# Does light have mass?

1. May 24, 2005

### sclancy

does light have mass? i thought it did because it couldn't escape a black hole. i need to know. thanks.

2. May 24, 2005

### quasar987

If you just want to know, the answer is 'no'.

For a small proof, see

https://www.physicsforums.com/showpost.php?p=534072&postcount=5

Relativity gurus will do a better job than me at explaining why they cannot escape black holes, but the short answer is that one does not need mass to be affected by the gravitationnal field, only energy. And photons have energy proportionnal to their frequency: E=hf.

Last edited: May 24, 2005
3. May 24, 2005

### pervect

Staff Emeritus

See http://math.ucr.edu/home/baez/physics/Relativity/SR/light_mass.html

4. May 24, 2005

### rbj

wouldn't it be more accurate to say that the short answer is "light has no rest mass" $$m_0$$ because if it had a rest mass, the relativistic mass which is

$$m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$$

would be infinite at the the speed of light $$v = c$$.

since a photon has energy

$$E = \hbar \omega$$

and energy has an equivalent mass

$$E = m c^2$$

does not each photon have an inertial mass that is

$$m = \frac{E}{c^2} = \frac{\hbar \omega}{c^2}$$?

at least it has momentum that is

$$m c = \frac{E}{c} = \frac{\hbar \omega}{c}$$.

is that not true?

5. May 24, 2005

### Crosson

And then tell a long story about what rest mass is...

To me, mass is assumed to mean rest mass. Relativistic mass is a totally unnecessary concept.

6. May 24, 2005

### The Bob

Light does not have mass. Light is pure energy (if I am correct). A black hole will pull anything in due to its gravitational field. Light is not faster than light and nothing is. As light can be pulled in, anything can be.

7. May 24, 2005

### pervect

Staff Emeritus
The problem is that that's not a short answer! People who want the whole, full, answer (and not the short answer) can read the FAQ entry I quoted (it's only a click away) which gets into everything you said and a bit more.

8. May 24, 2005

### RandallB

$$\hbar$$

I didn't find $$\hbar$$ in the links.
Could you referr me somewhere that discribes $$\hbar$$ a bit.
How and where it's used, name, value, units, maybe some history.
Thanks
RB

9. May 24, 2005

### quasar987

$$\hbar$$ is Planck's konstant divided by 2pi. It is used in quantum mechanics. But $$\hbar$$ is not the subject of this post, so if you wish to talk some more about it, please create a whole new thread. Thx.

10. May 24, 2005

### rbj

fine, i guess. paraphrasing Einstein: "An explanation should be as simple as possible, but no simpler." i think to simply say "light has no mass" implies that "light particles, photons, have no mass" which sorta implies (since momentum goes to zero if mass or velocity does) that "photons have no momentum" which simply is false.

short or whole or full, the answer should be sufficiently accurate to not lead someone to erroneous conclusions of substance that do matter. it is not a difference of semantics.

perhaps a better explanation for the OP is that there is no such thing as graviational force considering general relativity. the reason that light (or anything else) does not escape the black hole is due to the severe curvature of space-time due to the concentration of mass (or energy, it's about the same) in the black hole. similarly to the thought experiment of Einstein regarding the Equivalence Principle, the one with the accelerated frame of reference in space (at 9.8 m/s^2) and the non-accelerated frame on the surface of the Earth, in both cases, a beam of light will be bent, from the POV of the observers in both frames, to the same degree. one is due to the acceleration of the frame of reference, the other is due to gravity.

11. May 24, 2005

### rbj

also used in the photoelectric effect. historically, it is first used in the photoelectric effect to relate the energy of these particles of light to the frequency of radiation.

the (relativistic) mass of a photon is $$m = \frac{\hbar \omega}{c^2}$$ where $$\hbar$$ is the reduced Planck's constant, $$\omega$$ is the angular frequency of the equivalent wave of the photon of light, and $$c$$ is the speed of light.

it is germane to the subject of this thread.

12. May 25, 2005

### dextercioby

Planck used "h" when claiming that the enegy of the em field vibrating mode was proportional to the frequency of the radiation.The character $\hbar$ was introduced by Dirac (some people call it Dirac's constant) around 1926.

Daniel.