Relativity of Simultaneity According to Bob a train
Relativity of Simultaneity
According to Bob a train wagon is moving to the right; Alice is inside
Two lasers emit photons. One of them, at the left wall inside the train wagon, emits a photon (event A) to the right. The other one, at the right wall inside the train wagon, emits a photon (event B) to the left. According to Alice, who is inside and exactly at the middle of the train wagon, events A and B are simultaneous because the two photons (one from A and the other from B) arrive at the same point (at the middle) and at the same time. The question is: But can we say that A and B are also simultaneous according to Bob (who is outside, at the railway station, observing the train wagon moving to the right)?
• According to Alice events A and B are simultaneous. • Bob, on the other hand, finds out that events A and B are not simultaneous. Indeed, according to him, event A occurs before event B. • In slide #7 the time axis represents Bob’s equiloc and the spatial axis Bob’s equitemp. • But, again in slide #7, the line passing though A and B is an equitemp for Alice. • We conclude that Bob’s equitemp is not parallel to Alice’s equitemp: Time is relative because simultaneity is relative.
• The only thing that is absolute, from the starting point, is that the speed of light is always one (in natural or geometric units). • This, by our convention, corresponds to light always traveling along lines at plus (or minus) forty-five degrees with respect to the horizontal direction.
CONCLUSION • Two observers (Alice and Bob) are moving away, from one another, with some (relative) velocity. • The two sets of equitemps (one set for Bob and another set for Alice) are not parallel – although they are parallel inside each set. • This geometric conclusion leads to the following physical conclusion: Simultaneity is relative; hence time is relative.
- Slides: 13