# If mass becomes inifinite when approaching the speed of light, then photons?

1. Jul 5, 2010

### colbertsparro

Alright, hi. I've posted one or two things on here, and have been thoroughly informed how incredibly stupid and unprepared I am to even type in the same domain as people with IQs that mine would factor into. Okay, so I read Hyperspace and am reading the Elegant Universe. I'm a dumb high school student who thinks physics is cool. I'll try to make this brief.
I was trying to explain to friend of mine that {I had been informed that} you cannot go faster than the speed of light because as you APPROACH the speed of light, mass becomes infinite, and that travelling AT the speed of light, mass IS infinite. Then he proposed, well, doesn't light go at the speed of light? Which seemed like a dumb question until I thought about it, and realized, well, how is it that the mass of photons does not become infinite, and how does even a PHOTON travel at the speed of light? I know it has wave-like properties and all, but... how does even LIGHT travel at the speed of light?
Responses with minimal mocking appreciated, written, of course, in the most dumbed down way possible, for my teeny tiny brain.

2. Jul 6, 2010

### Eynstone

Photons are massless. Be careful when an argument involves limits as something tends to the speed of light.

3. Jul 6, 2010

### hendriko373

You should be careful in considering the "mass" of an object in a relativistic theory. In special relativity the rest-mass is a form of energy but not all energy is rest-mass. Basically particles can be divided in two subclasses: those with a rest-mass (e.g. the electron) and those without (e.g. the photon). It is crucial in special relativity that the latter always travel at the speed of light (this is in fact a postulate) and their energy is determined by their three-momentum (or their frequency if you want). Particles with rest-mass can never attain the speed of light as this would require an infinite amount of energy to achieve this. Why photons have no mass or in the light of relativity: "why do they travel at constant speed" has no deep answer; we just happen to observe it in the laboratory.

4. Jul 6, 2010

### ZapperZ

Staff Emeritus

Zz.

5. Jul 6, 2010

### bcrowell

Staff Emeritus
The easiest way to approach this is to consider the case of a particle with very small, but not zero, rest mass $m_o$. Its relativistic mass is $m=m_o\gamma$. For a fixed energy, if we let $m_o$ approach zero, $\gamma$ approaches infinity, but the product remains finite. You can think of the photon, with zero rest mass, as the result of this limiting process.

6. Jul 6, 2010

### AJ Bentley

That's a reversal of cause and effect.

Several things happen as you approach light-speed - one of them is that mass increases.
The primary cause of that is time dilation and the Lorentz contraction of space.
Basically, you get less acceleration for the force you apply. Rather than start saying the Force must be changing, we elect to blame the Mass. (It just makes the arithmetic easier )

7. Jul 6, 2010

### Mute

On the contrary, the modern interpretation is to blame the momentum (and hence force). It is (perhaps) conceptually easier to suppose that the functional form or momentum deviates from the simple mv at high speeds rather than supposing that mass begins to increase at high speeds.

Plus if everyone just got on board with the 'blame the momentum' interpretation we wouldn't get so many questions about photon masses (though we might get more on photon momentum...).

8. Jul 6, 2010

### AJ Bentley

So it wasn't the Butler after all?