# What proof is there that light has zero mass?

1. Aug 21, 2008

### azzkika

What proof is there that light has zero mass??

I often come across the assertion that light has zero mass. i was wondering is this a proven fact or just an assumption because we dont currently have the technology to measure it??

i have thought of an experiment that may determine if light has mass. you wold need an exactly balanced set of scales housed within a sealed box covered in mirrors. on one half of the scales, the scales and balance weight are covered in mirrors, on the other they are balck as that absorbs most light i think. if a light is shone within this box for a period of time any absorbing light would register on the black side if it had mass. the scales wopuld need to be extremely precise however and set up to be vibration free and various other measures to eliminate any other contributory effect that could cause scale variation. only an idea, but i personally think it has to have a mass, though i know this is an amateurs opinion, and it's commonly believed to be massless.

Last edited: Aug 21, 2008
2. Aug 21, 2008

### ZapperZ

Staff Emeritus
Re: What proof is there that light has zero mass??

1. You make a hypothesis that light has zero mass

2. You then see the consequences of such assumption in terms of current theories.

3. You test the consequences and see if (i) it matches existing observations and (ii) it predicts new observations that haven't been seen yet. If those are all verified so far, then there's a good indication that Hypothesis 1 is correct.

4. You continue to explore other implications of #1, i.e. what else can it predict? Can those be tested? If at some point, these future tests indicate a possible contradiction, then that's when you come back and question of Hypothesis 1 is valid all the time. We haven't seen this occurring yet for light.

The statement that light has no mass isn't JUST about light itself. It has implication in everything from your GPS system to your modern electronics. So you yourself are a prime data point in showing that our assumption that a photon has no mass is valid.

Zz.

3. Aug 21, 2008

### jostpuur

I'm copying stuff from the pages 6 and 7 of the book Gravitation And Spacetime, Second edition, by Ohanian & Ruffini. They are speaking about gravitation, but also mention something about electromagnetism:

You cannot prove experimentally that the mass of a photon is zero, but you can prove that it is below some small upper limit. The authors of this book are not very precise with numbers on this topic here, but if somebody is interested, it is probably possible to find more detailed information about these experiments.

4. Aug 21, 2008

### ZapperZ

Staff Emeritus
Re: What proof is there that light has zero mass??

Unfortunately, this builds upon a number of multi-leveled assumption of still-unverified theory (gravitons?). I'd say that one has to show that the theory is actually valid with gravitons first before one can safely conclude such upper limit. Furthermore, one can't "proof" anything in physics (can you proof that a superconductor actually has zero DC resistivity?). Our present day observation of the consequences of the assumption that a photon has zero mass allows us to conclude that this assumption is valid. Till we experimentally discover otherwise, then anything is really yet-unverified speculation.

Zz.

5. Aug 21, 2008

### Staff: Mentor

Re: What proof is there that light has zero mass??

In relativity there is no single definition of "mass" that covers all the properties that we associate with "mass" in classical physics. Different definitions of "mass" emphasize different properties.

The assertion that light has zero mass depends on a certain definition of mass, namely the one for invariant mass a.k.a. "rest mass". It is a constant for a particular particle or object, and is considered a fundamental property of that particle. It is related to the particle's energy and momentum by $E^2 = (pc)^2 + (m_{invariant}c^2)^2$. An individual photon always has E = pc, therefore $m_{invariant} = 0$.

(Aside: Note that the energy and momentum carried by a classical electromagnetic wave also has the relationship E = pc.)

The invariant mass of a system of particles follows the same equation, using the total energy and total momentum of the system: $E_{total}^2 = (|{\vec p}_{total}| c)^2 + (m_{invariant}c^2)^2$. (In finding the total momentum, we have to take into account that momentum is a vector, of course.)

The other definition of "mass" that you often encounter in popular-level books and some introductory textbooks is the relativistic mass which varies with speed according to

$$m_{relativistic} = \frac {m_{invariant}} {\sqrt {1 - v^2 / c^2}}$$

It can be considered as property of the relationship between an object and an observer (reference frame). An object (including a photon) has relativistic mass which is proportional to its energy via $E = m_{relativistic} c^2$

I think it is generally accepted that the "black" side of your scales should weigh more, because it has absorbed the energy of the light. That does not necessarily mean that the light (photons) that were absorbed individually have mass! It depends on which definition of mass you are using!

Unlike classical mass, invariant mass is not "additive." The invariant mass of a system of particles is not, in general, the sum of the invariant masses of its parts.

On the other hand, relativistic mass is additive, at least for the kind of situation you describe.

Most physicists who actually work with relativistic particles (i.e. nuclear and high-energy particle physicists) prefer to consider "mass" as a fundamental property of a particle. Therefore, by convention, when most physicists refer to "mass" without any qualifier, they mean "invariant mass" and call it simply "m".

Unfortunately, this causes a lot of confusion among people who are learning relativity, because most popular-level books and some introductory textbooks discuss relativistic mass. These books usually call relativistic mass "m" and invariant mass "$m_0$".

It also causes a lot of arguments here on PF, and on other forums, about whether relativistic mass or invariant mass is "better" or more worthy of being called simply "mass."

Last edited: Aug 21, 2008
6. Aug 21, 2008

### Raap

Re: What proof is there that light has zero mass??

Nvm, jtbell explained it neatly.

7. Aug 21, 2008

Staff Emeritus
Re: What proof is there that light has zero mass??

I agree that's not the best example, but the argument is still okay. I'd describe the argument this way: we use the Maxwell theory, which has a zero photon mass. There's also the Proca theory, which has the photon mass as an input parameter, and at m=0, it reduces to the Maxwell theory.

One then asks how large can m be before the differences between the two theories, and the answer to that question is the incredibly small mass that is quoted.

Note that this is purely a classical argument.

When one goes to a quantum theory, a massive photon means that gauge invariance is broken. This causes massive problems. If you break the photon's U(1) symmetry, you end up with an electrically charged particle with a mass comparable to the photon's mass that's the analog of the Higgs. The existence of such a particle means the electron would be unstable with a lifetime well under a second - that's not the world in which we live.

The other problem is that this permits charge nonconservation. There are some excellent reviews by Okun in the literature, but the short summary is that there are extremely stringent constraints on this.

8. Aug 21, 2008

### humanino

Re: What proof is there that light has zero mass??

There is a very pleasant discussion if I remember correctly in Feynman's lecture on gravitation. I could summarize here later tonight if somebody does not have the book and requests it.

9. Aug 21, 2008

### peter0302

Re: What proof is there that light has zero mass??

If we confine a gazillion (N) photons to a small region - say put it in a mirrored box - would we have any way of knowing that there was NOT a mass inside the box equal to Nhv/c^2 without looking inside?

10. Aug 21, 2008

### Topher925

Re: What proof is there that light has zero mass??

I know modern physics says that light does not have mass but it very clear that light does have momentum. How can photons have momentum but no mass according to modern physics?

11. Aug 21, 2008

### jostpuur

Re: What proof is there that light has zero mass??

https://www.physicsforums.com/showpost.php?p=1285138&postcount=6 [Broken] Do Photons Have Mass?

Last edited by a moderator: May 3, 2017
12. Aug 21, 2008

### peter0302

Re: What proof is there that light has zero mass??

You don't even need quantum mechanics to understand this. Light carries energy which gets absorbed by electrons. Newton told us that for every action there is an equal and opposite reaction. The action of the electron absorbing the photon must therefore be accompanied by some kind of motion (after all, the electron can gain neither charge nor mass). That's why the photon "has" momentum.

Maybe you'd be more comfortable if we said the photon "imparts" momentum?

13. Aug 21, 2008

### Raap

Re: What proof is there that light has zero mass??

Isn't the Sun's mass diminishing as it radiates photons?

14. Aug 21, 2008

### lightarrow

Re: What proof is there that light has zero mass??

Yes, and then? Mass is not additive, as jtbell explained. It means that it's not true that system's mass = sun's mass + photon's mass.

When you add (subtract) an amount E of energy to a body which stays stationary, its mass increases (decreases) of the amount E/c^2, independently of the way or the kind of energy you give it, so if it's light or anything else, it's the same. For example, you can heat it, you can spin it, ecc.

No need for photons to have mass.

15. Aug 21, 2008

### Landru

Re: What proof is there that light has zero mass??

Can it be said that photons have mass by virtue of having energy which is itself mass in another form?

16. Aug 21, 2008

### Staff: Mentor

Re: What proof is there that light has zero mass??

Note that in classical electrodynamics, the electromagnetic field carries both energy and momentum. In general, momentum and energy are not conserved by the particles alone, when they interact via electromagnetic forces. However, when we include the momentum and energy carried by the field, the total momentum and energy are conserved.

17. Aug 21, 2008

### lightarrow

Re: What proof is there that light has zero mass??

Among the experiments to measure the photon's mass I remember one in which the inverse square law is tested through the test of Gauss' theorem (it was on Scientific American ~ 20 y. ago). Essentially it was measured the residual charge inside a set of 5 metallic screens. If the photon had a mass we should be able to measure such a residual charge. Nothing of that kind has been found yet, with that as with other kinds of experiments and this fix an experimental limit for the photon's mass of which has been said, and that you can find in the Particle Data Group: < 10^(-18) eV.

18. Aug 21, 2008

### ZapperZ

Staff Emeritus
Re: What proof is there that light has zero mass??

The sun give out a lot of STUFF, including neutrinos (which we know to have mass). How are you able to simply attribute for the sun's diminishing mass to only the radiated photons?

Zz.

19. Aug 21, 2008

### Raap

Re: What proof is there that light has zero mass??

Hmm, what about gravity then, it does affect photons, does it not? Were they truly massless, shouldn't they remain unaffected?

But how then can we measure the Sun's mass without also including the possible mass of photons? I mean, isn't it likely that photons are part of the building block of e.g. quarks( or perhaps some even smaller block that we haven't discovered yet) ? Supposedly when we collide these smaller particles photons are often at least part of the end-result, right?

How are photons kept inside of fundamental particles anyway?

20. Aug 21, 2008

### ZapperZ

Staff Emeritus
Re: What proof is there that light has zero mass??

I am sure you would have realized by now that something THAT obvious would have an explanation. And there is. Please search the Relativity forum here because that question has been asked numerous times on here.

Zz.

21. Aug 21, 2008

### samalkhaiat

Re: What proof is there that light has zero mass??

22. Aug 22, 2008

### lightarrow

Re: What proof is there that light has zero mass??

Photons have energy and that's enough for Sun or anything else absorbing energy to increase its mass, or giving off energy to decrease its mass (if it stays still in your ref. frame).
Look at this equation:

$$\Delta E^2\ =\ (c\mathbf{p})^2\ +\ [(\Delta m)c^2]^2$$

Here $$\Delta E$$ is the energy absorbed (or released) by a system which momentum is $$\mathbf{p}$$ and $$\Delta m$$ is its mass increase (or decrease) after the process.

If the body is stationary, that is $$\mathbf{p}\ =\ 0$$ , then an increase $$\Delta E$$ in its energy corresponds to an increase $$\Delta E/c^2$$ of its mass. NO need for the particles or anything else carrying the energy $$\Delta E$$ to have mass.
Who told you that?

23. Aug 23, 2008

### Raap

Re: What proof is there that light has zero mass??

But couldn't it be argued that the photons *are* the energy, not just a carrier? Is there anything that directly contradicts this?

You're saying they aren't? So when a photon combines with matter in some way, it transfers its energy and cease to exist? That's what I'm confused about.

24. Aug 23, 2008

### Staff: Mentor

Re: What proof is there that light has zero mass??

Energy is a property of an object or system, not an object in itself.

Yes. And when matter radiates photons, they are created during the emission process; they were not previously stored within the radiating object and then released.

25. Aug 23, 2008

### azzkika

Re: What proof is there that light has zero mass??

you dudes are too clever. thanks for puzzling my brain some more, i really need to get on a proper physics course. i still think it must have mass even if it is close to zero. but i could be wrong.