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I read the related answer to whether photons have size, and the answer seemed to be it depends. If a Photon, or a rather an E&M wave has a magnetic and electric field, should things be able to feel this? I know electrons do get 'sloshed' in these fields, but what is the range of influence of a photon? How much space do the waves physically occupy?

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One has to have clear that the terminology "photon" describes an elementary particle.

Elementary particles are described concisely in the framework of quantum mechanics. In this framework an elementary particle, the photon in this case, can have two behaviors. Either as a classical physics point particle with an x, y,z position , i.e. no extent in space, or as a probability wave , which means that a statistical accumulation of individual photons from the same starting conditions will display an interference pattern as a classical wave would. In the wave manifestation the extent of the locus where the photon may be found is bounded by the Heisenberg Uncertainty Principle. This last tells us that the better we know the momentum of the photon, the less localized the locus of finding it is.In this sense the probable extent of a photon can be made as large as our knowledge of its momentum p=h/lamda , the planck constant over the wavelength.

Now nature and the physics models we have developed to describe and predict its behavior is continuous between the photon framework of quantum mechanics and the classical electromagnetic waves of maxwell's equations. , the frequency of the photon is the frequency of the wave it will build up when present in large numbers. Electromagnetic waves can have the extent one designs and the limits are the limits of the ability to produce them and direct them. Radio waves are all over the place.

anna v
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  • But so then, if radio waves are all over, and they have magnetic field components, why don't pieces of iron they encounter get moved as the radio wave goes by? As a wave, I don't understand how physically large of an influence their fields have. –  Jan 30 '14 at 06:30
  • Think of the antenna. Its electrons respond to the electric and magnetic fields of the radio waves. The size of the antenna shows the extent of the influence. The extent of the influence classically is the time the wave lasts otherwise with the velocity of light the extent is very large. only geometry limits the sizes and wavelengths how much of the wave interacts, classically – anna v Jan 30 '14 at 06:36
  • So then why don't pieces of metal, like iron bars, move back and forth from incident radio waves? –  Jan 30 '14 at 07:06
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    it is all a matter of frequencies and the amount of energy, moving metal takes a lot of energy. Sometimes there are hums, no? – anna v Jan 30 '14 at 07:36
  • I wasn't aware that there are! That's amazing. –  Jan 30 '14 at 08:55
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Perhaps a good way of thinking about it is that a photon is produced by some process: a free-space decay of an atom in free space, to a stimulated emission in a laser cavity, etc. These processes have a spread in energy(frequency) known as their bandwidth. Since frequency and time are conjugate variables in QM, the temporal length of the photon is constrained by the Fourier transform of the bandwidth, and since we know the propagation velocity of the photon, this defines it's length. The transverse dimension of the photon is given by the mode of the resonator that produced it (the dipole pattern of the atom, or the Hermite-Gauss mode of the laser cavity).

As an example, consider an atom in a laser cavity which has a mode waist of 1mm, and a bandwidth of 1 MHz (assume that the natural line width of the laser is much larger to keep it simple). The photon emitted from the cavity would be distributed along a volume which is transversely 1mm in diameter and longitudinally is c/1MHz ~ 300m long. As mentioned above, one typically views this as the probability envelope of a the photon so that over many identical realizations of the single photon event, one would find the above probability distribution in space or time.

From the standpoint of pure quantum optics, one formally considers a resonator in which the E-M field is a standing wave and has a lowest energy ground state. From here you find that the Hamiltonian is that of a harmonic oscillator and has single excitation (Fock) states which represent single photon. To think of photons in free space, one typically extends the dimensions of the resonator to infinity. This allows you to sleep better at night because it's rigorous, but I find viewing photons as described above more useful for understanding physics.

Orko
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At very low energy, the difference between photons and E&M waves becomes clearer: After every spin-flip in a hydrogen atom, "something" with E=6 µeV and spin=h/(2*pi) is released. Is that "something" a photon? Nobody can detect a photon with such a low energy. But if you have a radio receiver at 1420 MHz, you get a clear signal. The electric component of the wave accelerates electrons in a wire called dipole antenna and you can measure a weak current. Where is a photon? Radio receivers do not detect photons!

If the atom releases a photon, something transforms it to a long wave packet. Where? Is the intermediate photon necessary? Perhaps the atom emits the wave packet. How? Nobody knows.

The optimal length of the dipole (0.1 m in this case) corresponds to the diameter of the wave packet: a shorter dipole provides a weaker signal, a longer dipole brings no additional gain.

The coherence length of this wave packet is about 60,000 m. You can calculate using the FWHM = 5 kHz, measured in astrophysics. This huge wave packet is a big contrast to a point-like photon.

9herbert9
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