# Speed of light

1. Jul 24, 2004

### Kamataat

Hi!

I understand that according to E=mc^2 any normal object can't reach the speed of light because the energy of its motion increases its mass and thus you'd need an infinite amount of energy to reach c. However, it is said that objects with no mass (i.e. photons) travel at the speed of light. Why is it said that they have no mass? Isn't it true that even they have a rest mass (because their energy can never be zero even at rest according to the Heisenberg Uncertainity Principle)? If so, then how can they reach the speed of light if they have a mass like any other object or particle?

P.S. I know only high school mathematics and physics so please try to avoid anything more serious. I only want to get a simple explanation of the principles.

- Kamataat

2. Jul 24, 2004

### pmb_phy

This is a topic which comes up quite often. The answer is that the inertial mass (aka relativistic mass), defined as the ratio of the magnitude of the particle's momentum to the particle's speed, increases with increasing speed and that the proper mass (aka rest mass) is not a function of speed. Different people use the term "mass" to refer to different things. Some use it to refer to inertial mass while others use it to refer to proper mass.
When they say that they are not refering to the particle's inertial mass, they are refering to the particle's proper mass, i.e. the one that is not a function of speed.
According to current observations, photons do not have rest mass. And it is incorrect to claim that the energy of a photon is zero. The energy of a photon is related to the photon's inertial mass m through E = mc2.

Pete

3. Jul 24, 2004

### Kamataat

So photons don't have a proper mass, but do have an inertial mass? But if the inertial mass increases with speed, then how can a photon reach the speed of light?

- Kamataat

4. Jul 24, 2004

### pmb_phy

The inertial mass is a function of speed only for tardyons and not for luxons. A tardyon is defined as a particle that always moves with a speed v < c whereas luxon is defined as a particle that always moves with speed v = c (To be complete: A tachyon is defined as a particle which always moves with speed v > c). Therefore, since relativitiy tells us that photons always travel at the same speed, c, the inertial mass of a photon is not a function of speed.

Pete

5. Jul 24, 2004

### Mk

Obviously, particles that have only rest mass or only inertial have their own catogory of matter?, how are they diffrent?

6. Jul 24, 2004

### Mk

Oooops, I ment:

obviously, particles that have only rest mass or only inertial don't have their own catagory of matter. How are they diffrent than stuff that has both?

7. Jul 24, 2004

### Mk

By the way, is dark matter if it exists another form of matter? The diffrent forms of matter differ in how much empty space is in it and the density of the empty space. Right or no right so far? Is it the bonds, how long the chains are? Where do you draw the line between the diffrent types of matter? Is there a list or system or something where, it says where you draw the line, between the now 7 types of matter? I guess I just want to know how they are diffrent past all the, solids hold their shape stuff

-A confused person all of a sudden

Muy big thanks :)

8. Jul 24, 2004

### PRodQuanta

I believe the equation for proper massless particles looks like this: $$E^2={m^2}{c^4}+{p^2}{c^2}$$where p=momentum
This formula is used in x-ray and gamma ray astrophysics.
Obviously if the particle were at rest, p=0, which would bring you back to $$E=mc^2$$