# Can relativistic mass be used in place of total energy?

I was doing some practice questions regarding relativistic kinematics and I just had a question, We write total energy of an object as; $$E^{2} = m_{0}^{2}c^{4} + p^{2}c^{2}$$

Where $$m_{0}$$ is the rest mass. Now if we replace $$m_{0}$$ with it's relativistic alternative;

$$m = \gamma m_0$$ Where $$\gamma$$ is the Lorentz factor.

Can I remove the kinetic energy term $$(p^{2}c^{2})$$, since the kinetic energy is now counted as the mass increase or am I missing something?

I was doing some practice questions regarding relativistic kinematics and I just had a question, We write total energy of an object as; $$E^{2} = m_{0}^{2}c^{4} + p^{2}c^{2}$$

Where $$m_{0}$$ is the rest mass. Now if we replace $$m_{0}$$ with it's relativistic alternative;

$$m = \gamma m_0$$ Where $$\gamma$$ is the Lorentz factor.

Can I remove the kinetic energy term $$(p^{2}c^{2})$$...

Yes, you can write: $$E = \gamma m_0 c^2\;,$$ which can be squared to see that: $$E^2 = \gamma^2 m_0^2 c^4\;.$$

As a notational aside, I would personally advise against using the notation $$m$$ for relativistic mass, since many many people prefer to use $$m$$ for rest mass. I.e., just use $$m$$ for rest mass and use $$\gamma m$$ for relativistic mass.

• One problem with $\gamma m$ notation is that it doesn't work if the rest mass is zero. And, of course, using it indicates no respect for the history of $E=mc^2$, its cultural significance, and its profound implications. Commented Jan 20, 2023 at 13:00
• This is the Physics Stack Exchange, not the Hypothetical Cultural Significance Stack Exchange....
– hft
Commented Jan 20, 2023 at 17:13
• How is your preference for $\gamma m$ anything beyond a cultural statement? Commented Jan 20, 2023 at 18:08
• Why do you feel the need to die on this hill?
– hft
Commented Jan 20, 2023 at 19:49
• Who's dying? Not me. But physics itself is in a bit of trouble, losing sight of the fundamental phenomena. youtube.com/watch?v=aIhk9eKOLzQ Commented Jan 20, 2023 at 20:00