Special Relativity

1. Special Relativity Time Dilation, The Twins Paradox and Mass-Energy Equivalence.

2. Classical Relativity 1,000,000 ms-1 1,000,000 ms-1 • How fast is Spaceship A approaching Spaceship B? • Both Spaceships see the other approaching at 2,000,000 ms-1. • This is Classical Relativity.

3. Einstein Postulates that c is a universal constant • All measurements of Light Speed gave same value. • Did not seem to matter whether we were moving towards or away from light source. • This means that you will ALWAYS measure light at same speed. • You cannot ride along with the light beam. • He also derives the equation E = mc2

4. Einstein’s Special Relativity 0 ms-1 300,000,000 ms-1 1,000,000 ms-1 • Both spacemen measure the speed of the approaching ray of light. • How fast do they measure the speed of light to be?

5. Special Relativity • Stationary man • 300,000,000 ms-1 • Man travelling at 1,000,000 ms-1 • 301,000,000 ms-1? • Wrong! • The Speed of Light is the same for all observers

6. V Time Travel! • Time between ‘ticks’ = distance / speed of light • Light in the moving clock covers more distance… • …but the speed of light is constant… • …so the clock ticks slower! • Moving clocks run more slowly!

7. v = 0.8c v = 0.9c v = 0.99c v = 0.9999c

8. Relativistic Mass • E = mc2 • Objects have energy due to their mass! • If objects get more energy the mass must increase! • TRUE OR FALSE: • An object has more mass when you heat it up. • An object has more mass when you lift it up high. • An object has more mass when it is moving.

9. Relativistic Mass • E = mc2 • Objects have energy due to their mass! • If objects get more energy the mass must increase! • TRUE OR FALSE: • An object has more mass when you heat it up. • An object has more mass when you lift it up high. • An object has more mass when it is moving. ALL TRUE!

10. Relativistic Mass • When you fuse hydrogen to make helium the resulting nucleus is lighter than the parts used • When you break Uranium apart the resulting products are lighter than the original nucleus. • This “Mass Defect” accounts for energy released in nuclear reactions. • Also explains why you cannot accelerate objects to light speed.

11. Explanation of the Lorentz Transformations • Man on the train sees light take this path:

12. Explanation of the Lorentz Transformations • Man on the train sees light take this path: • We see the light take this path

13. Explanation of the Lorentz Transformations • Man on the train sees light take this path: • We see the light take this path • Which is longer because of the train’s motion

14. Explanation of the Lorentz Transformations • Man on the train sees light take this path: • We see the light take this path • Which is longer because of the train’s motion • Light always travels at c • We see train moving (hence t1) • Pythagoras’ theorem tells us: ct1 ct2 vt1

15. Derivation of Time Dilation. OK, so this is WRONG OR BUT…

16. The Lorentz Transformations • Time does appear to slow down for travellers:

17. The Lorentz Transformations • Time does appear to slow down for travellers: • You always “think” that your reference frame is stationary! • You will never see see another person move faster – they always appear slower.

18. Let’s try an example • Suppose a muon is created in the upper atmosphere (they are, btw). • It has a lifetime of 2.2 x 10-6 seconds. • How far can it travel? (assume it travels at c)

19. Let’s try an example • Suppose a muon is created in the upper atmosphere (they are, btw). • It has a lifetime of 2.2 x 10-6 seconds. • How far can it travel? (assume it travels at c) • So how come we see them 100,000 meters below?

20. “I wish I was a muon too” • If a muon knows it is travelling fast… • And It travels through the atmosphere (which is 100,000 meters thick) • And it has already had the diagnosis (that it only has 2.2 μs to live) • Does it “think” that it can exceed light speed?