Special Relativity

Learning Objectives

State the two postulates of Einstein's special relativity.

Describe the consequences of these postulates: time dilation and length contraction.

Explain the concept of mass-energy equivalence (E=mc²).

The Physics of High Speeds

Published by Albert Einstein in 1905, the Theory of Special Relativity revolutionized our understanding of space, time, and motion. It applies to inertial (non-accelerating) reference frames.

The Two Postulates

The entire theory is built on two surprisingly simple postulates:

1.The Principle of Relativity: The laws of physics are the same for all observers in uniform motion. There is no 'absolute' state of rest.

2.The Principle of the Constancy of the Speed of Light: The speed of light in a vacuum (c) is the same for all observers, regardless of the motion of the light source or the observer.

This second postulate is radically counterintuitive. If someone on a train moving at 0.5c shines a flashlight forward, both a person on the train and a person standing on the ground will measure the speed of that light as exactly c, not 1.5c.

Consequences of the Postulates

These seemingly simple rules lead to extraordinary consequences for objects moving at speeds close to the speed of light (relativistic speeds).

Time Dilation: From the perspective of a stationary observer, a clock that is moving relative to them will appear to tick more slowly. 'Moving clocks run slow.'

Length Contraction: An object will appear shorter in its direction of motion to an observer who is moving relative to it. The object's length is measured to be shortest in the dimension parallel to its motion.

Relativity of Simultaneity: Two events that are simultaneous for one observer may not be simultaneous for another observer in a different reference frame.

Mass-Energy Equivalence

The most famous result of special relativity is the relationship between mass and energy:

E = mc²

This equation shows that mass and energy are two forms of the same fundamental quantity.

It implies that a small amount of mass can be converted into a tremendous amount of energy (as c² is a huge number). This is the principle behind nuclear power and nuclear weapons. It also implies that energy has mass; an object gains mass as its kinetic energy increases.

Key Terms

Special Relativity: The theory, formulated by Albert Einstein, that the laws of physics are the same for all observers in uniform motion and that the speed of light in a vacuum is the same for all observers, regardless of their motion.
Time Dilation: A difference in the elapsed time as measured by two clocks, either due to them having a velocity relative to each other, or by there being a gravitational potential difference between their locations.
Length Contraction: The phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame.
Mass-Energy Equivalence: The principle, described by Einstein's famous equation E=mc², that mass and energy are two forms of the same entity and can be converted into one another.