What proof is there that light has zero mass?

[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 don't 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.

 

[ZapperZ]

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 don't currently have the technology to measure it??

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.

 

[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:

There are some general properties of relativistic field theory that place tight restrictions on a possible alternative to the inverse-square law.

...

The general potential consistent with field theory turns out to be

$$V(r) = -Gmm'\frac{e^{-r/\lambda}}{r}$$

...

Incidentally: The value of $$\lambda$$ is related to the mass of the graviton, a (hypothetical) particle of spin 2, which is to gravitation what the photon is to electromagnetism.

...

If we rely on the observational limit given by the inequality [4], we obtain

$$m_{\Gamma} < 10^{-59} g$$

It is interesting to note that by setting analogous observational limits on possible deviations from Maxwell's equations, we find that the limit on the mass of the photon is of the same order of magnitude,

$$m_{\gamma} < 10^{-59} g$$

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.

 

[ZapperZ]

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.

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.

 

[jtbell]

I often come across the assertion 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 have thought of an experiment that may determine if light has mass.

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."

 

[Raap]

Nvm, jtbell explained it neatly.

 

[Vanadium 50]

Unfortunately, this builds upon a number of multi-leveled assumption of still-unverified theory (gravitons?).

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.

 

[humanino]

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.

 

[peter0302]

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?

 

[Topher925]

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?

 

[jostpuur]

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?

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

 

[peter0302]

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?

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?

 

[Raap]

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

 

[lightarrow]

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

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.

 

[Landru]

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

 

[jtbell]

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.

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.

 

[lightarrow]

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.

 

[ZapperZ]

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

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.

 

[Raap]

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

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.

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?

 

[ZapperZ]

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

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.

 

[samalkhaiat]

The other problem is that this permits charge nonconservation.

Full stop. Well done, it can be shown that the electric charge is conserved if and only if the matter fields couple to a MASSLESS photon.

regards

sam

 

[lightarrow]

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.

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?

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.

How are photons kept inside of fundamental particles anyway?

Who told you that?

 

[Raap]

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

Who told you that?

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.

 

[jtbell]

But couldn't it be argued that the photons *are* the energy, not just a carrier?

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

So when a photon combines with matter in some way, it transfers its energy and cease to exist?

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.

 

[azzkika]

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.

 

[lightarrow]

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.

It's not true that you 'could' be wrong. You are wrong
This is not just a theory, it's something established and measured. But of course you're completely free to believe what you want...

 

[Raap]

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 object and then released.

But how can we know this for sure without having perfect knowledge about how the the particles are built up? Like, what evidence is there that photons are constructed and deconstructed, instead of them just combining and uncombining with the radiating object( without ceasing to exist )? And what makes us so sure that energy isn't, in its smallest form, some sort of particle on its own? Are there actual evidence to support those claims, or is it just something we have assumed because we had no reason to think otherwise?

And assuming the photon thing is true, doesn't that just bring up a bunch of other questions? E.g. what creates the photons, how are they created and what are they created with?

 

[azzkika]

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!

if this is true, how does a massless thing impart mass to something when there is no mass to impart, if light has no mass. i am told light has no mass yet when absorbed makes a thing heavier. i cannot understand this.

 

[jtbell]

Suppose we have a stationary object with momentum p = 0, invariant mass ("rest mass") $m_0$, and energy $E = m_0 c^2$. It absorbs a photon that has momentum $p_{ph}$ and energy $E_{ph} = p_{ph} c$.

Momentum and energy are both conserved. Therefore the energy of the object afterwards is

$$E^{\prime} = E + E_{ph} = m_0 c^2 + E_{ph}$$

and the momentum of the object afterwards is

$$p^{\prime} = 0 + p_{ph} = p_{ph}$$

The invariant mass of the object afterwards can be found from

$$E^{\prime} = \sqrt {(p^{\prime} c)^2 + (m_0^{\prime} c^2)^2}$$

$$m_0^{\prime} c^2 = \sqrt {(E^{\prime})^2 - (p^{\prime} c)^2}$$

Substituting $E^{\prime}$ and $p^{\prime}$ from above gives

$$m_0^{\prime} = \sqrt {m_0^2 + 2 m_0 \left( \frac {E_{ph}} {c^2}} \right) }$$

which is larger than $m_0$.

 

[Vanadium 50]

But how can we know this for sure without having perfect knowledge about how the the particles are built up?

This is science. There's no such thing as "for sure". Nevertheless, there is extremely strong evidence for this. An electron that has absorbed one photon (or a million) is identical to one that has absorbed zero, which is identical to one that has emitted one - or a million.

 

[morphemes]

I think these three hypotheses are even more interesting
(Y≡∞)
(Y≡{})
({}≡∞)

I think the obvious implications of such a hypothesis is enormous. No matter how we stack it, modern scientists are playing a dirty trick on us in failing to adequately distinguish Law from Theory. However, I think there is a very well established scientific law that further reinforces the hypothesis that ({}≡∞).

Within the laws of thermodynamics we find the conservation of energy. Which we all know states that energy can not be created or destroyed. This is interesting because it implicates that the physical universe is an isolated system. No energy in & no energy out. However, what it does not imply is the structure of such a system. WE may imagine an isolated system to be like a seed or an egg. Within such a system energy is stored but not exchanged with the outside world. However, what is not commonplace is to imagine the inversion of such a system. A perpetual empty set ({}) that is infinite (∞) in scope. By virtue of this empty set, we can more accurately explain the existence of our physical (massive) universe.

If we have an empty set, however difficult it is to imagine, we have the necessary ingredient needed to create an event similar to the 'big bang'. We have an absolutely perfect vacuum. Which means that the event that triggered the spontaneous combustion of our physical universe would have encountered zero resistance, thus accounting for its expansion.

However, what is lacking is an explanation for the existence of mass. Quantum mechanics are on the way to providing just such an explanation. Elementary particles are theorized to be orbits. Not particles, necessarily, but force orbits akin to shock waves. Perhaps of a higher dimensional form, but pure orbits nonetheless. These orbits could only arise if given enough space to travel through. Perhaps at one time they did have mass, within their respective elements, but those elements have dissolved, leaving only the reverberation of their motion. This is energy, and it could be everywhere all the time. These elementary particles will easily replace the 'big bang' theory once we have knowledge necessary to prove their nature.

However, what else implied here? Well, we have a natural polarity of energy which is observed in the application of electronics. Positive and negative forces. In the case of light, I believe our science overlooks the significance of dark. We have suburb descriptions of 'white' and 'black' but we have failed to expand upon them.

If we observe the night sky, cloudless and spectacular. WE see stars scatted on a vast darkness. Physicists speculate the existence of 'dark matter' however, the darkness could be described as the opposite polarity of our suns light. Moving away from the sun, the light appear bright when one faces it, but turn around and you cast a shadow. This shadow may not necessarily be what we imagine it to be.

We know that high velocity particles move right through us on a daily basis. If light travels as fast as it is theorized to travel, what is holding it back from moving right through us? Well, other questions arise, such as the fact that light doesn't appear to travel through objects, however, this can be accounted for if light is an infinite force with negative and positive polarity. Within a surface that reflects light, if we are to imagine ourselves inside, we see darkness. However, light travels through it's self. In the case of magnetic force, positive and negative are repulsed. This is absolutely true with light as well, only in a slightly different way. If light always dominated dark, then the stars in the sky would illuminate the entire sky, however they do not seem to do so. If we imagine light as a clockwise orbit & dark as counterclockwise, perhaps we may begin to understand.

However, we want proof of light having no mass. Well, the current mass of light is calculated by its luminosity and the space it contains, which is completely backwards if light is to have mass. We do not measure the mass of a water molecule by the size of a body of water and its dampness. The current mass of light equation already implies that light is without its own mass. Which is interesting.

Possible proof arises if one speculates an experiment where one is able to extract a photon from a volumeless container or the inversion. Which seems impossible. However, 'impossible' has long been the bane of scientific advancement.

Simply, we have no proof. Only a strong hunch.

 

[Galap]

Currently, our best experimental evidence for light being massless is that within extremely small margins of error, we have measured that it travels at C.

 

[humanino]

There is a very nice discussion about light mass in Feynman's lectures on gravitation, paragraph 2.2 (difficulties of speculative theories). If you are interested in the question, I strongly urge you to read this paragraph. Nowhere else have I ever read a more lucid and enlightening discussion on this matter.