Quantum Zeno Effect - Explained

[daisey]

I've heard an interesting explanation of how the Quantum Zeno effect works, but I am still confused. Here is a summary of that explanation, as I understood it...

When constant observations (or a series of observations taken at very short intervals) are made of a system in a superposition of state 1 (un-decayed) and 2 (decayed), the chances are greater the wave function describing the system will collapse into state 1 since the system never has time to evolve into state 2.

Now I'm not a mathematics expert (or probability expert), but the above explanation seems correct to me only if the time clock that governs how long it on average takes the system to decay starts over from the beginning with every observation. Otherwise even with constant observation the system will eventually decay. Does the "time clock" in fact start over with every observation?

 

[cosmik debris]

I think the explanation is that if the probability of a certain measurement is evolving from state 1 to state 2 and you measure it early on in it's evolution the probability will be high that you will measure state 1, that will reset the state to state 1. If you measure late in the piece the probability will be higher that you will measure state 2, and that will set the system to state 2. So if you measure lots of times early on the probability will favour state 1. Or something :-)

 

[tansic]

If I am not mistaken, (which I may be), particles have not been known to travel forward in time; only backwards, so, by this, the time-clock does reset.

 

[daisey]

I think the explanation is that if the probability of a certain measurement is evolving from state 1 to state 2 and you measure it early on in it's evolution the probability will be high that you will measure state 1, that will reset the state to state 1. If you measure late in the piece the probability will be higher that you will measure state 2, and that will set the system to state 2. So if you measure lots of times early on the probability will favour state 1. Or something :-)

When you say above "when you measure", do you mean to say "when you start measuring"? Does the Quantum Zeno effect not work reliably when the observer begins taking measurements late into what is considered (I guess) the so-called half-life of the subject particle?

 

[cosmik debris]

Any measurement gives you one of a range of values at random, which value you get is governed by the probability associated with each value. After the measurement the state is "reset" to the value you measured. If you measure frequently you are constantly resetting the state. Have a look at the measurement problem, there are plenty of articles on it.

 

[Greg-ulate]

Any measurement gives you one of a range of values at random, which value you get is governed by the probability associated with each value. After the measurement the state is "reset" to the value you measured. If you measure frequently you are constantly resetting the state. Have a look at the measurement problem, there are plenty of articles on it.

My opinion is that the copenhagen interpretation of quantum mechanics leads to some confusion. I would not say the state is "reset". The state is one of two things (1) Un-decayed, or (2) Decayed. You only know the state at the time of measurement. Quantum Mechanics allows you to predict with very high accuracy what is the probability of measuring state (1) vs state (2) with the information available, that is, "What state was it in last time it was measured?" and "How long has it been since the measurement was performed?"

The wavefunction gives you the relative probability of state (1), (2). The wavefunction is not a physical thing. The wavefunction "collapses" when you perform a measurement only because something about the system is known where before it was only one possibility out of several. The act of measurement often times disturbs the system so much that our prior knowledge of the system is now corrupt so we have to calculate a new wavefunction to predict what happens to the system after the measurement. This is when people start to use words like decoherence which makes it seem like they are saying more than they really are.

In the simple example of particle decay, the measurement does not necessarily disturb the system in any way, since the experiment could just be a geiger counter sitting near a sample, and each measurement shows whether or not a decay product has been generated.

For example, 22Na decays into a positron with very low energy such that as soon as it appears it is annihilated by a stray electron. Because momentum is conserved, the two photons must be emitted in opposite directions so that their combined momentum is near zero, equal to the momentum of the positron and electron center of mass. So you put a pair of detectors on opposite sides of the sample and you wait until you see two photons register at the exact same time and you know that one of the 22Na has just decayed. You did not affect the 22Na in any way by this experiment, however, your knowledge of the state changes every time you look at your measurement. Based on your knowledge of the system you can predict what will happen, thus you can write a new wavefunction each time. Each time you verify that the decay has not occurred you can rewrite your wavefunction starting with a definate state (1) and begin evolving the wavefunction into a superposition of (1) and (2) based on the properties of 22Na that you know. All this means is that as time goes on, it becomes more likely for your detector to register a decay.

Its like if you flip 10 coins at the same time once per second. How long will it take on average to get all heads? A decay event is like getting all heads. On average, it takes some time between events like getting 10 heads in coincidence, even though the likelihood is equal each time you flip. Imagine each nucleus is flipping coins at a constant rate and when they come up all heads the nucleus decays. If I had 11 coins, it would on average take twice as much time between getting all heads.

According to the present interpretation of particle physics, stable nuclei have a greater number of internal configurations (states) that do not represent decay, so after any given length of time they are less likely to appear in a configuration that does represent a decay event.

 

[mfb]

The wavefunction is not a physical thing.

Depends on the interpretation.

In the simple example of particle decay, the measurement does not necessarily disturb the system in any way, since the experiment could just be a geiger counter sitting near a sample, and each measurement shows whether or not a decay product has been generated.

This does not give the quantum zeno effect, the timescale of a decay process (this is not the decay time) is too short.

According to the present interpretation of particle physics, stable nuclei have a greater number of internal configurations (states) that do not represent decay,

?
According to nuclear physics, stable nuclei are in their ground-state (other states might be metastable). That is a single configuration.

 

[K^2]

The simplest way to understand Quantum Zeno is to forget about quantum mechanics for a moment.

Imagine two polarizers at 90° to each other. I send the beam of unpolarized light through the setup. After passing first polarizer, beam becomes polarized, and none gets through second polarizer. What can I do to change that without touching either of the two polarizers? I can put in more polarizers in between each one rotated slightly compared to its neighbors, forming a twist between the original two. Now the beam can get through. If the polarizers are ideal and I used infinitely many of them, there would be no loss beyond that of original polarization. In a realistic case, some intensity would be lost, but it's still a great improvement over no light getting through at all. Basically, this is principle behind LCD screens.

Now, if we look at the ideal case from perspective of QM, each photon passing through is a particle with specific polarization. Each polarizer it passes through is a measurement. The difference with the way that QZ is usually stated is that rather than system decaying (state rotating over time) I rotate coordinate system of the measurement. Otherwise, the effect is exactly the same. By having infinitely many measurements, I force the polarization of each photon to stay in an eigen state of my measurement, id est, aligned with polarizer. As a result, the photon passes through each one with 100% probability, rotating as it moves along.

Notice that even in the ideal case, there is absolutely no magic from perspective of classical electrodynamics. Electromagnetic wave excites oscillations along the preferred direction in a polarizer. If the directions mis-match by some ε, amplitude drops as ε². So in the limit of infinitely small rotations, the amplitude remains constant and polarization gradually rotates. The quantum description is effectively the same thing. We simply drop some details of how the polarization of EM wave is related to physics of a polarizer and what exactly constitutes a measurement.

This is true for Quantum Zeno in general. The statement of the effect is very broad, and so it can look a bit crazy. How is it that the observation prevents the nuclear decay? But if you describe the actual decay process, how the energy is converted into energy of some observable product, like gamma radiation, and how exactly you propose continuously measuring this gamma emission without losses, you'll arrive at a setup that really does keep the nucleus stable. And in that setup, the interaction that prevents decay will be explicit.

There is absolutely nothing unusual about Quantum Zeno effect. It simply happens to be a very general mathematical description which might look suspicious when you don't consider the details.

 

[Greg-ulate]

Yeah but there's all sortsa junk inside them that have many degenerate states. Thats where all those quark-gluon feinman diagrams happen, is it not? Nobody really knows exactly what's going on in there yet, that's why we don't know where the spin comes from on a proton. I actually worked with those RHIC guys in grad school ^^b

Oh, I see now that the Quantum Zeno Effect is specifically about a system in which the measurement is an active process, not passive like the situation I described. I read a little bit in a book and on wikipedia. They describe the measurement process to couple the system to its environment, a source of thermal noise. This might increase the multiplicity of states (more coins), or interrupt the flipping action