# What does the wave principle of light actually represent?

Light has a dual nature, one of photons and the other of waves. But energy doesn't really travel in waves. So what do the wave represent?

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The rays represent the (macroscopic) path followed by the photons. –  Wouter Mar 20 '13 at 15:58
@Wouter if the number of rays is infinite and each consists of photons then the number of photons and thus the energy of the light wave, even for a finite time, must be infinite. –  ketan Mar 20 '13 at 16:05
No, the rays do not consist of photons, they are the paths that the photons follow. There is a very crucial difference. –  Wouter Mar 20 '13 at 16:22
In response to the v2 form of the question: energy does travel in waves. Take a look at this wikipage to see how this relates to photons. –  Wouter Mar 20 '13 at 16:39

Light has a dual nature, one of photons and the other of waves. But energy doesn't really travel in waves. So what do the wave represent?

Let us be clear in our terminology and the domain to which we apply it.

Our everyday life is lived with classical mechanics and classical electricity and magnetism (as long as we do not use the net and transistors and the other paraphernalia of modern life). Classical theories are well developed mathematically and are applicable in the domain where hbar can be considered practically zero. Particularly for light Maxwell's equations have been validated in this domain and describe light as a wave. This wave is a propagating changing electric and magnetic field and is a wave in the four dimensional space time, there are peaks and valleys. It displays the classical wave behavior of interference and dispersion.

These carry energy, a universal example is simple sunlight.

Now you use the word photon. The photon is one of the elementary particles of the standard model. This means that we are no longer in the classical domain but in the quantum mechanical domain when we speak of light as a collection of photons. It means that it behaves sometimes as a particle, (photoelectric effect) i.e. it has a specific (x,y,z,t) value and sometimes as a probability wave , i.e. according to a quantum mechanical wave function the square of which gives the probability of finding a photon at a specific (x,y,z,t) which probability has a wave like variation in space because it is the solution of a wave type differential equation describing the dynamics of the situation. Note, it is the probability which shows a wave nature, not the "particle" itself.

Now the wave nature of Maxwell's equation and the wave nature of the probability function are mathematically reconcilable, so that the frequency of the classical wave is the nu in the energy of the photon in E=h*nu. In addition Lubos Motl has an interestin article about the collective emergence of classical light from photons in his blog, though it needs a background in physics to understand it.

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But energy does travel in waves. Consider the waves on the surface of a lake for example. Electromagnetic waves (light) carry energy to your radio where they wiggle the electrons in the antenna.

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'Energy travels in waves.' What does that mean? Do photons travel up and down the wave, or do the crests and troughs represent the amount of energy at a point? –  ketan Aug 11 '13 at 3:47

Er...

Light has a dual nature, one of photons and the other of rays.

Close. The dual nature is of photons (particles) and waves.

Rays are a visualization tool, and should not be thought of as physical in and of themselves.

They represent the nominal path of photons (an idea not well defined in modern theory, BTW, but still a useful visualization) and/or the local direction of wave propagation.

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It is important to first get some terminology straight:

• The wave particle duality of light is the principle that light exists in the form of both a stream of particles (photons) and a wave. In some situations, light will behave as a stream of particles (e.g. during the photoelectric effect and blackbody radiation). Other times it will behave as a wave (which is observed as it undergoing effects such as diffraction, constructive and destructive interference, and polarization).

• A photon is a single packet of energy.

• A wave is the uniform propagation of energy. As such it does travel as a wave. The peaks in the wave contain the highest point of energy, and the points directly between peaks contain no energy at all. The energy flux of an electromagnetic wave, known as the Poynting vector, is represented by the following equation: $$\vec{S}(t)=\frac{1}{\mu_0}\vec{E}_0\vec{B}_0cos^2(kx -\omega t+\phi)$$

So put simply, the wave principle of light represents the energy of light distributed over a continuous interval. The particle principle represents the energy existing in discrete "quanta" or "packets". The wave-particle duality principle is the observation that both are accurate.

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