Relativity and Time Dilation

Special Theory of Relativity

• The observational consequences of special relativity differ from Newtonian theory only at speeds close to that of light.
• Newton's theory was adapted for slow speeds, whereas 19th-century electrodynamics probed fast motions.
• Einstein's achievement was to simplify electrodynamics and show that unusual behavior at high speeds is due to space and time.

Frames of Reference

• Newton's laws determine how matter moves through space as a function of time.
• Einstein's special theory of relativity proposed revolutionary changes to human concepts of time, space, and gravity.
• The theory is based on two main postulates: constant speed of light for all observers and the same physical laws for observers moving at constant speeds.

Development of the Theory of Relativity

• Until the end of the 19th century, Newton's laws and ideas about space and time were thought to be sufficient to understand motion.
• Maxwell's unified theory of electromagnetism disrupted this, requiring a radical modification of Newtonian concepts.
• Einstein combined experimental results and physical arguments with his own insights to formulate the new principles of space, time, matter, and energy.

The Math Behind Time Intervals

• The new time interval T1 measured by S1 is T1 = 2T, where (ct)^2 = d^2 + (vt)^2.
• Solving for t gives d/c - v^2/2d or T1 = (c/√(1 - v^2/c^2))T0.

General Theory of Relativity

• The General Theory of Relativity is a generalization of the Special Theory of Relativity.
• It was driven by philosophical questions, such as why inertial frames of reference are special and why we don't feel gravity's pull when falling.
• The happiest thought of Einstein's life was trying to fit gravity into relativity, which was necessary to modify Newton's theory.

Test your understanding of relativity and time dilation concepts, including the differences between proper time and relativistic time. Solve for time intervals and explore the general theory of relativity.