Is electromagnetic wave a matter itself?

[Markovnikov ya]

What is the relationship between photon and electromagnetic wave?

I am trying to understand light, it is so weird. Light is not an electromagnetic wave, since it has different speed in different mediums. Light does not have mass (the mass that can be derived from the energy is not a real mass), so its not a particle either. What is it?

Back to my original question about EM wave being a matter. Well, it has energy, it has speed of distribution, it exerts pressure on reflecting or absorbing particles, so it must have a mechanical momentum, if it has momentum, then it must have mass. So it has all the components necessary to be considered matter. But its speed in any medium is the speed of light. But you cannot say the same thing about light, its speed changes with change in refractive index of the medium.

Ok, you are saying that electromagnetic wave is a lot of photons. But the waves' speed changes as the refractive index of the medium changes. Yet photons can only exist while moving with the speed of light. Maybe that is where some of the photons are absorbed by the medium (or reflected). Yet the light still exists (because some photons got through the medium without change in speed?), only with smaller intensity? But then I don't understand. EM wave moves in any medium with a speed of light, no matter what the refractive index is. Then why doesn't the EM wave of light disappear when some photons are absorbed?

I guess the question would be: WHy is any light absorbed at all if EM wave is supposed to travel at a speed of light through all mediums? It means that light is not EM at all! my head hurts.
Or does it mean that light is light and EM wave is EM wave. And classical EM wave does not have any photons?

 

[ZapperZ]

An electromagnetic wave is a lot of photons.

Zz.

 

[cwilkins]

EM waves are a steam of particles. This is true to the extent that any device capable of measuring light will discover that these "waves" interact with the detector in a discrete manner.^[1] That is to say, individual particles hit the detector one-by-one. In case you are wondering why you can't see this yourself, most streams of light completely saturate the detector (e.g. your eyes) or otherwise render it incapable of distinguishing the particles. The point is that light is composed of particles, even if there are a lot of them.

Particles of light (photons) do not have mass in the inertial sense, but they do have energy and momentum stored in their internal fields.^[2] These are the properties of light which allow it to interact. For example, an atom may be struck by a photon and its energy could be absorbed in the form of an electron whose quantum state is excited (e.g. it jumps to a higher orbit around the nucleus, or it might be knocked off of the atom entirely). I cannot tell you what it would look like to watch this absorption take place, only that the photon is destroyed and the internal electric and magnetic field energy is somehow given to the electron, which it uses to reach a higher energy state. The reverse process can happen, too, which is why you might still see light coming through the other side of a material with which light has been absorbed. To answer your related question, it doesn't matter what speed light travels, only that contact is made and energy is transferred.

There are several reasons why the stream of particles behaves like a wave. In a classical sense, the electric and magnetic fields which constitute the photon satisfy a "wave equation." This means that a photon travels with a well-defined propagation speed, which is the speed of the light, as well as a frequency and wavelength. Second (and less intuitively), the electric and magnetic fields are quantized, which leads to wave-like quantum mechanical effects. The main quantum effect is that there is some sort of probability distribution for where on the detector photons are "likely to arrive." In the end, though, it is still a stream of particles, which is why the wave still seems to exist even though parts of it have been destroyed.

I would recommend Feynman's QED for a good intuitive and mostly math-free explanation of how light and matter interact.

References:
[1] R. P. Feynman, QED, p. 15 (2006)
[2] D. J. Griffiths, Introduction to Electrodynamics, p. 355 (1999)