infinite space

There are a few different things to consider in evaluating a question like yours. First consider this:Spacetime appears to be a continuum (according to our best observations at this time which may later prove to be incorrect), and it is the nature of a continuum that it is infinitely divisible. In more direct terms, between any two non-congruent spacetime coordinates, there exists infinitely many spacetime coordinates. For another perspective, recall in simple geometry how there exists infinitely many points on a line segment drawn bewteen any two non-congruent points. In the same way there exists infinitely many spacetime points between any two non-congruent spacetime coordinates.Next, consider what you mean when you ask "Is there infinite space?" Do you mean "Does there exist infinitely many spacetime coordinates/intervals?" The answer to that is obviously yes if spacetime is indeed continuous. If you mean "Is spacetime unbounded?" or "Is there a maximum spacetime interval?" the answer is somewhat more tricky. Stephen Hawking offered the "No Boundary Condition" in his book A Brief History of Time which proposed a finite region of spacetime that had no boundaries (somewhat like the surface of a sphere), however some recent data from WMAP seemed to reveal a generally flat spacetime and thereby falsify that proposal. At that point it seemed that spacetime was unbounded, and that its expansion is in fact accelerating.Even the Big Bang, which had previously been considered a boundary to the universe in the past, is now hardly considered that at all. The Big Bang has recently been conjectured to represent the collision of P-branes or M-branes (here my recollection is sorta fuzzy) in accordance with String Theory in the Ekpyrotic Model. Max Tegmark has also conjectured beyond the BB in his Many Worlds model which interestingly enough also encapsulates the Everett interpretation of Quantum Mechanics at the Level III multiverse.The latest news that I've heard on this front, however, is that the universe has now been considered finite and shaped like a soccer ball. This comes in accordance to observed density fluctuations in the cosmic microwave background which were inconsistent with an entirely flat spacetime, and the math makes the most sense if the universe is instead shaped like a dodecahedron. Here's an article about those observations: Universe is Finite, "Soccer Ball"-Shaped, Study HintsSo I suppose the most honest answer to your question is: We're not certain. Some cosmological models say yes, others no.

Actually I think it would be more correct to say that it appears spacetime is bounded in the past, but boundaries on a continuum do not make it finite in every sense of the word -- especially in the case of a thing as relativistically plastic as spacetime. IOW, there may be a maximum spacetime interval from the past to the present, however unless spacetime is discrete (which our latest observations seem to refute), there may still be an infinite number of intervals in the past.Also it is important to note that the Big Bang singularity is really only a feature of our mathematical model, and it is not necessarily a feature of reality. So it is overly presumptive to state that we "know" the universe has a finite history. Several of the latest models actually challenge that notion. I don't think that is a realistic expectation since stars do not shine forever, and additionally we would only expect a finite number of stars to be in close enough proximity to us that their photons would have had sufficient time to reach our planet. IOW, some stars would be so infintely distant from us spatially that no amount of time would permit their photons to reach us.I suspect there is some confusion among the various usages of the term "universe" in this thread. In general, it should be taken to mean "everything that exists," but in the context of some cosmological models like Tegmark's Multiverse it is used (actually abused, IMHO) to represent "this patch of spacetime we presently observe" or "this bubble amongst many other bubbles." If we adhere strictly to the first definition in this paragraph, a beginning to "everything that exists" would be logically inconsistent, or at the very least claiming that we have observed such a beginning would be unsupportable.[This message has been edited by ::, 11-10-2003]

and... You are absolutely correct. My wording lent the dodecahedral universe theory entirely too much credit. Your links are excellent resources, and I thank you for supplying them.

I have to say that I concur with V-bird in this case. Space-time is an abstraction that we create in our minds from our points of view relative to things in reality. It has no substance. It has no external reality. It's a coordinate system that we use to affix references to the substantial things we experience.

I believe that physicists treat it as what's called a "tensor field," and the analogy of an empty stage for the play of matter and energy I think is quite apt. See tensors defined here. As you'll read, they are simply geometric constructs. Geometric constructs have mathematical reality, but as such they are abstractions, meaning we build them up in our minds according to what and how we observe material reality behaving relative to us and itself. Basically the abstraction process is a continuous "measuring" of everything's postion and velocity relative to yourself and the rest of the universe. Measurements are observations, and observations only exist in the minds of observers.[This message has been edited by ::, 03-24-2004]