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I have my head around wave-particle duality, however people tend to refer to light as either a wave or a particle in different situations. If I were to consider light as a particle am I still regarding it as an oscillating electric wave and magnetic wave? And are these waves a reason we can consider light a wave or is it purely a quantum effect?

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  • $\begingroup$ A particle is a packet or indivisible unit of light. A wave is light that oscillates at a certain frequency. Not the best definitions, a bit vague. $\endgroup$ – Alexander Hulse Oct 18 '13 at 22:02
  • $\begingroup$ Check out my answer and others to the link that Phyllipe gave above. One can think of the second quantized EM field: its state changes in discrete units - if you like, photons are the discrete "messages" the EM field swaps with other fields as the interact to build up the behavior that defines our World. When the EM field is in a one-photon state, the means of the electric and magnetic field observables do indeed propagate in spacetime EXACTLY following Maxwell's equations - so you can't get much "wavier" than that, even though there is only one photon. I'll write this up better tomorrow ... $\endgroup$ – WetSavannaAnimal Oct 19 '13 at 13:33
  • $\begingroup$ ...as an answer if someone doesn't get to it first. $\endgroup$ – WetSavannaAnimal Oct 19 '13 at 13:33
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Purely quantum effect, wave and particle are, at the same time, all roughly correct (although not wave in the sense of being like a water wave and not a particle in the sense of a tiny billiard ball). The idea of "wave sometimes" and "particle sometimes" is pretty outdated. Here's how I like to think of things.

There is one fundamental object in all of this - this is the second quantized EM field.

This one everpresent and everywhere object helps define the behaviours that we witness in our World by interaction with the other quantum fields that fill (and define) space.

It is the communications that are the discrete particles. The interactions of the EM and other field are brought into being by "messages" swapped between the fields. These "messages" we call photons. Just like a telephone call, or a data packet through the internet, these messages are "discrete". You can't have half a telephone call! But, just like a telephone call or a data packet, a photon can have different effects depending on which modes of the second quantized EM field make it up and with what superposition weights in those modes it has. The quantum observables define the statistical distributions of the outcomes of interactions the second quantized EM field has with the other fundamental fields.

Imagine the EM field in a one photon state: say it is formerly in the quantum ground state and an excited atom has spontaneously radiated into it, i.e. sent a "one photon" message to the unique quantum EM ground state. Then the means of the electric and magnetic field observables propagate in space and time precisely following Maxwell's equations. For the simple one-photon state, the means of the electric and magnetic field observables as functions of position and time wholly and uniquely define the second quantized EM field's state, in the same way as a simple Poisson probabilitu distribution is uniquely defined by (but is not equivalent to) its mean.

So our second quantized EM field has one "particle" in it, and the means of the $\vec{E}$ and $\vec{B}$ observables wholly define the field in this state. These means fulfill Maxwell's equations - which are EXACTLY the relativistic wave equation for one photon in free space. You can't get "wavier" than something whose Cartesian components fulfill D'Alembert's wave equation!

I think this is why Dirac made his famous statement "each photon interferes only with itself" because, unless there is entanglement, foretell the behavior of a classical field by doing the same for each photon and interpreting the probability density as the classical energy density for the corresponding photon states that make it up. His statement is not altogether true because it doesn't hold with entanglement present. See my answer to the Physics SE question How can we interpret polarization and frequency when we are dealing with one single photon?.

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My understanding is this: The wave is a description of the probability of a photon showing up at some particular place and time. It's particle nature is not expressed until the wave function collapses, when a detector detects it.

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