# Wave-particle duality

## Main Question or Discussion Point

Photons are always called 'particles'. But through many experiments (by scientists such as Geoffrey Taylor), it has been found that photons show some strange characteristics which resemble those of waves. In fact scientists also reveal that electrons also show wave-like nature(in fact they have frequencies). So what can we call them-waves or particles? Or none of them? And how is the Heisenberg's uncertainty principle applicable here?

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Fredrik
Staff Emeritus
Gold Member
"Particles" is the appropriate word, but these are quantum particles, not classical particles. A classical particle can be thought of as small massive spheres, but quantum particles can't. If you're interested in how they are different, I can recommend the book "QED: The strange theory of light and matter", by Richard Feynman. It's a short book that doesn't use mathematics.

Personally I prefer the term "warticle" ;p

some think its particles guided by pilot waves (DeBroglie). heisenburg's uncertainty principle applies because quantum entities are expressed by probabilities, and these probabilities have standard deviations, and it is the product of the standard deviation in momentum times that of position that has a bound defined by heisenburgs principle. typically wavelike entities have better defined momentum because the DeBroglie wavelength is what shrodinger used to motivate his equation (i think).

http://plato.stanford.edu/entries/qm-bohm/
http://en.wikipedia.org/wiki/Uncertainty_principle

I sometimes used to picture them like packets, like a tiny box with a piece of wave inside, a space-limited (and time-limited) wave impulse.

If you imagine each of them like in the attached picture then each is "space-confined", but many of them together forming a beam can be seen as a continuous wave (because the envelope is a piece of squared cosine, if you put many of them one after the other in the proper position and sum them all you should get a constant envelope).

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Photons are always called 'particles'. But through many experiments (by scientists such as Geoffrey Taylor), it has been found that photons show some strange characteristics which resemble those of waves. In fact scientists also reveal that electrons also show wave-like nature(in fact they have frequencies). So what can we call them-waves or particles? Or none of them? And how is the Heisenberg's uncertainty principle applicable here?
Some people use the term wavicle.

Pete

The uncertainty principle is, in fact, linked to Fourier theory. It is a principle of the Fourier transform of all signals (waves) that the time duration and temporal bandwidth product is limited to:

$$\Delta t \Delta \nu = 1$$

Further, the spatial frequency k is propotional to the momentum of the "wavicle" (with a constant 1/h-bar). So, we find that the width of the wavicle is constrained to:

$$\Delta x \Delta p = hbar$$

So the link between the uncertainty principle and the wave property of matter is mathematical in nature. The wave property of matter, on the other hand, requires experimental evidence.

For reading, google for "bandwidth time product". The Stanford Exploration Project has nice slides.

reilly