Experimental violation of HUP in its original form

[bcrowell]

Violation of Heisenberg's Measurement-Disturbance Relationship by Weak Measurements
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...?

 

[lugita15]

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...?

The key is the word "weak" in the title of the paper. A weak measurement is where, instead of measuring the position and momentum of a single particle, you compute the average position and momentum of an ensemble of particles in the same (potentially mixed) quantum state; see this blog post by Demystifier. You can do this with, in principle, arbitrary precision as long as you have sufficiently many particles, regardless of what precision you use to measure the position and momentum of each particle. But this arguably doesn't actually violate Heisenberg's uncertainty principle, in either of the two formulations you referred to, since your individual particle measurements are still constrained by the HUP.

 

[bcrowell]

The key is the word "weak" in the title of the paper. A weak measurement is where, instead of measuring the position and momentum of a single particle, you compute the average position and momentum of an ensemble of particles in the same (potentially mixed) quantum state

Aha, that makes a lot more sense. In that case, why is the result surprising at all? It seems obvious to me that you can do better than Heisenberg if you're given multiple chances and then take and average.

 

[RobinSky]

Thanks all! I saw this article also recently but I had a hard to understand why this would violate the HUP. First because I'm not an expert of its concept and the language used in the article did not make me any smarter.
I was very sad when I read it, because i find the HUP as a very beautiful statement, and finding it incorrect would make me more than sad.

 

[StevieTNZ]

If you 'weakly' measured the polarisation of a photon, would that measurement give you a definite polarisation outcome?