The Zeno effect is named after the [Greek] philospoher [Zeno] who lived in the fourth century B.C. Zeno presented several [paradoxes] regarding [infinity], most known are [Achilles and the Tortoise] and [the flying arrow].

Anyhow, the quantum Zeno effect was proposed by [George Sidarshan] and [Baidyanaith Misra] of [University of Texas] in [1977]. It suggested, just like [Norton_I] says in the previous writeup, that continuous measurements on a quantum level would slow down quantum decay. This is often referred to as [a watched pot never boils] (see [FFalcon]s writeup in that node).

In [2000] [Abraham Kofman] and [Gershon Kurizki] of the [Weizmann Institute] in [Israel] suggested the opposite effect, the [anti-Zeno effect], or [boiling the pot by watching]. They argued that the time frame in which the Zeno effect is valid, is very short. If you do not measure the effect often enough, then the effect will instead be that of speeding up the decay.

Both these theories can co-exist, and a recent article in [Nature Science Update] reports on how [Mark Raizen] and colleagues at the University of Texas have managed to prove both these theories, for as complicated systems as atoms. Previously only the Zeno effect had been experimentally proven, and that was on one particle systems only. Raizen used [Sodium] atoms, which naturally decays through [tunneling]. By measuring the system every millionth of a second, the decay slowed considerably. When instead measuring the system every five millionth second, the decay increased over the natural level. Thus, they seem to have proven both the Zeno effects on a never before seen level of complexity.

The rest in this writeup is for background only. I'll try to explain a little more in detail what these two are, in terms of [quantum mechanics]. The quantum Zeno effect is due to what is called the collapse of the [wave function]. As you may or may not know, the wave quantum mechanical wave function for a particle is a [probability distribution], which squared gives us the probability of finding the particle for a certain location. When the particle is measured upon, its wave function is said to collapse into a single defined state. As soon as the measurement is done, a new wave function will govern the particle.

Anyhow, the key is that if you measure the location - or any other quantum characteristic - often enough, you will effect the natural speed of events, such as decay. I'll use a common example: The event where an [excited] particle returns to its [ground state]. (See my [laser] writeup for a short piece on energy states)

The probability for a particle to go from a higher, called 2, to a lower energy state, called 1, is

P_2-1( t ) = a · t²

where P is the probability, t the time you wait between measurements and a is some kind of constant. Now, the probability for the particle to stay in the higher state is thus

P_2-2( t ) = 1 - a · t²

Now, consider that you wait n times longer between measurement, ie you wait n · t. Then the equation would change to

P_2-2( t ) = 1 - a · ( n · t )² = 1 - a · n² · t² (1)

This equation shows that if you never ceased measuring the particle, n ⇒ 0, then the probability P ⇒ 1, which makes sense. The particle will never decay if we measure it constantly.

If you instead measure the particle 2 times, with the interval t, the probability for the particle to be in the same state 2 becomes the product of each of the probabilities, or

P_2-2( t ) = ( 1 - a · t² )²

By using the [binomial approximation], this can be written

P_2-2( t ) = 1 - 2·a·t^2

which in turn can be generalized to measurement n times of intervals t to (by approximation)

P_2-2( t ) = 1 - n·a·t^2 (2)

Comparing equations (1) and (2), we see that the more often we measure, the greater the probability for the particle to remain in state 2. In equation (1) we measure once after n·t wait, while in (2) we measure n times during the n·t time.

For the anti-Zeno effect, the theoretical argumentation is that decay events have some sort of [memory time], and that the valid intervals for measurements are incredibly small. In fact so small, that the energies needed for measurement could well destroy the measured particle. This is due to the [uncertainty principle], which makes the variations in energy large over small times. Researches say that if the intervals are not fast enough, then the effect could well be the [reverse]. How this anti-Zeno effect theory will be affected by the new results mentioned further up, remains to see.

Source: Scientific American and Andrew Hamilton at Dalhousie University for formulae.

quantum Zeno effect (idea)