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First off I have found several different definitions of duality and complementarity, so if anyone has a clear idea on what it meant with these terms please do share.

Now, what I mean is the following: in the wave-particle picture for light and for massive particles, can all phenomena be interpreted in both pictures, or do certian problems rely exclusively on one picture?

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  • $\begingroup$ If you're interested in the application of these terms to experiments like the double-slit experiment where interference patterns are either observed or not observed depending on whether we know which path was taken, Wootters and Zurek came up with a technical definition of the "complementarity" between interference and which-path information in a 1979 paper, not available free online but you can read some discussion of it in this paper (pdf link). $\endgroup$ – Hypnosifl Dec 11 '14 at 15:43
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    $\begingroup$ Neither term has any functional meaning in modern physics. I would suggest to treat them as historic artifacts. $\endgroup$ – CuriousOne Dec 12 '14 at 0:45
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In physics, complementarity is a fundamental principle of quantum mechanics, closely associated with the Copenhagen interpretation. It holds that objects have complementary properties which cannot be measured accurately at the same time. The more accurately one property is measured, the less accurately the complementary property is measured, according to the Heisenberg uncertainty principle

On the other hand, the wave–particle duality is the concept that every elementary particle or quantic entity exhibits the properties of not only particles, but also waves. It addresses the inability of the classical concepts "particle" or "wave" to fully describe the behavior of quantum-scale objects.

To answer your question more specifically, any quatum system exibits both phenomena simultaneously, so they are not alternative interepretations of the same phenomenon, but rather two different characteristics shared by any quantum system.

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The second answer is correct, some problems need wave-treatment, others may be treated with the particle approach.

Let's make clear the specific of each case: in the quantum theory an object (which typically is microscopic) is described by a wave-packet. In some experiments, and for some particles, this wave-packet is small (we say in this case that the particle is well-localized).

As long as we pass it through beam-splitters, but we just examine its passing through bubble chambers or ionization chambers or different materials, we may be able to treat it as a particle. Also, when the object is big, i.e. its linear dimensions >> wave-length, we can treat it as a classical object.

But if the wave-packet is sufficiently long, and we pass it through a beam-splitter, e.g. Mach-Zender beam-splitter, the two instanciations of the wave-packet meet on the screen at the exit a sufficiently long time for producing an interference pattern. For understanding why packet-length is important you need to read about coherence length.

Now, there is also another issue about particle vs. wave behavior. Even if the wave-packet is split into two, i.e. a transmitted and a reflected packet, when you place detectors on the transmitted path and on the reflected path, in only one of the two detectors will be produced a click. Only one of the two wave-packets gives a response. Why? The particle is one, we have a single particle, not two.

Do you understand how it is possible, why one wave-packet gives a response and the other doesn't? Don't you understand? Well, welcome to the club! Nobody understands! The quantum objects behave in a strange way. And though, this is the answer, the particle is one. This is also a particle-like feature of the quantum object.

Good luck!

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    $\begingroup$ Actually, it's completely trivial to understand why single particle wave packets can only produce a single quantum event in an absorbing detector: there are NEITHER particles NOR are there any wave packets. There is only one quantum field which changes one of its quantum numbers. When the physical terms of particles and wave packets were invented by humans we simply didn't know that. Today we do, but unfortunately, it seems to be next to impossible to remove false ideas from the imagination of the public once they have established themselves as self-evident truths. $\endgroup$ – CuriousOne Dec 12 '14 at 9:53
  • $\begingroup$ @CuriousOne: you think it's trivial? Imagine the beam-splitter on a cosmic station, the transmitted part of the wave-packet flying to a lab at 1 light-year distance, and the reflected part to another lab also at 1 light-year distance from the station, but in opposite direction. Then the field has to occupy a volume of 2 light-years length. A detection takes less than a nanosec. Do you imagine all this field changing a quantum number in less than 1 nanosec.? Signals with velocity 2x$10^9$ light-years/sec. should run through this field, for ensuring that only at one lab a detection will occur. $\endgroup$ – Sofia Dec 13 '14 at 1:01
  • $\begingroup$ This experiment has been done over distances of tens of millions of light years, if I am not mistaken (by measuring the coherence of light from far away galaxies). You are, however, giving a great example of an argument that puts human scales at the center of a physical argument. To YOU, a length scale of a light year seems very long. To quantum electrodynamics it's obviously of no measurable importance. $\endgroup$ – CuriousOne Dec 13 '14 at 1:03

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