# Mass and relativity

1. May 24, 2010

### Fuz

I know that KE is relative, because velocity is relative. I also know that the more energy an object has, the more mass it has. Whats got me confused is when an object is accelerated to a certain velocity, its mass increases do to increases in KE, but that velocity is relative to what ever you want it to be relative to. This must imply that the increase in mass of the object is also relative. How can this be possible?

Thanks
Fuz

Last edited: May 24, 2010
2. May 24, 2010

### Staff: Mentor

That is the so-called "relativistic mass", and it is generally deprecated for exactly the reason that you point out. Instead, the more common mass in modern physics is the "invariant mass" which is frame invariant meaning that all reference frames agree on its value.

3. May 24, 2010

### cesiumfrog

Why is this a problem, if you were happy accepting that the length is relative?

It's not just possible but necessary: in the reference frames where the object is moving slowly, a certain force will readily make the object accelerate. But in the reference frame where it is already moving close to the speed of light limit, the same quantity of force must produce a smaller degree of acceleration, which requires the object's inertia to be relative.

It may be worth noting that the phrasing of your question may be contentious here. Not everyone uses the term mass (as you have) to refer to the ratio of force to acceleration, and of momentum to velocity, and to give Einstein's famous equation its most profound significance. Many prefer using mass to describe rest-energy, which is invariant and is a defining property of fundamental particles (although its quantity is not even simply additive, and is somewhat distanced from the concept of gravitation). Some people try to insist others adopt their convention.

4. May 24, 2010

### Passionflower

Very true, often those same people who show disrespect for actual physical measurements (e.g. Bondi k-calculus) and instead gloat on mathematical frames and coordinate system in their mistaken belief that those are more real, and then trying to police others into thinking like them.

5. May 24, 2010

### cesiumfrog

Hermann Bondi? Could you explain what you mean?

6. May 24, 2010

### Fuz

Thanks cesiumfrog, but I'm still confused. I thought that when we accelerate an object to near the speed of light, it gains mass making it harder to accelerate that object. Is that mass gained just an illusion, like how we feel heavy when traveling up a roller coaster but our mass isn't actually changing?

7. May 24, 2010

### DrGreg

It's worth pointing out that the ratio of force to acceleration, and the ratio of momentum to velocity, are not equal, except in the special case where the force is at right-angles to the velocity (or the velocity is zero). That's another reason why "relativistic mass" is deprecated.

$$\textbf{p} = \gamma m \textbf{v}$$
$$\textbf{f} = \gamma m \textbf{a} \mbox{ when } \textbf{f} \cdot \textbf{v} = 0$$
$$\textbf{f} = \gamma^3 m \textbf{a} \mbox{ when } \textbf{f} || \textbf{v}$$
$$\mbox{where } \gamma = 1/\sqrt{1-v^2/c^2}, \, \, m = \mbox{ constant rest mass}$$​

Last edited: May 24, 2010
8. May 24, 2010

### Passionflower

Not the same, in the roller coaster case we increase our proper acceleration. What we feel is nothing but the stresses on our body caused by the increase in acceleration.

9. May 24, 2010

### Fuz

I know. I was just trying to give the analogy that in the seat it feels like we're gaining mass (or getting heavier). Thats besides the point though.

I'm just wondering whether I truly gain mass when I move forward due to KE.