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Categories: Special relativity | Equations

List of relativistic equations

Special relativistic equations

Definitions

m₀ = rest mass
v = velocity
c = velocity of light in a vacuum

Speed parameter

$\beta = \frac{v}{c}$

This is the speed parameter which occurs in the Lorentz factor. A consequence of this is that as v, the speed of the moving body, approaches c, the speed of light, the speed parameter approaches one and therefore the Lorentz Factor approaches infinity.

Lorentz factor

$\gamma = \frac{1}{\sqrt{1 - \beta^2}}$

This factor describes the change in measured times and lengths by observers in relative motion.

Relativistic momentum

p = γ m 0 v

Kinetic energy

T = (γ - 1) m 0 c 2

Because γ diverges to infinity as v approaches c the kinetic energy also approaches infinity. Therefore it is not possible to accelerate a body to the speed of light with a finite amount of energy.

E = kinetic energy + rest mass energy

Note that at one time in presentations of special relativity, it was common to introduce a quantity called the relativistic mass, defined as m=γm₀. In modern treatments of special relativity, mass is always defined as the mass measured by a comoving observer, and is therefore synonymous with the rest mass.

Equations

$E = \gamma m_0 c^2 = \left( m_o^2 c^4 + c^2 p^2 \right)^\frac{1}{2}$

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