Post of the Day
September 1, 2000

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Rat's Broadband Bandwagon

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Subject:  Electrons, Photons, and All That
Author:  squark

Now that optical networking is a hot thing and the word photonics pops up on a daily basis, it might be useful to review some basic facts about electrons, photons, and their interactions. When you hear "experts" talking about electrons turning into photons or electrons travelling in copper wires at the speed of light, I think it's time to brush up on some physics!

Photons are quanta of electromagnetic (EM) radiation such as radio waves, light, X-rays, etc. Each photon carries an energy E=hf, where h is Planck's constant and f is the frequency of the EM wave. The value of E depends on how the photon was created. Photons created in atomic transitions can have only certain discrete energies (typically a few eV's), reflecting the spacings of atomic energy levels. Lasers are an example of this. Photons are also created by accelerating charges, in which case their frequency spectrum is continuous and extends all the way from zero to "infinity". The brightness of a source such as a flashlight or an FM station antenna is determined by the number of photons it emits, and not by their frequency.

A large number of photons make up what we call a (classical) EM field. The reason we don't notice the quantum nature of light in everyday life is that the number of photons is normally huge. For example, a 100 W light bulb emits about 10^19 visible photons per second (even though most of the power goes into heat rather than light). The eye sees that as a continuous stream of light.

In addition to these real photons there are also "virtual" photons which mediate the forces between electrons and other charged particles. For example, the reason two electrons repel each other is that they exchange virtual photons between them. The quantum theory describing the interactions of electrons and photons (both real and virtual) is called Quantum Electrodynamics (QED).

There is a big difference in the way electrons move in an electrical wire and the way photons move in an optical fiber. When you send a light pulse down an optical fiber, the photons travel all the way to the other end (let's ignore attenuation and dispersion for now). The speed of the signal is typically 2/3 the speed of light in vacuum, and the mechanism that keeps the light in the fiber is known as total internal reflection. When you send an electrical pulse down a wire, the electrons barely move. Let me be very precise here as to what this means. The velocity of each "free" electron in the wire has two components: thermal velocity and drift velocity. Thermal motion is the random bouncing around that the electrons do simply because of the temperature of their surroundings; typical thermal velocities in a room-temperature conductor are 100 km/sec for electrons. But this thermal motion does not give rise to a macroscopic current because the motion has no preferred direction. The current is due to the drift velocity which all electrons acquire due to an applied electric field generated by the "battery" (or whatever drives the current). Since the applied field has a direction, all electrons pick up a drift velocity in that direction, and you have a current.

It turns out that in all practical situations the drift velocities are very small indeed. For example, if you have a 1 amp DC current in a typical copper wire, the average electron drift velocity is well below 1 mm/sec, i.e. literally a snail's pace. For an AC current the electrons merely oscillate by minuscule amounts about their equilibrium positions. What happens then when you switch on a battery or a power supply is that the applied electric field "jolts" nearby electrons, which get a little bit closer to their neighbors down the line and therefore repel them more strongly, thereby giving them a jolt, which in turn .... etc. etc., all the way down the wire. You have a disturbance propagating along the wire at very high speed even though the electrons move very little. We call this disturbance an electrical pulse, and it is being transmitted by the EM field (i.e. by virtual photons, in the language of QED) rather than by any significant flow of electrons. The situation is fully analogous to a pipe full of water: if you jolt a piston at one end, you'll have a pressure wave propagating rapidly down the pipe even though there is very little water flow in the pipe. If you jolt the piston back and forth very quickly, you'll effectively have a steady pressure in the pipe, and that allows you to transmit power to the other end without any net flow of water.

An optical fiber can carry much more information than an electrical cable. But the reason has nothing to do with the speed of photons vs. the speed of electrons. It is simply that the short wavelength of light (of order 1 micron) allows you to construct very short pulses. You cannot make short pulses by superposing radio waves (wavelengths range from meters to kilometers).

In practice, a light pulse propagating in an optical fiber gets attenuated and it also spreads in time. The spreading is due to dispersion, i.e. different wavelengths making up the light pulse propagate at different velocities. It becomes necessary to "regenerate" the signal by converting the light pulses into electrical pulses for amplification and reshaping, and then back into light pulses again. An alternative is optical amplification, using semiconductor lasers or what have you, and people are working on that. But you never, ever "convert electrons into photons" or vice versa - that would violate charge conservation and lepton number conservation, for starters. And respecting absolute conservation laws of physics is not just a good idea, it's THE LAW!


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