# Ultrarelativistic limit

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Particles which go near the speed of light are called ultrarelativistic.

The ultrarelativistic limit is the maximum velocity that a particle can move at. Albert Einstein found the equation for energy: E=mc². This means that energy is equal to a certain amount of mass. However, this is a simplified version of his equation. The longer version of his equation is E2=m2c4+p2c2. (Mathematically, if you ignore the p2c2 and take the square root of the equation, you get E=mc2). p2c2 refers to the velocity of a particle multiplied by a very large number.

Einstein then went on to show that a particle can never achieve the speed of light, because you get a divide by zero error from the equation for kinetic energy, $E_k = m_0 ( \gamma -1 ) c^2 = \frac{m_0 c^2}{\sqrt{1-\frac{v^2}{c^2}}} - m_0 c^2,$. Look at the denominator (bottom) of the equation, ${\sqrt{1-\frac{v^2}{c^2}}}$. "v" refers to the velocity of the particle. If its velocity reaches the speed of light (which is "c" in this equation), $\frac{v^2}{c^2}$ will equal one, and since that would leave one minus one in the denominator, there would be a divide by zero error.

Particles which go below the speed of light (all particles which have mass) are called tardyons. Theoretical particles which go above the speed of light are called tachyons.