# What is the density of light?

• Niflheim
In summary, photons have no mass because they are made up of energy and that energy is solely due to how light behaves.f

#### Niflheim

What is the density of light?

I'm relatively new to Physics and very new to the forum, so please forgive any (potentially) hilarious mistakes or stupidity in my question, knowledge, and use of the thread.

But really, what is the density of light? Light is a particle like anything else, and all particles have a density, so what is it? How does it impact light's interactions with matter/energy/fields? Are any of light's properties dependent on its density? Do different light particles have different densities? Any answers/insight would be greatly appreciated.

Thanks for any/all replies!

• Symmetry777
Welcome to PF!

If you are talking about mass density, no, light does not have mass so it doesn't have density.

• Symmetry777
Thanks!

When you say that light has no mass, do you mean literally, or in the same way that we say the electron adds no mass to an atom? If the former, than how can it exist as a particle without mass? Is the particle just a grouped together bunch of light waves or something?

• Symmetry777
• Beenigma and Symmetry777
Photons are among the gauge bosons with zero invariant mass. Electrons have mass 0.511 MeV/c^2, 9.10×10−31 kg

• Symmetry777
Interesting. And yes I know electrons have mass, I thought you meant that they had a near zero mass.

Thanks so much for the replies! I'm off to look into the zero mass particles now, they seem interesting.

• Symmetry777
Thanks!

When you say that light has no mass, do you mean literally, or in the same way that we say the electron adds no mass to an atom? If the former, than how can it exist as a particle without mass? Is the particle just a grouped together bunch of light waves or something?
Electrons do add mass to an atom. Who told you they do not ?
The mass of neutral protonic hydrogen is m_p+m_e - Eb.
One could say that the electron adds anything between m_e and m_e - Eb, slightly less than m_e.
Note that m_p ~ 2000 times m_e, so the addition is small.

• Symmetry777
Okay, just to clear things up a bit, yes guys, I know that electrons have mass. When I said that I was asking if he meant exactly zero mass or so close to zero as to be irrelevant, like how we don't add the mass of the electrons to an atom's mass number since it is mostly irrelevant.

and all particles have a density,
Particles do not have a property "density". Density is something you can consider for a large amount of particles (like "the density of air molecules in the room" only. A volume with light inside will have a photon density (photons per volume) and an energy density (energy per volume).

It is expected that photons are exactly massless. If they have mass (you can never measure something exactly), it has to be extremely tiny.

• Symmetry777
Two more things:
- There are several properties of light that can be termed density. Energy-momentum density (including, energy density, momentum density, energy transport density, stress density), angular momentum density (orbital and spin). number density (but this is just the same as energy density).
- Imagine a massless resonator with an infinite quality value, containing a resonant electromagnetic field.
Such an object would have a purely electromagnetic mass. Thus confined light can have mass, the density of which is simply the energy density in the rest frame.

Thanks, that helps clear it up a bit.

Hello! I'm also new here, and I find this question very interesting.

Do we say photons have no mass because they are definitely massless? Or is it because their mass is so small that there is no device/method known to mankind yet that can measure to such a small degree?

Hello! I'm also new here, and I find this question very interesting.

Do we say photons have no mass because they are definitely massless? Or is it because their mass is so small that there is no device/method known to mankind yet that can measure to such a small degree?
Welcome to PF.

Photons are definitely* massless. Scientists speak with precise wording, so when someone says "massless", that's what they really mean.

*to within the limit of science's ability to say "definitely"

• 1oldman2
An incoming beam of coherent photons, when absorbed, will exert a force on the absorbing body similar to force of an incoming ball that is caught. It is possible to calculate this force, so in some ways, light behaves like moving massive particles, but its mass is entirely due to its energy and its energy is entirely due to its motion.

Wouldn't density be in direct relation to frequency... If measured in a beam of light wouldn't a higher frequency contain a higher density of photons than a lower frequency?

Wouldn't density be in direct relation to frequency... If measured in a beam of light wouldn't a higher frequency contain a higher density of photons than a lower frequency?
Higher frequency means that each photon is more energetic, not that there are more of them. Are you imagining photons arranged on a beam of light like a string of beads, all riding the beam, each one wavelength from the next? That picture would be wrong on multiple levels.

Thus confined light can have mass, the density of which is simply the energy density in the rest frame.

Hi my2cts,

Are you saying that if one can confine light, for instance, inside a cavity, it is possible to attach a rest mass to this oscillating electromagnetic field?
Could you please indicate some reference? It happens that I have great interest in this subject. Thank you in advance.

Best wishes,

DaTario

it is possible to attach a rest mass to this oscillating electromagnetic field?
Photons have 0 rest mass, 0 inertia, 0 gravitational impact on matter. Perhaps the effect of the photonic fields leads to an increase in the mass of the matter it affects, but the fields themselves do not warp space in a gravitational sense.

Are you saying that if one can confine light, for instance, inside a cavity, it is possible to attach a rest mass to this oscillating electromagnetic field?
It is possible to assign a mass to the whole system (cavity+radiation). This mass increases if you increase the amount of light in it, as the rest energy of the system increases.
Photons have 0 rest mass, 0 inertia, 0 gravitational impact on matter.
Photons do have a gravitational impact on matter, because they have energy. They also have momentum.

• Revolucien
So if we use a magnifying glass redirecting photons from a larger area to a smaller area would that increase density of photons at the focal point? You know the point where the ants catch fire.

So if we use a magnifying glass redirecting photons from a larger area to a smaller area would that increase density of photons at the focal point? You know the point where the ants catch fire.
Of course.

So if measured density at this focal point is based on the energy and momentum of the photons, and the frequency determines the energy and momentum of the photon...my question from earlier (#17)- Isn't photon density in direct relation to frequency? A higher frequency will take more energy and momentum creating a higher density at a measured point. Sorry, if I'm missing something basic just trying to understand.

They also have momentum.
But photons can't accelerate or decelerate. Their velocity remains the same regardless of "energy" they contain...

Isn't photon density in direct relation to frequency?
The density of the waves per distance increases with frequency, but a photon is still one photon. It can only land in one place.

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So if measured density at this focal point is based on the energy and momentum of the photons, and the frequency determines the energy and momentum of the photon...my question from earlier (#17)- Isn't photon density in direct relation to frequency? A higher frequency will take more energy and momentum creating a higher density at a measured point. Sorry, if I'm missing something basic just trying to understand.
You seem to be missing that a beam of light is not a single photon. Leaving aside the question of whether the notion of photons is useful in understanding light at this level (it is not), there are a lot of photons in a beam of light. More photons packed in a smaller area = higher light intensity in that area.

I agree a beam of light is not a single photon, didn't really question that, but my focus was more towards your final sentence "More photons packed in a smaller area = higher light intensity in that area." That basically says what I was saying, Photon Density(More photons packed in a smaller area) = Energy( higher light intensity in that area), my only addition is the "energy in the photon is directly associated with its wave frequency" (Planck-Einstein relation), then frequency is in direct relation to density.

my only addition is the "energy in the photon is directly associated with its wave frequency" (Planck-Einstein relation)

That applies to a single photon.

then frequency is in direct relation to density.

What do you mean with the density of a photon?

If a beam light is combination of many photons, isn't the density is measured from the energy produced from the those photons.

If a beam light is combination of many photons, isn't the density is measured from the energy produced from the those photons.

Density is mass per volume and doesn't depend on energy only. But I don't think this is what what you are trying to talking about.

If I took a cylinder 10cm diameter x 1 meter long as my volume measurement, then through one tube had a red beam of light, and through another had a blue beam of light, the blue beam would have a higher energy per volume than the red. Since I can calculate the amount of energy difference and I know the speed of light, can't I calculate mass?

Light traveling in free space has no mass. Light that is trapped in a cavity has invariant mass, and therefore a density.

Photons are massless, so there is no mass density involved. They have energy, so there is an energy density. There is also number density, which scales with energy divided by frequency and is independent of frequency.
Photons in a resonant cavity do represent mass, but this is mass of the system of cavity plus photons and not photon mass.

An incoming beam of coherent photons, when absorbed, will exert a force on the absorbing body similar to force of an incoming ball that is caught. It is possible to calculate this force, so in some ways, light behaves like moving massive particles, but its mass is entirely due to its energy and its energy is entirely due to its motion.

Yes, photons have momentum proportional to frequency, but not mass, so they do exert force on massive objects. Look up light sails, or thermonuclear warheads for examples of the practical use of that momentum.