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jadrian
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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?
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 Schrodinger equation at all. That is why a particle can be stationary, but still not have zero momentum. So the HUP is saved!enroger0 said: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 said: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 Schrodinger 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!
lugita15 said: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 Schrodinger 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!
jadrian said: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?
The QTM Zeno effect is a phenomenon in quantum mechanics where frequent measurements or observations of a system can prevent it from undergoing a change. This is relevant to the Heisenberg Uncertainty Principle because it suggests that the act of measuring a particle's position can affect its momentum and vice versa.
No, the QTM Zeno effect does not contradict the idea of the Heisenberg Uncertainty Principle. In fact, it provides further evidence for the uncertainty principle by showing that frequent observations can affect the behavior of particles in quantum systems.
Yes, the QTM Zeno effect has been observed in various experiments involving quantum systems. For example, in the delayed-choice quantum eraser experiment, frequent measurements were shown to affect the interference pattern of particles, providing evidence for the QTM Zeno effect.
The QTM Zeno effect challenges our classical understanding of the physical world and highlights the unique behavior of particles at the quantum level. It also has implications for quantum computing and communication, as frequent observations may be necessary to maintain the integrity of quantum information.
The QTM Zeno effect is a well-established phenomenon in quantum mechanics and has been observed in numerous experiments. However, there is ongoing debate and research surrounding its exact mechanisms and implications for the Heisenberg Uncertainty Principle.