1 The Principle of Relativity Holds There is

1. The Principle of Relativity Holds: There is no detectable or physical difference between ‘rest’ and ‘constant velocity motion’… so called, inertial frames of reference. 2. The Speed of Light is Constant: The speed of light will be measured to be identical within any inertial frame of reference, even those in relative motion to one another.

Relativistic Addition of Velocities: u = uo + v 1 + uov/c²

Time Dilation “Moving clocks run slowly. ” ∆t = 1 ∆t₀ 1 - v²/c²

Time Dilation : Gamma Factor g g = 1 1 - v²/c²

Time Dilation “Moving clocks run slowly. ” ∆t = 1 ∆t₀ 1 - v²/c²

Time Dilation : Cosmic Ray Muons

Frisch-Smith Experiment: 1963 Classical Physics: Almost all muons passing by Obs. A will “decay” by the time they reach Obs. B Modern Physics: The high speed of the muons relative to us will slow their “clocks” down… and many will make it!

Frisch-Smith Experiment: 1963 In fact… Very few do. Most should decay.

Hafele-Keating Experiment: 1971 Atomic clocks aboard moving airliners experienced “less time” than clocks at rest on the ground.

The Twin Paradox

Length Contraction ∆x = “Moving rulers shrink. ” 1 - v²/c² ∆x₀

There is a planet orbiting Alpha Proxima, 4. 4 lightyears away. If we were to choose to travel to it, this table would show the influence of Special Relativity: Speed (relative to Earth) Earth time Our time Distance 30, 000 m/s (0. 1 c) 44 years 43. 8 years 4. 38 lightyears

There is a planet orbiting Alpha Proxima, 4. 4 lightyears away. If we were to choose to travel to it, this table would show the influence of Special Relativity: Speed (relative to Earth) Earth time Our time Distance 30, 000 m/s (0. 1 c) 60, 000 m/s (0. 2 c) 44 years 22 years 43. 8 years 21. 6 years 4. 38 lightyears 4. 31 lightyears

There is a planet orbiting Alpha Proxima, 4. 4 lightyears away. If we were to choose to travel to it, this table would show the influence of Special Relativity: Speed (relative to Earth) Earth time Our time Distance 30, 000 m/s (0. 1 c) 60, 000 m/s (0. 2 c) 120, 000 m/s (0. 4 c) 44 years 22 years 11 years 43. 8 years 21. 6 years 10. 1 years 4. 38 lightyears 4. 31 lightyears 4. 03 lightyears

There is a planet orbiting Alpha Proxima, 4. 4 lightyears away. If we were to choose to travel to it, this table would show the influence of Special Relativity: Speed (relative to Earth) Earth time Our time Distance 30, 000 m/s (0. 1 c) 60, 000 m/s (0. 2 c) 120, 000 m/s (0. 4 c) 240, 000 m/s (0. 8 c) 44 years 22 years 11 years 5. 5 years 43. 8 years 21. 6 years 10. 1 years 3. 3 years 4. 38 lightyears 4. 31 lightyears 4. 03 lightyears 2. 64 lightyears

There is a planet orbiting Alpha Proxima, 4. 4 lightyears away. If we were to choose to travel to it, this table would show the influence of Special Relativity: Speed (relative to Earth) Earth time Our time Distance 30, 000 m/s (0. 1 c) 60, 000 m/s (0. 2 c) 120, 000 m/s (0. 4 c) 240, 000 m/s (0. 8 c) 285, 000 m/s (0. 95 c) 44 years 22 years 11 years 5. 5 years 4. 6 years 43. 8 years 21. 6 years 10. 1 years 3. 3 years 1. 4 years 4. 38 lightyears 4. 31 lightyears 4. 03 lightyears 2. 64 lightyears 1. 37 lightyears

There is a planet orbiting Alpha Proxima, 4. 4 lightyears away. If we were to choose to travel to it, this table would show the influence of Special Relativity: Speed (relative to Earth) 30, 000 m/s (0. 1 c) 60, 000 m/s (0. 2 c) 120, 000 m/s (0. 4 c) 240, 000 m/s (0. 8 c) 285, 000 m/s (0. 95 c) 298, 500, 000 m/s (0. 995 c) Earth time Our time Distance 44 years 22 years 11 years 5. 5 years 4. 6 years 4. 4 years 43. 8 years 21. 6 years 10. 1 years 3. 3 years 1. 4 years 5. 3 months 4. 38 lightyears 4. 31 lightyears 4. 03 lightyears 2. 64 lightyears 1. 37 lightyears 0. 44 lightyears

There is a planet orbiting Alpha Proxima, 4. 4 lightyears away. If we were to choose to travel to it, this table would show the influence of Special Relativity: Speed (relative to Earth) 30, 000 m/s (0. 1 c) 60, 000 m/s (0. 2 c) 120, 000 m/s (0. 4 c) 240, 000 m/s (0. 8 c) 285, 000 m/s (0. 95 c) 298, 500, 000 m/s (0. 995 c) 299, 642, 000 m/s (0. 9995 c) 299, 777, 000 m/s (0. 99995 c) Earth time Our time Distance 44 years 22 years 11 years 5. 5 years 4. 6 years 4. 4 years 43. 8 years 21. 6 years 10. 1 years 3. 3 years 1. 4 years 5. 3 months 4. 38 lightyears 4. 31 lightyears 4. 03 lightyears 2. 64 lightyears 1. 37 lightyears 0. 44 lightyears

There is a planet orbiting Alpha Proxima, 4. 4 lightyears away. If we were to choose to travel to it, this table would show the influence of Special Relativity: Speed (relative to Earth) 30, 000 m/s (0. 1 c) 60, 000 m/s (0. 2 c) 120, 000 m/s (0. 4 c) 240, 000 m/s (0. 8 c) 285, 000 m/s (0. 95 c) 298, 500, 000 m/s (0. 995 c) 299, 642, 000 m/s (0. 9995 c) 299, 777, 000 m/s (0. 99995 c) Earth time Our time Distance 44 years 22 years 11 years 5. 5 years 4. 6 years 4. 4 years 43. 8 years 21. 6 years 10. 1 years 3. 3 years 1. 4 years 5. 3 months 1. 7 months 4. 38 lightyears 4. 31 lightyears 4. 03 lightyears 2. 64 lightyears 1. 37 lightyears 0. 44 lightyears 0. 14 lightyears

There is a planet orbiting Alpha Proxima, 4. 4 lightyears away. If we were to choose to travel to it, this table would show the influence of Special Relativity: Speed (relative to Earth) 30, 000 m/s (0. 1 c) 60, 000 m/s (0. 2 c) 120, 000 m/s (0. 4 c) 240, 000 m/s (0. 8 c) 285, 000 m/s (0. 95 c) 298, 500, 000 m/s (0. 995 c) 299, 642, 000 m/s (0. 9995 c) 299, 777, 000 m/s (0. 99995 c) Earth time Our time Distance 44 years 22 years 11 years 5. 5 years 4. 6 years 4. 4 years 43. 8 years 21. 6 years 10. 1 years 3. 3 years 1. 4 years 5. 3 months 1. 7 months 16 days 4. 38 lightyears 4. 31 lightyears 4. 03 lightyears 2. 64 lightyears 1. 37 lightyears 0. 44 lightyears 0. 14 lightyears 0. 04 lightyears

There is a planet orbiting Alpha Proxima, 4. 4 lightyears away. If we were to choose to travel to it, this table would show the influence of Special Relativity: Speed (relative to Earth) 30, 000 m/s (0. 1 c) 60, 000 m/s (0. 2 c) 120, 000 m/s (0. 4 c) 240, 000 m/s (0. 8 c) 285, 000 m/s (0. 95 c) 298, 500, 000 m/s (0. 995 c) 299, 642, 000 m/s (0. 9995 c) 299, 777, 000 m/s (0. 99995 c) Earth time Our time Distance 44 years 22 years 11 years 5. 5 years 4. 6 years 4. 4 years 43. 8 years 21. 6 years 10. 1 years 3. 3 years 1. 4 years 5. 3 months 1. 7 months 16 days 4. 38 lightyears 4. 31 lightyears 4. 03 lightyears 2. 64 lightyears 1. 37 lightyears 0. 44 lightyears 0. 14 lightyears 0. 04 lightyears According to a light wave… moving at the speed o f light… 299, 794, 458 m/s (1. 00000 c) 4. 4 years no time no distance

The Andromeda Galaxy is 2, 500, 000 lightyears away. If we were to choose to travel to it, this table would show the influence of Special Relativity: Speed (relative to Earth): 299, 777, 000 m/s (0. 99995 c) Earth time: 2, 500, 125 years Our time: 25, 000 years Distance: 25, 000 lightyears