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Classically it was said that measurement leads to a collapse of the wave function. However, if there wouldn't be any limit on the process on measurement itself, strange things can happen, e.g. a particle that is confined to a small region by a very strong potential could by measuring its momentum with high precision be made to be spread out instanteneously all over space. Likewise, if a particle is detected at one location, then its momentum is measured with very high precision, at any moment after that it can be detected arbitrarily far away.

In Feynman's lectures on physics, he goes into the explicit measurement process in the double slit experiment, where light is used to detect which slit the electron passed through. As long as the photons can detect the slit the electron went through, the interference pattern is destroyed. When the frequency of the light is reduced to diminish the impact, the interference pattern keeps being disturbed, up to the moment when the wavelength of the photons is so large that they are not able to determine which slit the electron passed through.

Likewise, in this answer by John Rennie to the question how it can be that if you measure the momentum of a particle with very high precision its uncertainty may extend over one light year, he explains why (doing this with light at least) a measurement with that precision would take a year.

As another example, in this answer by DanielSank to the part of my question where it was asked how it could be that a measurement of a particle in a box with infinite walls could be made to tunnel out by making a measurement, it was suggested that there is a fundamental limitation on the precision of the measurement.

In all three examples it looks like the restrictions on the measurement process are exactly conspiring to avoid any undesired behaviour to occur. Is there any fundamental reason for that?

Thanks!

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Well, I don't think DanielSank meant that there is a fundamental limit on precision of measurement. I wouldn't call all of this a "conspiracy". It's rather the self-consistence of physics that seems like a conspiracy. :) –  Bubble Jun 15 at 22:26
    
thanks Bubble. Maybe that was imprecise, would it have been better to say that the precision is fundamentally limited by how much you are willing to disturb the system? Or maybe the time you allow the measurement to take? –  doetoe Jun 15 at 22:35
    
Also I think the self consistency of physics is a pretty fundamental reason for the conspiracy! However it is not so clear that the only way out is that any measurement must disturb the system just (or at least) enough to make everything work out fine. Also it is not obvious that those situations really violate the consistency of physics or that they just make physics even stranger than it already is. In the first two examples I mentioned, the way out was made pretty explicit for a very specific setup, but they were also just specific examples. –  doetoe Jun 15 at 22:42
    
@Bubble actually I didn't say fundamental limit, but fundamental limitation, e.g. on the time or energy required to get to a certain level of precision. In the last example the higher the potential, the more energy should have to be put into the measurement, which would allow the particle to escape –  doetoe Jun 16 at 22:29

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