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Lee A. Rozema, Ardavan Darabi, Dylan H. Mahler, Alex Hayat, Yasaman Soudagar, Aephraim M. Steinberg

http://arxiv.org/abs/1208.0034

This paper says there are two forms of the Heisenberg uncertainty principle (HUP), one involving measurement and one involving the intrinsic spread in the quantum state. I'd always thought that the intrinsic one was more fundamental, and that the measurement one was just a heuristic justification for it. According to the paper, Heisenberg originally proposed the measurement one, and the relation he gave was too strong; the paper shows experimental violations of it.

One thing I can't decode from the paper (which is pretty technical) is how badly they claim the measurement version can be violated. Is it basically good to within a factor of 4 or something? If so, then it doesn't seem terribly interesting. After all, there are various ways to measure uncertainty, so the unitless constant in front of the HUP isn't really all that fundamentally exciting, as long as we know it's of order unity.

Or can the violation be arbitrarily large? That seems implausible.

I don't understand how the measurement version can be violated when the intrinsic one isn't. The intrinsic one limits what there *is* to know, so how can you measure information that doesn't even exist...?