How do electromagnetic waves wave?

Electromagnetic waves have a physical crest and trough as observed in microwaves and radio waves. I understand that is electromagnetic field vectors that wave, not the photon. But how do they wave? What does causes them to change direction?

• Why do you think that "photons manage to go up [...] and go down"? See physics.stackexchange.com/q/90646/50583 for a question about the relation between the notion of an electromagnetic wave and a photon Sep 27, 2017 at 23:11
• @ACuriousMind I read and does not answer my question. Maybe I am not grasping the concept; Is there a more intuitive way to answer my question? I see the physical affects of the wave in a microwave where we see the heat spots, so I am still not sure how the waves go up and down or that visualization is wrong? Sep 27, 2017 at 23:38
• The visualization is wrong if you're not aware that the only spacial direction that matters in the usual drawing is that of the propagation: those up/down and left/right arrows for the electromagnetic field mean to depict the electric and magnetic intensities, not a spatial extension - ideally it's a light ray and the associated fields don't extent beyond the ray "border" (which has zero "radius"). And yes, your question is loaded, it'd be better to ask several different questions. Oct 9, 2017 at 19:29
• To reopen this question (v4) consider to only ask one subquestion per post. Oct 10, 2017 at 6:53

It is important to remember that an electromagnetic wave is exactly what it says on the tin: an electro-magnetic wave, i.e. it contains both an oscillating electric and an oscillating magnetic field.

When the amplitude of one of the fields decreases, it causes also a change in the other field, and vice versa. This is due to Maxwell's equations, which link the changes of electric and magnetic fields in time and space.

A helpful picture to visualize what is going on in such a wave is the following:

As you can see, the electric field alone propagates as a sine wave, as does the magnetic field. However, it matters that they are both propagating along the same direction and have the same phase, while their polarization (the direction their field vectors point in) are 90° offset.

Maxwell's equations specifically state that a change in space of the electric field ($\nabla \times \vec E$) causes a change in time in the magnetic field ($- \frac{\partial \vec B}{\partial t}$). The second equation goes the other way around: a change in space in the magnetic field ($\nabla \times \vec B$) causes a change in time in the electric field ($\frac{1}{c^2} \frac{\partial \vec E}{\partial t}$).

For microwave ovens, it is not useful to try to analyze the heating process in terms of photons and electrons. This process is understood as AC electric fields acting on water molecules with an electric dipole moment. An electric field will polarize water (the relative permittivity of the liquid is about 80), doing work on the molecules. When the field is turned off, the orientation of the molecules will relax to randomness again. So energy is transformed to heat.

The more often this happens, the higher the rate of heating. In a household microwave oven this is done $2.45\cdot10^9$ times per second, but the exact frequency is not important.

Photon's only move in their direction of travel, it is the electric field vector and magnetic field vector that oscillate, making them waves.

The presence of these fields induces fields in adjoining space, thus the energy in the field travels, wave like.

• How the electromagnetic field vector and magnetic field vector creates a physical change in other objects? I mean, electromagnetic force is only exchanged via photons, right? So photons, would then create another photon? And if photons travel in one direction or direction of travel, how the electrons in the food change their kinetic energy to heat only on specific points not on other? I am positive you have a clear answer, just curious. Sep 27, 2017 at 23:47
• It looks like his question is more about standing waves in a microwave, like why there are more photons in the middle that at the walls. Thus I've deleted my answer, you are on your own now :) Sep 27, 2017 at 23:53