# If the concept of relativistic mass is rejected...

1. Aug 28, 2015

### hidex

Then why did they find out it's harder to accelerate particles when they are near the speed of light?

Even the lorentz equation indicates that the dimension is mass (rest mass / lorentz factor).
Infinite energy is required to accelerate an object approaching to the speed of light, but what did the object gain if it's not relativistic mass ?

2. Aug 28, 2015

### Orodruin

Staff Emeritus
3. Aug 28, 2015

### Staff: Mentor

Kinetic energy. The work-energy theorem still applies:$$W = K_{final} - K_{initial}\\K_{final} = K_{initial} + W$$ However, the relativistic equation for kinetic energy is different from the non-relativistic one: $$K = \frac{mc^2}{\sqrt{1 - v^2/c^2}} - mc^2$$ rather than $$K = \frac{1}{2}mv^2$$

Last edited: Aug 28, 2015
4. Aug 28, 2015

### ZapperZ

Staff Emeritus
5. Aug 28, 2015

### vanhees71

Yes, and read the paper by Okun mentioned there. You find it online here:

http://www.stat.physik.uni-potsdam.de/~pikovsky/teaching/stud_seminar/einstein_okun.pdf

Also see

6. Aug 28, 2015

### robphy

By the way, $$K = \left(\frac{1}{\sqrt{1 - v^2/c^2}}-1\right)mc^2$$

7. Aug 28, 2015

### Staff: Mentor

Yep, I inadvertently omitted the $-mc^2$ term from my version of the equation, then went back and added it.

8. Aug 28, 2015

### pervect

Staff Emeritus
Acceleration is the rate of change of velocity, but in special relativity velocities don't add normally. By "add normally", I mean that in Newtonian physics, if we have three objects, $O_1$, $O_2$, and $O_3$, if the velocity between $O_1$ and $O_2$ is $v_{12}$ and likewise the velocity between $O_2$ and $O_3$ is $v_{23}$ and the velocity between $O_1$ and $O_3$ is $v_{13}$, then we expect that $v_{13} = v_{12} + v_{23}$

This is not true in special relativity, $v_{13}$ is not equal to $v_{12}+v_{23}$.

So let us apply this relation to a hypothetical rocketship, that after 6 months of proper (shipboard) time, reaches half the speed of light relative to it's starting point. We ask the following question: "What happens in another six months shipboard time?"

Well, the rocketship's velocity relative to its starting point is equivalent $v_{12}$ in the above example, and by the problem statement this velocity is 0.5c. The velocity of the rocket at 12 months relative to it's velocity after six months is like $v_{23}$, and because the rocektship accelerates at a constant rate, we can say that $v_{23}$ is also equal to 0.5c.

But $v_{13}$, the velocity of the rocket relative to its starting point, is not equal to $v_{12} + v_{13}$ which is 0.5c + 0.5c = c. It's lower than that.

We don't need to introduce the concept of "mass" or "energy" at all to make this statement, so any explanation that relies on the concepts of "mass" or "energy" in an attempt to "explain" the behavior is introducing superfluous concepts that aren't really required.

9. Sep 1, 2015

### harrylin

Thus a concept that was easy and simple for Feynman and his students, was a "confusing concept" for Okun. "Everyone his own" I suppose...