There are some things that confuse me about electromagnetic waves, and I haven't found good answers anywhere. Consider the following equation: E=E0 e i(wt-kx) (here E and E0 are vectors, I couldn't find the right symbols). The things that confuse me are the following: 1° We say that the power of the exponential is the phase of the wave. So at every instant it would correspond to the angle on the unit cercle. If the wave is linearly polarised, we could represent it as a cosine, so, on the graph, each phase would have different amplitude. But here is the confusion, the phase is not related to the amplitude - which is also confirmed given that the amplitude of the exponential is always 1, but given the graph of cos, it would seem to me that E0 should be multiplied by a value smaller than 1 of we are not on themaximum point (which is wrong, I know, but please help me visualise this in another way that would help clear my confusion). 2° For a linearly polarised function (the subject of my confusion could be extended to all waves however, but this is simpler to explain) the wave could be expressed as Ecos(wt-kx). How could this function be graphed in dependance of both t and x at the same time, to keep its form? This is what I don't understand. If we take x as a variable, then it's clear that on y (for example) we have its amplitude, but how does t enter the game? 3° (Bonus question) This is a bit unrelated to the previous two, but how could a beam of light be carrying Electric and Magnetic fields? This means that light should interract somehow with itself and other photons due to the field. I suppose it doesn't, because for there to be an interraction there needs to be a force, but since light has no mass there can be no force. Is this why a photon is called the EM force carrier?