Can a photon move more slowly than the speed of light and behave 'non-relativistically,' so to speak. Perhaps another way to express my thought is: could we stop a photon from moving?
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When photons go through a material, like glass or water, they travel more slowly. There are materials in which they can go very slowly. But that does not reduce their energy. – Mike Dunlavey Jun 30 '15 at 00:39
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What materials are these? Could we then capture a photon, or make it radiate enough energy to make ir behave differently? – Alex Hinkle Jun 30 '15 at 00:41
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Its energy is a function of its frequency (color) not of its speed. – Mike Dunlavey Jun 30 '15 at 00:42
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Are they not related on some level, speed and energy? Can we turn 'off' the color of a photon? – Alex Hinkle Jun 30 '15 at 00:45
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1@MikeDunlavey saying that the thing moving slowly when light travels in a dielectric is a "photon" is really dicey. – DanielSank Jun 30 '15 at 00:47
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In vacuum, the energy of a photon is related to its wavelength, or equivalently to its frequency. It turns out that a photon's frequency is independent of its speed. Photons in vacuum always travel at the same speed ($3 \times 10^8$ m/s). When light travels inside matter you get interference between the usual thing we call a photon and the polarization of the material itself. This can lead to the resulting wave travelling more slowly than the speed of light, but beware anyone who calls this a "photon", for that can be very misleading. – DanielSank Jun 30 '15 at 00:50
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1@DanielSank and it gets WAY more dicey if we're going to talk slow-light experiments, where the excitation is some hybrid spin-wave/photon thing – zeldredge Jun 30 '15 at 00:50
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@zeldredge totally agree. – DanielSank Jun 30 '15 at 00:50
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It's not dicey, at all. Photons that are coupled to electrons, plasmons etc. are part of quasi-particles. That's no different from an electron that is bound to an atom. The atom has completely new properties compared to both its nucleus and electrons and it has to be treated as a different entity. – CuriousOne Jun 30 '15 at 00:54
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Now we're talking! – Alex Hinkle Jun 30 '15 at 00:56
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so like an atom made with photons – Alex Hinkle Jun 30 '15 at 00:57
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@CuriousOne but the different components of the polariton have different dispersion relations, even. People even talk about the "photonic" component of the excitation. Ultimately, when we say "the photon is traveling slowly" we're teaching vocabulary, and I think it's fair to say that in this case being simplistic about the vocabulary is misleading. – zeldredge Jun 30 '15 at 00:57
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@zeldredge: So? All that means is that the combined object does not have trivial properties. If you are going into this with the idea that everything has to behave like little hard balls then you will be constantly fighting with reality. Look at phonons and their band structure. That's as close to a classical object in qm as one can get and it's still not trivial. – CuriousOne Jun 30 '15 at 01:00
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conceptual physics is sometimes misleading, however think of it instead as using lies to tell the truth. – Alex Hinkle Jun 30 '15 at 01:01
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People are addressing the speed question, but just to be clear: a photon can be very low energy. For instance, radio waves are much lower energy than gamma rays, even though both are made of photons (and, in vacuum, both travel at the speed $c$). What determines the energy of a photon is the frequency of the excitation (frequency of the corresponding light wave), which is related to the energy by Planck's constant, $E = h f$. This doesn't affect its speed, and it doesn't really have anything to do with "relativistic" concerns--photons themselves are not necessarily present in relativity.
Usually relativstic/nonrelativistic is the kind of distinction you get to make with massive particles, since you can talk about their energy compared to $m c^2$. If they have low kinetic energy it will be roughly $T \approx \frac{1}{2} m v^2$. Since a photon NEVER has such an energy, being massless, this doesn't really come up much. Of course, since we usually care about photons only when they interact with massive particles, relativistic concerns can pop up if the photon energy is large compared to the mass of the particle in question (see Compton scattering for instance). It's just never so clear-cut as "oh, this is an infrared photon, let's treat it classically always."
zeldredge
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This answer is correct, the energy of a photon has nothing to do with it's speed, and since $c = \nu\lambda$, there is no way that it can have $0$ frequency, so taking into account that the energy of a photon is $E = h\nu$, where $h$ is Planck's constant, the energy cannot be zero either, but it can be very low as this answer explains. – iharob Jun 30 '15 at 01:26
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@AlexHinkle You can see that having $0$ energy is equivalent to having $0$ frequency, since $E \propto \nu$, so it can't have $0$ frequency because that would require it to stop, and hence it can't have $0$ energy. Note, that the fact that photons are massless implies that they should Always move at the speed of light, that is in contrast to a particle that has mass, which Can never move at the speed of light. – iharob Jun 30 '15 at 01:33
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but it has energy and can interact with em fields and g fields, can we impart mass to it? – Alex Hinkle Jun 30 '15 at 01:37
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2@AlexHinkle - "so how do we get a photon to 'stop'?" That happens all the time. When a photon is absorbed into a material, it delivers all of its momentum into the material, and it stops. Of course, it ceases to exist as a photon, but you can't have everything. – WhatRoughBeast Jun 30 '15 at 01:39
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@AlexHinkle as @WhatRoughBeast has mentioned, when it "stops", then mass appears out of nothing, it's energy becomes a particle + an anti-particle. The process can happen in reverse too. – iharob Jun 30 '15 at 01:40
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@AlexHinkle The creation of an electron + a positron would. You can read about it here to start, and then search for a robust source for the topic. – iharob Jun 30 '15 at 01:41
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Refractive Index is when light travels more slowly in a medium.
Here is an example of light being slowed down to 38 miles per hour.
The speed of a photon does not affect its energy. It has zero mass, therefore zero kinetic energy. The energy it has is due to its frequency (color), and nothing else.
(However, it does have momentum!)
Mike Dunlavey
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5For the hapless future student reading this: when we say "light" travels slowly in a medium we really mean "the collective excitation of the electromagnetic field arising from the radiation source and the resulting polarization of the medium" travels more slowly than does light in a vacuum. Beware this extremely important distinction. – DanielSank Jun 30 '15 at 00:51
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@Daniel: You're absolutely right. I'm trying to keep it simple for an OP who is clearly a newbie to physics. – Mike Dunlavey Jun 30 '15 at 00:54
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Oh, for sure. It's just that this, like so many other topics, suffers from a lot of explanations which make it sound obvious but are completely fragile and fall apart when subject to the tiniest further inquisition. For this reason I personally prefer to keep things as simple as possible. Start with light in a vacuum. The speed is fixed and in particular independent of energy. Let the student understand this first. Then we can talk about media, but I'd insist on being explicit that the thing travelling in that case is a mix of the medium's polarization and the free radiation. – DanielSank Jun 30 '15 at 00:59
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One of my strongest personal convictions in physics is that we should not give students those matter-of-fact simple answers which turn out to be completely bogus on further inspection. We should strive to be explicit about the boundaries of our answers. I say this because of how hard it was for me during my student days to sort this kind of thing out, and it was usually because of abuse of terminology, etc. /soapbox – DanielSank Jun 30 '15 at 01:01
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So the answer is that light in a vacuum cannot, however the electromagnetic properties of a physical medium can keep the light from shooting off into space or being adsorbed for short periods of time; 'slowing' the light down. – Alex Hinkle Jun 30 '15 at 01:09
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@DanielSank I'm glad people on this site think like this. I am often told I am pedantic for not thinking of light in a medium as "light" but a quantum superposition of the EM field excited states and excited states of the medium" but we're definitely not talking about photons alone in a medium, so I too think this is a highly important distinction. – Selene Routley Jun 30 '15 at 01:13
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@WetSavannaAnimalakaRodVance Please note that quantum mechanics is absolutely not needed when discussing the difference between bare light and light in a medium. Classical physics admits hybridized modes just fine. In my experience this is one of the most misunderstood topics among card-carrying physicists. For some reason everyone thinks you need quantum for everything: avoided level crossings, hybrid modes, etc. – DanielSank Jun 30 '15 at 01:15
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@DanielSank Indeed Iwo Bialicki-Birula in quite a few of his works as well as do I in JOSA-A explore the equivalences between the classical and quantum descriptions of light in a medium. If you interpret solutions of Maxwell's equations as describing a one particle excited state of the EM field as in, e.g. Chapter 1 of Scully and Zubairy, then any ME solution can be interpreted as one of three things: a classical light description, a coherent state and a 1-photon Fock state. Put ME together with 2D systems describing atoms and you've got either quantum superpositions or classical modes. – Selene Routley Jun 30 '15 at 01:35
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1@AlexHinkle Absolutely not. If it slows down, its interacting with something, so you haven't got a vacuum any more. – Selene Routley Jun 30 '15 at 01:36
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Although it has been said in other comments and answers, it bears repeating succinctly: photons (as far as any experiment can tell) are massless and therefore always move at the universal, invariant speed of light. There is NO non-relativistic description of the photon. Even the "classical" description of light - Maxwell's equations - can be interpreted as the propagation equation for a lone photon - aka a one-particle state of the electromagnetic field, and you may know that Maxwell's equations are Lorentz invariant: they are fully relativistic equations and were always so as soon as Maxwell wrote them down - indeed historically they were the first model of a relativistic description, whence people derived special relativity. So there is no nonrelativistic classical description of light either.
When we see "light" in a medium, we are seeing a quantum superposition of excitations both of the electromagnetic field and of excited atom / molecule states. So it's really "photons" together with "other stuff" and the photon part still moves at $c$ exactly. The full superposition can move at speeds less than $c$, which means it also has a rest mass. Indeed, the "particles" of an optical frequency disturbance in a glass of index 1.5 have a mass of the order of $10^{-6}$ electron masses, as I calculate here.
Also, as Daniel Sank points out, there is an equivalent classical description of the superposition - hybrid modes - and, when you think of Maxwell's equations as the propagation equation of the one particle EM field state, the mathematics of the two descriptions is identical.
Selene Routley
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I will reply to this because the checked answer is not answering the question.The question is about photons, the answer is about light. It is as if the question were about atoms and the answer is about density of material. The question is asked about photons, the quantum mechanical framework is relevant to it. The checked answer is about light which is in the classical electrodynamics framework.
Photons are elementary particles with very specific attributes, one of which is zero mass and always moving in vacuum with velocity c, the velocity of light. Light is built up out of zillions of photons in confluence. .
As also WetSavannaAnimal explains in his answer the two frameworks can be rigorously connected mathematically but still photons and light are two distinct physical manifestations each belonging to a different physics framework, and the classical emerges from the quantum underlayer in a mathematically demonstrable way.
To the question:
Can a photon move more slowly than the speed of light and behave 'non-relativistically,' so to speak. Perhaps another way to express my thought is: could we stop a photon from moving?
No, a photon can never move more slowly than the speed of light in vacuum, because as an elementary particle it is either in vacuum or interacting with another elementary particle or field. Its interactions can be elastic, inelastic or total absorption by kicking an electron of an atom to a higher energy level. You can only stop a photon by total absorption/disappearance.
It is the synergy of zillions of photons with the molecules of the specially prepared medium that produces the effect of slowing light velocity in a medium referred in the checked answer.
