# How can photons be massless?

E=MC2 according to general relativity. But photons supposedly have no mass, so E=(0)C2=0. But E≠0, because the simple act of existing requires energy, and light interacts with normal matter via the electromagnetic force all the time, which again requires energy. Moreover, photons have been shown to oscillate between various different kinds/wavelengths, which apparently requires mass to occur (at least according to leading authorities on neutrinos). So how can photons be massless?

Relevance

E = Mc^2 has nothing to do with the energy of a photon but rather how much energy it takes to form a lump of matter of a goven size (mass).

The energy of a photon = (Planck's constant * speed of light) / wavelength

http://en.wikipedia.org/wiki/Photon

Light has mass?

Light particles (Photons) are pure energy and exist only when in motion. We can debate if photons have mass. Because of Einstein's E = Mc^2 matter and energy are 2 forms of the same thing. Since photons have energy it can be argued that they have Relativistic Mass. On the other hand, Einstein was uncomfortable with the concept of Relativistic Mass because:

Many contemporary authors such as Taylor and Wheeler avoid using the concept of relativistic mass altogether:

"The concept of "relativistic mass" is subject to misunderstanding. That's why we don't use it. First, it applies the name mass - belonging to the magnitude of a 4-vector - to a very different concept, the time component of a 4-vector. Second, it makes increase of energy of an object with velocity or momentum appear to be connected with some change in internal structure of the object. In reality, the increase of energy with velocity originates not in the object but in the geometric properties of spacetime itself.

http://en.wikipedia.org/wiki/Mass_in_spe%E2%80%A6

http://en.wikipedia.org/wiki/Mass%E2%80%93energy_e...

Scroll Down to “Relativistic Mass”

In any case, photons have zero Rest Mass.

When we get into Relativity, “mass” has 2 different meanings. There is “Rest Mass” and “Relativistic Mass” and they are NOT the same thing.

• What do you mean by 'mass'?

Strange question to begin an answer with, I know, but let's consider it for a moment. If you were talking about a car, then mass is some property of the car related to the 'amount of material' and describes the relationship between the force you apply and the acceleration that results. Is this sense of 'mass' applicable to a photon? How much 'material' makes up a photon? What 'force' do we apply to change its acceleration?

You might say 'electromagnetic forces' and you'd be right. But electromagnetic forces are the result of photons. So does the concept of mass have any meaning for a photon interacting with other photons or with matter? Can we explain what happens without invoking a 'mass' for photons? Well, yes we can!

Of course, you could define mass as the property of objects that produces gravitational forces. But gravity is the curving of spacetime by mass/energy distributed within it. A star has mass, but a photon moves through spacetime, so it doesn't need mass to be deflected by the star - it simply follows the curved spacetime path and is deflected. But again, we don't need mass to describe what happens to the photon.

So, the short answer is, photons are massless because the concept of 'mass' isn't necessary to explain any of our observations involving photons!

• Anonymous
8 years ago

The energy of a photon, is a constant times its frequency. The formula you remember, is for the energy of a particle or body at rest, with mass m.

"Moreover, photons have been shown to oscillate between various different kinds/wavelengths"

No. They do not do this.

To have mass, would violate conservation of charge.

• Better ask, "How can they not be massless?" After all, they travel at, duh, the speed of light. And I suspect you know what happens to the inertia of a rest mass, m, when v = c, it's velocity reaches light speed.

Your assertions are so filled with misinformation, I hardly know where to begin.

But let's tackle "photons have been shown to oscillate between various different kinds/wavelengths, which apparently requires mass to occur (at least according to leading authorities on neutrinos" What you are referring to is the so-called neutrino oscillation, but...this is important...that's not wave frequency oscillation. That's oscillating between three kinds of neutrino. In other words, there is but one neutrino but it oscillates through three different phases to show up as three different kinds of neutrino.

And the reason this neutrino oscillation forces us to conclude that neutrinos have mass is because those phase changes have a periodicity. That is, they indicate time passing for that neutrino. And that means...drum roll please...the neutrino cannot be going the speed of light (time would stand still if it did) so the neutrino has to have some mass, m. You see, only things going light speed and time stands still for them are massless.

But photons are going the speed of light and they are eternal, time stands still for them. So they must be massless. And I prove that below under source. Check it out.

Another bad assertion, e = mc^2 is the source of energy for a photon, so e = 0 as m = 0 for photons. The mass-energy equivalent term, e = mc^2, is not the only source of energy for particles. There is also kinetic energy. In fact, we can show that E = Mc^2 is total energy, e = mc^2 is the mass equivalent energy, and k = Mvc is the kinetic energy. They are related by E^2 = e^2 + k^2; so when m = 0 so that e = 0, the total energy is E = Mc^2 = Mvc = k the kinetic energy, which you can see when v = c is the speed of the particle. M is the relativistic inertia of the particle. [See source.]

Source(s): From the special theory of relativity, relativistic inertia is M = m/sqrt(1 - (v/c)^2) where m is rest mass, as in e = mc^2, and v is the relative speed of the mass. We multiply both sides by c^2 and rearrange the terms to give E^2 = e^2 + k^2; where E = Mc^2, e = mc^2, and k = Mvc. Now let the mass, m, go v = c, light speed. In which case k = Mvc = Mcc = Mc^2 = E. So now we have E^2 = e^2 + E^2 and E^2 - E^2 = e^2 = 0. Then e = mc^2 = 0. Since c > 0 always, that means m must = 0 when v = c. You know, like massless photons. QED.
• I have no idea why anything you said means light can't have mass.

You said E=(0). You are wrong.

E=mc² is not the whole equation. It is just a famous abbreviation of it.

The whole equation is:

E² -(pc)² =(mc² )²

p here is the momentum of the "thing" in question.

There is an equation for the momentum of light in the 2nd link I provided. yes light can have momentum even if it is massless

Since light can have momentum we use the whole equation to make this shortened version:

E² -(pc)² =(mc² )²

E² -(pc)² =(0*c²)²

E² -(pc)² =0

E²=(pc)²

E=pc

Thus the speed of light times the momentum of the particular photon equals its energy

• What Justin said.

BTW where did you learn that photons oscillate between various different kinds/wavelengths? I've never heard of that.

• You have misused the formulas for photon. ( Virus do not get rid the pupils)