Changes

where <math>p</math> is the momentum defined by <math>\gamma m v</math>, <math>\gamma</math> is the standard Lorentz factor, and <math>\tau</math> is the proper time. Force F defined this way is a vector and thus can handle the directional aspect of the relativistic effects better than the concept of relativistic mass can.

where <math>p</math> is the momentum defined by <math>\gamma m v</math>, <math>\gamma</math> is the standard Lorentz factor, and <math>\tau</math> is the proper time. Force F defined this way is a vector and thus can handle the directional aspect of the relativistic effects better than the concept of relativistic mass can.

The abandonment by physicists of the concept of relativistic mass, however, has the consequence of undermining the traditional claim under relativity that

Ultimately, the concept of relativistic mass should be viewed as a language for interpreting the equations of relativity that has since become less popular. Relativistic mass <math>m</math> was defined in such a way that the equation <math>E=mc^2</math> became true in all inertial reference frames. One can rephrase this equation as saying the following: If <math>p</math> is the 4-momentum of a particle, then the square of the magnitude of <math>p</math> satisfies:

:<math>m - m_0 = \frac{E}{c^2}</math>  

<math>||p||^2 = -p_x^2-p_y^2-p_z^2+E^2 = m_0^2c^4</math>  

in any inertial reference frame. In other words, the magnitude of the 4-momentum, in any inertial frame, equals the rest mass <math>m_0</math> of the particle (in units where <math>c=1</math>). While this is equivalent to the statement <math>E=mc^2</math>, where <math>m</math> equals relativistic mass, the latter statement in terms of the 4-momentum is more natural from the point of view of Minkowski geometry.

 

:<math>E = m c^2</math>

==Evidence for Relativity==

==Evidence for Relativity==