Bill

Albert Einstein (1879–1955). Relativity: The Special and General Theory. 1920, XXXI. The Possibility of a “Finite” and Yet “Unbounded” Universe.

Its Einstein's theory, which has been largely confirmed by experments conducted over the past few decades (so far as I understand it, anyway ).

== Bill

Shadowy Man

Bill:

Yes, a closed universe (i.e. positive curvature) would be finite yet unbounded.

However, virtually every cosmological experiment performed in the last couple of decades indicates that the universe is flat. The flatness of the universe goes pretty much uncontested among cosmologists.
In fact, the standard Big Bang Theory pretty much demands that the universe be flat (an explanation for the flatness can be found in Inflationary theory).

A flat universe would have Euclidean geometry, and could possibly be an infinite Minkowski space-time.

Now, as someone pointed out in a different thread, you need to distinguish between curvature and topology. There are configurations of topology that are finite but still have flat curvature. But whether or not we live in one of those universes is hardly an established fact.

I wasn't questioning the possibility of a finite, unbounded universe only your certainty with which you seem to believe that that is what our universe actually is.

Bill

You question my certainty of a "finite (but unbounded)" space/time continuum when it is your own certainty of a flat geometry that ought to be questioned. Your statement that "[t]he flatness of the universe goes pretty much uncontested among cosmologists" is either untrue or extremely misleading. Let me give you a quote from an on-line college-level introductory course: So, the source of this idea of a flat universe is the UNCONFIRMED theory of cosmic inflation, and only because that theory seems to require a flat universe in its present forumulation.

The actual experimental evidence tends to demostrate the third possibility: that the universe is "open" (as stated on the same page I took the above quote from). But it seems that nobody wants to believe that option, so they make up so-called "dark matter" (indetectable quantities of matter that make their theories true) to make up the "missing mass" that would make the universe "flat." Well, if the proponants of a "flat" universe can make up enough "missing mass" to convert an "open" universe to a "flat" universe, then it won't take much more "missing mass" to get it to a "closed" universe, will it?

Of course, most of those conjectures were created before the recent experiments which tend to show that the expansion of the space/time continuum is accellerating! An increasing rate of expansion would strongly argue that the "open" universe model is the correct model.

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But I really think that this equivocates a lot of the terms we've been using because it is my understanding that Einstein's view of a "finite (but unbounded)" universe was based on topology, and as you go on to note: True, but it has been my understanding that Einstein's General Theory of Relativity tends to suggest a "finite (but unbounded)" space/time continuum for us to exist in, and the closest thing we have to an actually confirmed theory here is Einstein's General Theory of Relativity.

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All of this pretty-much misses the point I was trying to make, which is that the source of human intuition is an evolved reference set which lacks any real experience with actual infinities, so it isn't surprising that our intuition would lead us down the apparently-erroneous path towards a belief that actual infinities do not exist (or are "impossible," as theists argue, right before they propose that their God is the only actual infinity....).

Another point which General Relativity seems to prove is that there is at least one additional dimension of space (the dimension of space through which the usual three dimensions can all be simultaneously curved in order to create gravity and other things which have been verified about the General Theory of Relativity). That additional dimension of space (a "fourth spatial dimension," if you prefer) may well be "rolled up" in a tiny cylindar or however you wish to postulate its existence, but it clearly does exist. And, just about as clearly, our "Big Bang" space/time continuum does not extend into that fourth spatial dimension, giving rise to at least the conjecture of an infinite number of parallel universes that might exist at various points along that fourth spatial dimension.

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In any case, the point at issue was really whether an "actual infinity" exists in reality. The "flat" and "open" models of the universe present no problems in that regard, since they instantiate actual infinities. It is only the "closed" (either by curvature or by topology) model which denies an "actual" infinity, so my point about the probable logical conclusion remans valid, regardless of the ultimate conclusion(s) of science on these various topics.

== Bill

Jet Grind

This is from secularhumanism.org.

Shadowy Man

You actually have it backwards. The experiments suggest a flat universe. One of the triumphs for the Inflationary Universe is that it has an explanation for the flatness.

Maybe you should check out some of the results from the Wilkinson Microwave Anisotropy Probe instead of relying on on-line introductory courses. That page looks very out of date.

From "First Year Wilkinson Microwave Anisotropy Probe Observations: Determination of Cosmological Parameters", by D. Spergel et al.:


This is not the origin of dark matter. Dark matter is needed to explain galaxy rotation curves and galaxy cluster dynamics, among other things.
You show a very crude understanding of dark matter, and its place in modern cosmology.


Like I said, go check out the WMAP results. Cosmology has been a very active field over the last decade or two, so its easy to get behind.

That is one possible space-time continuum that is suggested by GR, but not the only one, and not the one that appears to be confirmed by experiment.

Bill

It would have been nice if you had supplied an actual link to the WMAP site.

Well, I see that the claims for the results of this mission are far from modest, in that virtually all of the major unknowns of cosmology are claimed to be resolved to a high degree of accuracy. Pardon me if I at least think to myself that "it would be really strange if it were all really this simple."

Most interesting to me is the claim that the universe is 13.7 Billion Years Old, plus or minus 1%. If that is accurate, it would allow me to settle a bet made years ago when the accuracy was only about plus or minus 20% of 13 billion years (obviously, those text books claiming "about 15 billion years" will need to have a minor rewrite).

But the mission timeline shows that the first data was only released in February of this year, so there hasn't really been time for peer-reviewed papers to be presented and for the holders of contrarian views to capitulate. In other words, its a little early for you to be claiming all this new stuff to be "settled," and all of my older information to be "out of date." After all, there is still that little annoyance of the apparent increase in the rate of expansion of the universe to be dealt with.

But I agree that it is an exciting development, if it proves to hold water. (And, as I noted earlier, it really doesn't change the argument over "actual infinity" by much; the new results would still allow a marginally closed universe to exist, and arguments favoring closure to at least some degree are still logically compelling to at least some of us. )

== Bill

Bill

One issue that apparently the Wilkinson Microwave Anisortopy Probe (WMAP) experiments must necessarily leave unresolved is the question of whether our space/time continuum is totally flat or merely locally flat (all of this presumes that the accuracy of the results is subsequently verified and accepted by the bulk of cosmologists). The main experimental report claims an error rate of plus or minus 0.02 from a measured mass-energy density value of 1.02, which would imply a very slight positive curvature to the local area (to which these measurements are necessarily constrained). To get to an exactly flat density value, all of the error margins would need to bias over towards a value of 1.00 when it seems far more likely (from a purely statistical point of view) that the actual exact value would be somewhere within the allowable range of 1.00 through 1.04, with a slightly positive curvature implied for all values greater than 1.00 itself (by definition).

But to repeat myself here, the WMAP experiment necessarily only measures the curvature of the local area. Areas outside of the local area, but still within the overall space/time continuum within which we exist, could easily be curved more or less and we would not be able to measure (or in any way verify) those differences.

To understand my claim here, we need to also understand a bit about inflationary theory, which is the "currently live" theory for describing the early evolution of our space/time continuum after the so-called Big Bang. Here is a technical description taken from the work of one of the main proponants of inflationary theory: Everything observable to humans today falls within one of the approximately 100,000 "causally disconnected regions" within the entire space/time continuum. We might say for certain that the geometry of space appears to be flat within our particular region, but the geometry of space could be different in each of the other approximately 99,999 causally disconnected regions and we would never be able to know without waiting for a very long time (as the passage of time allows effects constrained to the speed of light to penetrate further and further through space, regions which were previously causally disconnected can connect together, but to connect vastly-separated regions of space will require incomprehensible lengths of time).

With modern instrumentation, we can peer back in time to very near to the Big Bang itself (relatively speaking). But we do so only within our little local region of the entire space/time continuum which, with about 100,000 equal-sized regions, extends outwards from ourselves towards the edges of the universe (space/time continuum).

One of the arguments for a non-flat geometry (at least not perfectly flat) is that assertions of this sort would be meaningless if the universe were actually infinite in size. To visualize this for a moment, think of a sphere with the Earth (or the Milky Way Galaxy) at the center, and a radius of 13.7 billion light years. That is the rough definition of our "local region." There are about 100,000 such local regions (according to inflationary theory, above), and they are all piled together within the entire volume of the space/time continuum within which we exist. The implication of this assertion is that the entire volume of the space/time continuum is roughly 1,000 billion light years across. 1,000 billion light years is large, but it is far short of "infinite," and a perfectly flat geometry would necessarily imply an infinite volume of space within our space/time continuum.

Given that size, it would take about 500 billion years for the observable universe to expand to the point where it was as large as the total universe is today. That is about 36+ times the amount of time from the Big Bang to the present, and of course, since the universe continues to expand, we would by no means be able to observe the entire universe (space/time continuum).

Anyway, there is a lot that we don't know about cosmology, and even what we think we do know will remain substantially uncertain, at least until we work out a viable "Theory of Everything" (incorporating quantum gravity into our existing cosmological theories).

== Bill

thomaq

Bill, thanks for your reply, its helping me alot. i have a question for clarification. what do you mean by "finite (but unbounded) space time continuum"? is this just what we commonly think of as "our" universe when in actuality it is part of a "bigger" universe? kind of like our finite existence that is only a segment of the infinite universe? please let me know if i am understanding it right.

now, with all due respect i have to completely disagree with the assertion that "an actual infinite amount of moments must exist necessarily." i think it is more than just "intuition" that is appealed to when commenting on the impossibility of an actual infinite. it is logic that is appealed to. if an infinite amount of people have to sit down before i do, when will i sit down? the answer is never. to say that "because we are in the present, necessarily an actual infinites must exist" is the completely wrong and illogical conclusion. the logical conclusion is that because the present exists, actual infinities must NOT exist. now i think what a naturalist should admit, is that, as of now, 2a by itself (not considering other alternatives) is irrational. it is not rational to accept it by default, it is more rational to say, as of now, naturalism offers no rational answers for the existence of the universe. maybe this will change in the future . what do yo think?

SteveD

thomaq,

You forgot option 3.

Not enough information, therefore don't know.

You seem intent on painting naturalism as irrational based only on conjectures about the existence of the universe. I would like to point out that finding things that natralism hasn't explained does not falsify naturalism. To falsify naturalism you would have to demonstrate that supernaturalism is true.

Steve

thomaq

so would you agree that the options i brought up are irrational?

i'm not trying to prove or falsify anything really, just strictly examining the rationality of the naturalist explanation for the universe.