Does the Quantum Zeno Effect Contradict the Heisenberg Uncertainty Principle?

[jadrian]

in q zeno effect, measuring, or observing a particle will effect its outcome. however, its been said on this forum that the hup is there whether we observe it or not. contradiction?

 

[lugita15]

Depending on your interpretation of quantum mechanics, the quantum Zeno effect can be thought of as not depending on human observation at all. You can have a machine carry out the measurement then when you look at the machine's readout you'll say exactly the same effect has occurred. Of course, you can always take the unfalsifiable position, ala Schrödinger's Cat, that the wavefunction of the particle-and-machine system was in a superposition of states until you walked into the room and observed the machine readout, at which point the wavefunction collapsed.

 

[StevieTNZ]

HUP = Heisenberg uncertainty principle? I don't follow your post...

If you are talking of that principle, I see no contradiction

 

[lugita15]

I assume jadrian was asking how to reconcile the view that Heisenberg's uncertainty principle has nothing to do with human knowledge or observation with the quantum zeno effect. And my reply is that there's no particular reason to connect it to humans, because the same result occurs regardless of whether it is performed by humans.

 

[StevieTNZ]

I see it as no issue, because the repeated observation would be about one of the "non-compatible with others" observables. Or in the case that the system doesn't collapse, and you stop it from doing so- no need to worry about HUP.

 

[enroger0]

I kind of understand the question OP asked and I'm puzzled too.

If I understand it right, q zeno effect means when you measure the state of a system, wave function collapse into one of the eigenstate, and if you repeat the measurement fast enough you'll get the same state because the wavefunction doesn't have enough time to "spread out".

So say you measure the position of say an atom, you get its point position in space, if you do it at an high enough frequency the atom would seems as if "frozen" in same position. This does sounds like violation of HUP?

 

[lugita15]

I kind of understand the question OP asked and I'm puzzled too.

If I understand it right, q zeno effect means when you measure the state of a system, wave function collapse into one of the eigenstate, and if you repeat the measurement fast enough you'll get the same state because the wavefunction doesn't have enough time to "spread out".

So say you measure the position of say an atom, you get its point position in space, if you do it at an high enough frequency the atom would seems as if "frozen" in same position. This does sounds like violation of HUP?

It's not. The HUP states that you cannot have a quantum state that has both a definite position and a definite momentum. In the quantum Zeno effect, you are forcing the particle to stay in a position eigenstate, so its momentum will be totally indefinite. But you may ask, if the position isn't moving then isn't the momentum automatically zero? No. There is Ehrenfest's theorem that states that the expectation value of the momentum is the derivative of the expectation value of position with respect to time (times mass), but this theorem only covers the behavior of expectation values when the quantum state is undergoing unitary time evolution. But if constant position measurements are made of it, then its wavefunction cannot evolve according to the Schrödinger equation at all. That is why a particle can be stationary, but still not have zero momentum. So the HUP is saved!

For the record, I think the OP was asking about a different issue, the question of whether human knowledge matters.

EDIT: I just wanted to add that while you shouldn't just naively apply Ehrenfest's theorem to find the expectation value of the momentum, because unitary time evolution is not occurring, it turns out that you happen to get the right answer anyway if you do apply it. That's because, since the position uncertainty is zero, the momentum uncertainty is infinite, so the momentum is equally likely to take any value from negative infinity to infinity, which means that its average value is zero!

 

[enroger0]

It's not. The HUP states that you cannot have a quantum state that has both a definite position and a definite momentum. In the quantum Zeno effect, you are forcing the particle to stay in a position eigenstate, so its momentum will be totally indefinite. But you may ask, if the position isn't moving then isn't the momentum automatically zero? No. There is Ehrenfest's theorem that states that the expectation value of the momentum is the derivative of the expectation value of position with respect to time (times mass), but this theorem only covers the behavior of expectation values when the quantum state is undergoing unitary time evolution. But if constant position measurements are made of it, then its wavefunction cannot evolve according to the Schrödinger equation at all. That is why a particle can be stationary, but still not have zero momentum. So the HUP is saved!

For the record, I think the OP was asking about a different issue, the question of whether human knowledge matters.

EDIT: I just wanted to add that while you shouldn't just naively apply Ehrenfest's theorem to find the expectation value of the momentum, because unitary time evolution is not occurring, it turns out that you happen to get the right answer anyway if you do apply it. That's because, since the position uncertainty is zero, the momentum uncertainty is infinite, so the momentum is equally likely to take any value from negative infinity to infinity, which means that its average value is zero!

Good explanation, though momentum uncertainty is infinite, its average value is indeed zero. If we can observe at extreme resolution we might find the particle doing random walk under repetitive measurement, for what little time wavefunction gets to evolve.

 

[jadrian]

It's not. The HUP states that you cannot have a quantum state that has both a definite position and a definite momentum. In the quantum Zeno effect, you are forcing the particle to stay in a position eigenstate, so its momentum will be totally indefinite. But you may ask, if the position isn't moving then isn't the momentum automatically zero? No. There is Ehrenfest's theorem that states that the expectation value of the momentum is the derivative of the expectation value of position with respect to time (times mass), but this theorem only covers the behavior of expectation values when the quantum state is undergoing unitary time evolution. But if constant position measurements are made of it, then its wavefunction cannot evolve according to the Schrödinger equation at all. That is why a particle can be stationary, but still not have zero momentum. So the HUP is saved!

For the record, I think the OP was asking about a different issue, the question of whether human knowledge matters.

EDIT: I just wanted to add that while you shouldn't just naively apply Ehrenfest's theorem to find the expectation value of the momentum, because unitary time evolution is not occurring, it turns out that you happen to get the right answer anyway if you do apply it. That's because, since the position uncertainty is zero, the momentum uncertainty is infinite, so the momentum is equally likely to take any value from negative infinity to infinity, which means that its average value is zero!

i don't regard human obsrvation as any different from machines observation. both would have effect on the future

im more concerned with its implications on true randomness and how we could possibly effect it if both situations are assumed to be governed by it.

 

[Cthugha]

in q zeno effect, measuring, or observing a particle will effect its outcome. however, its been said on this forum that the hup is there whether we observe it or not. contradiction?

Eh? Any state which you keep going back to repeatedly using the quantum Zeno effect still has uncertainty associated with it and is therefore obviously in no way contradicting the HUP. How did you get that impresssion?