# Special Relativity

The Theory of Special Relativity is a branch of physics dealing with the behavior of inertial frames of reference moving at very different speeds. It does not cover the behavior of non-inertial frames of reference which are instead covered by General Relativity.

It is an axiomatic theory, derived from two main axioms:

- The laws of physics are the same in all inertial frames (the principle of relativity)
- The speed of light is determined by the laws of physics

From these it can be concluded that in all inertial frames the speed of light must be measured to be the same constant value. In order to accommodate these several assumptions which seem commonsense must be thrown away. All the derivations can be performed purely through thought experiments combined with calculation

### The major changes of special relativity

Note: it is important for this section to know that

\[\gamma=\dfrac{1}{\sqrt{1-\dfrac{v^2}{c^2}}}\]

Where \(v\) is the speed of the object or frame under consideration.

- Different inertial frames measure the distance between two points to be different; the proper distance and the measured distance will (see length contraction)
- Different inertial frames measure the time between two events to be different (see Lorentz transformations)
- Mass and energy are interchangeable through the formula \(E=mc^2\)
- The overall energy of an object including it's Kinetic is \(E^2=m^2c^4+p^2c^2 =(\gamma mc^2)^2\)
- The momentum of an object is defined as \(p=\gamma mv^2\)
- The formula \(F=ma\) no longer holds, however the alternative \(F=dp/dt\) still does.