What is the energy distribution of light if it has an infinite length?

Question

Electromagnetic wave

I have read in one of the answers here on phys.SE that light has actually an infinite length. But then what is the energy distribution of that electromagnetic wave?

@JeffDror Yes: http://physics.stackexchange.com/q/74316/ Emilio says: Well-defined 10 nm photons are as spatially large as 1 km photons - infinitely big. — Evariste Galois, Jan 23 '14 at 19:29
The answerer was not saying that light has infinite length. He was just saying that to claim your light beam has exactly a given wavelength it must have an infinite length. Physically, there will always be some wavelength distribution in a given beam and the light will not in fact be infinite. — JeffDror, Jan 23 '14 at 19:34
@JeffDror So how to calculate the length of a photon? (not the wavelength) — Evariste Galois, Jan 23 '14 at 19:42
Ah, okay. That is the length the photon travels. It is not the "length of a photon". Every object can travel an infinite distance assuming that it doesn't interact with anything. This is true of the photon as well. As for the energy distribution, consider a fixed patch of surface area of a sphere that is 1 meter squared. If you are close to the source of light, most of the light will travel through this surface area so the light appears very intense. — mcFreid, Jan 24 '14 at 13:10
As you move very far away, the fixed patch of surface area becomes very small compared to the rest of the surface area of the sphere (i.e. the light has spread out). So, the intensity decreases. — mcFreid, Jan 24 '14 at 13:10
Oh I shouldn't do this: Technically, at least as Feynman saw it, a photon is an instantaneous interaction between the emitter and receiver. Actually, two such interactions, since there's that pesky advanced solution photon that gives a kick back at the emitter. So... you can sort of say "infinite length" for a single photon, as viewed from our ordinary passage of classical time, with the energy per unit of length simply being the energy of one photon divided by that length. And somehow I don't think that was the intent of the question, but points like that are just so nicely weird... — Terry Bollinger, Feb 23 '14 at 01:07

score 2 · Answer 1 · edited Apr 24 '14 at 07:09

What is the energy distribution of light if it has an infinite length?

You are confusing two frameworks here, instead of fusing them.

Light classically is an electromagnetic wave traveling with velocity c. It does carry energy and this is given by the Poynting vector,

the Poynting vector represents the directional energy flux density (the rate of energy transfer per unit area, in units of watts per square metre ($W·m^{−2}$)) of an electromagnetic field

It describes well the energy the earth gets from the sun which allows us to be here and communicate.

The wave, a laser beam pointed to space for an interval delta(t) will travel at the velocity c and dissipate finally angularly into single photons. Thus there is no infinite length of travel for a beam of light.

Photons are the quantum of light, the smallest bit of light, traveling with velocity c and carrying part of the energy of the original beam as $E=h\cdot\nu$.

Photons travel in empty space until they hit a target where either they lose energy or their energy is degraded enough to be absorbed in some atom/molecule by raising the energy level of an electron.

So in both forms there exists an expression for energy, and the wave dissipates into single photons at very large distances, which eventually may disappear as explained above. Single photons that do not meet obstacles travel very far, as seen by the light reaching us from stars and galaxies and the beginning of the big bang, as cosmic microwave background. Their energy is given by the $h\cdot\nu$ of the time of detection.

score 0 · Answer 2 · answered Jan 23 '14 at 23:35

Light doesn't has infinite length, it travels infinite length (if it is allowed without distraction i.e, without the absorption of energy). You have the bulb in your home working under the principle of heating effect of electric current. Once you switch on the bulb, light travels with the speed of $3X10^8$ m/s, just imagine how fast it will be. Lets assume that you switch on the bulb and switch it off swiftly. lets think hypothetically that you are seeing the situation in slow motion. Once the light is switched on and switched off, light travels and collides with the walls of the room. If the wall of your room is $30$m away from the bulb, then you will see first collision to the wall at $3$ns. At the end of $1$s you would had seen about $10^8$ collisions if there was no absorption of energy by the molecules of the wall. But there is the absorption of energy after each and every collision. If it wouldn't been, there was no requirement of keeping on the bulb all while, it would have been enough if you switch it on once and switch it off. After each and every collision, atoms of the wall absorb energy and at the end of $1$s you will see no light (light energy is absorbed by wall). If your room had no walls, light would had spread in all directions and it would travel infinite length (if there is no absorption of energy after that).

What is the energy distribution of light if it has an infinite length?

2 Answers2