Ah. Well, that’s just one of those little irritations that we have to deal with a lot in the field. You see, it really doesn’t matter which one has the plus and which one has the minus; what matters is that time and space separations get opposite signs. The convention used in the site you linked to is the one I prefer, with
but it really doesn’t matter. The reason I used the other one is that it looks a bit more like the Pythagorean theorem the other way around, that’s all.
To get the picture with (ds)[sup]2[/sup] defined the way I did, just rotate the entire picture on the site by 90[sup]o[/sup] and change the sign. Either one is equally good and it’s just a matter of preference as to which you use.
Point taken. I didn’t mean to be pedantic but it’s just that when I was in school when we would get a complex/imaginary solution to a real world problem we would start hearing “danger Will Robinson” and start getting panicky.
No, that’s actually good. Obviously, if one is doing real world problems, one wants to get results that mean something, and for the most part, getting an imaginary solution to a problem like “how fast was Bob driving” is a bad thing.
Unfortunately, you have to be able to get both positive and negative answers for (ds)[sup]2[/sup], and at that point, it just becomes a matter of convention as to which you prefer to get more often. And on this particular issue, there isn’t really a convention yet.
Or rather, there are too many conventions. Most folks doing General Relativity follow the lead of Misner, Thorne and Wheeler (in this and most other notational issues), and therefore use plus signs on space and a minus sign on time. The advantage of this is that ordinary space looks the same way that we learned in junior-high geometry. Particle physicists, though, I understand usually use a minus sign on space and a plus sign on time. The advantage of this is that world lines of real particles then have a positive (ds)[sup]2[/sup]. It really only becomes a problem when you have a paper that doesn’t specify which convention it’s using.
Heh, Misner, Thorne, and Wheeler actually opens with a Table of Sign Conventions, full of + and - signs from sources back over the decades, which shows that there is absolutely no standard convention, or at wasn’t in 1973.
