# What does it mean (how is it visualized) for a particle to act as a wave?

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?

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Possible duplicate: physics.stackexchange.com/q/33333/2451 –  Qmechanic Nov 6 '12 at 22:13
The wave nature is what evolves with time and the particle nature is what is observed. This link may help: upload.wikimedia.org/wikipedia/commons/e/e7/… –  Dimensio1n0 Jun 18 '13 at 9:41

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 milimeters. 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.

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Thanks for the really detailed post and the concept of proxies. Surely mathematics isn't "the final" proxy to observe and learn? There may be others? –  Jason Oct 17 '12 at 7:38
Mathematics itself has several levels used in physics, and those are continually expanding as research progresses. The question becomes esoteric to mathematics, imo. –  anna v Oct 17 '12 at 10:35

At the moment of impact, however, the entire wave field disappears and a photon appears.

Any source that is content to describe scientific theories in terms of black magic is worse than useless.

How can I visualize "a wave"?

You can visualize it as y=sin(x). The wave's strength oscillates both over time (if you stand in one place and watch it pass), and space (if you "freeze" it in time). Light is more complex than more familiar waves (eg, waves in water), in that it's made up of oscillating electrical and magnetic waves.

So the photon actually duplicated itself?

No, it hasn't duplicated itself, just spread itself out so that it can pass through two slits simultaneously (just like a wave in water would do). The "collapsing" occurs due to the quantization of light, which is evident when the light gets absorbed by matter.

Realize that trying to visualize is a very limited vehicle for understanding quantum-scale physics. Since such tiny scales are out the domain of our ordinary sense perception, all we have available is hypothesis based on experiments. So, to understand a theory is to understand the paradoxes and experiments that gave rise to it; in the case of the wave-particle duality, that would be (among others) the double slit experiment, as you mentioned. On the quantization of light, a good class of experiments to ponder is those of emission/absorption spectra of elements.

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Visualization is difficult since, for example, the 'waves' that we're talking about a probability amplitude density waves. (In fact, we (teachers) should probably discourage initiates into the subject from trying to do this outright.)

One thing that has always helped when I describe this to folks is something I got from Paul Tipler's undergrad book (!) a long time ago when I was a teaching assistant. He makes a very useful distinction: when an electron (as a canonical example of a quantum 'particle') propagates it behaves in a wavelike fashion; when it exchanges energy with other systems, it does so discretely, like a particle.

In this sense then the 'duality' of quantum mechanics is less paradoxical and perhaps less seemingly contradictory. Electrons behave as waves and particles but never 'at the same time.'

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Particles in quantum mechanics are always particles and act as particles. E.g. an electron or a photon are always defined as particles according to the Standard Model and Wigner representation. E.g. an electron is defined as a particle with mass $m_e$, spin 1/2 and charge e and always behaves as a particle, never as a wave. As emphasized in CERN website "everything in the Universe is found to be made from twelve basic building blocks called fundamental particles".

There is not need for a wave-particle duality in modern interpretations of quantum mechanics (in fact quantum mechanics can be formulated without wavefunctions) and the wave-particle duality term is often considered a "myth", Klein prefers the term "misnomer". The historical roots of the wave-particle duality myth are explained in Ballentine's celebrated textbook Quantum Mechanics: A Modern Mechanics Development:

"Are ”particles” really ”waves”? In the early experiments, the diffraction patterns were detected holistically by means of a photographic plate, which could not detect individual particles. As a result, the notion grew that particle and wave properties were mutually incompatible, or complementary, in the sense that different measurement apparatuses would be required to observe them. That idea, however, was only an unfortunate generalization from a technological limitation. Today it is possible to detect the arrival of individual electrons, and to see the diffraction pattern emerge as a statistical pattern made up of many small spots (Tonomura et al., 1989)."

As stated by Klein:

"The miraculous "wave-particle duality" continues to flourish in popular texts and elementary text books. However, the rate of appearance of this term in scientific works has been decreasing in recent years."

Look Akira Tonomura’s video clip .wmv .mpeg for a beautiful demonstration of the appearance of statistical wave pattern on a double-slit interference experiment when a large number of independent single particles (electrons) impact the detector.

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In advanced formulations of QM, wavefunctions are substituted by kets, density matrices, Wigner distributions... Have you heard of some ket-particle, matrix-particle, or distribution-particle duality? No, because there is none. Moreover, wavefunctions are not waves, are functions. –  juanrga Oct 21 '12 at 11:07
Thank you! It was -4 some days ago. I would like to know two things: (i) why do they appeal to a hypothetical wave-particle duality, when $\Psi$ is not a physical wave but a mathematical function? and (ii) what term would they use in those advanced formulations of QM, where there is no wavefunction $\Psi$? E.g. in the Wigner-Moyal formulation of QM the state of the system is given by the Wigner distribution W and the evolution equation is not the Schrödinger equation but the Moyal equation $\dot{W} = \{H, W\}_{M}$. –  juanrga Oct 22 '12 at 14:59
I really think, this answer is spot on. –  Iota Mar 12 '14 at 21:04