I have no background in physics. This isn't for homework, just for interest.
In quantum physics, it's described that a particle can act as both a particle and a wave.
Quoted from HowStuffWorks "Wave-Particle Duality"
Today, physicists accept the dual nature of light. In this modern view, they define light as a collection of one or more photons propagating through space as electromagnetic waves. This definition, which combines light's wave and particle nature, makes it possible to rethink Thomas Young's double-slit experiment in this way: Light travels away from a source as an electromagnetic wave. When it encounters the slits, it passes through and divides into two wave fronts. These wave fronts overlap and approach the screen. At the moment of impact, however, the entire wave field disappears and a photon appears. Quantum physicists often describe this by saying the spread-out wave "collapses" into a small point.
I have trouble visualizing a particle transforming into a wave and vice-versa. The quote says that light travels away from a source as an electromagnetic wave. What does that even look like? How can I visualize "a wave"? Is that supposed to look like some thin wall of advancing light? And then, the quote says, at the moment of impact, the wave disappears and a photon appears. So, a ball of light appears? Something that resembles a sphere? How does a sphere become something like an ocean wave? What does that look like?
My (completely uneducated) guess is, by a particle becoming a wave, does that mean that this expansive wave is filled with tons of ghost copies of itself, like the one electron exists everywhere in this expansive area of the wave, and then when it hits the wall, that property suddenly disappears and you're left with just one particle. So, this "wave", is really tons of identical copies of the same photon in the shape and form and with the same properties of, a wave? My guess comes from reading about how shooting just one photon still passes through two slits in the double-slit experiment. So the photon actually duplicated itself?
Best Answer
What we observe in nature exists in several scales. From the distances of stars and galaxies and clusters of galaxies to the sizes of atoms and elementary particles.
Now we have to define "observe".
Observing in human size scale means what our ears hear, what our eyes see, what our hands feel, our nose smells , our mouth tastes. That was the first classification and the level of "proxy", i.e. intermediate between fact and our understanding and classification, which is biological. (the term proxy is widely used in climate researches)
A second level of observing comes when we use proxies, like meters, thermometers, telescopes and microscopes etc. which register on our biological proxies and we accumulate knowledge. At this level we can overcome the limits of the human scale and find and study the enormous scales of the galaxies and the tiny scales of the bacteria and microbes. A level of microns and millimeters. We observe waves in liquids with such size wavelengths
Visible light is of the order of Angstroms, $10^{-10}$ meters. As science progressed the idea of light being corpuscles ( Newton) became overcome by the observation of interference phenomena which definitely said "waves".
Then came the quantum revolution, the photoelectric effect (Particle), the double slit experiments( wave) that showed light had aspects of a corpuscle and aspects of a wave. We our now in a final level of use of proxy, called mathematics
The wave particle duality was understood in the theory of quantum mechanics. In this theory depending on the observation a particle will either react as a "particle" i.e. have a momentum and location defined , or as a wave, i.e. have a frequency/wavelength and geometry defining its presence BUT, and it is a huge but, this wavelength is not in the matter/energy itself that is defining the particle , but in the probability of finding that particle in a specific (x,y,z,t) location. If there is no experiment looking for the particle at specific locations its form is unknown and bounded by the Heisenberg Uncertainty Principle.
What is described with words in the last paragraph is rigorously set out in mathematical equations and it is not possible to understand really what is going on if one does not acquire the mathematical tools, as a native on a primitive island could not understand airplanes. Mathematics is the ultimate proxy for understanding quantum phenomena.
Now light is special in the sense that collectively it displays the wave properties macroscopically, and the specialness comes from the Maxwell Equations which work as well in both systems, the classical and the quantum mechanical, but this also needs mathematics to be comprehended.
So a visualization is misleading in the sense that the mathematical wave function coming from the quantum mechanical equations is like a "statistical" tool whose square gives us the probability of observing the particle at (x,y,z,t). Suppose that I have a statistical probability function for you, that you may be in New York on 17/10/2012 and probabilities spread all over the east coast of the US. Does that mean that you are nowhere? does that mean that you are everywhere? Equally with the photons and the elementary particles. It is just a mathematical probability coming out of the inherent quantum mechanical nature of the cosmos.