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:

Post a Comment