1. Modern Physics (PC300) Class #5 Cool, but not as fast as we are talking about! Notes: Test a week from Tuesday Old tests are avail. Homework due Wednesday Last four due the Friday after Sim due Friday

3. Two Observer Spacetime Diagram: Time x t O t’t’ @ x’=0, t’=n  -> n  t 2 - x 2 x=  t Moore confusing ->  = separation between marks on t & t’ axis Slope=1/  t=  t’

4. Two Observer Spacetime Diagram: Length O x tt’t’ Length Contraction x’x’ Slope= 

5. Two Observer Spacetime Diagram: Hyperbola Relationship O x tt’t’ x’x’ 1/x 2 At ds=1, x-0 -> t varies depending on speed t2-x2=s2t2-x2=s2

8. From Moore p.108

9. Deriving Lorentz Transformations Ox tt’t’ x’x’ Q tQtQ xQxQ tQ’tQ’ xQ’xQ’ P  t PQ  x OP t PQ =  t’ OQ x OP=  x’ OQ Inverse Lorentz Transformations Normal Lorentz Transformations Generalized Normal Lorentz Transformations

11. R6S7

13. The Barn and Pole Paradox: Home Frame Pole Rest Length (L 0 ) = 10ns Home Frame: Pole moving at  = 3/5 -> L=8ns Barn Length (L 0 ) = 8ns An instant in time when the pole is entirely in barn with doors shut. Seems to Make Sense

14. The Barn and Pole Paradox: Other Frame Other Frame: Barn moving at  = -3/5 -> L=6.4ns Pole Length (L 0 ) = 10ns How can the pole 10ns long fit into a 6.4ns barn? The runner with the pole does not observe that the pole is enclosed in the barn. Front of pole reaches end of barn @ -6ns End of pole reaches front of barn @ 0ns when pole has already left

19. O t’t’ x’x’ x t Pole The Barn and Pole Paradox Resolution

20. Lots of Barn and Pole Problems

22. The Cosmic Speed Limit Nothing can travel faster than the speed of light!

23. Geometric Analogy

24. What is Causality?

25. Causality Connected events must occur in certain order. THEOREM: The Cosmic Speed Limit

26. The Cosmic Speed Limit No information can travel faster than the speed of light! Causality is conserved!

27. Einstein Velocity Transformations Inverse Normal

28. Moving On Relativistic Kinematics Relativistic Dynamics