Hardy's Paradox: Explained in Plain Terms

[gonzo]

I just saw a reference to Hardy's Paradox, but the only explanations I've found seem to be overly techincal. Can someone explain what this paradox is to me in relatively starightforward terms? Thanks.

 

[slyboy]

Hardy and Kwiat wrote a nontechnical description of the experiment intended for High School Teachers:

L. Hardy and P. Kwiat. "The mystery of the quantum cakes". American Journal of Physics 68 33 (2000)

 

[gonzo]

Are we talking about the same thing? I'm thinking about the paradox with the electron and positron going around a path and that they should annhilate each other but then they don't but then they have to, and then you get some weird thing with the answer like one of the paths has to have a negative probability and then it works out.

 

[caribou]

I read a version of the paradox in a book that is sufficiently different from the original that I'm not sure how to describe the original. I guess I'd need to read that as well.

I know that you end up with apparent faster-than-light effects or negative probability from paradoxes like EPR, Hardy, GHZ and the like if you use the older interpretations of quantum theory.

Hardy's paradox requires a violation of the consistency conditions of the more modern consistent histories interpretation of quantum theory but I'm not entirely sure what that means physically other than its making statements that quantum theory doesn't allow.

I'm still learning all this myself.

 

[slyboy]

Well, it is possible to describe Hardy's paradox in a few different ways that are essentially equivalent (i.e. different physical setups that lead to the same conclusion). There is the original version involving the interferometers and paticle-antiparticle annihilation, but you can rewrite the whole thing in terms of an ordinary Bell-inequality type experiment with 2 spin-1/2 particles (although you still need a post-selection to get the result). The latter setup is essentially what is described in the "quantum cakes" article.

The original Hardy's paradox is best understood by first looking at the Vaidman-Elitzur bomb (otherwise known as interaction-free measurement). This involves just a single interferometer, but I can't find a good nontechnical account of this on the web. You might try http://www.users.totalise.co.uk/~idmon/quant5.htm.

Now, suppose you combine 2 Vaidman-Elitzur setups, with a particle in one of them and its anti-particle in the other. In place of the bomb you just overlap one arm of each interferometer, so that the particles will annihilate if they are both in that arm. This is Hardy's setup.

 

[Caroline Thompson]

I read a version of the paradox in a book that is sufficiently different from the original that I'm not sure how to describe the original. I guess I'd need to read that as well.

I know that you end up with apparent faster-than-light effects or negative probability from paradoxes like EPR, Hardy, GHZ and the like if you use the older interpretations of quantum theory ...

I don't think everyone is talking about the same thing in this thread, but perhaps the original idea was to do with his "ladder" test for entanglement. This is similar to the Bell inequalities in effect, though in a perfect experiment it would require no inequality. It was tested in 1997 -- see:

Boschi, D, S Branca, F de Martini and L Hardy, “Ladder Proof of Nonlocality without Inequalities: Theoretical and Experimental Results”, Physical Review Letters 79, 2755 (1997)​

As someone else implied, the experiment depends for its interpretation on the same "fair sampling" assumption that is needed in most Bell tests. Since it is far from clear why the sample should be fair, the experiment is unconvincing.

[For the basic logic that tells you why the sampling is unlikely to be fair, see one of my "Chaotic Ball" papers, e.g. http://arxiv.org/abs/quant-ph/0210150 ]

Caroline

 

[slyboy]

Yes, there is considerable confusion about what "Hardy's paradox" and "Hardy-type non-locality" actually is. The reason is that Hardy is pretty good at coming up with different types of nonlocality experiment and has come up with a few different ones since the early nineties.

Actually, he once told me that he usually has no idea what people mean when they talk about "Hardy nonlocality" in the abstracts of their papers.

 

[lowflier]

There's a recent article in The Economist (about March 2009) that makes sense in layman's terms AND references (in the New Journal of Physics)an experiment that CONFIRMS another reported in the Physical Review Letters - both confirming that Hardy really was "right-on" in his prediction! They found values LESS THAN ZERO for the polarized photons interaction which serve to confirm Hardy's Paradox. Check it out (but DON'T LOOK)