Historically wave and particle has been perceived as totally different phenomenons (before 20th century). Now is it widely accepted and there are experimental results to show that in fact both matter and light have a dual nature. Let's take light for example. Depending on the experiment it could behave as a wave(as in interference and diffraction) and it could be taken as a particle (as in explanation of photoelectric effect). If it has properties of both wave and particle at the same time, shouldn't we be able to explain the experiments with both wave and particle nature and not selecting either wave or particle? Why particle or wave, why not particle and wave? Please help me understand it and this question has been bugging me for quite some time now. I understand the standard explanation of both but I am having trouble putting them together. If there is anything I am missing please provide some link or reference to read.
[Physics] If matter and light have dual-nature, shouldn’t we able to explain the observed phenomenons using either wave or particle
photonswave-particle-duality
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What they actually measured was not particle behavior. It was just a quantized energy transfer to the probing electrons. That corresponds to the absorption of individual photons, but it doesn't mean the Surface Plasmon Polariton (SPP) field was acting as a particle. It just interacted locally with the electron, as it must. Typically particle-like behavior happens when decoherence happens. In the two slit experiment, a superposition of a photon hitting the screen in two separate places is dynamically unstable and will decohere. Consequently, we only observe a single flash at a single point. Nothing like this happened in their experiment. They set up a standing wave in their SPP, and tossed electrons to image the interference fringes. If any interaction is to happen, it will happen at the electron's position, and if any decoherence is to take place in order to secure particle-like behavior, it will happen when the electron is detected. The SPP itself never acts like a particle -- it just acts like a quantum object, which, of course, it is. This paper would be much improved without mentions of confusing notions of wave particle duality. They have cool results as it is; anything else is spurious.
Here is a very good article explaining what it actually is, thereby clarifying the paper's findings.
There have been attempts to describe the photoelectric effect by taking the EM field as a classical wave. For a discussion see a previous question "Can the photoelectric effect be explained without photons?". One of the answers describes that the photoelectric effect can be well explained considering the EM field more or less as a classical wave. To explain other experimental data though a quantized version of EM waves is needed.
On the second part of your question "And how is it that particle nature defeats the wave theory?" The above does not mean that these "wave quanta" (or photons) are particles in the sense of being localized objects flying around in space until they "hit" an atom kicking out an electron. A photon as a quantum of the waves is not localized or trackable as what one would think of a particle. Some physicists refere to these photons as particles which could lead to confusion (e.g. through which slit did they fly in these double slit experiments), but the bottom line is that even if you call these quanta particles they certainly do not defeat the quantum version of the wave theory.
Best Answer
Light and matter are neither particles nor waves. We use the particle and wave analogies to allow us to apply some level of intuition to the effects. The interference effects in light (and matter interference experiments) follow similar equations to waves in water so when we want to talk about the interference, we call light and matter a wave. When we want to talk about effects such as the absorption of a discrete quanta of light in the photoelectric effect or the billiards like collisions of two atoms in a gas, we talk about light and matter as particles.
Reiterating: light and matter are neither particles nor waves... they are something else, something different than a sum of the two catch phrases. That difference generates amazing effects that defy our macro-world based intuition.
As for calculations, quantum field theory (QFT) treats both matter and light in a way that handles both the wave and particle like effects in one theory. One thing to note: light and matter have significantly different properties in QFT. The 'particle' properties of light are not the same as the 'particle' properties of matter.