For how long does a measurement collapse a wave function?

Ivan Seeking

I assume that some speed limit must exist that limits how often we can measure something - if is exists, perhaps the Plank time unit governs this? Do we know this answer? Does this relate to the speed of quantum computers?

jeff

Wave function collapse is irreversible:

The value of an observable once measured will not change in a system that remains otherwise undisturbed, and the fact that measured values of the same observable of a system that was disturbed in between measurements will not in general agree is not the result of some restorative process directly inverse to the initial collapse.

Obviously, insulating quantum computers from disturbances that would collapse the wavefunction carrying out some given computation is key.

Of course, limits on how quickly information may be gathered is limited by causality, and the basic unit and meaning of information may ultimately be tied to physics at the planck scale.

Ivan Seeking

Interesting. I thought it a basic principle of QM that we can only know that state of a system at the time of the measurement and immediately thereafter. After this, the state of the system cannot be known. This statement is false?

jeff

According to what the axioms of QM actually say, yep.

Ivan Seeking

I was checking an old text book and perhaps I confused the idea of random states with perturbed states? The language is clear that a measurement only tells us about the state of the system at the time of the measurement. I guess this emphasis is motivated by the idea that in real experiments, other things will affect the state of the system?

I do see what you mean though. The II postulate [in my text] does state that a measurement of observable A, yielding value a, leaves the system in the state φ. Conservation laws would seem to do the rest.

Still, it does seem that no truly isolated system can exist. Are we discussing an idealized system that cannot exist?

ranyart

You would be correct to understand that in measurement,there is a optimum distance, an optimum place, and an optimum Time for a single event to occur. If for instance you viewed an event with an energy that is comparably 'slower', it is the TIME factor that changes, the distance between you and the event does not change.

Watching a video in slow motion, you are recieving he same amount of information, at a 'reduced' rate over an 'extended' time.

jeff

Yes: Whatever "apparent" deviation from these axioms we've seen in real systems have always been attributable to our inability to perform ideal experiments rather than to a failure of the axioms themselves.

Ivan Seeking

Gees. I read your answer and thought, great, we're done. But something has been nagging me and I finally realized what. Doesn't a fundamental argument exist that unique states only exist when measured? This is what I kept thinking was the motivation for the language of my old QM text. I am sure that I have heard this used as an escape clause for various paradoxes…say for example when we talk about the energy in a field. I will try to explain the violation of concepts that I am alluding to here.

Doesn’t the whole idea of superposition fail if any measurement permanently collapses the wave function for an isolated wave/particle? In fact, if we do consider one wave/particle thingy, and if we assume that it exists as in a superposition of eigenstates, then we must assume that nothing else has ever “measured” the thing. Otherwise, it would seem that we are asserting a solution to Schrödinger’s Cat paradox. That is to say that the concept of superposition only references populations of particles. However I am quite sure that no consensus exists as to what constitutes a measurement, so we can’t know if a thing has been measured. Also, I was not aware that any consensus exists as to the proper interpretation of the Schrödinger’s Cat paradox. So, are you speaking from a particular school of thought, or am I again misunderstanding the basics of QM?

ranyart

You are mis-interpreting the whole of shroedingers cat?..the cat is representative of a standing wave, It's inside of a box! You are external, the box forms a junction of where your observational limits are defined, and it works both ways, the cat inside cannot see you unless the box is removed, collapsed.

You cannot isolate the cat from the box, yourself from seeing the cat without the box, its the events that are always extended, there are always distructive obstacles in line's of sight when trying to isolate anything, even a single particle!

Ivan Seeking

I understand this.

Sorry, I don't follow your point. I suspect that you are misunderstanding my comments...I'm not sure. Can you tell me what I am saying that motivates your comments?

jeff

A collapsed wave function is still a wave function, since measurement of an observable must by the uncertainty principle leave us with a quantum superposition of all possible values of it's conjugate, i.e. if we know position we don't know momentum.

Ivan Seeking

Jeff, thanks. You have helped to clear up twenty years of confusion. [:)] I will stew on this awhile but I think you hit bullseye.

Ivan Seeking

I am curious about your views on a statement that comes from the Quantum Cosmologists: When I look at a gauge, I don't collapse its wave function, instead I jump into a superposition of eigenstates. As I understand the reasoning, if we can collapse any wave function, then we can infer that we should be able to collapse the wave function of the universe; which it seems that we can't. So, to collapse any wave function is to create a paradox.

Edit: Also, how do you feel about live-dead cats? Do you feel that a single qm entity can exist in a true superposition of states, or do you think this only applies to large populations of particles?

planetology

There are quite a few experiments that I think show individual particles are superpositions of states. For instance, the double-slit experiment with individual electrons shows the same interference pattern after enough electrons have been put through it one at a time as a full electron beam; also the work of Abner Shimony and others attempting to resolve the EPR paradox using Bell's theorem has this interpretation in my view. And there are some polarization experiments with individual photons going through multiple polarizers.

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