Chapter 1: Introduction

• The equation equals MC squared is famous but few people know its meaning or origin

• Deriving the equation and understanding its meaning

• Insight into Einstein's theory of special relativity

Chapter 2: Mechanics and Frames of Reference

• Mechanics describes how bodies change position in space over time

• Observing the motion of a stone dropped from a moving train

• Stone appears to descend in a straight line from the train's frame of reference

• Stone appears to fall in a parabolic curve from the platform's frame of reference

• Using a system of coordinates to describe motion relative to a frame of reference

Chapter 3: Principle of Inertia and Inertial Frames of Reference

• The fundamental law of mechanics: A body continues in rest or uniform motion in a straight line unless acted upon by an external force

• Principle of inertia

• An inertial frame of reference is a non-accelerating frame of reference

• Einstein's theory of special relativity focuses on inertial frames of reference

Chapter 4: Principle of Relativity

• Introduced by Galileo in his dialogue concerning the 2 chief world systems

Chapter 2: Particular Moving Clock

• Einstein's experiment with the speed of light

  • Spaceship traveling at 200,000 km/s relative to the road

  • Beam of light travels past at 300,000 km/s relative to the road

  • Speed of light relative to the spaceship is 100,000 km/s

  • Experiment shows light traveling 300,000 km/s relative to spaceship and road

  • Conclusion: Sense of space and time is not the same for a person standing still and a person moving

• Measuring the duration of time

  • Simple clock with parallel mirrors separated by one meter

  • Light signal reflects off mirrors, making a tick every time it moves up and a tock every time it comes down

  • Two clocks with same length are synchronized

  • Light always travels at the same speed

• Comparison of stationary and moving clocks

  • Stationary clock takes time T Naught for one tick-tock

  • Moving clock on a train takes longer path due to train's motion

  • Observer sees light taking a zigzag path in the moving clock

  • Path taken by light in moving clock is longer than in stationary clock

Chapter 1: Introduction

• The train is moving with velocity V relative to the platform

• The time taken for light to travel from bottom mirror to top mirror is big t

Chapter 2: Pythagoras' Theorem

• Using Pythagoras' theorem to find a relationship between the sides of a right angle triangle

• CT squared = 1 squared + vt squared

• Rearranging for t, the time taken for a tick of the moving clock: t = 2 / square root of (c squared - v squared)

Chapter 3: Time Dilation

• Expressing t in terms of t naught, the time taken for the tick tock of the stationary clock: t = t naught / square root of (1 - v squared / c squared)

• Gamma (γ) is the factor that tells us the difference between t and t naught

• If v = 0, then gamma = 1 and t = t naught

• If v > 0, then gamma > 1 and t > t naught

• All moving clocks run slower by the same amount to preserve the principle of relativity

• Time dilation is the difference in elapsed time between stationary and moving frames of reference

Chapter 4: Time Dilation at the Speed of Light

• As v approaches c, gamma approaches infinity and t tends to infinity

• The tick tock of the moving clock would get slower and eventually freeze

Chapter 5: Conclusion

• Time dilation is a prediction of Einstein's theory of special relativity

• Time itself appears to be slower in the moving train

Chapter 3: Energy Of Object

• Usane Bolt example

  • Calculating time dilation factor

  • t is essentially the same as t naught

• Time dilation with muons

  • Muons created in upper atmosphere decay after 2.2 microseconds