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Photons are known to travel at a speed of $\rm 299 \ 792 \ 458 \ m / s$ in vacuum. Photons can be absorbed, or absorbed and re-emitted by matter. They slow down to $\rm 225,000,000 \ m/s$ in water with a refractive index of $1.3$, to $\rm 200,000,000 \ m/s$ in glass and to $\rm 125,000,000 \ m/s$ in diamond. So its speed can be varied with variations in the medium.

What happens if the photons can be virtually brought to a stop and is not absorbed by matter? Can the photon exist in a state where it has an energy of $\rm E = h \nu$, but having no velocity?

Qmechanic
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schizoid_man
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    The most intriguing property of BECs is that they can slow down light. In 1998 Lene Hau of Harvard University and her colleagues slowed light traveling through a BEC from its speed in vacuum of 3 × 108 metres per second to a mere 17 metres per second, or about 38 miles per hour. https://www.britannica.com/science/Bose-Einstein-condensate – Gert Apr 22 '21 at 20:24
  • @Gert light is composed of photons, photons are not light but elementary particles in the standard model,. – anna v Apr 23 '21 at 05:12
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    @Jonas, by 'virtually' schizoid probably means 'almost exactly'. E.g the chances of their being life on Mars is virtually nil – John Hunter Apr 23 '21 at 06:21
  • @schizoid_man: do you mean to ask if it is meaningful to discuss the 'rest' state of a photon in the same way that one might discuss (or posit existence of) the rest state of, e.g., a massive fermion? – TLDR Apr 23 '21 at 06:33
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    Somehow this question has points of contacts with this one of mine https://physics.stackexchange.com/q/612110/ – Alchimista Apr 23 '21 at 09:30

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You are confusing photons with electromagnetic waves, light.

They slow down to 225,000,000 m/s in water with a refractive idex of 1.3, to 200,000,000 m/s in glass and to 125,000,000 m/s in diamond. So its speed can be varied with variations in the medium.

This is not correct . Light,the electromagnetic wave, slows down. Light is made out by the superposition of a large number of photons, but photons are not light. They are elementary particles with mass zero and will always , when they exists, move with the speed c of light in vacuum, even within matter.

See this simple experiment

dblslphot

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.

to understand how photon wave functions interfere and show the interference fringes expected by light, even though the individual footprint is a dot in (x,y,z,t). The wave nature of photons is a probability wave, it needs an accumulation of photons to appear.

In a medium individual photons will interact randomly at random angles, always at the speed of light ( more complicated than hitting the screen in the link) they will take complicated paths . If the medium is transparent and the classical light does not change color, it means they will make a large number of elastic collisions which extend the path length traveled by individual photons and will be seen as the slowing of the electromagnetic wave, light.

anna v
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    @ anna-v are you saying that the individual photons will always travel at c, though the light wave as a whole might travel slowly, like in a medium? – schizoid_man Apr 23 '21 at 16:06
  • @schizoid_man yes, that is what I am saying, the path of light is from a superposition of photon wave functions. – anna v Apr 23 '21 at 18:16
  • OP: I guess a useful analogy can be a person walking always at the same speed but in a dense wood. Trees forced her to stay longer in the forest, but her speed doesn't change. Anna can correct because it is just an analogy, it might have cons that at the moment I don't see. – Alchimista Apr 24 '21 at 08:10
  • @Alchimista a randomness introduced by the trees , i.e. not being able to run straight, yes. Except in quantum terms for a single photon it is probablities that introducea randomness – anna v Apr 24 '21 at 08:22
  • I’m not sure it’s necessary to invoke a longer path length for photons to explain slowing of the wavefront. Virtual transitions have a short lifetime corresponding to a time delay between absorption and coherent re-emission of photons interacting with the material (resulting in a phase delay of the electromagnetic wave). – Gilbert Apr 25 '21 at 00:35
  • @Gilbert The photons in the experiment shown in the answer have on mass four vectors and do travel different paths. Virtual is a different story , I agree. Though then one would not be having zero mass particles and there is no meaning to their velocity, except that it mathematically adds up out of the medium as classical light collectively smaller. – anna v Apr 25 '21 at 04:11
  • If absorbed I now think a photon would lose it's momentum. And then we would get into questions about "conservation of energy" in respect of electron repulsion. The answer does not mention "lenght" of path, although this is a easy, common sense solution in respect of unchanged speed of light. Must there be some exchange of energy between electron and photon, when there is no absorption, only refraction? It's the direction that changes. That may be beyond energy/mass, in my opinion. That's what non-mentioning "length" of path brings up. – Peter Bernhard Nov 18 '22 at 14:03
  • @PeterBernhard see my answer here https://physics.stackexchange.com/questions/254085/same-photon-or-different-photon/254092#254092 and keep in mind that at particle level we have four vectors describing their energy momentum, that transform from inertial frame to inertial frame with Lorentz transformations http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/vec4.html – anna v Nov 18 '22 at 14:23
  • My last comment, in fear of chatting: you said so before, and it is good. There is curvature in medium... I am only beginning to see. Lorentz may be underrated... If a real straight line is seen as a curve, why not just the opposite... – Peter Bernhard Nov 18 '22 at 16:29
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It depends how you're defining "motion". As you're talking about photons as opposed to light generally, I'll talk from the quantum perspective rather than just classical waves. See these related questions for more on the different perspectives:
Do photons actually slow down in a medium, or is the speed decrease just apparent?
What is the mechanism behind the slowdown of light/photons in a transparent medium?

Remember that whilst we say that photons/light slows down in a medium, the individual photons still locally propagate at $c$ in between interactions (described by QED). So slowing photons down means increasing the number of interactions with other forms of matter (i.e. absorption and emission). Getting to your question:

What happens if the photons can be virtually brought to a stop and is not absorbed by matter?

The answer is that either that they're absorbed and not emitted, which doesn't seem to mean what you intended, or the answer to your title question is yes, the massless photons can only exist in a state of motion. "Brought to a stop" doesn't make sense if we're talking about photons themselves.

Eletie
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Perhaps this question is answerable in a purely classical electromagnetic wave setting.

You need to be aware that there are different definitions of "speed" for waves. The speed of light is a "phase velocity", which is not really a velocity (see below).

The phase velocity is more the ratio between frequency and wavelength. Both are physically well defined and measurable parameters. The different speed of light (or refractive index) is now, in its essense, just a measure that a wave has different wavelength at same frequency in some media.

So why it is dangerous imagining the phase vecloity "speed of light" as an actual speed?:

  • An (infinitely long) light beam does not have a "speed". Still the "speed of light" is well defined and changes with medium.
  • A wave-packet e.g. a a light burst (or the front of a just-turned-on light beam), actually does not generally propagate with a speed equal to the phase velocity. The right term is the group velocity or the front velocity of the wave. Just in vaccuum these velocities happen to be the same. But they are generally not. They are changed by the medium and the waveguide the light is confined in.
  • In a wave packet the ratio between wavelength and frequency is still the phase velocity, but the envelope may move much slower (or faster) in a medium and/or waveguide.
  • Consider a cavity, that is in its simplest form just two parallel mirrors. With hypothetical ideal mirrors one can store light or photons in it with an intensity distribution which is stable over time. So there is no "movement".
  • Perhaps you want to check out the Slow Light field where scientists try to design structures which allow for extremely low group velocity. This sounds more fancy than it is. Essentially this works by some sort of resonator or cavity where the light is circulating or "stored".

So to answer your question: Yes, in a ideal resonator photons can be brought to stop without being absorbed. The energy-frequency relationship for photons is not affected and still valid. Your confusion most likely is due to the definition(s) of velocity. Velocity is not well defined for a single photon, but only for waves, and even there different velocities exist, accounting for the nature of waves.

Note: In the RF there are superconducting cavities, which come very close to the ideal, lossless resonator.

Andreas H.
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  • To OP: A couple of points in this answer (cavity) show the connection that I brought up in my previous comment (that under your question). – Alchimista Apr 24 '21 at 08:38