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If waves are defined as the oscillation of a medium, why are electromagnetic waves called waves as they do not need a medium to travel through?

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The definition of a wave is not that it is the oscillation of a medium. Waves are called waves because they are solutions to a wave equation, which is, for a generic "excitation" $A(t,x)$ depending on the time $t$ and some spatial coordinate $x\in\mathbb{R}^n$, of the general form

$$ \frac{\partial^2 A}{\partial t^2} = c^2\Delta A$$

where $\Delta$ is the Laplacian for the spatial coordinate. The wave equation, in turn, is called a wave equation because it is precisely the equation that governs the archetypical system where a wave occurs - that of masses linearly connected by springs.

While a wave equation may arise from considering a medium, a medium is not necessary for a wave equation to occur, as Maxwell's equations and the disproof of almost all luminiferous aether theories show.

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  • $\begingroup$ Might you want to include the wave equation in the post? $\endgroup$ – Kyle Kanos Feb 20 '15 at 20:44
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    $\begingroup$ Just a thought: it may be worth explicitly stating that a wave is not defined as the oscillation of a medium. $\endgroup$ – David Z Feb 20 '15 at 23:24
  • $\begingroup$ This equation is for linear waves. Waves are something more general. See wiki before posting such answers. $\endgroup$ – Mikhail Genkin Feb 21 '15 at 1:58
  • $\begingroup$ @MikhailGenkin that's hardly a problem. EM waves are also linear in classical field theory. $\endgroup$ – Ruslan Feb 21 '15 at 6:08
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    $\begingroup$ -1 Saying "waves are called waves because they are solutions to a wave equation" completely inverts the rationale. The equation is called the wave equation because it describes waves. Waves came first, and the equations describing them came second and were named after them, not the other way around. $\endgroup$ – user541686 Feb 21 '15 at 10:16
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In addition to the other answers, back in the olden days they were thought of as oscillations in the ether. As a result of the Michelson-Morley experiment back in 1887, physicists began to think that there was no ether. But the term didn't change.

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    $\begingroup$ This best answers the actual question. $\endgroup$ – chowey Feb 20 '15 at 22:15
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Electromagnetic waves are called waves because there are waves (propagating disturbances), waves in the electromagnetic field.

These electromagnetic waves, like material waves, transport energy. According to the Wikipedia article "Wave"

In physics, a wave is disturbance or oscillation (of a physical quantity), that travels through matter or space, accompanied by a transfer of energy.

(emphasis mine)

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The electromagnetic waves satisfy the Maxwell equations for waves.

They don't need a medium for propagating, because these waves are their own energy-carriers, the photons. By that, they differ from water waves whose energy is propagated by the intermediation of the water molecules, or sound waves whose energy is propagated through the molecules of the media through which the wave passes.

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To give an answer we have to remember the historical facts. While making a light source point like and for better visible results nearly monochromatic one can see behind an edge an intensity pattern (fringes) right and left from the geometric line of the shadow. Hence the intensity pattern are something equal to water waves light has to have wave characteristics. It was not ask, why the maxima and minima of interfering water waves are moving. The sketch Thomas Young used for his explanation looks like the fringes from light. But in our days the real picture is that the the interference pattern of water waves are moving. Are the fringes from two light sources are doing the same?

What light is doing and water waves never do is that behind an edge only light produces fringes. In both cases there is diffraction but they are from different cause. Water waves disperse in their medium and that is the reason they "occupy" all the available medium around. This is not the case for light. The diffraction of light is limited to a narrow area left and right the geometric line of the shadow where the bright fringes and the zero intensity fringes are existing both in the geometric shadow and on the other side too. With the knowledge that physical fields are quantized and with the knowledge that photons and the surface electrons from the edge material are interfering one can count A and B together and interpret the fringes as the manifestation of of this common field. The next needed step from scholarly opinion is that two edges moved close enough to each over give a "harmonic" fringe pattern. Even if one use a well composed double slit this is nothing else as 4 edges.

To do the last step it has to keep in mind that the discovery of electromagnetic radiation is connected with radio waves. Radio waves are modulated EM radiation. Radio waves are made from oscilating electrons. Since Einstein we know, that the EM radiation from excited electrons is quantized and this quanta later were called photons. The frequency of this photons has nothing to do with the frequency of the generated radio wave. But what we see is the result of a huge number of syncronized photons: In sum they poduce a electric and a magnetic field, both perpendicular to each over and perpendicula to the direction of propagation (exactly so in vacuum). It is possible to conclude from this manifestation of electric and magnetic fields to the nature of photons? Yes, it is. Once emmited a photon is a indivisible unit of propagating energy with oscilating electric and magnetic field components.

One point more. In the near field of an antenna the maxima of electric and the magnetic fields are shifted by 90°. As you know, photons could be influented and their field componets could be rotated (polarization of light, irefringence, ...). It seems not impossible that the photons in radio waves do synchronize each other and this is the reason for antennas far field.

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