# Mass in special relativity

1. Jun 27, 2011

### Zac Einstein

According to Einstein's theory, when an object travels at the same speed as the speed of light, it's mass will be much bigger and it's weight too.
How and why?.......because of energy?

2. Jun 27, 2011

### danR

It will have an increased energy equivalent to mass, but not 'mass' proper as it pertains to matter-mass. For example, you cannot convert that added 'mass' into new energy to drive a photonic spaceship even faster. This was a conceptual error I made until someone corrected me.

3. Jun 27, 2011

### bcrowell

Staff Emeritus
A material object can't travel at c. A correct way to state this would be that as you increase an object's speed, its inertia increases. The amount of inertia increase is small if the speed is small compared to c. As the speed approaches c, the inertia approaches infinity.

These days, most physicists prefer not to refer to this effect as a mass increase. Usually we write the relationship as $p=m\gamma v$, where p is momentum, m is the mass, v is the velocity, and $\gamma=1/\sqrt{1-v^2/v^2}$. The mass m is taken to be constant, and the factor of gamma gives the relativistic effect.

There is a variety of ways of proving this theoretically. One is that if you try to use p=mv without the gamma factor, then collisions that obey conservation of momentum in one frame will not obey conservation of momentum in another, because velocities don't add linearly in relativity.

4. Jun 27, 2011

### Zac Einstein

Excuse me sir, I didn't really understand what did you mean by this equation $\gamma=1/\sqrt{1-v^2/v^2}$ and how the factor of gamma gives the relativistic effect, sir? Ehh! This is really confusing
I'm 15 and they don't teach relativity to Tenth grades but I can't wait untill they do so I learnt it by myself.

5. Jun 27, 2011

### Polyrhythmic

It's actually supposed to be

$\gamma=1/\sqrt{1-v^2/c^2}$,

where c is the speed of light. This factor is central to special relativity and gives you the velocity dependence of quantities like energy or momentum. You immediately see that for v=c, that quantity blows up and becomes infinite. That's one good way to see that approaching c is impossible for massive objects.

6. Jun 27, 2011

### bcrowell

Staff Emeritus
Oops, thanks for the correction, Polyrhythmic!

Zac Einstein, if you want to learn some relativity, I'd suggest starting with An Illustrated Guide to Relativity by Takeuchi.

7. Jun 27, 2011

### Zac Einstein

Yes sir, but I understand relativity......but there are some points which are a bit confusing 'cause of the high math level

Thank you, sir

8. Jun 28, 2011

### bcrowell

Staff Emeritus
The Takeuchi book is nice because it uses only very basic math.

9. Jun 28, 2011

### Zac Einstein

Thanks thanks thanks thanks, sir