1. The Twins “Paradox”
© D Hoult 2011

2. Event 1: A and B meet and set clocks to zero

3. B sends pulses of light at 12 second intervals (on his/her clock)

4. 12 seconds

5. 24 seconds

6. 36 seconds

7. 36 seconds
C is moving at the same speed relative to A (but in the opposite sense to B)

8. 48 seconds

9. C takes a look at B’s clock and copies the time (48 seconds) to his/her clock

10. C takes a look at B’s clock and copies the time (48 seconds) to his/her clock
C also sends pulses every 12 seconds

11. 60 seconds

12. 72 seconds

13. 84 seconds

14. 96 seconds

15. Event 2: C meets A

16. Total time between event 1 (B meets A) and event 2 (C meets A) according to the clocks of B and C “combined” is therefore

17. Total time between event 1 (B meets A) and event 2 (C meets A) according to the clocks of B and C “combined” is therefore 96 seconds

18. What is the time between these same two events according to A ?

19. Event 1: A and B meet and set clocks to zero

20. Let the relative speed be such that k = 3/2

21. Let the relative speed be such that k = 3/2 (that’s pretty fast !)

22. 18 seconds

23. 36 seconds

24. 54 seconds

25. 72 seconds

26. 80 seconds

27. 80 seconds (v changed to -v so k is now 2/3)

28. 88 seconds

29. 96 seconds

30. 104 seconds

31. Total time between event 1 (B meets A) and event 2 (C meets A) according to the clocks of B and C “combined” was 96 seconds

32. Total time between event 1 (B meets A) and event 2 (C meets A) according to the clocks of B and C “combined” was 96 seconds
Time between event 1 (B meets A) and event 2 (C meets A) according to A’s clock is 104 seconds

33. Total time between event 1 (B meets A) and event 2 (C meets A) according to the clocks of B and C “combined” was 96 seconds
Time between event 1 (B meets A) and event 2 (C meets A) according to A’s clock is 104 seconds
The “stay at home” twin is a little older that the space-travelling twin !

34. Time measured by A is TA
Time measured by B (and C) is TB

35. Time measured by A is TA
Time measured by B (and C) is TB
Number of pulses sent (after t = 0) is N
Interval between transmitted pulses is t

36. Time measured by A is TA
Time measured by B (and C) is TB
Number of pulses sent (after t = 0) is N
Interval between transmitted pulses is t
TB =

37. Time measured by A is TA
Time measured by B (and C) is TB
Number of pulses sent (after t = 0) is N
Interval between transmitted pulses is t
TB = N × t

38. Time measured by A is TA
Time measured by B (and C) is TB
Number of pulses sent (after t = 0) is N
Interval between transmitted pulses is t
TB = N × t
TA =

39. Time measured by A is TA
Time measured by B (and C) is TB
Number of pulses sent (after t = 0) is N
Interval between transmitted pulses is t
TB = N × t N N 1
TA =
× t × k +
× t × 2 2 k

40. Time measured by A is TA
Time measured by B (and C) is TB
Number of pulses sent (after t = 0) is N
Interval between transmitted pulses is t
TB = N × t TB TB 1
TA =
× k + × 2 2 k

41. Time measured by B (and C) is TB
Time measured by A is TA
Time measured by B (and C) is TB
Number of pulses sent (after t = 0) is N
Interval between transmitted pulses is t
TB = N × t TB TB 1
TA =
× k + × 2 2 k
conversion chart between space-twin and stay-at-home-twin times