasma composed of a fifty-fifty mixture of atomic nitrogen and carbon-14. You understand that in a nuclear sense, carbon-14 is really just an excited state of nitrogen, because that is what it decays to in 7000 years of so. I said just open a little door and let one atom out at a time. You might assume that there is a 50-50 chance that you get a carbon atom and an equal chance that you get a nitrogen atom. But according to those guys with their density matrices, I have just as much right to declare that each atom is in a 50-50 superposition of carbon and nitrogen…and experimentally, no one can prove me wrong!
In my original post I added a couple of stipulations: first, that the atoms might be in any number of superpositions, e.g. 80-20 or whatever, so long as they averaged out to 50-50. Secondly, that there was a real issue with the assumption that any machine was capable of letting out exactly one atom at a time. Maxwell’s demon and all that, but I think it goes even deeper.
No matter. That’s not why I brought up the question today. The reason is that in his original post, this Andrew fellow promised that pending the answer to this question, he would have a follow-up question. I was eagerly awaiting the follow-up and it never came. Somehow Andrew just disappeared.
The reason I was waiting for the follow-up is that I think I know where Andrew was going with this. It’s something I have been arguing for years and constantly getting shot down for. It’s about whether the universe is really as described by Copenhagen, with it’s quantum leaps and collapse of the wave function, or whether Schroedinger was on the right track when he looked for the natural time-evolution of the wave function. This is the question:
In the Copenhagen interpretation, we say that a gas consists of atoms in the ground state and a variety of excited states. The probability of finding an atom in an excited state is inversely and expontially proportional to the energy of that state. From time to time an atom jumps from one energy level to another, emitting or absorbing a photon. The probability of such transitions is calculated according to something called Fermi’s Golden Rule.

Following Schroedinger, I have an alternate description of the universe. I say that the same gas consists of atoms in a superposition of states. When you look at an atom in a superposition of eigenstates, you find that the charge distribution is not stable: it oscillates at frequencies corresponding to the difference in energy levels between the eigenstates. Because you have an oscillating charge distribution, it emits and absorbs radiation like a tiny antenna. The amount of radiation emitted and absorbed is calculated according to Maxwell’s Equations.
The question I ask, which is the question I believe Andrew meant to ask, is the following: is there any way to experimentally distinguish my model of the universe, my “cheap knock-off”, from the Copenhagen Model, the “real McCoy” according to everybody who is anybody. I’m saying there isn’t. Anybody care to disagree?

No comments: