Why do we say that electromagnetic wave is oscillating? Or does light propagate really in a wavy form like this image?
What is making the photons oscillate and how is it oscillating is it oscillating back and forth (and if oscillating back and forth how does it move if its moving back and forth at the same point?)?
Why do we say that the EM field is constantly changing when in the above picture its constant? (we know that a compass is not able to follow an electromagnetic radiation because the EM field is constantly changing)
Answer
In light propagation, oscillation does not mean any movement in space. It is the value of the electromagnetic field, at one given point in space, that oscillates.
The picture that you quote does not represent the movement in space, but the electromagnetic field value as a function of time.
Compare to waves in water: if you put a little boat on the water, the boat will actually go up and down when a wave passes by, showing that the water is indeed going up and down. For electromagnetic waves, there is no matter or photons that go up and down.
Instead, you have to imagine that there is a little arrow associated to each point in space: this little arrow is the electric field direction. Another arrow, at the same point, is the magnetic field. These two arrows change size and direction with time, and in fact they oscillate. But remember they only are related to one point in space. The next point in space will have different arrows. The whole space is filled with many arrows, one at each point, and they interact with each other. This interaction allows for the oscillation of one of them to be transmitted to the next one, and the next , etc.
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