# Q & A: photons, mass, gravity, light, rest mass, invariant mass, energy, momentum

Q:
If photons are massless, how come light are affected to gravity? dosent gravity only effect particles with mass? So for light to be bent or curved by gravity dosent that mean that photons have to have mass?
- Stian Dahl (age 21)
Vestfold Norway
A:
Although we've answered this question before, it comes in so often that it seems time to try to put a compact, easily searchable version of the answer up again. As a brief preview of the more complete answer, a photon has energy, which is equivalent to mass, and therefore interacts via gravity with everything else.

Much of the confusion arises because the word "mass" has been used in two different ways in physics. The "m" in E=mc2 is (as the equation makes clear) just another symbol for energy, expressed in different units. This same "m" also appears in the equation for momentum p=mv, where v is velocity. Light has energy and momentum, so it has "m" in this sense. This m is the same thing that appears in General Relativity (or even Newtonian gravity) as the source of gravitational effects. So light is definitely affected by gravity. Since light has energy, it is also a source of gravitational effects on other objects, although not a very strong one under ordinary circumstances.

Now when people are describing the "mass" of different objects, including particles, it's much more convenient to talk about the rest mass, also called the "invariant mass", the mass a particle has in a frame in which its momentum is zero. That way you don't have to ask what reference frame you're using, and can just give a specific mass for each object. In that sense, the mass of a photon is zero. However, that's not the term that enters into the gravitational equations.

Although the "invariant mass" is indeed invariant under choice of reference frame, it is not invariant under choice of how to group things into objects. For example, take two similar blips of light traveling opposite directions. Each one has energy E, momentum |p|=E/c, and an invariant mass of zero. Since the momenta are opposite, we are already using the reference frame in which the momentum of the two-blip object is zero. The invariant mass of the two-blip object is then 2E/c2, not zero. Even when things have no interaction, the invariant mass of the sum is not the sum of the invariant masses. A big box of photons has energy, zero average momentum, and thus has some invariant mass. It acts gravitationally just like anything else with the same energy and no momentum.

Mike W.

(published on 01/09/2011)

## Follow-Up #1: light, gravity, again

Q:
Light has no mass, so how can it be effected by gravity?
- Philip (age 21)
England
A:

etc.

(published on 02/23/2011)

## Follow-Up #2: light, mass, momentum

Q:
I read in this forum that light has no mass but does have momentum. Now I learned from basic physics that momentum is equal to the product of mass times velocity with units kg.m/sec. So this is in contradiction with the statement of light not having mass, as no mass than no momentum, right?
- petrus snel (age 55)
france
A:
Once more into the breech. I've marked this as a follow-up.

Mike W.

(published on 07/28/2012)

## Follow-Up #3: Higgs: inertial, gravitational, and rest masses

Q:
recently the scientific world was shocked at the discovery, or rather proof of the Higgs bosons existence by the CERN Labratory near Geneva. resistance to inertia in our universe (otherwise known as Mass) is caused by the Higgs field. Photons, whether they are particles or waves seem not to interact with this field at all acording to their speed, however they are still affected by gravity. my question; is it necessary for a particle to have mass in order to interact with gravity and more importantly, is it necessary for a particle traveling the speed of light to not have mass.
- Mark Cliffod (age 18)
Santa Fe
A:
In various forms, this is probably the question we see most often. I've switched the follow-up number to the most compact relevant answer. That answer covers the background, but not the Higgs part. Interaction with the Higgs field (or something like it)
gives some particles rest mass. The other particles, lacking rest mass, still have inertial mass, which is identical to gravitational mass.

On another point, I'm curious why you say that "the scientific world was shocked at the discovery, or rather proof of the Higgs bosons existence". This particle has been expected for decades. It would have been shocking if it weren't there. The particle seen has not yet been pinned down to be the simplest sort of Higgs particle, but it is some sort of rest-mass-generating boson.

Mike W.

(published on 07/27/2012)

## Follow-Up #4: can gravity make light accelerate?

Q:
The idea that light has no mass but can have an energy value seems wrong to me. Following Einstein's E = m x c^2 Light has a value in energy because any photon or single packet of light has measurable energy value. Therefore the equation says there must be a mass for this energy to exist. Assuming light therefore has mass a few situations become possible. It means that light can have a force applied to it in the direction which means. The energy added (from the force applied) could increase the speed of the light beam thus making is faster than the current speed of light which shows that the current speed of light is not the universal speed limit. OR The energy is turned into mass, because energy was only added in mass form to the beam of light which means increases in the overall mass of the beam of light thereby increasing the lights inertia and causing it to slow. So my question really is asking if you can critique this theory, is it possible? If it was possible does this help explain any other natural phenomenon that is current unexplained? (I have limited knowledge in physics up to my last year of high school for official study on the field. So if you could explain in simpler physic terms how it is wrong. At least as simply as you can please.)
- Andrew (age 21)
New Zealand
A:
Andrew- We've dealt with the question of light's mass many times before, so I've marked your question as a follow-up to some of those earlier ones.

We've only dealt briefly with the issue of light "accelerating". Why not have a look at and then follow-up for more clarification?

Mike W.

(published on 10/11/2012)

## Follow-Up #5: Do photons have mass?

Q:
E=mc^2 says If an object is moving at speed of light and has energy it should have mass so, does that mean that photons have mass too?
- Hamuda (age 16)
Maldives
A:

Mike W.

(published on 05/14/2013)

## Follow-Up #6: momentum of a massless particle

Q:
I just read one of your statements in which you said that E=m^2.c^4+p^2.c^2 and for a photon, E=pc as the mass of a photon is 0. what i want to ask is that, if p=m.v and for a photon v=c, then E=pc=(m.v)c=(m.c).c= mc^2? So we again reach E=mc^2 and well, if photons dont have mass then energy is 0..which is not possible, So when we say E=pc, how do we know the momentum of a massless particle, is there any equation or anything for it?
- Anushka (age 16)
India
A:

I've marked this as a follow-up to ones that may answer it. The key is to pay attention to the different uses of the symbol "m", either as rest-mass or as the factor in p=mv.

"How do we know the momentum of a massless particle?"  There are several ways. One is to directly measure the momentum by measuring, for example, the force exerted on a mirror by a stream of photons. Here one uses  that p is conserved and also that the particle number can be determined using universal quantum relation E=hf, where E is energy, h is Planck's constant, and f is frequency.  Another way is to use an argument from Maxwell's equations that requires E=pc if momentum is to be conserved. That gives a momentum density in terms of the electric and magnetic fields.  It can be converted to a momentum per particle again using E=hf.  Another way is to look for the missing momentum in events involving a few massive particles and a photon or two.  Other ways include  using the universal quantum relation |p|=h/λ, where λ is the wavelength.  λ can be measured with diffraction gratings or other methods.

Mike W.

(published on 06/04/2013)

## Follow-Up #7: mass, light, and matter

Q:
As we know that mass is to matter.any think havin mass will be matter...so light does'nt have any mass and it being a property of matter then how you considerd it as a mass.
pakistan
A:

Inertial mass is a well defined quantity that appears in physical effects, such as momentum conservation and gravity. Those effects show the inertial mass (not rest mass) of light. There's more discussion in the earlier part of the thread in which I've put your question.

I'm not sure what the word "matter" means.

Mike W.

(published on 12/21/2013)

## Follow-Up #8: gravity and light

Q:
This question is confusing me since i heard about it in E= mc^2 light has E=0, m=0 then, how it has mommentum and with out mass how it get effected by gravity?
- Suroj Dey (age 14)
India, ASSAM
A:

Mike W.

As we have said many times the full equation for energy is E2 = p2 + mc2  where p is the momentum.    LeeH

(published on 04/18/2014)

## Follow-Up #9: photon energy

Q:
Why aren't you using the formula E = hc/(wavelength) or E = h(frequency) to describe the energy of a photon in these answers?
- Travis (age 27)
Richland, wa
A:

Actually, we do happen to use E=hf in one answer. Most of these questions, however, center on the relation between momentum and energy and gravity, not on the size of the quantum packets.

Mike W.

(published on 03/24/2016)

## Follow-Up #10: gravity and mass

Q:
While I understand pretty much everything in this. My question relates to photons and gravity (specifically gravitational lensing). Is it a fair statement to say that F_g= [G(E/c^2)*m_2]/r^2? If so, why are photons, being a quanta of EM force/force carrier, the only gauge boson to interact with 3 (but not four?) fundamental forces? I know EM and weak merge to form electroweak (in theory) at very high energies and W bosons have electric charges but I'm uncertain how this relationship works or why photons interact with weak but weak force carriers don't interact with EM (maybe I'll just have to wait until I take QM). But I just realized digressed from my main inquiry, why do photons, a massless EM force carrier interact with gravity (I get the equation and substitution aspect) but AFAIK W and Z bosons, which are massive, do not? (If this doesn't technically count as being related to the question, I apologize.)
- Sam L (age 33)
Phoenix, AZ
A:

They all interact via gravity.

Mike W.

(published on 01/19/2018)

## Follow-Up #11: light, mass, and energy again

Q:
How can light have momentum and, furthermore; how can light have energy if a photon is massless? Einstein says that E=mc^2 which means that since light is massless, it�s energy should be 0. I�ve read that since light is massless that all of its energy comes from its momentum which is demonstrated by E=pc. However, in Newtonian physics momentum is equal to 1/2mv^2 which is an equation that again relies on mass. According to Einstein, momentum of a photon is instead found by p=h/λ. This results in a number that does not equal 0 which should answer my question. But if I�m right in saying that Planck�s constant is a description of energy contained within a quanta of light; isn�t energy still dependent on a particle�s mass?
- Austin (age 18)
South Carolina
A: