In my experience, when E=mc² is written, physicists generally mean relativistic mass, making the formula extract, whereas m_0 is used for rest mass, as seen in the expansion E = m_0c² + m_0v²/2 + O(v⁴)
Where does that expansion come from? As far as I can tell, m0v^(2)/2 only gives you the kinetic energy of the object where v << c, in which case the difference between relativistic mass and rest mass is negligible?
In my experience, when E=mc² is written, physicists generally mean relativistic mass, making the formula extract, whereas m_0 is used for rest mass, as seen in the expansion E = m_0c² + m_0v²/2 + O(v⁴)
Where does that expansion come from? As far as I can tell, m0v^(2)/2 only gives you the kinetic energy of the object where v << c, in which case the difference between relativistic mass and rest mass is negligible?
And where does the O(v^4) term come from?