Sunday, June 28, 2009

Quantum Zeno's Paradox or Quantum Zeno Effect


Zeno's had a number of paradoxes, but the one I mean here is - there is an arrow flying through the air. It has to be somewhere. Let's say it is a one foot from a certain tree. Well, if it is one foot from the tree, then it is at rest there, since it is no where else. If it is at rest, it is not moving, therefore motion is impossible.

In the atomic world, observations can affect the behavior of atoms, just as Zeno's detailed examination of motion seems to make the arrow stop.

Observing an atom with a photon or a radiowave disrupts the atom, and prevents it from evolving into another state. This notion is called the Quantum Zeno Effect.

In the quantum mechanical jargon, observation collapses the collapses the wavefunction to the pure eigenstate of the measurement. Evolution between states follows an exponential distribution, which can be expanded in a Taylor series for short times. At sufficiently short times, the leading terms show that the probability of changing states is reduced. More physically, the atoms starts out in a defined state, and displacement from that state is proportional to time squared, as if it were on a random walk through configuration space.

In 1997 this was observed at NIST in beryllium atoms, but they were unable to measure the beryllium sufficiently fast to keep it from reacting - in that case relaxing to a ground state.

Wayne Itano has shown that this using a very simple quantum mechanical argument. Practically one can't measure it fast enough to stop a reaction, but you can slow it down. That is shown in the figure above. The first calculation is a Taylor series expansion for short times, and the second calculation is the same but factoring in that the actual experimental observations have a duration. "n" is the number of observations in a period of time.

This shows that, perhaps strangely, measuring something by hitting it with a low energy photon is enough to slow its reaction rate. This leads one to believe that there is something real about "collapsing a wave function," because then the atom takes longer to get to a different state.

As with the previous post, I am concerned with the book Biocentrism by Lonza on my other blog. Lonza's point is that hitting a beryllium atom with radio frequency pulses is "observing it," and the mental energy of the "observer" is part of the process. Itano points out that measuring is not the same as observing.

All that is necessary for Itano's theory is that radio frequency pulses be shot at the beryllium atom. No one needs to measure what fraction of the radio frequency pulses are absorbed, and no person needs to think about it. For this effect to work, all that is necessary is for the quantum state of the beryllium to be re-set.

Secondly, poetic language about preventing a nuclear explosion by thinking continuously about stopping it is not called for. It is a great heroic image though. The essential part is not the thought, but rather the irradiation of the constituent nuclear fuel with probing electromagnetic radiation.

I tend to think the metaphysics is getting carried away with itself.