In Newtonian language a photon oscillates to get his frequency. In the quantum field theory the photon is an excitation of the electromagnetic field. But are these excitations also limited by the speed of light giving the frequency of a photon a maximum?
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$\begingroup$ Where do you see the link between the speed of light and the frequency of a photon? One is the time of an oscillation of the electric field, the other one is the speed with which it propagates through space. $\endgroup$– user_naCommented Aug 6, 2017 at 9:27
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$\begingroup$ related(?) physics.stackexchange.com/questions/43063/… $\endgroup$– SecretCommented Aug 6, 2017 at 9:40
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$\begingroup$ "In Newtonian language a photon oscillates to get his frequency." [citation needed] In Newtonian language, there is no such thing as a photon, there are only electromagnetic waves. $\endgroup$– ACuriousMind ♦Commented Aug 6, 2017 at 13:50
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$\begingroup$ @user_na the idea is that a frequency corresponds to a wavelength, a wavelength pertains to a wave, and a wave involves motion of something in something — so if the frequency is high enough, maybe that motion is fast enough to run afoul of relativity. It's not true, but it's a valid line of thinking and a valid question if you don't know why it's not true. Relativistic electron orbitals are a thing, for instance. $\endgroup$– hobbsCommented Aug 6, 2017 at 15:30
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$\begingroup$ (You have to imagine something like a "classical photon" (yes, I know that's a contradiction) vibrating perpendicular to its direction of motion, "at its own frequency". Which, among other things, has the problem that light wouldn't travel at the speed of light.) $\endgroup$– hobbsCommented Aug 6, 2017 at 15:38
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2 Answers
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Wow, wave particle duality can be tricky to quote Feynman. A photon of frequency f does not wiggle as it goes along! what wiggles is the particle probability psi field ..and the wavepacket advances corresponding to movement of particle.
First the classic EM picture: the oscillations of the electromagnetic field are not displacements in space of anything which moves. The electric field has direction but its magnitude does NOT correspond to any physical real world displacement. Similarities or analogies with strains in an elastic ether medium were abandoned long ago and there was never found any conversion factor from field strength to physical distance. Any such conversión factor would surely fail quickly. For example microwave diffraction through a hole in a metallic highly conducting surface is well studied and verified in the field of radar. IF the field strength corresponded to an actual sideways displacement of some ether (like with earthquakes) then at larger amplitudes the wave would sort of get too big to pass through properly and there would be some effects of amplitude dependence. Of course NONE are observed, there is no amplitude depedence (non-linearities) in radar scattering, and there is no suggestion of such in millions of experiments across the whole electromagnetic spectrum. With solids it is different!, solid body transverse elastic sound waves of super large amplitude passing through a small aperture should have serious consequences and nonlinearities will be observed even at smaller amplitudes as it will be kind of smelling or feeling sideways, like a wave on string can pass through a hatch if the amplitude is not too big. Hope that helps. Possibly in the days of ether hypothesis people considered these problems? Nowadays no physicist or electrical engineer would ever contemplate that kind of view. But I guess we should be careful and understand why we dismiss ideas. Curious!
In the more fundamental quantum picture there will be oscillations of the psi field (mod square gives the probability density) for photon particle which again is a number at a given space location which doesnt correspond to any actual spatial displacement of anything material.
IN either picture there is no spatial movement of anything corresponding to a mechanical oscillation and so there is no suggestion to apply the speed limit c (velocity of light) to such vibrations. The speed limit c does not apply to how fast temperature can change , or the money in a swiss bank account either. However it could apply to say earthquake displacements though the velocities are very much to low to notice. So there is no limit on frequency or amplitude of EM photon wave imposed by the universal speed limit.
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1$\begingroup$ An advice: At the present version, this only addressed the first question, not the second one (whether there is a frequency maximum for photons). Suggest to edit the answer to address both questions $\endgroup$– SecretCommented Aug 6, 2017 at 9:47
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$\begingroup$ So the (classical?) view that the electric and magnetic field are perpendicular on each other isn't right either? $\endgroup$– MarijnCommented Aug 6, 2017 at 16:44
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$\begingroup$ Aren't sideways displacements of em-waves also not making polarization filters functioning? $\endgroup$– MarijnCommented Aug 7, 2017 at 20:50
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$\begingroup$ The word "paragraph" leaps to mind. :-) $\endgroup$ Commented Aug 16, 2017 at 2:20
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As the photon is not "oscillating" in anything, there is no theoretical maximum energy for a photon. Remember that there is zero evidence for the existence of the "luminiferous aether" that was supposed to be the medium that light oscillates in.
Under current theories, the shortest possible distance is the Planck length, about $1.6*10^{-35}m$. If a photon has a wavelength that short, its frequency is about $1.8*10^{43}Hz$. Yellow light has a frequency of about $5*10^{14}Hz$, so at the Planck length the frequency would be almost $10^{30}$ times (a billion billion billion billion billion times) higher.
It's possible that this is a limit to photon frequency, as a photon with this energy might be a black hole by itself. Problems with this idea include the fact that, like a black hole, a proton is thought to be a point, a singularity. All our mathematics break down at singularities, so all predictions are off, at least until we have a theory of quantum gravity.
If it doesn't become a black hole, a photon with that much energy will interact with other particles (and even the earth's magnetic field) to create new particle-antiparticle pairs, and thus cease to exist. That would be a practical rather than a theoretical limit to the photon's energy/frequency.
But, until we can create photon energies that high, we have to assume that a photon has no maximum energy. At present, the highest recorded photon energies are rare cosmic ray events, with energies above $100 TeV$, or frequencies above $10^{28}Hz$, still a factor of $10^{15}$ away from the Planck limit. At these energies, a photon has about the same energy as a ping pong ball.
