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

[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 ?

 

[Orodruin]

Please read this Insight: https://www.physicsforums.com/insights/what-is-relativistic-mass-and-why-it-is-not-used-much/

 

[jtbell]

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 ?

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 $$K = \frac{1}{2}mv^2$$

 

[ZapperZ]

In addition to the responses above, read this on why even Einstein stopped using the term "relativistic mass" once he realized how misleading and inaccurate that term was:

https://www.physicsforums.com/threads/relativistic-mass.642188/#post-4106101

Zz.

 

[vanhees71]

In addition to the responses above, read this on why even Einstein stopped using the term "relativistic mass" once he realized how misleading and inaccurate that term was:

https://www.physicsforums.com/threads/relativistic-mass.642188/#post-4106101

Zz.

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

http://svr1dx.ud.infn.it/URDF/laure...erDoes_mass_really_depend_on_velocity_dad.pdf

 

[robphy]

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

 

[jtbell]

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

 

[pervect]

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 ?

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.

 

[harrylin]

In addition to the responses above, read this on why even Einstein stopped using the term "relativistic mass" once he realized how misleading and inaccurate that term was:

https://www.physicsforums.com/threads/relativistic-mass.642188/#post-4106101

Zz.

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