1. Relativity of Simultaneity
© David Hoult 2011

2. If two events occur very close together (in space) then it is easy to decide if they occurred simultaneously or not

3. If two events occur very close together (in space) then it is easy to decide if they occurred simultaneously or not
However, with events having a very large spatial separation…

4. If two events occur very close together (in space) then it is easy to decide if they occurred simultaneously or not
However, with events having a very large spatial separation… things are not so simple !

5. Observer A holds a long support with two mirrors

6. The mirrors are equidistant from A

7. Observer A sends two pulses of light, simultaneously towards the mirrors p and q

8. The light pulses are reflected by p and q and

9. The light pulses are reflected by p and q and are observed to arrive back at A simultaneously

10. We ask the question:

11. We ask the question:
from A’s point of view (in A’s frame of reference) did the two events, light reflecting from p and light reflecting from q, occur simultaneously ?

12. We ask the question:
from A’s point of view (in A’s frame of reference) did the two events, light reflecting from p and light reflecting from q, occur simultaneously ?
N.B. we are assuming that the distance s is very great, say, millions of km or, why not even a few light years…

13. We ask the question:
from A’s point of view (in A’s frame of reference) did the two events, light reflecting from p and light reflecting from q, occur simultaneously ?
N.B. we are assuming that the distance s is very great, say, millions of km or, why not even a few light years… this is a thought experiment !

14. Knowing that the distances, s are the same and that light always travels at the same speed, A must conclude that the two events occurred simultaneously

15. Now consider a second observer, B

16. Now consider a second observer, B who carries a very long ruler

17. B is very close to A and observes the light pulse experiment

20. B makes the same observations and will reach

21. B makes the same observations and will reach the same conclusion

22. Now consider A and B to have a large relative speed

23. Now consider A and B to have a large relative speed
Consider A to be moving to the right

24. Now consider A and B to have a large relative speed
Consider A to be moving to the right in B’s frame of reference

25. Some time later the situation (from B’s point of view) will be something like…

29. B’s conclusion is that the light will hit p before it hits q… for B the two events (light reflecting from p and light reflecting from q)

30. B’s conclusion is that the light will hit p before it hits q… for B the two events (light reflecting from p and light reflecting from q) were NOT simultaneous !