# Proton Twin Slit Experiment?

1. Nov 10, 2006

### ianbell

Have single protons or neutrons or anything "bigger" been experimentally confirmed to "interfere with themselves" and "act like waves" the way single electrons and photons do, in experiments such as the twin slit expt?

All I have been able to find on this is the somewhat lame
http://www.fnal.gov/pub/inquiring/questions/double-slit.html.

TIA.

2. Nov 10, 2006

### zbyszek

Check out A. Zeilinger who has done interferences of fullerens (60-, 70- atoms), and W. Ketterle who interfered two condensates (10^5-10^6) of rubidium atoms.

3. Nov 10, 2006

### StatMechGuy

I think questions like this come up due to issues with where the "quantum" or "classical" regime are. So I'll try to answer this question by answering that question.

From the standpoint of classical mechanics, the quantum regime occurs when

$$S = \int_{t_0}^{t_f} dt L(q, \dot{q},t) \sim \hbar$$

that is, when the classical action gets on the order of a few integer multiples of $$\hbar$$. This analysis fails for macroscopic quantum phenomena, such as superconductivity or superfluids.

From a quantum mechanical standpoint, the classical limit is achieved from the standpoint of the propagator by looking at

$$K \sim \int \mathcal{D}[q(t)] e^{i S/\hbar}$$

Now, to obtain the classical limit from here, we look at $$\hbar \rightarrow 0$$. From the stationary phase approximation (see Erdelyi, for example), we know that the path that contributes the most to the integral is that for which $$\delta S = 0$$, that is, for stationary action. But that's just D'Alembert's principle, that

$$\delta S = \delta \int_{t_0}^{t_f} dt L(q, \dot{q}, t) = 0$$

from which we obtain the Lagrange equations of motion. This is how one might try to get at the classical limit from the standpoint of path integrals. Unfortunately, again, it is very difficult to account for superconductors and other macroscopic quantum mechanical effects in this manner.

I think the key is to be able to look at the dimensional quantities that depend on $$\hbar$$, such as the correlation length or whatnot, that are intrinsic to the problem, and in the case where such dimensional considerations allow one to consider $$\hbar$$ to be very small, those problems exist in the "classical regime".

Crossover approximations such as WKB are themselves quite interesting, but I have to run off to an appointment now. Perhaps someone else could take that.

4. Nov 12, 2006

### ianbell

Thanks. Just what I wanted.