In honor of Einstein’s birthday tomorrow (which also happens to be pi day!), let’s talk about relativity.

Albert Einstein’s general theory of relativity pertains to gravity. He developed this theory between 1907 and 1915. Essentially, this theory states that the observed gravitational effect between masses results from their warping of spacetime.

Einstein’s general theory of relativity narrows down into the equivalence principle, which states that gravitational forces are equivalent and practically indistinguishable from accelerated (or inertial) reference frames. This concept results in the following formula: (Inertial mass)(Acceleration) = (Intensity of the gravitational field)(Gravitational mass)

Albert Einstein furthered his work through the study and postulation of special relativity. Special relativity encapsulates many features, including defining the relationship between energy and matter. In this theory, Einstein suggests that the speed of light is a constant which remains he same in any inertial frame and that all inertial frames are equivalent under the laws of physics. The famous equation E=mc^2 originates from special relativity!

Einstein’s famous theories of relativity have resulted in a variety of interesting paradoxes.

**Ladder Paradox**: Assume there is a ladder moving through two open doors at relativistic speed. The open doors are shorter than the ladder’s rest length, so if the ladder was not moving it would not be able to fit inside. This ladder undergoes length contraction, the phenomenon that a moving object’s length is measured to be shorter than its proper length. To a stationary observer, the ladder can fit through the doors, but through an observer moving with the ladder, the ladder will not contract and fit through the doors. However, this paradox can be resolved through the fact that simultaneity is relative. The ladder is said to fit into the garage if both of its ends can be made to be simultaneously inside the garage, and since this is relative, so is the answer to whether or not the ladder can fit.

**Twin Paradox: **Assume that there are two identical twins. One of these twins makes a journey into space and comes back to find that the twin who remained on earth has aged more. Due to the fact that each twin sees the other moving, each twin should have found the other to have aged less. This paradox can be resolved in one of two ways. Firstly, the traveling twin has two inertial frames, one for the outbound journey and one for the inbound journey. Secondly, the traveling twin is undergoing acceleration, making them a non-inertial observer.

Despite an abundance of these paradoxes, Einstein’s theory of relativity remains strong to this day.

Happy (almost) birthday Albert!