This page is only intended to provide a high level overview of Special Relativity. The goal is to demonstrate how Newtonian laws are adjusted to drive SR via only applying Einstein’s SR postulates. All of SR is derived from two remarkably easy to understand postulates.

  1. The laws of physics take the same form in all inertial frames of reference.
  2. The speed of light has the same measured value in all inertial frames.

In teaching SR, often these postulates are applied to Newtonian physics by presenting an observer in one inertial frame and translating what each observe to the other’s observer’s frame. This may be derived by walking the student through the concept of “loss of simultaneity” and apply a conversion of values observed in one frame to the other. In each frame Newtonian laws are applied with the adjustment of time and space is no longer the same for all observers. When teaching this way, it is easy for the student to transition from classical mechanics to relativistic mechanics.

By applying this concept of transformation from one inertial frame to another, new definitions for classical concepts are derived. In some cases, new concepts are discovered. Listed below are some of these. In all cases the primed frame is the frame in motion relative to the unprimed frame.

  1. An Inertial Frame’s relative velocity to another Inertial Frame is observed as equal in both framesets.
\(\begin{equation}\label{eq101}\tag{1}
v’ =v
\end{equation}\)

2. The scalar transformation between two inertial frames is:

\(\begin{equation}\label{eq102}\tag{2}
\gamma =\sqrt{\frac{1}{1-\frac{v^2}{c^2}}}
\end{equation}\)

3. Relativistic Momentum

\(\begin{equation}\label{eq103}\tag{3}
p =\gamma m v
\end{equation}\)

4. Rest Energy (the same value in any inertial frame)

\(\begin{equation}\label{eq104}\tag{4}
E_0 = m c^2
\end{equation}\)

5. Relativistic Kinetic Energy

\(\begin{equation}\label{eq105}\tag{5}
T =E_0 \left( \gamma – 1 \right)
\end{equation}\)

There is much, much more to Special Relativity. This small discussion and short reference list is primarily for understanding the bridge from Newtonian mechanics to General Relativity as described on this site. I highly recommend studying Einstein’s SR through online courses or available books. One of my favorite SR books is Special Relativity in General Frames by Éric Gourgoulhon, it may be purchased on Amazon here.

Next -> Time Dilation and Rest Energy