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Physicists resolve a paradox of quantum theory


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"For nearly a century, the widespread interpretation of quantum mechanics suggests that everything is uncertain until it is observed, and that observation inevitably alters reality," says Professor Steinberg. "However, in the 1990s, a technique known as 'interaction-free measurement' seemed to promise the ability to 'see without looking,' as a Scientific American article put it at the time. But when Lucien Hardy proposed that one could never reliably make inferences about past events which hadn't been directly observed, a paradox emerged which suggested that whenever one attempted to reason about the past in this way they would be led into error."
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Please give us an observation or even an opinion as a starting point for discussion,...


I'd like to concur with Phi's request. It's no fair just mutely revealing a remarkable development like this without adding some comment of your own, to get the ball rolling.


Also I'd personally like very much to know what your take on this is, Kedas.

Lundeen Steinberg experiment could be major. I'd like to know Swansont's take on it. Potentially very exciting as I see it.


So comment, for Pete's sake, Kedas, and let's see what other people say too!:D


One point I guess is that it got accepted by PRL.

The abstract on arxiv does not have any information about peer review.

Here is the abstract


So we could read the whole article as of October 2008, but we didn't have a clue about what peer review would say. Publication in Physical Review Letters is a premium stamp of approval.


I'm printing off the Lundeen Steinberg article as we speak. They do a lot of explaining, it is written comparatively clearly as these things go---some clear language along with the math.


The original 1992 paper by Lucien Hardy which posed the so-called Hardy Paradox is linked here:


A free preprint is not available. It was published in PRL and has been cited 67 times


We should learn a little about Lucien Hardy (I know he's bigtime, and at Perimeter Institute, but didn't know details)


"Lucien Hardy received his Ph.D. at Durham University (1993) under the supervision of Professor Euan J. Squires. He has held research and lecturing positions in Maynooth, Innsbrook, Durham, Rome, and Oxford. Since 2002, he has been a member of faculty at Perimeter Institute for Theoretical Physics in Waterloo, Ontario, Canada. His primary research area is quantum foundations. In particular, he is interested in applications of quantum foundations to quantum gravity and quantum information. In 1992, he found a very simple proof of non-locality in quantum theory, which has become known as Hardy's theorem. In Rome, he collaborated on the first experiment to demonstrate quantum teleportation. In Oxford, he worked on obtaining an alternative set of postulates for quantum theory. He is currently working on building a framework appropriate for a theory of quantum gravity."


More background is at wikipedia on the EPR paradox


which refers to a 1993 Hardy paper:


which also made it into PRL and has been cited 37 times, not bad for a grad student.

Anyway, somehow it seems advisable to get some understanding of so-called Hardy Paradox, also I've heard of something called Hardy's Theorem which may be related.


If it should turn out that the Lundeen Steinberg experiment is important it will probably be because Hardy's contribution is. We are having company this morning and I may not be able to get enough time to investigate Hardy paradox until later today.

Edited by Martin
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I haven't had time to look at it. I was disappointed in the article though — I don't think it explained very much at all. I still don't know what the Hardy paradox is.


Glad you gave it an initial glance! The Hardy paradox setup was originally stated involving an electron and a positron---more of an unrealizable thought experiment. What Lundeen Steinberg did was realize the same basic scheme with two photons instead of an e+ e- pair. Let's look at the original thought experiment as shown in Figure 1. BTW I see there is a typo, writing H instead of Y in the caption to figure 1, but it seems trivial.


I've tried to extract what I think are two key passages the first from page 1 and the second from page 3 of their paper.


"Hardy’s Paradox is a contradiction between classical reasoning and the outcome of standard measurements on an electron E and positron P in a pair of Mach-

Zehnder interferometers(seeFig. 1). Each interferometer is first aligned so that the incoming particle always leaves through the same exit port, termed the “bright” port B (the other is the “dark”port D). The interferometers are then arranged so that one arm (the ”Inner” arm I) from each interferometer overlaps at Y. It is assumed that if the electron and positron simultaneously enter this arm they will collide and annihilate with 100% probability. This makes the interferometers “Interaction-Free Measurements” (IFM)[6]: that is, a click at the dark port indicates the interference was disturbed by an object located in one of the interferometer arms, without the interfering particle itself having traversed that arm.


Therefore, in Hardy’s Paradox a click at the dark port of the electron (positron) indicates that the positron (electron) was in the Inner arm. Consider if one were to detect both particles at the dark ports. As IFMs, these results would indicate the particles were simultaneously in the Inner arms and, therefore should have annihilated. But this is in contradiction to the fact that they were actually detected at the dark ports. Paradoxically, one does indeed observe simultaneous clicks at the dark ports[7], just as quantum mechanics predicts..."


"...Examining the table reveals that the single-particle weak measurements are consistent with the clicks at each dark port; as the IFM results imply, the weakly measured occupations of each of the Inner arms are close to one and those of each of the Outer arms are close to zero. The weak measurements indicate that, at least when considered individually, the photons were in the Inner arms.


However, if we instead examine the joint occupation of the two Inner arms, it appears that the two photons are only simultaneously present roughly one quarter of the time. This demonstrates that, as we expect, the particles are not in the inner arms together.


So far, we seem to have confirmed both of the premises of Hardy’s Paradox: to wit, that when DP and DE fire, N(IP) and N (IE) are close to one (since the IFMs indicate the presence of the particles in Y) – but that N(IP & IE ) is close to zero (since when both particles are in Y, they annihilate and should not be detected).


This is odd because in classical logic, N(IP & IE) must be ≥ N(IP) + N(IE) − 1; this inequality is violated by our results.


Although N(IE) is 93% and N(IP ) is 92%, the data in Table 1 suggest that when E is in the Inner path, P is not, and vice versa; hence the large values for N(IE & OP) = 64% and N(OE & IP) = 72%. The fact that the sum of these two seemingly disjoint joint-occupation probabilities exceeds 1 is the contradiction with classical logic..."


BTW I see that A. M. Steinberg used to be at UC Berkeley and also at the Washington NIST. Given your metrology connections, you may have heard of him in some other context (or actually met the guy for all I know :D). This is the first time I've seen his name.


Just to be explicit about the notation in case others read this, IP means photon P goes by the inner path, OP means it goes by the outer. Similarly IE and OE. So N(IP & IE) is the percentage of trials where both photons went by the inner path.

The two photons are called P and E because they play the roles that were played by the positron and the electron in Lucien Hardy's original thought experiment.

Swansont please correct any mistakes or misinterpretation you happen to see here.

The figure 1 diagram is not all that complicated so if anyone is curious about what are the inner and outer paths thru the optical apparatus they can check out the paper. It is just 4 pages. Looks like an ordinary laser optical experiment to me, like I could see any day of the week just by walking over to the Physics building on campus. So far I don't see what was especially hard about what they did, but I still have a lot to understand about it.

Edited by Martin
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...I was wondering if this is related to the Heisenberg's Uncertainty Principle...


OK so that is your comment/question. I think our SFN policy is that one doesn't just post a news item (no matter how interesting it sounds). One posts the news item together with some question you have about it. Or some reflective comment about it. So there is something of your thought out there as well as the bare news.


I'm glad you found this.


I don't know if it is as important or interesting as it sounds. Could be.


It definitely does have some relation to the H.U.P. Most things in quantum mechanics seem to, one way or another.


One thing I would say is that in quantum mechanics a particle does not have a path. Trajectories do not exist.


If a particle starts at point A and arrives at point B then you cannot say what path it followed.


This is a true contradiction to common sense and macroscopic everyday experience.


In this experiment, one can identify cases where both particles behave as if they traveled along the inner pathways of the apparatus. And yet, if they had trajectories, they would have crossed. But they did not cross!


The only way to make sense, as the authors describe it, is to use negative probabilities. I don't like the idea. I am only starting to think about it. For me, now, all I can say is that particles don't have trajectories, or they follow all possible trajectories at once with a certain amplitude assigned to each. And even if one's reason says that the particle MUST have followed a certain trajectory, yet it did not.


See if you can find some more popularization/outreach material about this. Maybe it would help. I can't really offer anything helpful at this point.

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OK, I had a very quick glance, and it's very intriguing. The idea that the paradox relies on the particles annihilating/interacting when (classically) their paths should overlap gives me pause, though — how do we know that the interaction takes place all of the time? I assume that's measured independently and there's a statistically significant deviation from that in the "dark" coincidences.


I tried emailing the article to me at home and it doesn't seem to have worked, despite it being relatively small, so I'll have to address that tomorrow, and a more thorough read will have to wait.

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Quantum theory is the theoretical basis of modern physics that explains the nature and behavior of matter and energy on the atomic and subatomic level. In 1900, physicist Max Planck presented his quantum theory to the German Physical Society. Planck had sought to discover the reason that radiation from a glowing body changes in color from red, to orange, and, finally, to blue as its temperature rises. He found that by making the assumption that energy existed in individual units in the same way that matter does, rather than just as a constant electromagnetic wave - as had been formerly assumed - and was therefore quantifiable, he could find the answer to his question. The existence of these units became the first assumption of quantum theory.

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