Does Einstein's relativity of simultaneity mean that two events cannot be simultaneous or that we cannot prove that two events occurred simultaneously?
An artist's impression of Gravity Probe B — a spacecraft used to test Einstein's theory of general relativity.
Image Credit: NASA
The answer to this question is, in a sense, both. There are two distinct cases. In one case, two events cannot be simultaneous; in the other case, they can be, but not everyone will agree that they are.
These two cases are called "timelike" and "spacelike". In the case of timelike events, a particular observer will measure that there is enough time for a light ray to go from one of the events A (the earlier one, obviously) to the other one, B. In that case, all observers moving with constant velocity with respect to the first one will agree that event A came before event B. No observer will see A and B as simultaneous.
In the case of spacelike events, a particular observer will measure that A and B are sufficiently close in time (and/or sufficiently far apart in space) that no light ray could make it from A to B. All observers who are moving with constant velocity with respect to the first one will also conclude that no light ray could make it from A to B.
But some of these observers will say that A and B are simultaneous, some will observe that A came before B, and others will observe that B came before A. The concept of ordering in time is no longer meaningful (because according to relativity, all observers are equally "right") but the statement that the two events A and B are spacelike does have meaning.
Alan Chodos, PhD
Associate Executive Officer
American Physical Society
Lipton from Massachusetts