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Comment by Strilanc | Hacker News Reader

If I understand correctly, what's going on is... Suppose you have a system rotating between state |0> and state |1>, like f(t) = cos(t) |0> + sin(t) |1>. If you measure at time t, you get |0> with probability cos(t)^2. After measuring, the system starts rotating again, but reset to |0> (assuming you measured that). If you measure n times per rotation period, the chance of measuring the state |0> every time (i.e. of effectively keeping the system in the |0> state) is (cos(τ/n)^2)^n per period. That converges to 100% as n gets large.

So, by measuring more and more frequently, you can effectively stop a system like that from transitioning between states.

It's an interesting example of measurement unavoidably affecting quantum systems, where the problem clearly isn't due to kicking or perturbing the state.

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So, imagine you have a ball and a slope

       o
    __/\__

(ball should be on top in the middle).

The ball will slowly start rolling down one or the other side of the slope (because gravity).

You have a robot hand that keeps checking if the ball is still on top by grabbing it and then releasing it right in the middle. There is some leeway when the hand grabs the ball but none when it releases it.

    __|__          _|_
    | o |    =>    |o|

So effectively, if you do this fast enough, you keep "resetting" the ball on top of the slope.

Is this a good analogy?

Not really. A minor problem is that it fails to capture the fact that this process will also hold the qubit stable in the |1> state. More importantly, it fails to capture the limiting behavior of the success rate; it should move smoothly towards 100% as the measurement frequency increases but the ball-and-slope would instead jump discontinuously from not working to working as the hand went from being too-slow to fast-enough.

A better example might be... a series of polarizing filters? If you have a series of polarizers but skip all the way from vertical to horizontal with nothing in between, no light gets through. If you put a diagonal polarizer between the horizontal and vertical, some light gets through. If you have a big long series of very gradual steps from vertical polarizer to horizontal polarizer, almost all the light gets through. More frequent measurements causing the zeno effect is like to adding more gradations of polarizer direction causing the all-light-gets-through effect.

Er, I am fairly sure that polarizer example doesn't work, and still no light gets through, as polarizers don't rotate the light, but simply cut off components that are orthogonal to the polarization direction. So stacking slightly rotated filters through to 90 degress would still leave you with no light.

EDIT: On second thought, it might just be you wording making it seem weird. The analogy works if you don't look at the whole stack, but the after adding each polarizer. Still, the same effect is had as simply gradually rotating the 2nd polarizer.

You're one of the lucky ten thousand today. [1]

Following a vertical polarizer with a horizontal polarizer will block all light. But putting a diagonal polarizer in between will result in some of the light getting through. You can find videos and explanations of this effect on youtube [2] [3].

1: https://xkcd.com/1053/

2: https://www.youtube.com/watch?v=gm2LCsM_S5o

3: https://www.youtube.com/watch?v=KM2TkM0hzW8

Hah, nice! Looking at it now, of course it makes sense. I guess I just short-circuited by thinking of the polarizer as blocking light only, and not that the reduction in intensity is the result of the projection of the previous wave direction onto the new wave plane!

EDIT: not that this makes the quantum effects any clearer ;)

This is correct

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