# Can a photon have mass when travelling through a medium?

I know that a photon has no mass when it is travelling at the speed of light, however my question is, can a photon have mass when travelling through a medium, i.e. when its speed is less than c?

I have done some reading but cannot find an answer. From this reading I have got the following:

We have the following standard equation:

E2 = p2 c2 + m02 c4,

where p is the momentum and m0 is the rest mass of the object.

Now for a photon travelling in a vacuum at the speed of light, its energy is hf, where h is Planck's constant and f is the frequency. Also we have that the momentum of a photon in a medium is

p = (hf) / (cn),

where n is the refractive index, given by

n = c / v.

Therefore, by looking at the energy of the photon in a vacuum and in a medium we would get the following:

h2f2 = h2f2c2 / (c2n2) + m02c4
h2f2 = h2f2v2 / c2 + m02c4

Rearranging for m0, gives

m0 = (hf / c2 ) * sqrt(1 – v2/c2).

Hence this implies that when a photon is travelling at the speed of light it would have zero mass. However if it was not travelling at the speed of light, then it would have mass, with its maximum occuring when v=0, i.e. just before the photon is destroyed.

So what are you thoughts regarding this?

P.S. hopefully I have posted this in the correct section.

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Khashishi
Where did you get the expression for momentum of a photon in a medium?

can a photon have mass when travelling through a medium, i.e. when its speed is less than c?
Is it still a photon when traveling through a medium and does it make sense to describe it independent from the medium? Obviously the common mass of media and photon remain constant but splitting it between media and photon is not as easy.

BiGyElLoWhAt
Gold Member
I think you're confusion is coming from assuming a photon can travel at a speed of less than c.

One of the primary postulates of relativity says that no matter the observer, the instantaneous speed of a photon is c. In a vacuum it's always c. In a medium, it's also always c, the only difference is the photon tends to hit stuff like oxygen and nitrogen molecules when traveling through air, for example.

When a photon hits an atom, it is absorbed, causing a spike in energy, causing an electron to jump to a higher energy level (maybe a level of orbit or 2) then that electron jumps back down to find equilibrium, re-emitting a (the) photon, and that takes time. This is why taking a measurement of the speed of light varies in a medium vs. a vacuum. Again, the instantaneous speed is always c.

Orodruin
Staff Emeritus
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When a photon hits an atom, it is absorbed, causing a spike in energy, causing an electron to jump to a higher energy level (maybe a level of orbit or 2) then that electron jumps back down to find equilibrium, re-emitting a (the) photon, and that takes time. This is why taking a measurement of the speed of light varies in a medium vs. a vacuum. Again, the instantaneous speed is always c.
Of course, this is a quantum mechanical process and you really cannot tell whether this has happened - only that it affects the propagator and disturbs the dispersion relation of the photons. This is known as coherent forward scattering and effectively is the same as sub-light-speed propagation.

BiGyElLoWhAt
Gold Member
It is if you say ##c \approx \frac{\Delta x}{\Delta t}##, but not if you say ##c = \frac{dx}{dt}##

Of course no one knows what's actually happening; but this model works. If you want to consider it as a photon travelling v<c, go ahead, but I choose to view it the other way, as it seems more consistent with things like, say, relativity.

Orodruin
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The point is that you do not have to get a velocity which is Lorentz invariant as the presence of the medium in itself breaks Lorentz invariance by defining a preferred frame (its rest frame). When doing computations within a medium, it becomes very natural to use the particle density within the medium rather than looking at every single particle. This is well motivated as long as the typical size of a wave packet is larger than the distance between the scatterers and this is typically true when a photon goes through a medium. The mathematical background is the domain of finite temperature and density (FTD) within thermal field theory. This effect is not unique to photons but also the propagators of other particles are affected in, e.g., a plasma, and these effects have to be taken into account when doing computations regarding the early Universe. It also appears in neutrino oscillations through the MSW effect.

In a sense, saying that the photon in a medium always travels with speed c but is some times interrupted by scatterings is not completely unlike saying that the electron always travels with speed c but is interrupted by scattering on the Higgs field.

I think you're confusion is coming from assuming a photon can travel at a speed of less than c.

One of the primary postulates of relativity says that no matter the observer, the instantaneous speed of a photon is c. In a vacuum it's always c. In a medium, it's also always c, the only difference is the photon tends to hit stuff like oxygen and nitrogen molecules when traveling through air, for example.

When a photon hits an atom, it is absorbed, causing a spike in energy, causing an electron to jump to a higher energy level (maybe a level of orbit or 2) then that electron jumps back down to find equilibrium, re-emitting a (the) photon, and that takes time. This is why taking a measurement of the speed of light varies in a medium vs. a vacuum. Again, the instantaneous speed is always c.
"Do Photons Move Slower in a Solid Medium?" ?

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lightarrow

TheDemx27
davenn
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When a photon hits an atom, it is absorbed, causing a spike in energy, causing an electron to jump to a higher energy level (maybe a level of orbit or 2) then that electron jumps back down to find equilibrium, re-emitting a (the) photon, and that takes time. This is why taking a measurement of the speed of light varies in a medium vs. a vacuum. Again, the instantaneous speed is always c.
That is what I learnt some years back from the Feynman lectures

which doesn't gel with other teachings eg .....

and it still leaves me sometimes scratching my head

Dave

BiGyElLoWhAt
Gold Member
The point is that you do not have to get a velocity which is Lorentz invariant as the presence of the medium in itself breaks Lorentz invariance by defining a preferred frame (its rest frame). When doing computations within a medium, it becomes very natural to use the particle density within the medium rather than looking at every single particle. This is well motivated as long as the typical size of a wave packet is larger than the distance between the scatterers and this is typically true when a photon goes through a medium. The mathematical background is the domain of finite temperature and density (FTD) within thermal field theory. This effect is not unique to photons but also the propagators of other particles are affected in, e.g., a plasma, and these effects have to be taken into account when doing computations regarding the early Universe. It also appears in neutrino oscillations through the MSW effect.

In a sense, saying that the photon in a medium always travels with speed c but is some times interrupted by scatterings is not completely unlike saying that the electron always travels with speed c but is interrupted by scattering on the Higgs field.
I'm not talking about the math, I'm not saying it's not useful to view light as moving <c in some situations. That is a rather analogous situation with the electron and the higgs field, but the difference between the 2 situations is that the interaction between the e^- and the higgs boson gives the e^- mass, whereas the interaction between the photon and whatever it's hitting does not.

BiGyElLoWhAt
Gold Member
You can see the process of a photon being "absorbed" or reflected, or however you want to call it, in abundance with optical tweezers/trap. It uses the scattering of photons and the momentum changes associated with them to create a central force (which requires a time interval) on the object (the ones I worked with were rather transparent, that's how we were able to pick them up on camera).

When a photon hits an atom, it is absorbed, causing a spike in energy, causing an electron to jump to a higher energy level (maybe a level of orbit or 2) then that electron jumps back down to find equilibrium, re-emitting a (the) photon, and that takes time.
That is not what happens in a solid medium, e.g. glass:
You can't make it simple as you say.
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lightarrow

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BiGyElLoWhAt
Gold Member
A solid has a network of ions and electrons fixed in a "lattice". Think of this as a network of balls connected to each other by springs. Because of this, they have what is known as "collective vibrational modes", often called phonons. These are quanta of lattice vibrations, similar to photons being the quanta of EM radiation. It is these vibrational modes that can absorb a photon. So when a photon encounters a solid, and it can interact with an available phonon mode (i.e. something similar to a resonance condition), this photon can be absorbed by the solid and then converted to heat (it is the energy of these vibrations or phonons that we commonly refer to as heat). The solid is then opaque to this particular photon (i.e. at that frequency). Now, unlike the atomic orbitals, the phonon spectrum can be broad and continuous over a large frequency range. That is why all materials have a "bandwidth" of transmission or absorption. The width here depends on how wide the phonon spectrum is.

On the other hand, if a photon has an energy beyond the phonon spectrum, then while it can still cause a disturbance of the lattice ions, the solid cannot sustain this vibration, because the phonon mode isn't available. This is similar to trying to oscillate something at a different frequency than the resonance frequency. So the lattice does not absorb this photon and it is re-emitted but with a very slight delay. This, naively, is the origin of the apparent slowdown of the light speed in the material. The emitted photon may encounter other lattice ions as it makes its way through the material and this accumulate the delay.
Seems rather consistent with what I'm saying. I'm not saying every photon gets absorbed via interaction, but... see above, or click the link and read it for yourself.

Is it still a photon when traveling through a medium and does it make sense to describe it independent from the medium? Obviously the common mass of media and photon remain constant but splitting it between media and photon is not as easy.
I would argue that it is still a photon when travelling through a medium, for example I can still see using light when standing the in the medium of air or water. Also you state that “obviously the common mass of the media and photon remain constant”, why would this obviously be the case, since the equations above would seem to imply that whilst travelling through a medium it could add a very tiny amount to the media+photon object. Moveover the amount of mass added would be dependent upon the speed of the photon within that medium. The only way I can see of checking this would be to weigh an object that is able to slow photons down considerable and then re-weigh it when passing high energy gamma or xrays through it and seeing if the objects weight changed ever so slighty.

That is not what happens in a solid medium, e.g. glass:
You can't make it simple as you say.
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lightarrow
Furthermore Lightarrow's link on “what ahppens in a solid” gives a very good argument of why we can consider the tranmission speed of a photon in a medium to be less than c.

Equally the argument that the photons are absorbed and re-emitted surely falls when you consider an amplitude modulated radio-wave. If this was absorbed and then re-emitted when it passed through a medium (which it clearly does), then the signal would be lost he moment the original wave was absorbed.

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A photon always carries momentum, according to ## E = pc##. But we know it must be massless, otherwise it cannot travel at the speed of light: ## m = \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}##.

Simon Bridge
Homework Helper
The possibility of massive photons has been considered, but I have not heard of anyone postulating that photons gain mass in media.
If so, then it would be the only fundamental particle to gain mass as it slows down.

In the QED description, photons travel at c between interactions and the "slow photon" becomes an emergent effect.
In a medium the interaction can be with the "free field", but it's basically with charged particles, ... which leads to the FAQ description.
It is usually equivalent to describe the region inside a media as having a different value for the speed of light similar to how electrons in a semiconductor can be treated as being more massive.

Objects have mass via the Higgs mechanism ... so there is another way to approach the question: is there anything about the media that would result in a different coupling with the Higgs field for photons?

Anyway - whatever approach one decides on - the consensus is that photons do not gain mass as a result of slowing down in high refractive index materials. There are treatments which talk about an effective mass for photons though.

Other discussions:
http://physics.stackexchange.com/questions/1898/do-photons-gain-mass-when-they-travel-through-glass

Lecture in which photon mass is presented in a Field Theory approach:
http://folk.uio.no/finnr/talks/Oberwolz.pdf (slides)

Papers using photon effective mass in different contexts:
http://arxiv.org/pdf/physics/0207128.pdf
http://hal.archives-ouvertes.fr/docs/00/63/12/35/PDF/Effective_mass.pdf
... boils down to what you want to call "a photon".

Ravi Mohan
for example I can still see using light when standing the in the medium of air or water.
Even if the chromophors of your eye absorbs photons only this doesn't mean that the photon was a photon before and not part of some kind of composition of photons and phonons.

Also you state that “obviously the common mass of the media and photon remain constant”, why would this obviously be the case
Because mass is a conserved property.

The "Photon" page at Wikipedia, last paragraph of the "Experimental checks on photon mass" section states

"Photons inside superconductors do develop a nonzero effective rest mass; as a result, electromagnetic forces become short-range inside superconductors."

but it does not elaborate on whether "nonzero effective rest mass" is quite the same as inertial mass, passive or active gravitational mass, rest mass, the inverse of the effective mass tensor, the Higg' field explanans, or something like virtual mass / added mass (fluid mechanics).

The possibility of massive photons has been considered, but I have not heard of anyone postulating that photons gain mass in media.
If so, then it would be the only fundamental particle to gain mass as it slows down.

In the QED description, photons travel at c between interactions and the "slow photon" becomes an emergent effect.
In a medium the interaction can be with the "free field", but it's basically with charged particles, ... which leads to the FAQ description.
It is usually equivalent to describe the region inside a media as having a different value for the speed of light similar to how electrons in a semiconductor can be treated as being more massive.

Objects have mass via the Higgs mechanism ... so there is another way to approach the question: is there anything about the media that would result in a different coupling with the Higgs field for photons?

Anyway - whatever approach one decides on - the consensus is that photons do not gain mass as a result of slowing down in high refractive index materials. There are treatments which talk about an effective mass for photons though.

Other discussions:
http://physics.stackexchange.com/questions/1898/do-photons-gain-mass-when-they-travel-through-glass

Lecture in which photon mass is presented in a Field Theory approach:
http://folk.uio.no/finnr/talks/Oberwolz.pdf (slides)

Papers using photon effective mass in different contexts:
http://arxiv.org/pdf/physics/0207128.pdf
http://hal.archives-ouvertes.fr/docs/00/63/12/35/PDF/Effective_mass.pdf
... boils down to what you want to call "a photon".
To start with I would personally describe a photon as a single EM wave of any frequency.

Secondly, do I understand you correctly with regard to QED. Are you saying that photons travel at the speed of light in all medium until they interact with a charge particle at which point, I assume they would be absorbed and then re-emitted, with this process taking time and thus the resultant speed of the photon through the medium is reduced? If this is indeed the case, how does QED explain the transmission of AM radio waves through the atmosphere, since if a wave with AM is absorbed, the “new” photon emitted would surely not have the same if any AM?

In terms of a photon being the only fundamental particle that increases mass with decreasing velocity then I would argue the following. To start with if we take another fundamental particle, e.g. an electron, then when we try to accelerate it speed, we are adding energy to it, some of which expresses itself as mass. In the case of a photon, I would argue that it always has a fixed amount of energy, which when travelling at the speed of light is given by hf. However, when a photon is travelling at less than the speed of light, some of that “momentum energy = hf / n” is expressed as mass. Moreover, E=mc^2 would imply that mass is just a dense form of energy and thus it would follow that in the case of a photon its energy is just being expressed in different forms, depending upon its environment. Another way that this could be viewed, is that if mass is a dense form of energy, then when a photon slows down its wavelength decreases. Thus the total volume occupied by the photon has decreased, but its total energy remains the same. Hence it could be argued that the slower the photon is travelling the more densely packed its energy becomes and thus the more mass it has. Furthermore this argument would appear to hold with dealing with the other fundamental particles, since when they are being accelerated, their energy is increased but the volume they occupied hardly changes. Thus this increased energy density at that point represents itself as an increase in mass.

Additionally, if we accept that a medium is able to slow a photon down from the moment it enters (i.e. the head of the wave enters its) until it leaving (i.e. the tail of the wave leaves it), rather than taking the view that the photon always travels at c, between the interactions; then it could be seen that it is this that causes the change between the photon and the higgs field. In fact it could be argued that it is the electromagnetic fields of the charged particle in the atoms, which are affecting the speed of the photon (which in itself is an EM propagation).

jtbell
Mentor
I would personally describe a photon as a single EM wave of any frequency.
What exactly is a "single EM wave?"

Nugatory
Mentor
To start with I would personally describe a photon as a single EM wave of any frequency.
That description is completely incorrect (although you can be forgiven for believing it, as many bogus descriptions written for non-scientists are floating around).

It's best not to talk about "the speed of a photon" if it can possibly be avoided. "Speed" is generally understood to mean change in position over time. That definition doesn't work very well for a photon, which has no definite position except at the moment that it is absorbed or emitted.

(This might also be a good time to remind everyone of the PF policy on personal theories)