AC and Maxwell's Equations
A rotating magnet turns a nearby compass needle
A power station turns a distant motor using coils. Here there is no direct connection shown, there is a capacitor with an electric field across it as shown by the voltmeter. I have stopped time in the animation to show that the voltage is zero when the current is maximized.
A real capacitor and inductor (coil)
In this model of a coil and a capacitor, an alternating current (AC) is shown. Electrical charges build up on one side of the capacitor, producing a an electrical field between the plates of the capacitor as shown by the dark arrows. When the capacitor can hold no more charge the current reverses and gradually increases, driving a magnetic field (shown by the N and S for North and South) until the current reaches a maximum and there is no more voltage across the plates of the capacitor. Having exhausted the potential energy of the voltage the magnetic field now begins to collapse and continues to push the current in the same direction, this time building up a voltage in the capacitor with opposite polarity, shown by the plus and minus signs. When the magnetic field is zero (as it must eventually become), the voltage is at a maximum and when the magnetic field is at maximum the current is also at a maximum and the voltage is at zero. Thus we see in the coil a kind of flywheel with inertia, reluctant to start moving and reluctant to stop once it is, and the capacitor is a kind of spring, eager to return from its stretched or compressed condition. On the right can be seen voltage (red/blue) and the magnetic field (gold/purple) with a teal vector representing constant energy.
For a radio transmitter a continuous wave train is emitted radially, and this simulation shows the effect of doppler shift also. Travelling away from the red/blue source dipole the purple dipole sees no energy at all, whereas the gold dipole sees the emitted frequency doubled.
Although mathematically the same, things are a little different for a photon; photons are single pulse of energy, not a wave train.
How you picture a photon in your mind is a matter of subjectivity, it can be like this three-dimension representation:
or like this two-dimensional representation, showing wave superposition from which we obtain directionality. Androcles' third law: For every photon there is an equal and opposite rephoton. The rephoton goes away from you and so is not detected.
This is in agreement with Faraday's Law for induction embodied in Maxwell's equations,
which says the electric field is proportional to the change in the magnetic field. Some purists want that to read curl E = -dB/dt but really the electric field is wherever the conductors take it. In this motor is parallel with the shaft, curling around the iron, but also across the brushes. "Curl" is misleading.
A magnetic field which is not changing produces no electric field, and an electric field that is not changing produces no magnetic field. The motor will generate when the shaft is driven and an electric field will appear across the brushes.
We can represent the voltage applied to a capacitor as a complex quantity
(ref: http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/info/signals/complex/react.html)
In the case of a photon (which seems to be a huge mystery to many), we have the same operation but without any electrons or any wires or coils. The same laws apply, the magnetic field exists away from the coil and the electric field exists in the space between the plates of the capacitor. Both these spaces are empty, although it is possible to fill them with matter such as air. When we do that we say we have a dielectric and a diamagnetic material that can affect the operation, but it is not a requirement for the process to occur. Thus the vast reaches of space across which light reaches us in packets of energy from individual atoms need contain no aether with properties of permittivity or permeability, these are properties of matter and not a requirement for the transmission of energy. All that is necessary and sufficient is that magnetic and electric fields must exist in the vacuum of space. The "wave" nature of the photon is simply a misinterpretation of such concepts as "wavelength", for the wave shown above is a wave not in space, but in time. "Now" is shown by the black vertical line and as time passes the trace shows the voltage and gaussage* as it once was, not how it is now. It doesn't actually exist "now", but it did "then". There is no wave"length", only wave duration. The horizontal axis is the time axis, not a distance axis. The "poles" of the photon are it's centre and the surface of a sphere at infinity, for there is no electric or magnetic field except between poles.
To understand what a photon is, think of a coil and capacitor with the hardware missing. How fast it moves is not a requirement for its operation.
* I'll call it 'gaussage' for want of a better word. Electrical pressure is "voltage" named after Volta, magnetic pressure would analogously be gaussage named after Gauss.
> [hanson]
> Another way to look at photon representation via a sinusoidal EM
> parameter display would be by citing/using the **fundamental**
> observation that/of
>
> "A collapsing E-field generates an expanding M-field & visa
> versa and these first principles / conservation laws say that
>
> 1) If there is no field of neither M nor E: Nothing happens
> 2) If there is a field present but no change: Nothing happens.
> 3) If there is a Magnetic Field that starts to collapse, an E field arises.
> 4) If M becomes zero, the E will be max+ at pi/2, then
> 5) E starts to collapse at p/2 down to 0 at pi while
> M rises from 0 at pi/2 to max at pi... ...etc & analog to/till 2pi