"Worlds lived. Worlds died. And the universe was never the same again."- DC Comics, 1985
Posted on 06/25/2003 7:42:21 AM PDT by Junior
As a matter of fact, he's one of the premier experts on cosmology in the world (and a colleague of mine here at Penn). When it comes to testing cosmological models against hard observational data, there's none better.
The Big Bang theory stipulates that at the beginning the volume of the universe was zero. After that, it expanded (extremely rapidly) and continues to do so, such that the total volume of the universe grew and continues to grow at a high but finite rate.
That refers to our horizon, but not to the whole. In the standard Friedmann cosmology, the volume of the universe can be represented as the "surface" of a 4-dimensional hypersphere. We have a finite horizon, or "Hubble volume"--the volume of the universe that is receding from us at a velocity less than the velocity of light--but the whole is (in principle) finite, too: it eventually curves back upon itself.
[Geek alert: read carefully what I said. In any cosmological model, there will be parts of the universe that are receding faster than light. This does not violate special relativity, because these regions are out of causal contact with us.]
The question remains: what is the radius of that hypersphere? It could be anything, according to Friedmann; it's just something you have to measure. On Earth, for example, you can measure the radius of the Earth simply by noting that an equilateral triangle, 10 million meters on each side, will have interior angles of 90 degrees each, rather than the 60 degrees of a small equilateral triangle.
We now (as of 4 months ago) have a similar measure for the largest possible triangles that can be drawn in our Hubble volume. No matter how big, the interior angles sum to 180 degrees. This corresponds to a hypersphere of infinite radius; in other words, the universe is flat.
This agrees with the theoretical prediction of Inflationary Cosmology.
[Geek alert: the curvature could also have been negative, in which case the universe would have a hyperbolic shape, rather than a hyperspherical shape.]
Looking back on my life, there are a number of really smart things that I almost did. Now I find out that somewhere out there, I actually did do them. How cool is that?
In fact, the volume of the universe must be finite, if Big Bang cosmology or any other cosmology that depends on expansion is true. The Big Bang states that the universe was at one point finite in size (a singularity or near-singularity) before it started expanding. You cannot expand a finite space for a finite period of time (13-15 billion years) and reach infinity. For that matter, you cannot expand something that is already infinite at all.
Likewise, if the volume of space is finite, the mass and energy contained in it must be finite as well, as you cannot fit an infinite amount of mass into a finite container.
I understand that he's writing at the popular level, but he really should be more careful in the use of his terms. The fact is that "infinite" is a purely conceptual word (and a poorly conceived word at that), and not one that can be observationally or even logically sustained. The author here is misusing it, meaning instead "an incoceivably large amount."
I myself tend towards a more Aristotelian worldview for a simple reason: We know that not all mathematical models correspond to reality. For example, suppose my boss asked for an estimate on how many people it would take to complete a certain project. And then suppose that I use a quadradic equation to make my estimate and end up with the numbers 4 and -3 for x. Could I then go to my boss and say, "Well, it'll either take me four people or negative three people"? Is there a conceivable universe in which -3 people would be the correct answer?
To me, the fact that the universe corresponds so well to mathematics is not evidence that the math is the real and my senses are the unreal, but that it was designed by a very good Engineer.
What a great idea for a made-for-TV movie!
"Worlds lived. Worlds died. And the universe was never the same again."- DC Comics, 1985
"Worlds lived. Worlds died. And the universe was never the same again."- DC Comics, 1985
We have worlds enough, but not time. The same data that revealed the infinite extent of the universe also measured the rate of expansion as a function of time. The expansion is growing ever faster. In a finite amount of time, the universe will expand so fast that any surviving stars will be flung from their galaxies; after which, the planets from their stars; the stones from their planets; the atoms from their stones; electrons from their atoms; protons from their nuclei; quarks from their protons. Perhaps even the quarks will be destroyed.
Love while you can. For humility, we have the WMAP data.
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