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697 bytes removed ,  21:34, June 15, 2009
→‎Mass increase: removed claptrap about "language" and "more natural", and restored the clear point about relativistic mass that had been overwritten
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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.
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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:
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<math>||p||^2 = -p_x^2-p_y^2-p_z^2+E^2 = m_0^2c^4</math>
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The abandonment by physicists of the concept of relativistic mass, however, has the consequence of undermining the traditional claim under relativity that
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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.
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:<math>m - m_0 = \frac{E}{c^2}</math>  
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also popularly known as
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:<math>E = m c^2</math>
    
==Evidence for Relativity==
 
==Evidence for Relativity==
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