- #51
bossman27
- 204
- 0
arindamsinha said:
Sorry I haven't checked this thread in a few days so I didn't get back to you earlier. Even without reading all of the latest posts, I'm sure you have been getting good information and have gained some valuable insight.
That said, I am responding to this quote because it is not quite correct. It is correct that causality, as we usually mean it, is a sufficient but not a necessary condition for preserving the temporal order of events across all reference frames. It is not correct that the order would be preserved, "even if there wasn't enough time for a message to necessarily pass between the two events." In fact, the definition of a light-like interval is that light (a message) had exactly enough time to traverse the space between the two events between their occurences. That was actually the basis of the value (.018... seconds) that I calculated; if \Delta t was exactly that value, we would have a light-like interval, and both spatial and temporal order would be preserved (though keep in mind the actual values calculated in different references frames would vary, we are just saying the sign of all of those values would agree). If \Delta t was any greater than that value, then we have a time-like interval; here not only light but matter could also, in theory, traverse the distance in time to carry a message; in this case only temporal order is guaranteed to be preserved. (that is, the sign of \Delta t' will be preserved)
The short version is: the requirement for the preservation of temporal order is exactly that light had at least enough time to make it from event A to event B. That is, the "calculable time gap" is the amount of time it takes to send a message (light) from point A to point B. We would say that even if it isn't really possible within the context of the situation (like two crashes A and B in NY and London), the laws of relativity cannot immediately rule out the possibility that A caused B, if light could have traveled between them in time. You could also think of the light as being in the form of a radio signal, if that makes the situation more plausible to you.
To reiterate one last time, when we're talking about determining the type of interval in SR, and hence the possibility of causality... "could event A have caused event B?" is equivalent to asking, "could a beam of light have made it from the occurrence of event A to the occurrence of event B?" (disregarding obstacles of course)
And again, I encourage you to read up or watch some youTube videos on Minkowski diagrams and light cones. I am very certain that this would really make everything I and others have described more visually intuitive for you.
Here we would say that an interval between A and B is:
1) Time-like if: event B is inside event A's future light cone.
2) Space-like if: event B is outside event A's future light cone.
3) Light-like if: event B lies on the edge of event A's future light cone.
-- This will all make sense when you see/draw the diagrams.
