# Photons in 1 cubic meter

#### benzun_1999

hi,

just out of curiosity. What is the maximum number of photons that can be accomodated in 1 cubic meter?

-benzun

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#### Gokul43201

Staff Emeritus
Gold Member
Photons are pointlike Bosons, so there is no limit that I'm aware of.

#### Norman

Gokul43201 is correct. But it may be somewhat confusing to many people. One might think, "Well, so what if they are pointlike bosons- If I take a pencil and make a bunch of points on a (small) piece of paper, it will only take a finite (but maybe tremendously large) number of points to fill up the paper. So why can an infinite number Photons be put into a set amount of space?"

This is a good thought process, that I am sure crosses many students minds at least once, but is ultimately wrong. The definition of a point-like particle or even better a point is that it is an object that is dimensionless geometrically and the only property that can be given to it is a location. So a point-like particle doesn't take up any volume in your space, so you could add as many as you please. I hope that helps.
Cheers,
Norm

#### Nereid

Staff Emeritus
Gold Member
Another way to ask this question might be "what is the maximum energy - in the form of photons - that can be crammed into 1 m^3?"

A good piece of trivia is the photon density, or energy density due to photons, of a chunk of space ... 1 au from the Sun, out in the EKB, at the surface of the Sun, at its core, ... I once found a website with a cool table of this trivia, but I seem to have lost the bookmark

#### rayveldkamp

Because photons don't obey the Pauli Exclusion Principle, does this mean we can have an infinite number of photons at a single point in space?

#### marcus

Gold Member
Dearly Missed
benzun_1999 said:
hi,

just out of curiosity. What is the maximum number of photons that can be accomodated in 1 cubic meter?

-benzun

the short answer, as Gokul said, is there is no limit to the number of photons that can go into a 1 cubic meter box.
but there are some things to consider

collapse to black hole:
if the energy density is too high in the cubic meter box then it will collapse

what does "accomodated in" the box mean, if the wavelength of the photon is a kilometer?

==============
Benzun, this is a question where it matters very much how you say it.
If you say "How many photons per cubic meter can coexist in a cubic kilometer, or a cubic lightyear?"
then you will get a nice big number because you can include very weak photons with very long wavelengths!

But if you insist on imagining a 1 cubic meter box and say "How many can coexist in this box?" then, in order to be reasonably sure that the photon is in the box you must allow only photons of wavelength less than, say, a meter, or even 10 centimeters. So then there will be a lower cutoff on the energy of an individual. So then, if you put too many in, it will collapse to make a black hole.

I will be happy to calculate (or several other people could do it) for you if you will please just say clearly what you want to know.

=============
in the meantime, nobody seems to have mentioned yet the beautiful idea of TEMPERATURE
a good question is about thermal photons at a given temperature

If you are in a room which is , say 293 kelvin, then the walls and everything are giving off infrared heat photons. There are far more of them than there are of visible light photons so let us focus just on the thermal kind. A good question is, how many thermal photons per cubic meter in a room at usual room temperature?

so maybe Benzun you will ask some more questions and we can broaden the discussion?

#### marcus

Gold Member
Dearly Missed
Nereid said:
Another way to ask this question might be "what is the maximum energy - in the form of photons - that can be crammed into 1 m^3?"

A good piece of trivia is the photon density, or energy density due to photons, of a chunk of space ... 1 au from the Sun, out in the EKB, at the surface of the Sun, at its core, ... I once found a website with a cool table of this trivia, but I seem to have lost the bookmark
Please do not weep Nereid, surely the bookmark will turn up sometime!
And meanwhile we will do what we can. It is not so hard to find the number of sunlight photons in open space at this distance from sun.

the solar constant is 1370 watts per sq. meter
http://scienceworld.wolfram.com/astronomy/SolarConstant.html

and one divides this by 3E8 meters per second to find the joules in a cubic meter
and one finds the energy density of sunlight at this distance from sun:

4.57 microjoules per cubic meter

Now in thermal black body radiation the energy of the AVERAGE PHOTON is 2.701kT. this 2.701 is one of nature's beautiful numbers.
and sunlight is very much like blackbody radiation at temperature 5700 kelvin

so I just have to look up boltzmann k = 1.38E-17 microjoules per kelvin
and multiply by 2.7 and 5700
2.12E-13 microjoules (behold it is the average photon energy in sunlight!)

and then I only must divide 4.57 by 2.12 and I see that in a cubic meter of sunlight (at this distance from sun)
there are 2E13 photons

that is, 20 trillion photons in a cubic meter of sunlight

I have rounded off, it is just a rough answer, but it is the right OOM
(as i know from other calculations which serve as check)

#### marcus

Gold Member
Dearly Missed
Nereid said:
Another way to ask this question might be "what is the maximum energy - in the form of photons - that can be crammed into 1 m^3?"
OOM I would say 1048 joules

or since this is just rough OOM calculation, call that 9E47 joules
which would act like an equivalent mass M = E29 kilogram

why can you not cram a mass greater than M into a spherical cubic meter volume?

because the Schwarzschild radius for that mass is
2GM/c2 = (13/9) E(29 - 11 - 18) meters = 13/9 meters
so you could not cram that much light even into a spherical volume with a radius of 1 meter

I have said 9E47 joules of light could not be crammed into a cubic meter sphere but probably with a more careful calculation one could show that
already 4E47 joules is too much

yes, I checked, 4 x 1047 joules is already too much light to
put in a cubic meter

#### benzun_1999

sorry for the late reply, i got carried away. this is wat i am thinking. since there exist a maximum density(mass per unit volume) for any particle in space before it colapses, i was just wondering if any such maximum energy equivalent exists. since EM radiation is the most common form of energy i thaught by figuring out how much can coexist in one cubic meter one can find that energy density. There is a limit for everything even energy. does this limit have any implication on the speed of light is yet another question that bothers me.

-benzun

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