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 FFalcons 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
The probability for a particle to go from a higher, called 2, to a lower
energy state, called 1, is
P2-1( 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
P2-2( 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
P2-2( 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
P2-2( t ) = ( 1 - a · t2 )2
By using the binomial approximation, this can be written
t ) = 1 - 2·a·t^2
which in turn can be generalized to measurement n
times of intervals t to (by approximation)
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
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.