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Quantum Mechanics.

Could anyone help me to understand the concept involved?

Double slit experiment can be easily understood by Wave nature of light, but while explaining it with photons, it required a lot of mathematics (Englert–Greenberger duality relation). Can anybody tell me what is the physical interpretation of theory rather than using probability functions?

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The physical interpretation of the theory is that it is a gadget calculating and using probability functions. So I guess it means that the answer to the question "What is the physical interpretation of theory rather than using probability functions" is "Nothing". –  Luboš Motl May 18 '11 at 10:48
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I can't figure out what you're asking at all. Have you tried reading through the other questions about the interpretation of quantum mechanics to see if someone else already asked what you want to know? –  Mark Eichenlaub May 18 '11 at 11:55
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Quantum Physics (as all other areas) is what it is at face value. Quantum mechanics is a method of taking some input and calculating an output. For a discursive explanation see Feynman or a favourite of mine John Gribbin's work. –  Nic May 18 '11 at 12:39
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Possibly related: physics.stackexchange.com/q/6738/2451 –  Qmechanic Jun 17 '11 at 19:12
    
I recommend Feynmann's book QED. I believes he does it without maths, by drawing arrows or something like that. –  WIMP Jul 21 '11 at 7:07
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3 Answers

I don't know how you can understand it as photon by Englert–Greenberger duality relation, which is in itself derived from the wave nature. When light behaves like a wave, consider it as a wave; don't try to comprehend it as photons.

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One of the comments gives the "gadget interpretation" of QM, also known as the "Ithaca interpretation", or more colloquially, "shut up and calculate". The idea of this interpretation is that quantum mechanics is a black box gadget where you put in some inputs, and you get out a probability distribution for outputs as given by the Born interpretation. This distribution can be calculated using wave functions, density states, or path integrals, but none of them should be taken as "real". These are only computational tools to let us compute the right probabilities.

On further thought however, if Nature is a black box gadget with no internal structure (or if we're not allowed to talk about its internal structure), then why does QM have limitations? Why can't we score better than ${1\over 2}+{1\over 2\sqrt 2}$ in the CHSH game? Why can't we search a quantum database of size N with less than $\mathcal{O}(\sqrt N)$ searches? Why can't a quantum computer play a perfect game of chess or go in polynomial time? Why can't quantum computers solve the halting problem? At this stage, a practitioner of this interpretation will tell you, that's because that's just the way Nature is, followed by "shut up and calculate". Needless to say, this answer is very unsatisfactory.

Far more likely, the limitations of QM most likely suggest there is an internal structure to QM. If QM has an internal structure, it's our duty to find out what that is.

Another objection is that we're actually inside the gadget, or at least, it seems as if we're inside the gadget. If the gadget has no internal structure, then how do you describe the view from within? Is it really "Nothing", as suggested by Lubos?

Also, where do we draw the boundaries of this gadget (the Heisenberg cut aka Schnitt), and what is the preferred basis (or preferred POVM to be more precise) for the probability distribution?

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Well, I will try some simplification as I assume you are a student and have not yet started a serious course on the subject.

The word "quantum" means "a specific quantity". The verb "quantized" means that some physically measurable quantities, as energy, angular momentum, and others, have been observed to come in quanta rather than continuously.

Easy examples are colour spectral lines in the spectrum of excited atoms, which instead of showing a continuous frequency spectrum have sharp peaks. These peaks indicate that at that frequency excessively many atoms change energy levels by emitting a quantum of energy which is observed as that line in the spectrum, way over the background.

Quantum mechanics theory was created to explain and predict quantized behaviours in physical observables at the atomic level and below, but also in super fluids and super conductors which have macroscopic extent but quantized behaviours.

And it is a theory which deals with probabilities and needs a mathematical background to comprehend.

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I don't think this is accurate. Quantized doesn't mean discrete spectrum. There are observables with continuous spectrum. –  MBN Jun 17 '11 at 19:25
    
@MBN do not confuse necessary with sufficient. A discrete spectrum is sufficient show up the need for a quantum interpretation. It is not necessary to display a discrete spectrum in order to be composed by quanta. –  anna v Jun 18 '11 at 4:47
    
Yes, but if it isn't necessary then it is not a characterizing property. Then why put it in the definition! –  MBN Jun 19 '11 at 1:38
    
@MBNIt is not in the definition. I call it an example, and actually discrete spectra are part the experimental proof of what nailed quantum theory as physical. –  anna v Jun 19 '11 at 18:18
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May be I misunderstood, but when the sentence starts with "The verb "quantized" means..." it seems like a definition. Anyway, you know quantum physics better than me, I had no intention in arguing with you. I was just making a small remark, because someone may get that impression, that quantized means discrete spectrum. –  MBN Jun 20 '11 at 18:42
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