What does that sin wave of a photon represent? [duplicate]

I had an interesting thought in one of my classes, when we were talking about photons... I thought that if the speed of light is the fastest speed, and light goes in a straight line, then how come the motion of a photon is a sin wave which would be a greater velocity by a ratio of a length of a sin wave between 0 and 2 pi and 2 pi.

Of course I realise that the motion of a photon is not a sin wave. The position of a photon is random within a certain area, but has probabilities of being in particular places (quantum mechanics). The sin wave represents some kind of field, but I am not sure what, and how it relates to a photon.

• A minor point: The mathematical notation is $\sin{x}$ but that function is actually called “the sine function”, with an e, and the waves are called “sine waves”. Nov 5, 2018 at 18:57
• Possible duplicate of How do electromagnetic waves wave? Nov 5, 2018 at 19:42
• The fields rotate rather than oscillate: physics.stackexchange.com/questions/360638/… Nov 6, 2018 at 6:41

In a classical electromagnetic wave of a particular frequency (for example, red light), the magnitude of the electric field and the magnetic field oscillate in time at each point in a sinusoidal way, and the magnitude at each time changes in space (in the direction of the wave) in a sinusoidal way. So it is these two fields that are doing the “waving”, both as a function of time and as a function of position.

But these fields are not material things moving back and forth in space. It is just that, at each point, with time they get strong in one transverse direction, then weaker, then strong in the opposite direction, then weaker, etc. And, looking along the direction of the wave at a particular instant, they are strong in one transverse direction, then weaker, then strong in the opposite direction, then weaker. The direction of the two fields is perpendicular to the direction of the wave, and also perpendicular to each other.

When this classical theory is quantized, photons are the quantum excitations of this electromagnetic field, but before understanding what that means you should understand the classical picture of electromagnetic waves as oscillating transverse vector fields. As you realized, the photons do not move on a sinusoidal trajectory. Actually, they don’t have a meaningful trajectory at all because, as quantum particles, their position and momentum cannot be simultaneously measured with complete accuracy. However, they behave as if they move in straight lines at the speed of light.

Additional to G. Smiths answer I want tell you the story backwards in time.

Light, or more broad, electromagnetic radiation is emitted as a stream of photons. Excited subatomic particles, mostly excited electrons, fall back in less excited states and this time they emit photons. The light ends by the absorption of photons by subatomic particles. In short, EM radiation behaves in both the emission and the absorption like a stream of particles.

Years before scientists had learned how to produce electromagnetic waves. Pushing and pulling electrons forth and back in an antenna rod, these electrons get accelerated or rather excited. To be precise, at the beginning Hertz uses spark discharges but anyway in both cases excited electrons are involved. Hertz could measure the pulsating electric (and magnetic) field and it was discovered that EM waves - called radio waves, because they were used for information transfer - have an electric field component and a magnetic field component; both perpendicular to the direction of radiation and - in vacuum - both perpendicular to each other.

Since photons remain indivisible during their live (from the emission to their absorption), nothing prevents us to conclude that radio waves are a stream of photons. And since these photons are emitted from synchronized in acceleration electrons, these photons are moving also in a synchronized way. In short, the discovered field components of a radio wave could be made from the electric and magnetic fields of all the emitted photons. So each photon behave as a particle with oscillating electric and magnetic field.

The photon is not a wiggling particle in its trajectory. Only the intensity of the accompanying fields follows the sine function.