Comprehensive notes for Chapter 11 Special Theory of Relativity. Covers Inertial Frames, Postulates of Relativity, Time Dilation, Length Contraction, Mass-Energy Equivalence, and more.
Inertial Frame: A frame of reference where Newton's First Law holds true (non-accelerating frame). Example: A train moving with constant velocity.
Non-Inertial Frame: A frame of reference that is accelerating. Newton's laws do not apply directly without fictitious forces. Example: A rotating merry-go-round.
1. Principle of Relativity: The laws of physics are the same in all inertial frames of reference.
2. Constancy of Speed of Light: The speed of light (c) in free space is constant for all observers, regardless of the motion of the source or the observer.
Time Dilation: Time appears to run slower for a moving object relative to a stationary observer. t = t₀ / √(1 - v²/c²).
Length Contraction: Moving objects appear shortened along the direction of motion. L = L₀ √(1 - v²/c²).
Mass Variation: Mass increases with speed. m = m₀ / √(1 - v²/c²).
Equation: E = mc².
Significance: Mass and energy are interconvertible. Small amounts of mass can be converted into huge amounts of energy (e.g., nuclear reactions).
GPS satellites rely on relativistic corrections. Their clocks run differently due to speed (Special Relativity time dilation) and weaker gravity (General Relativity effects). Without these corrections, GPS accuracy would fail within minutes.