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Who hasn't heard about the double-slit experiment? It figures in any book of quantum physics. But there is something no one can explain to me : I understand why the light cannot be described only as a wave, but I do not understand why it cannot be explained only in terms of a particle, having some trajectory, following other laws of phyisics we may not know. Usually, every book in which I have tried to look for an answer considers that if it cannot be described as a classical trajectory (which is clearly the case in this experiment), then it is not a particle, that is, a material point. Could it not be a particle following new laws?

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Sorry, but such questions are somehow not working on this site -- they collapse into an useless random argument. –  mbq Mar 19 '11 at 17:54
    
@mbq, did You delete comments here? I missed two others in other threads today, but was not quite shure. –  Georg Mar 19 '11 at 18:11
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closed as not constructive by mbq Mar 19 '11 at 17:52

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I point out that Feynman, in his 1979 Douglass Robb Memorial Lecture, part I (actually entitled "Photons - Corpuscles of Light") on QED, video freely available at http://vega.org.uk/video/programme/45, asked this very question. He answered definitively that Newton was correct and that light was indeed a particle which, however, propagates according to the usual q.m. laws of adding complex amplitudes, thus reconciling its particle nature with observed interference phenomena. Furthermore see his closely related answers on this question at http://www.youtube.com/watch?v=_7OEzyEfzgg&feature=related.

The determining evidence ruling out waves includes 1. the photoelectric effect since waves can not cause ejection of electrons with the same frequency energy relationship, and the non relationship between the E field amplitude and energy 2. Compton scattering (not mentioned in his lecture) not explainable under a wave theory 3. An argument he alluded to relating to the equation for scattering multiple particles not corresponding any more to Maxwell's equations (which I don't quite follow). With the adoption of the probability amplitude propagation theory of QED, apparently no evidence is against the particle hypothesis. (I myself would also like to see a QED derivation of the old Einstein entropy density of black body radiation in a closed cavity, however, i.e. the one that looks like 1/2 particle and 1/2 wave)

Note related to a comment below:I previously (mis)attributed these arguments to his 1964 Messenger Lectures at Cornell, available online (only for PC's?) here and later published as "The Character of Physical Law", but the correct ref. is as above.

PS. I myself do not feel that the question is confused at all, and actually voted it up, but it is the sort of question that often gets many confused answers. I'm not too sure how we should handle this)

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I fixed your spelling of Messenger, added year, and URL to the lectures - via Bill Gates. +1 for your answer. I think it is a totally legitimate conclusion to say that Newton's corpuscular theory was right but the corpuscles have to become photons and adopt the wave properties previously associated with "classical waves only". –  Luboš Motl Mar 19 '11 at 17:58
    
I think I made a mistake, due to my confusion about the subject. I now understand a bit more the subject thanks to you (though I don't perfectly understand Feynman's English). What I should have written is: "Quantum mechanics is apparently the best theory we have to explain Yougn's experiment. But would it be possible the keep the classical concept of particle (I only mean by there a material point) with a new definition of trajectories deduced from a new kind of F=ma?" (The vocabulary may not be well chosen.) I suppose it is not, as quantum mechanics is more used today; but why? –  Isaac Mar 20 '11 at 13:36
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When we say it doesnt behave as a particle, we mean it doesnt behave as a classical particle. But it does behave as a particle, in the sense of an elementary particle, which share some characterstics with classical particles, and some with classical waves.

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As the other answers tell you there have been people trying to explain the two slit experiment with different mathematics than quantum mechanics.

Could it not be a particle following new laws? ,you ask. Calling a particle a material point .

The answer is no, experiments have confirmed that the quantum mechanical descirption is the valid one, generally, not just for the two slit experiment. Do look at the link in sb1's answer.

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Honestly - no experiment can prove that a law is correct. Whereas, experiments will agree with accepted theories - until we find new experiments that don't. –  Sklivvz Mar 19 '11 at 15:14
    
Well, from an experimentalist's point of view, exeriments try to falsify theories. Up to now quantum mechanics has not been falsified and in that sense it is still the valid theory, while alternate views have been falsified. –  anna v Mar 19 '11 at 16:33
    
Of course quantum mechanics is a valid theory. I didn't mean to imply anything different. But over and over, Nature has proven that things are rarely so simple as we think, and even when it looks like we have a good grasp of things... we don't. –  Sklivvz Mar 19 '11 at 16:49
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