Changes

===Mass increase===

===Mass increase===

We also see that as a body moves with increasing velocity its [[mass]] also increases.  

For decades the theory of relativity taught that as a body moves with increasing velocity its [[mass]] also increases.<ref>For example, this was taught as recently as in the 1991 edition of the Encyclopedia Britannica.</ref>

The mass, <math>m</math>, of an object as detected by a (relative) stationary observer is given by:

Under this view, the mass, <math>m</math>, of an object as detected by a (relative) stationary observer is given by:

<math> m = \frac{m_{0}} {\sqrt{1 - \frac{v^{2}}{c^{2}}}}</math>

:<math> m = \frac{m_{0}} {\sqrt{1 - \frac{v^{2}}{c^{2}}}}</math>

Where  

Where  

There is a logical difficulty, however, to an increase in relativistic mass.  Such increase would only exist in the direction of motion, and the rest mass would remain intact with respect to a force applied in a direction orthogonal to velocity.  But mass is not a vector, and the notion of the mass of an object having different values depending on the direction of an applied force is unacceptable.  Accordingly, most physicists today avoid Einstein's original reliance on relativistic mass and his suggestion that mass increases.  Instead, most physicists today teach that  

There is a logical difficulty, however, to an increase in relativistic mass.  Such increase would only exist in the direction of motion, and the rest mass would remain intact with respect to a force applied in a direction orthogonal to velocity.  But mass is not a vector, and the notion of the mass of an object having different values depending on the direction of an applied force is unacceptable.  Accordingly, most physicists today avoid Einstein's original reliance on relativistic mass and his suggestion that mass increases.  Instead, most physicists today teach that  

<math>F=\frac{d}{d\tau} p</math>  

:<math>F=\frac{d}{d\tau} p</math>  

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.

==Evidence for Relativity==

==Evidence for Relativity==