The speed of light is 299,792,458 meters per second. Does this number include the values above and below the x axis or only the values on the x axis?

I expect it includes the distance measured on the y axis as the photon travels above and below the x axis. Otherwise, an infrared would have to travel farther than an x-ray. Both would travel the same distance on the x axis, but the x-ray would would cross the axis more than the infrared. If they had the same amplitude, the x-ray would move more distance if the wave was stretched out into a straight line. If the infrared frequency is one and the x-ray frequency is ten times one, then the infrared travelled a distance A along the x axis.The x-ray must have moved ten times A to cross the same distance on the x axis.

If an x-ray has ten times the frequency (I know) and the same amplitude and the photon moves at the speed of light, it must move at ten times times the speed of the infrared. It does not do that. Therefore, the amplitude must be less.

The light from the x-ray may be brighter than the light from the infrared, but that is because there are more photons from the x-ray source and the collective effect of all the photons makes the light wave have more amplitude. If we took an individual photon from the x-ray, it must have less amplitude than an individual photon from the infrared.

This is a quantum problem that had probably been asked many times. Have I got it right so far?

No, it is just the x-axis distance if you have a free space traveling wave.

The 'length' of the Pointing vector.

Not an expert on the subject, but light study has been a part of several courses I took.

What I think is happening here is that you're missing the wave / particle duality of light. Or, more accurately, you're mashing the two together, when they don't go together. Light has a sort of quantum uncertainty. If you can observe it's wave nature, you won't know anything about the particle nature, and vice versa.

The image you're getting at is that photons sort of "ride the wave." That's not correct. In fact, when you observe photons individually, their wave nature is inobservable. Variations on the double slit experiment (namely putting a laser behind the slits to observe photons) will display this.

The wave and particle natures of light are separate. Photons do not travel in a sine wave fashion. This can be a really odd idea, and difficult to grasp, particularly if this is your first venture in to quantum uncertainty.

To quote a professor of mine, "light is EXACTLY like a wave... Except when it acts EXACTLY like a particle."

Try and wrap your head around the photon that has momentum but no rest mass.

Trying to understand light can truly bend your brain.  Now try to understand gravity and light together.  Simple stuff that affects everything and stops being simple when you get down to nuts and bolts understanding, and leaves you intellectually burnt.  Photons ruined my world.

Especially since they have no rest mass, yet gravity can 'bend' their path.


ETA:


 J. B. S. Haldane quotes (British geneticist 1892-1964)

Excellent way to sum up the issue





 

I'm a retard that can't link pics
 

Gravity does not bend their path, it bends the space they travel in. Light escaping from near the surace of a black hole will still travel c, even though the gravity is insanly high.

Phase velocity is the rate at which a electromagnetic wave will propogate through space. Typically it is c. The rate at which a wave traverses its axis is not limited to c. Your example of a x-ray vs an IR ray is good. Even though the x-ray has a higher frequency, they both move through space at the same speed, regardless of their frequency.

Think of it as if your in a vehicle and your kids are in the back seat jumping up and down. Regardless of how fast or slow you are going, your kids can jump up and down at a rate independant of your forward speed.

And a x-ray and IR ray do not have the same energy levels. e=hc/(l) where h is the plank constant 6.626 *10^-34, c is speed of light, and l is lambda, or wavelength. So lets say you have a adjustable power flash light. You turn it on and it emits a certain power level. If you adjust it to a high power level, you are increasing the number of photons emmited, not their power level. A mid-length IR wave is about 5um. A  x-ray has a wave length of about 5nm.  Using the formula above you get a IR wave having a energy level of about 4*10^-20 joules. I will convert to electron volts for easier numbers which is dividing this anser by the charge of an electron or 1.6*10^-19. This gives a IR wave an energy level of about .248 eV. Note: this is per photon. The x-ray will have an energy level of about 249 eV. This is about 4*10^-17 joules. So a x-ray is about 10^3 times more powerful than than a IR wave. Again, this is per photon. An x-ray gun would need a lot less photons to zap someone than a IR gun.