Temporarily Blah said:
Pervect, I'm not much for math(10th grade does algebra, how weak), so.. I have no idea what lim r->0 means.
Sorry, that expression is the process of taking the limit (in this case the limit as r approaches zero). It's only fully covered with calculus, though you can probably get an intuitive idea even with 10th grade algebra.
However, the sites shown are quite interesting, and I will look into those.
(Picky alert) "visualize", not "visualzie". X.X (/picky)
Sorry for the typo, but I'm afraid I do that a lot (I type very fast, and don't always use the spell checker).
Anyway, now for the random questions.
I heard of this theory: Due to the gravitational effects of a black hole, time will be slowed enough for all of the future to flash before the eyes of one falling into a black hole.
There's an easy answer to that question - it doesn't happen! At least not with a non-rotating black hole.
Take a look at the sci.phsics.faq on black holes, for instance
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html
Will you see the universe end?
If an external observer sees me slow down asymptotically as I fall, it might seem reasonable that I'd see the universe speed up asymptotically-- that I'd see the universe end in a spectacular flash as I went through the horizon. This isn't the case, though. What an external observer sees depends on what light does after I emit it. What I see, however, depends on what light does before it gets to me. And there's no way that light from future events far away can get to me. Faraway events in the arbitrarily distant future never end up on my "past light-cone," the surface made of light rays that get to me at a given time.
That, at least, is the story for an uncharged, nonrotating black hole. For charged or rotating holes, the story is different. Such holes can contain, in the idealized solutions, "timelike wormholes" which serve as gateways to otherwise disconnected regions-- effectively, different universes. Instead of hitting the singularity, I can go through the wormhole. But at the entrance to the wormhole, which acts as a kind of inner event horizon, an infinite speed-up effect actually does occur. If I fall into the wormhole I see the entire history of the universe outside play itself out to the end. Even worse, as the picture speeds up the light gets blueshifted and more energetic, so that as I pass into the wormhole an "infinite blueshift" happens which fries me with hard radiation. There is apparently good reason to believe that the infinite blueshift would imperil the wormhole itself, replacing it with a singularity no less pernicious than the one I've managed to miss. In any case it would render wormhole travel an undertaking of questionable practicality.
Note that the situation with a rotating black hole is unclear. Some simple models do predict what you describe (infinite blue shift, near the so-called "inner horizion"), but there is good reason to believe that these simple models are wrong (specifically, unstable). Working out the exact details of what happens in this case is very tricky, and I don't think there are definitive answer to the questions of what should happen when someone falls into a rotating black hole, and whether or not the inner horizon of a rotating black hole actually exists or not.
Next random question;
Does motion REQUIRE time? Looking at it mathematically, it seems so. However, I'm not much for the correlation between mathematics and relativity, so it seems unusual. Would "Quantum Foam" be able to move between amounts of Planck Time?
I don't share your distrust of math. It seems to me that if you want to define motion without time, the "ball is in your court". I can't think of anything in standard physics that suggests this.
If time breaks down in a singularity, how can anything around the singularity move?
If time stops at the speed of light, how does it have a finite traveling speed?
It's very unclear what happens in a singularity, though note that *near* a singularity there isn't any particular problem.
As far as the speed of light goes, anyone who measures the speed of light has to be going slower than 'c', so they don't have any problem defining or measuring time.
If time loops, does space loop? (Say, time travelling, assuming that the two are connected)
Usually it's thought of the other way around. If space loops (wormholes), then time can loop too - unless Hawking is right, and that wormholes that attempt to become time machines self destruct due to infinite vacuum pertubations.
Planck units - how are they determined? I understand Planck time is the amount of time light takes to move Planck Length, but how did they figure out the length? How about energy, and is there a Planck Mass?
This is getting long, so I'll refer you to the Wikipedia article on Planck units. Hopefully it will answer your question.
http://en.wikipedia.org/wiki/Planck_units
Wormholes - would humans only be able to see the ENTRANCE of them, due to their extension beyond space? Would we ride only on the surface of wormholes, or would we be able to look at the extra dimensions contained within?
The universe that we can percieve is only 4 dimensional. General Reltivity does not actually predict other spatial dimensions, they are a useful visual aid. You can use curved surfaces to visualize non-Euclidean geometry, but it is a mistake to assume that they *have to* exist just because you use them as visual aids. While you can assume they exist if you like, you will find that the "embedding" of 4-space in a higher dimensional manifold is not unique. You can also assume that they do not exist, and that the geometry of space is simply non-Euclidean.
What would happen if you had 2 wormholes pointing in different directions, but starting from the same point in space? Kind of hard to explain in words, but I will draw a picture later.
Unrelated - I heard 2-D beings could not live, due to the inability to have a digestive system. What if they simply absorbed their food through their being, and then deposited it after it's used for energy?
Anyway, lunch time is over, back to class. I'll try to check up after school(1.5 hours from now), but not likely.
Cya then!
I'm not quite sure what you're getting at with these last two questions, which seem to be drifting away from relativity again, and I'm also a bit tired from writing the long response ;-). Hope you find what I did write informative and useful.
