# Can a photon vibrate without any velocity or directional movement; Can it vibrate without moving? [closed]

I understand that light travels in a straight line unless gravity says otherwise. However, if it were theoretically possible to keep the energy in a photon without having any directional movement, what would happen? Would the photon dissipate and just transfer its energy to a nearby particle?

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• Non-moving photons are not a mainstream physics concept, at least not in vacuum. They are an oxymoron — a contradiction in terms — like a square circle. – G. Smith Sep 15 at 19:01
• Are you satisfied with zero average velocity? – Superfast Jellyfish Sep 15 at 19:53

Can a photon vibrate without any velocity or directional movement; Can it vibrate without moving?

Can a photon have a non-zero frequency $$\omega$$ while having a zero wave-number $$k$$ ?

No, it can't, because for photons in vacuum we have the following dispersion law $$\omega = c k \tag{1}$$ where $$c$$ is the speed of light. This linear dispersion law is equivalent to saying a photon has zero rest-mass.
This would be entirely different if the photon would have a non-zero rest mass $$m$$. Then the dispersion law would be $$\omega^2 =c^2k^2 + \left(\frac{mc^2}{\hbar}\right)^2 \tag{2}$$ where $$\hbar$$ is Planck's constant. (You can find more about massive bosons (in contrast to massless bosons) by searching for "Proca action" or "Proca equation").
From (2) we can see: For massive photons at rest (i.e. $$k=0$$) we would have $$\omega_\text{rest}=\frac{mc^2}{\hbar}$$ A massive photon at rest would just sit there and keep its energy.