Say I have sphere that is 13" in diameter. Someone looking at our expanding universe from outside would see the sphere growing. My question is this. If the sphere is 13" at midnight what size would be 6 hours later? If 6 hours is not enough to see a noticeable difference how long would it take to see it even grow by an inch?
Jim Mac Millan
This question is pretty vague and confusing, but I’ll give it a whirl…
First off, somebody can’t be “outside” our universe, because our universe is all that there is. But say, for shits and giggles, you’re God, and can do whatever the hell you want.
Fine, you’re God, and you’re looking at the universe from outside, as only God can. You wouldn’t see a sphere. Well, you’d see a kind of shape, that maybe is a “sphere” of sorts, but it would be a hypersphere. That means it would be a spatially-symmetric, finite, three-dimensional “surface” with no boundary. You and I, mere mortals, can’t picture such a thing, because we can’t see higher dimensional spaces, or even imagine them in a visual sense. The best we can do is use analogy. In this case, the analogy would be a sphere, which is a spatially-symmetric, finite, two-dimensional surface with no boundary. By no boundary, I mean you can’t fall off of it if you’re traveling on it, just like the surface of the Earth. There’s no edge. Try to imagine, if you can, something like this, only add a dimension to everything. Now you’re in a finite space that looks just like the world we live in, except, if its small enough, if you look in any direction, you can see yourself, from the opposite direction. If you look straight ahead, you’ll see the back of your head. If you look up, you’ll see the bottom of your feet. Repeated endlessly, like a hall of mirrors. If you travel in one direction, never turning, you’ll wind up back where you started. You’re on a three-dimensional sphere.
Yeah, so this is pretty mind-boggling. But you’re God, so it’s OK, you can handle it. OK, so now you want to know how fast it will grow? Hold on to your hat. First off, this thing, the universe, is growing in size in all three dimensions, as well as a direction that is at a “right angle” to up-down, forward-backward, and right-left. You can call this dimension “time”. So, you see, the question now of how “quickly” it grows becomes rather complicated. If you can observe the universe from “outside”, you are literally outside of space and time. To you, there is no “passage” of time from this perspective. You see it all, laid out before you, from beginning to end, the same way you can see all the world laid out before you from space. Time is just another direction, like up, or left, or forward. It’s “timeward”. If you look one way “timeward”, the universe is bigger “spaceward”. If you look the opposite way, it’s smaller. You could tick off increments of time and space, like we do on a piece of graph paper, and say, well, for every unit t, the universe increases or decreases in x, y, and z. It would be like drawing a line on a graph that had a certain slope. Actually, for the sake of simplicity, you, being God, might like to look at just a slice of the picture, just consider two dimensions, t and x, and trace on a piece of graph paper, what the change in the x dimension is over some distance t.
You would see a line that at first looks like a hyperbola; initially running almost parallel to the x axis, but eventually curving up to approach being parallel to the t axis, at least for a bit. Then, after a distance, the line starts to swing again towards the x axis, until it’s parallel again. Now you ask yourself “God, what would this look like to the humans?” Being God, you know the answer: The universe goes from the size of a proton to the size of a grapefruit essentially instantaneously. After that, its rate of expansion rapidly decreases as the creation of matter, and the gravitational force it exerts, slows down the inflationary phase of expansion. But, even at this stage, things are moving very fast. It takes almost a billion years before things slow down enough that clumps of matter (galaxies, and galaxy clusters) aren’t moving away from each other at a significant fraction of the speed of light. Eventually things, relatively speaking, almost come to a stop; but before they halt, all of the sudden they start moving apart again at an increasing rate; slow at first, but before too long infinitely fast. The end of the universe, the Big Rip.
Just as things are moving wickedly fast when the universe is huge compared to now, things were moving wickedly fast when the universe was very young. I would guess that, at the basketball-sized era you mention, to see an inch or so of growth, you would have to wait about 8.3x10^-12 seconds, or about the amount of time it takes light to go 2.5 cm, as the universe was expanding pretty close to the speed of light when it was that big.
The Hubble constant is roughly 55 kilometers per second per megaparsec. One megaparsec equals 1.215 X 10[sup]24[/sup] inches. 55 kilometers equals 2,165,354.3 inches.
No its not. Recent measurements with the WMAP experiment have conclusively pinned the Hubble constant at 72+/- 3 kilometers per second per megaparsec. Nowhere near 55.
Well whack me with an old book for pulling the number off APOD. :o
So now the hubble constant is 2,834,645 inches per second per 1.215 X 10[sup]24[/sup] inches, or 2.33 X 10[sup]-18[/sup] inches/sec per inch.