[From Bruce Gregory (2005.0401.1615)]

Bill Powers (2005.04.01.1251 MST)

Bruce Gregory (2005.0401.1155) --

I know that it is not easy to envision, but here are a few suggestions. Remember that the Big Bang did not occur anywhere _inside_ the observable universe, the Big Bang _created_ the observable universe. That is to say, the Big Bang occurred "everywhere" in the observable universe.

In all such 3-dimensional situations of which I know, the center of the explosion is contained within all the material it generated, and from the standpoint of any one piece, there is a vector you can draw back to where the original explosion was centered. A vector 180 degrees from that vector points away from the center, in a direction toward empty space.

But that's not the case for the Big Bang; the geometry is clearly not that of an ordinary explosion.

That's true, and the reason is that an ordinary explosion takes place within an existing space and time. The Big Bang fills the space and time it creates.

One way to think of it is that everywhere in the universe the density began to rapidly fall 13.7 billion years ago. As the density fell, structure formed, including the galaxies we see today.

It seems to me that this description deliberately omits any mention of size -- the description makes it sound as if there is a fixed volume within which the density of matter is decreasing. But the amount of matter (-energy) in the universe is not decreasing -- it is the volume that is increasing, the distances between the objects in the universe. Some matter may be falling through black holes into other universes, but that's a different question not related to expansion.

At the beginning the entire observable universe was smaller than an atom. After inflation it was roughly the size of grapefruit. That does not say that the observable universe is all there is. The observable universe is presumably embedded in a much much larger, possibly infinite universe. The density decreases because the volume is increasing as you say.

I don't think there is any way to get the effects we observe in a Euclidean universe. For the apparent center to be visible in all directions, there HAS to be some sort of nonEuclidean curvature. I think that what the omega constant must refer to is a departure from a uniform curvature, not the curvature itself. In other words, I suspect that omega = 1 means a universe with the same curvature everywhere, and departures from that value mean that the curvature increases or decreases as the hyper-radius grows. That is a totally uninformed guess, but it's the nearest I can get to making sense of this stuff.

Well you are creating a new physics, but there is nothing wrong with that. I have been describing the picture generated by the existing physics. You may have trouble imagining the effects we observe in a Euclidean Universe, but that's what the physics calls for.

The region we are seeing today was not always 13 billion light years away because of the expansion of the universe the region emitting the radiation was once much closer to us, but that is just a further detail.

Are you really satisfied with that? "Just a further detail" seems to be the whole problem. How can the region emitting the radiation be closer or farther from us -- in every direction? That is not Euclidean space as I know it.

Well, just imagine that we are in the center of the expansion. Then the emitting region was once closer to us, but the universe is expanding, so the emitting region is now much further from us.

If space is indeed flat, then mass does not curve it, and we can start dismantling the whole fabric of General Relativity, can't we?

No, fraid not. The overall curvature of space is determined by the average density of the matter and energy it contains. GR still applies, and spacetime is curved in the vicinity of matter. So while the Milky Way curves spacetime, the average curvature throughout the the observable universe is zero.

But that requires that mass cause negative curvature elsewhere to compensate for positive local curvature, and I don't think there's any provision in General Relativity for that. AQlso what you say denies itself: if curvature is determined by the average density of matter-energy, then the universe contains a very large amount of that and it has to be curved. If there is curvature anywhere, then the average curvature is positive.

In fact the total energy of the universe is exactly zero. The positive energy of mass and energy is exactly balanced by the negative energy of gravity. That's another way of saying that Omega is exactly 1.

Whatever the case, I think that the value of Omega we come up with will be whatever it is, perhaps exactly 1.

Yes. But that is like winning the lottery. Someone will win, but the changes that it is you are very small.

Well, the chances of holding a particular bridge hand, even a bust hand, are small -- but after the deal their probability is 100%.

The inverse square law is exactly as it is because space has three dimensions. At least that's what we believe. (Of course string theorists are convinced there a six more but they are curled up out of sight and don't effect the argument.)

That's in Euclidean geometry. So it's not true in our universe, if general relativity holds.

General relativity holds, as far as we know, and space is Euclidean. Those two statements are perfectly compatible.

The problem is that we're talking about theoretical notions that people are still arguing about. These are propositions, not facts. We're exploring the implications of certain theories as they would apply under extreme conditions, which is one good way of testing theories. One reason the old theories of the electron as a point-charge were abandoned was what happened in thought-experiments when you carried calculations to an extreme condition, arbitrarily close to the singularity. The self-energy of the electron, instead of being finite, went to infinity. So there was clearly something wrong with the theory, even though nobody knew at the time just what was wrong.

I think we're finding that when you take the basic concept of a Big Bang and an expanding universe to extreme conditions (small or large distances) you start seeing contradictions.

Well, the community of folks who study these things see no contradictions.

That's why people are still arguing. If all the questions like the ones I raise, and those raised by much smarter people, had been answered, the explanations would be clear and wouldn't rely on analogies -- illegimitate analogies, since they propose similarities to perceptions in an ordinary intuitive three-dimensional universe.

No. People are not arguing about the Big Bang. It is confirmed by a host of independent measurements. The unresolved issues are the nature of dark matter and dark energy. There are plenty of ideas but a paucity of data. Other questions are the exact nature of inflation (we have a hope of getting a handle on this from gravity-wave experiments), and what happened before inflation, which may always remain speculation. The only analogies involved are in attempts to relate the mathematics of the theory to everyday experience. The mathematics is perfectly consistent and unambiguous, just as the mathematics of QM is perfectly consistent and unambiguous. As Martin says, the problem is trying to think of this mathematics on a scale (everyday life) very different from the scale under investigation.

The six numbers Rees is referring to are constants in the laws of nature. It turns out that if these constants (which are arbitrary as far as we know) had somewhat different values, the universe would look nothing like it does today. Either stars could not form, or the heavy elements could not be created inside stars. Those sort of problems. Of course to take this argument seriously, you have to believe that we understanding something about the laws of nature. If you're not convinced of that, all bets are off.

Yes, that's my point. The ideas behind his proposals are nowhere near fully-developed enough to count as "laws of nature."

That simply is not true. We is talking about constants associated with well-established physics, not with speculation. Let me give you an example, Newton's gravitational constant G is perfectly well determined. However, it cannot be derived from first principles. As far as we know it is arbitrary. If you want to win a Nobel Prize, derive G from first principles. In other words, show, in Einstein's words, that "God had no choice" in determining the value of G. Once you accept the conservation of energy and the laws of thermodynamics, say, G _must_ have the value it does.

When the dust settles, we will see what we have then. When you say "arbitrary as far as we know" you point directly at the weak link in the deductions: hidden premises. What this phrase does is say that there are arbitrary assumptions behind these constants, so the conclusions remain true only as long as the assumptions are not modified or disproven. The fact that we are being led into absurdities and contradictions could be interpreted to mean that pure physics is vastly superior to human intuition. But it could also be interpreted as a "reductio ad absurdum" proof that there is something wrong in the premises -- especially those we are using without being aware of using them.

More than one Nobel Prize for the person who pulls this off. Needless to say, I'm not holding my breath.

A true believer knows the solution before he understands the problem.