Relativity of Simultaneity David Hoult 2011 If two

Relativity of Simultaneity © David Hoult 2011

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

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…

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 !

Observer A holds a long support with two mirrors

The mirrors are equidistant from A

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

The light pulses are reflected by p and q and

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

We ask the question:

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 ?

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…

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 !

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

Now consider a second observer, B

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

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

B makes the same observations and will reach

B makes the same observations and will reach the same conclusion

Now consider A and B to have a large relative speed

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

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

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

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)

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 !