black holes always liven things up

So in a really brief summary for any reader as confused as I am about astrophysics at the moment: The Schartzchild metric is metric derived from general relativity to describe objects falling radially into black holes. I won't try to write it here because it involves a lot of symbols that won't mean anything unless I spend an hour explaining them, and I'm sure it's on good old Wikipedia. So anyway, you can plug the coefficients of the Schartzchild metric into the general equation for a geodesic (describing the shortest path between two points in curved/non-Euclidean space), which is this unpleasant monstrous equation summed over multiple partial derivatives (but which thankfully simplifies for black holes because objects only move radially and not in the other spherical directions so the derivatives in those directions vanish). Anyway, so you can plug all this junk in (well theoretically you could; I'm not very good at it yet, which is unfortunate given our exam next Thursday). Once you do this you can write an equation for conservation of energy, and you can solve for the proper time, or the time measured by the falling object. This proper time is a defined equation that has its final value when the object falls completely into the black hole.

However, the interesting point of all of this math mumbo jumbo I'm talking about is that there are singularities in the coordinate time, or the time measured by things beyond the Schartzchild radius of the black hole. You get singularities because the integral used to solve for time has (r-Rs) in the denominator, where Rs is the Schwartzchild radius and r is the perceived radius of the falling object. Thus when r reaches Rs, you get the observer as seeing the object falling for infinite time.

Okay, while that is cool, that's not my main point here. My main point is that it's kind of sad actually to learn about this math. I read about this effect first when I was in sixth grade or so (I wasn't quite your normal sixth grader, I think, though I really tried for a while to appear dumb and wore way too much makeup). And I think the reason I really liked it, and all of the other astrophysics stuff I read from the age of eight onwards, was that it was, well trippy. I heard someone talking in the lounge at my dorm the other day. He said string theory sounded like someone on acid. He imitated the person by saying "what if everything is made of little tiny strings... woah" and the way he said it really did make it sound a bit like one of those things that people on LSD think are brilliant that everyone else thinks are crazy. And I think that's always why I've liked astrophysics, because it was so out there, because it bended my thoughts at every turn.

And it turns out that while I do like actually learning the math for these things that have amazed me for over half my life, in a way it's kind of sad. I'm the kind of person that would rather think about things that actually do the experiment, which I think differentiates me at this school (except maybe all the math majors are like that, but they're too far gone I think in their topologies). When I actually have to do the math (besides feeling upset at having to face my woeful failures in basic algebra), I feel like I'm kind of losing something, the clarity of the acid trip maybe, the "woah, dude, that's gnarly" aspect of it all.

So it's nice I guess to think that the reason the proper time and the coordinate time are different at the vanguard of the black hole is an integral denominator approaching zero, but it's not quite as nice as thinking that it's some crazy bent up quality of time itself that I can make up in my head because I don't know enough to make realistic predictions. I like my creative astrophysics ideas. I love the ideas a lot. It's just not quite so fun when I have to calculate derivatives.

Anyway, it doesn't matter I suppose because in the end I chose what I was best at (biology) and abandoned what interested me most in that acid-trip way. And while I was sad for a while, I don't regret it at all now. Because I can always sit around in my living room thinking about things stretching in black holes, but I can't really think about the psychedelic awesomeness of AMPA receptor endocytosis during depotentiation, and that's something I actually enjoy figuring out in a lab. So I think I'm doing the right thing.

But seriously, tiny vibrating strings whose curled-up radius determines the properties of the particles we actually "see" (in cloud chambers anyway)?

Gnarly, dude.