- #1

godw2718

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Below is what I posted on my facebook, and my friend's comments.

- my post on facebook -

A watched pot never boils.

The state of pot is either boiling or still. When we measure the state of the pot its state collapse into the 'boiling' or 'still' state. Suppose that its state becomes 'still'. When we keep 'measure' the state of the pot, it continues to collapse into the 'still' state, so it never boils. It's a Quantum Zeno Effect!

- friend's opinion -

think the reason that we cannot observe such phenomena at least in practical/actual situation is either that continuous measuring is not theoretically obtainable or feasible, or that the state of the pot, which should be represented by a wave function residing in the product space of each particle's ket, is not an eigenfuction of the measurement operation, but rather receives the measuring Hamiltonian as a time-dependent perturbation, creating discrete change on the system. (Therefore, we CAN observe the boiling process..!)

The latter sounds to me more plausible; we can even define "dynamic equilibrium" of the whole system by limiting the number of particles that are in the "boiling" state, where we have two possible states for each particle. The claim that the measurement Hamiltonian causes transitions among states of composite particles sounds quite valid.

- my comments -

I agree on your opinion about why we can't really observe the quantum Zeno effect in everyday objects. After I've heard about quantum Zeno effect, I become curious about why we can't observe quantum effect in macroscopic objects. And about quantum system of many body, equilibrium, phase transformation, and so on.

In terms of QM, we can only 'measure' the state of fundamental particles(or the energy of the particle is low enough for us to ignore the inner structure) because we measure the state of particle by exchanging what is called 'messenger particles'.

So while we are 'measuring' the state of particle 1, the state of particle 2, 3, 4, 5 evolves as the time goes on. So, we can't fix the state by the continuous measurement. (I just summarized your opinion. Is it what you meant?)

However, if all of the particles are 'identical', watching only one particle is equivalent to watching all the particles aver the universe. So, if we measure the state of particle 1, the effect is we fix the total wave function to the state that 'one' particle is in the state that we observed. Then, we can fix the state of second particle, and then third particle, and so on... So, I think(not quite sure...) we can observe the quantum Zeno effect in many body system.

In analogy, assume that there are 100 dogs, and 100 people. If every one person observe the one dog, all the dog remain calm, which corresponds to 'fix the quantum state of the system'.

Although I have much more questions about this topic, I'll stop here, and I'll tell you later after I get your opinion.

- and then, my friend -

I was in truth suggesting opinions of two opposite (in a way) nature: one is to look at the system as a composite of fundamental particles in which our measurement results in the wave function collapse of one particle, and the other is to look at the system as a whole where we consider the "entangled" system. (What you summarized I think is closely related to the former view. )

In suggesting the latter view, I was saying that the measurement Hamiltonian does not result in the eigenstate of the system as it would on an individual particle, therefore, resulting in time-dependent perturbation on each of the particle as a result. (That we can decompose the process of the Hamiltonian's operation on the entangled system as what I just mentioned is what I want to claim. At least, in that perspective. ) And, when it comes to taking the former view, which you just mentioned, where we view the system as a "composite" of individual particles, your claim that the Hamiltonian, since resulting in an eigenstate ("still," for example) on an individual particle, would result in the eigenstate on every particle should be slightly altered in order to produce the eigenstate of the whole system, for the Hamiltonian would (and should) have a dependence on displacement across the space (that is, H = H( x ) )

Therefore, when one system is in the eigenstate due to the measurement Hamiltonian, I suppose the Hamiltonian would have a somewhat different effect on each particle. (They may not be in the eigenstate when one is.) I think in order to obtain the eigenstate of the whole system, we should construct a set of local observer to each particle where we can neglect its effect on a distant particle, effectively producing the eigenstate on a particle to which a local observer is assigned. (Picture the system as having a set of particles in the vicinity of each is occupied by a "nearby" observer. (The distance between a particle (say, particle 1) and its assigned observer (say, observer 1) should be much shorter than the distance between particle 2 and observer 1. (I think you get the general idea.) I think in that setting we can almost approximate the effects of observer 1's on particle 2 as being ok-to-neglect time-dependent perturbation, and resulting in a state slightly (negligibly) varied from the eigenstate ("still" state) of each particle. In this view, I tried to make the process more feasible by combining my and your view on the problem, where you focus on the effect of the Hamiltonian on a composite of "identical" particles, and I was focusing on the possibility of spatial effect of the Hamiltonian, amplifying its perturbative properties when operated on particles that are not in the same physical specifications. (Apparently,the effect of the Hamiltonian on all particles should be different as long as we view the system as a composite, and not the whole entangled system, where we need not consider the individual effect of the Hamiltonian on individual particles. I think when considering the entangled system we only need consider the statistical effect of the Hamiltonian on the system.) I'll stop here, too, and wait for your comments/opinions/corrections on what I just have said.

p.s. Glad we can talk about this over the web! I am stimulated by our discussion.

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Actually, for me, it's hard to grasp an idea that measurements perturb the rest of the system.

Welcome to all new ideas and comments. Thank you.