Quantum Zeno effect and Heisenberg uncertainty principle

Question

The Heisenberg uncertainty principle forbids the existence of static atoms But in the Quantum Zeno effect observing atoms makes them stand still does the Quantum Zeno effect violate the Heisenberg uncertainty principle?

Answer 1

No, the quantum Zeno effect does not violate the Heisenberg uncertainty principle. Both are parts of ordinary quantum mechanics. Ordinary quantum mechanics does not have such basic inconsistencies as would be needed to make these two conflict with each other.

The Zeno effect can be understood as the result of repeated projection. After projecting onto any given quantum state, that state respects the Heisenbergy uncertainty principle. It cannot fail to; the principle is part of the mathematics. It is like Fourier analysis: you can't create a function which cannot be Fourier analysed.

If the state projected onto has a small position spread, then it will have a large momentum spread and this will cause it to start to evolve to a wider position spread. If you measure it again quickly enough then you can project it back to small position spread again. This measurement is an interaction with the system---quite a strong interaction in fact---and it causes this part of the evolution of the system. At every stage the uncertainty principle describes what can and cannot be true of the combination of position and momentum in the system state.

(By the way, for anyone interested in the quantum Zeno effect, there is in classical physics an effect that matches it closely. One considers classical waves such as light waves. Allow linearly polarized light to pass through a medium which rotates the polarization (called an optically active medium; some types of syrup or molasses do this). If you put a sequence of polarizing filters in such a medium, then the polarization vector is prevented from rotating, and in the limit of an infinite number of perfect filters, you also get perfect transmission.)

Answer 2

In the Quantum Zeno effect observing atoms makes them stand still

Not quite. The QZE just says that if we measure the system frequently enough then there isn't time for the state vector to change too much from it's initial measured state, hence it is very likely that our repeated measurements will yield the same result. Between the measurements the state vector evolves like it would in any other situation.

Answer 3

The uncertainty principle does not forbid the existence of static atoms. It only says that the more precisely the position is known the more uncertain the momentum is and vice versa. It is a limitation of what can be known, not on what can exist.