How can photons have frequency without vibration?

Question

If photons have frequency then they must vibrate. So i was wondering, what kind of vibration do photons have? But according to physicists, photons do not vibrate. Can someone explain me, how is that possible?

Answer 1

Look at this experiment, which shows in one page what is the meaning of frequency for light, electromagnetic wave, and what is the meaning of fequency for photons, elementary particls.

Figure 1. Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, and 500’000 frames.

The frame on the far right shows the classical interference pattern for electromagnetic waves of frequency $ν$ of the experiment.

The leftmost frame shows the footprints of the individual photons, a particle hitting a small area on the screen.

On the left it looks random. On the right one gets the distribution of the probability for photons of energy $hν$ to be at the (x,y) of the screen. It is the probability that waves for the individual photon,, the individual photon leaves a small footprint consistent with the standard model hypothesis that it is a point elementary particle with a wavefunction whose $Ψ^*Ψ$ gives the probability of finding the photon at a particular (x,y,z,t).

It can be shown that classical electromagnetic waves and their E and B fields that classically carry the energy of the electromagnetic wave, emerge from the superposition of zillion of photons with energy $hν$.

Similar double slit experiments exist for electrons and other particles and the same reasoning is behind the plots. It is the probability of finding the particle that waves, not the particle.

Answer 2

You are confusing to different concepts. The photon is a particle whereas the classical description of light is a wave, vibrating or oscillating electric and magnetic field vectors. The dual description is the hallmark of quantum mechanics and quantum field theory. The same could be said of material particles like the electron. They have an associated frequency but they do not "vibrate" in the traditional sense.

Material vibrations occur in acoustics and are oscillations in a material like air, water, or elastic solids (there are other examples). Our experience leads us to expect "vibrations" need a medium. For a long time people thought this was true of light and postulated an ether for light waves to travel in. In the late 1800s to early 1900s we discovered that there was no need for this and that we could describe "light" as oscillations in electric and magnetic field vectors. This is a classical mechanics description of light.

Experiments seem to indicate that light (which we thought of as a wave) has particle like properties and that matter (electrons, protons, etc which we thought of as particles) could behave like waves. This led to the development of quantum mechanics in which particle-wave duality is an underlying paradigm.

Any particle has an associated frequency and wavelength related to its energy and momentum. Similarly any quantized field (like light) has associated particles related to its irreducible quantum states.

In the context of QM and QFT any "particle" has a frequency even thought that particle is not necessarily vibrating in the classic sense of acoustics.

Answer 3

Start by having a read through the answers to Do photons truly exist in a physical sense or are they just a useful concept like $i = \sqrt{-1}$? As explained there, while it's tempting to imagine the photon as a little ball of light this is not the case. Unless the photon is being created or destroyed it is usually in a delocalised state and behaves like an electromagnetic wave rather than a particle. So the vibration is not like a particle bouncing to and fro. It is the oscillation of the electromagnetic field associated with the particle. Note that this oscillation is of the values of a field not a physical motion in space like the wave moving along a string.

All particles have oscillations like this when they are propagating as waves, and the oscillation is in the value of the wavefunction that describes the particle. For particles like electrons the physical meaning of the wavefunction is somewhat elusive, and we cannot simply relate a physical property to the oscillation. So while we can observe the wave like properties in diffraction experiments we cannot simply measure the oscillation of electrons as they pass. Light is something of a special case since the wavefunction is effectively just the complex field described by Maxwell's equations. So when we measure the oscillation of the electric and magnetic fields we are effectively measuring the oscillations of the photon.