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==Concerning the [[Afshar experiment]]==


There is one year already the physicist S. Afshar (see [http://www.irims.org/quant-ph/030503/ preprint]) working at Harvard university realized a very controversial experiment in order to refute the famous principle of Niels [[Bohr]] called [[complementarity]]. 
This experiment was described in an article of the British journal New scientist [(2457,  24 juillet 2004)]. It was clear for me since the beginning that the result was badly interpreted and that the reasoning of Afshar was misleading. 

In order to refute the claim of Afshar I would like, here, to explain briefly my reasoning.

[[Image:drezet.png|thumb|500px|Principle of Afshar's experiment.]]

The optical experiment represented on the figure included is essentially an extension of a ‘gedanken’ experiment proposed by Wheeler and called the delayed choice experiment.  A coherent light impinges on a screen containing two slits or apertures A and B. Light diffracts and produce interference fringes at large distance from the apertures. As well known we can use a lens L to observe these fringes in the focal plane (F). Alternatively we can decide to observe the image A' and B' of the holes in the image plane (I). This is simple and is only a problem of classical optics.

However difficulties arise if we consider the same problem with photon. Indeed a photon is a discrete entity which can produce a local click on a detector. If we suppose that light is made of particle how to explain the existence of the interference? This is the canonical problem called wave particle [[duality]]. Einstein and others, like de Broglie or Bohm, tried to justify this curiosity of nature  but Bohr found a simple solution to this problem which is to dismiss the entire issue by avoiding any reference to objective reality. For Bohr and Heisenberg it is a complete non sense to search an explanation for such quantum behaviour. Indeed such explanation(s) could not be experimentally tested.  

Bohr realized that effectively if you build up a model attributing a trajectory to photons then you should be able to observe experimentally these trajectories. If you can't do that your model is without any physical interest. However Bohr remarked that the observation of the path of the photon always disturbs the coherence of the wave and erase the interferences.
In the present context we have the choice between detecting a photon in the image plane or in the focal plane. This means that we have the choice between using each photon to build up the images A' and B' ('which path' information) or the interferogram. But since a photon can not be absorbed twice we can not make the two observations with the same particle. This is the reason why Bohr called this property complementarity. 

Now let go to the Afshar modification of the preceding experiment. Afshar decided to observe his photons in the image plane (I). Nevertheless he introduced in the focal plane a periodical grid of absorbing wires (in fact he worked just in front of the lens but this doesn't affect my reasoning). The wires are located at the exact minimum of the fringes. Naturally the experiment is not affected by this introduction because the intensity on the wires is close to zero producing consequently no additional disturbances or diffractions on the light propagation. The two spots in A' and B' are then unchanged. 

However since no photon are absorbed this give us information on the intensity at the wires location. We know then that the probability for a photon to cross the section of the wire is null and this is already something. Afshar believes that this information is sufficient to prove the existence of fringes in the plane. He is wrong. Naturally he is however right saying that clearly the intensity can not be uniform in the focal plane. But he can not really say what the shape of the fringes in this plane is. Bohr’s principle speaks about physical observation not about metaphysical expectation. To define experimentally the fringes he should use other photons that the ones recorded in the image plane. If you need an analogy you can imagine the following situation. You  are living in Paris and you can see from your beautiful flat (with a rent of 8000 $ per month) the apex of the Eiffel tower. Can you deduce from that the shape of the Eiffel tower? Obviously not... in the Afshar experiment every thing is the same.

This is clearly in disagreement with the conclusion of Afshar and is sufficient to refute all his reasoning.
==Remarks concerning Unruh's reasoning==
In august 2004 the well known physicist Unruh (see [http://axion.physics.ubc.ca/rebel.html]) proposed a simple counter argument (i.e. a gedanken experiment) in order to reveal the mistake in the reasoning of S. Afshar. The gedanken experiment of Unruh uses a Mach-Zehnder version of the original set up build by Afshar and seems to be in appearance an elegant alternative to the experiment described in [http://www.irims.org/quant-ph/030503/]. However in spite of its interest it can be finally observed that the reasoning of Unruh missed the essential point of the argumentation. In order to prove that we will analyse briefly Unruh's proposal.

The experiment starts with the splitting of a initial photon wave packet into two by a half silvered mirror. The two wave packet 1 and 2 are then redirected on a second beam splitter and separated into the beams 3 and 4. Finally using two mirrors and a last beam splitter we obtain the two beams 5 and 6 (corresponding to the two spots A' and B' in Afshar's set up). Unruh observed correctly that his set up is for the essential equivalent to the one build by Afshar. He remarked in particular that if no absorbing device is introduced in the interferometer then the photon will never follow the path 4. This is clearly equivalent to the existence of fringes in front of Afshar's lens. After crossing the last beam splitter the photon has a probability of 50% to be detected in 5 or 6. However, and this is fundamental, nobody can tell us with this set up from which path 1 or 2 comes the photon detected in 5 or 6. We can be tempted to close one of the two paths 1 or 2 in order to see effectively the path followed by the photon. If we do that we always record the photon in 5 if 2 is blocked and in 6 if 1 is blocked. Additionally the photon has the same probability to be in the arm 3 an 4 which means no interference. This is clearly the equivalent of the single slit experiment (i.e. a single path experiment).

Nevertheless by closing one of the two paths we have different physical situations. It is indeed evident that we can not reproduce the interference observed in 4 and 3 simply by adding the results observed in the two single path experiments. This is the reason why in the double path experiment of Unruh nobody can tell from which path 1 or 2 comes a photon detected in 5 or 6. It is then not true to tell that the photon observed in 5 (respectively 6) has a probability of 100% of coming from 1 (respectively 2) since nobody can test this fact experimentally without strongly disturbing the system. The same conclusion is valid with the lens. We observed two spots A' and B' but we don’t know if the photon detected comes from A or B: This is a metaphysical question for a quantum physicist. What we can deduce from the observation in 5 and 6 or in A' and B' is the number of photons coming from 1 and 2 but this is only a statistical result which should not be confused with the concept of which path information.

Now Unruh add a beam block in the arm 4. In the double path experiment this changes nothing because no waves propagate in this arm. This is clearly the same conclusion that the one obtained with the wires in the focal plane of the lens. However in the single path experiments the results are different since the beam going through 4 is blocked: the photon has now an equal chance to be recorded in 5 or 6. Unruh deduced from that that in the double path set up a photon detected in 5 or 6 has a probability of 50% of coming from 1 or 2. He then concludes that the experiment of Afshar doesn't conserve which path path information. However as analyzed previously the concept of which path information is dangerous and fallacious in quantum mechanics. Indeed by adding again the statistical prediction of the two single path experiments (i.e. by adding the number of particle observed )we can not create the 'fringes' present in 3 and 4. It is then wrong to tell that in the double path experiment with absorber in 4 the photon detected in 5 or 6 has an equal chance to come from 1 and 2. In reality nobody knows it and nobody can really test such assumption without changing dramatically the experimental situations. 

It can be added that the experiment of Afshar differs from the one proposed by Unruh on one point: if we introduce the wires in the single slit experiment the probability for the photon to be scattered or absorbed is only of few percents. This is far from the 50% of Unruh and this proves again that the essential point is not the hypothetical dualism between which path and interference but the complementarity between the observation in the focal plane and the image plane (Afshar's experiment). It can be observed finally that in Unruh's double paths experiment with absorber in 4 we can simultaneously measure the number of photon in 5 an 6 and be sure that no photon goes through the arm 4 (in the other case the absorber should count some photons). On this point the conclusion is different regarding Unruh's or Afshar's experiment since we explained previously that in the afsahr experiment the complete knowledge of the fringes and of the images can not be obtained with the same particles. 
The present discussion is not however in contradiction with our analysis of Afshar's experiment. Indeed in the experiment of Afshar the numbers of photons in the focal and image plane are associated with two non commutative observable (momentum and position) which are consequently complementary. It is then forbidden to build up simultaneously (i.e. by using the same particles) the two statistics in the two planes. But such constraint doesn't exist in the experiment of Unruh since the observation in 5 and 6 are not complementary of the observation in 4 and 3. Unruh's experiment is then not a test of complementarity and can not be compared to the experiment of Afshar.

==External links==
*Shahriar S. Afshar, 
**[http://www.irims.org/quant-ph/030503/ www.irims.org/quant-ph/030503/] (Preprint) 

[[:Category:Quantum measurement]]
[[:Category:Physics experiments]]