otseng wrote:
FarWanderer wrote:
I'm no expert, but it appears to me that if you are saying the universe can be both Euclidean and finite, you are disagreeing with wikipedia:
Yes, I'm disagreeing with Wikipedia. The only reason they would think that it is infinite is because of the mediocrity principle. If the universe was Euclidean, then in order for no place to be special, it would require positing an infinite universe.
Since we both agree that that an infinite universe makes no intuitive sense, then it must be that the assumption of the mediocrity principle cannot be true for a Euclidean universe.
Actually, I don't think a finite universe makes any more intuitive sense than an infinite one.
In fact, I find the idea of a finite Euclidean universe the most unintuitive model out of all that we have discussed, but you don't see me basing arguments off of my personal intuition.
otseng wrote:There's only two possible explanations. If the universe is non-Euclidean or the universe is Euclidean and we're at the center.
Like I said. Nonsense. False dichotomy.
You never did address stars moving on the other side of the center. Furthermore, stars on the sides of us would not appear to be moving.
You just didn't understand. Will try explaining again below.
otseng wrote:
Furthermore, what kind of alternative expansion of space are you proposing exactly? As far as I can tell from poking around some websites, "everything moving away from us in proportion to their distance" is precisely the same thing as "the metric expansion of space". As in, by definition.
No, it's not by definition the same.
The metric expansion of space is the increase of the distance between two distant parts of the universe with time. It is an intrinsic expansion whereby the scale of space itself changes. This is different from other examples of expansions and explosions in that, as far as observations can ascertain, it is a property of the entirety of the universe rather than a phenomenon that can be contained and observed from the outside.
http://en.wikipedia.org/wiki/Metric_expansion_of_space (emphasis mine)
Ok, I get it.
Doesn't change anything, though. The difference has nothing to do with relative location and motion of objects. The point is that even assuming a spherical expansion from the center of a universe, non-center viewpoints will still see everything receding at speed in proportion to distance just like the center will.
Now, to get back to your earlier concern about stars to the "side" of us or on the other side of the center. It's entirely a matter of geometry and algebra. It has nothing to do with the mediocrity principle. It's just math.
Take what you mean by "side" for example. It's mathematically impossible for two rays (a ray = a line with a starting point) to be precisely parallel to one another if they share the same starting point. This means that two distinct objects "shot" from the same point of origin at the same time will inevitably have the distance between them grow.
Try it on paper and see what happens. Take a point and draw strait lines extending from it. See if you can find a pair of these lines for which their tips don't diverge as they extend from their origin. You won't be able to.
As for things on the other side of the center, it's a bit harder to explain. You have to remember, things are moving away from the center
at a speed proportional to their distance from it. That means if there's something halfway between earth and the center, we'll be moving away from the center twice as fast as it is. Which means the distance between us and it will be growing, but at half the rate the distance is growing between us and the center.
Similarly, if there is something exactly opposite the center from us, it will be moving away from the center at the same speed we are. It will be twice the distance from us than the center is (our distance from the center, plus its distance from the center). We will also be separating from it at twice the speed we are separating from the center (our speed of separation from the center, plus its speed of separation from the center).
In other words,
whether the expansion is metric or not if everything that exists is moving away from a center at a speed in proportion to its distance from it, then everything that exists,
regardless of location, is separating
from everything else at a speed in proportion to the distance by which they are separated.
otseng wrote:Was the matter of earth not affected by this "exploding" force somehow?
Actually, I don't know what the force was. However, to my knowledge, nobody knows what caused the Big Bang to explode either.
I'm not asking about cause. I'm asking about applicability.
How do we know that the material that would later comprise the Earth wasn't affected by this same event? Why should we think it wasn't the case that it was thinly distributed over a hugely vast area in such a way that it took a relatively long time to coalesce?
otseng wrote:I'm ready to hear that story right now. I'm perfectly happy to debate both topics.
OK, if you insist. We'll go step by step.
Let's assume that at the very beginning, space-time existed. In this space-time, all the matter of the universe was in a spherical mass. The gravitational field around this mass would be so great that nothing can leave its event horizon. Would you agree that this would be equivalent to a black hole?
It sounds like you are saying that space-time is infinite and matter is finite.
Singularities aren't spherical. They are a single point that exerts a spherical event horizon. Though that would be simplifying things a bit. Black holes have a slight wobble, and by my understanding quantum physics puts a wrench in the idea that genuine singularities are even possible. It seems to
me that the very concept of "shape" brakes down within the event horizon.
As for all the mass of the universe being concentrated in one location in space, I'm not sure I'd label it a black hole. Whatever you call it, I have little idea what would be going on in there.
But to answer the question you probably want answered, it would require some kind of cause unknown to current science in order to break out of the event horizon. In your hypothetical, of course.