Infitine Space

[md65536]

It would not diminish GR to just refer to the curved path of objects, however, without the superfluous insistence on " curved spacetime" with ruts or grooves, or whatever which "guide" objects' trajectories.

And with that, I formally abandon this hopeless conversation. Thank you for your time.

[owl]

I transcribed this post from the time travel thread for relevance of content.

 

No one here has yet answered these obvious questions: If the universe is not infinite, how does it end, how is it "bounded", and finally, yet again, what could possibly be beyond any proposed wall out there but more space (whatever it contains,if anything)... infinite space? Just a logical, reasonable question from the realm of a-priori epistemology, a realm of science/philosophy which DrRocket would not have studied given his disdain for it.

DrRocket:

 

The only point in even addressing your posts is to mitigate the damage that might occur to people who are actually trying to learn a bit about relativity.

 

I think that it is a good thing to question scientific authority, especially when abandonment of reason is the requirement for "passing the tests" and getting your all-important credentials.

True science stays open minded, and I have many times said that I am not questioning the "mountain of evidence for GR," but only its reification of space, time, and spacetime. We are safe to just say what we see, like objects traveling in curved paths without saying that curved spacetime (without ontological examination) makes that happen.

 

I'll finish with one of my favorite quotes from Kelley Ross' "Ontology and Cosmology of Non-Euclidean Geometry":

 

...it never hurts to ask questions. The worst thing that can ever happen for philosophy, and for science, is that people are so overawed by the conventional wisdom in areas where they feel inadequate (like math) that they are actually afraid to ask questions that may imply criticism, skepticism, or, heaven help them, ignorance.(My bold)

 

These observations about Einstein's Relativity are not definitive answers to any questions; they are just an attempt to ask the questions which have not been asked. Those questions become possible with a clearer understanding of the separate logical, mathematical, psychological, and ontological components of the theory of non-Euclidean geometry. The purpose, then, is to break ground, to open up the issues, and to stir up the complacency that is all too easy for philosophers when they think that somebody else is the expert and understands things quite adequately. It is the philosopher's job to question and inquire, not to accept somebody else's word for somebody else's understanding.

[Iggy]

No one here has yet answered these obvious questions: If the universe is not infinite, how does it end, how is it "bounded"

 

Finite space does not imply an end or a boundary to the space.

 

That is the answer. It has been explained and repeated to death and you're still saying that no one has answered it like you didn't notice.

 

It's hopeless.

[Realitycheck]

Why can't it be bounded? It may just keep growing, but if there was a limit, there doesn't have to be more space or something on the other side. With all due respect, that is a self-imposed condition, besides being unknowable. Maybe the universe is spherical. If you keep going in one direction, you actually do wind up back where you started.

[StringJunky]

Finite space does not imply an end or a boundary to the space.

 

That is the answer. It has been explained and repeated to death and you're still saying that no one has answered it like you didn't notice.

 

It's hopeless.

 

Shotgun or razor blade?

 

.

[owl]

Iggy:

Finite space does not imply an end or a boundary to the space.

What do you think is the difference between finite and infinite. Maybe you just don’t know the difference. Infinite means endless, no end or boundary.

 

Reality check:

Why can't it be bounded? It may just keep growing, but if there was a limit, there doesn't have to be more space or something on the other side.

Think about the difference between empty space, which can not, logically, "end," and the stuff in space, which mayor may not be a finite amount of 'cosmos' out there... the stuff in space. What limit? Please describe!

 

With all due respect, that is a self-imposed condition, besides being unknowable. Maybe the universe spherical. If you keep going in one direction, you actually do wind up back where

you started.

 

Not really 'self imposed" but logically cogent, and I think irrefutable.

Think about "shape" as mentally imposed upon the universe... all there is, space and its known contents and beyond what we can know. Beyond that mentally imposed "shape" is... what? Even "nothing" as an answer is infinite space, regardless of what it may contain.

Yes, whatever is beyond our present cosmic event horizon is "unknowable." But we can know (and I do know) that there can be no "end of the universe" regardless of the fact that the infinite remains unknowable.

Somebody tell me about the end of the universe, and try to make sense.

 

This should answer you too, Stringjunky. I not let's talk.

[Iggy]

Iggy:

 

What do you think is the difference between finite and infinite. Maybe you just don’t know the difference. Infinite means endless, no end or boundary.

 

Seriously? Are you serious with this... again?

 

If infinite implies unbounded then it does not necessarily follow that finite means bounded. That would be a logical fallacy called denying the antecedent.

 

It is true that "infinite space" implies "unbounded". It is not true that "finite space" implies "bounded".

 

If you can't think about it logically then there is no point in thinking about it.

 

edited to add:

 

The difference between infinite and finite space: you can only put so many ping-pong balls in a finite space, there is no limit to the number you can fit in an infinite space. A compact, finite, and unbounded space is one that only holds so many ping-pong balls. If you filled up the space with ping-pong balls the thing preventing you from adding more is that every ping-pong ball is surrounded and filled in with other ping-pong balls. There is no boundary where one side has ping-pong balls and the other doesn't.

 

In euclidean space you would be correct. Space is either infinite and unbounded or finite and bounded. All you know is Euclidean space so you no doubt assume that what is true for Euclid is true in general.

 

Your error is in failing to conceptualize non-euclidean space and assuming that such a space is impossible. That is your failing and your faulty assumption. Non-euclidean spaces are just as valid as euclidean. Knowing which is correct is an empirical issue. It has to be measured. Even if you really, really, really like Euclidean space -- that doesn't make the universe Euclidean. Even if you really, really, completely, fail to understand non-euclidean space and have no idea what space-time is -- that doesn't mean they are impossible. It just means that you don't understand and you don't know what you're talking about.

Edited May 18, 2011 by Iggy

[csmyth3025]

Yes, whatever is beyond our present cosmic event horizon is "unknowable." But we can know (and I do know) that there can be no "end of the universe" regardless of the fact that the infinite remains unknowable.

Somebody tell me about the end of the universe, and try to make sense.

Can anything outside our obsevrable universe have any effect on events within our observable universe?

 

If not, then does it make any difference whether it's infinite or not?

 

Chris

[DrRocket]

Can anything outside our obsevrable universe have any effect on events within our observable universe?

 

If not, then does it make any difference whether it's infinite or not?

 

Chris

 

The "observable universe" is time-dependent and location-dependent.. If the universe continues to expand at a non-decreasing rate then anything outside of our Earth-bound observable universe "now" will forever be causally disconnected from us. This scenario is dependent on what "dark energy" really is and how it behaves in the future.

 

If the rate of expansion were to decrease, or if expansion were to reverse (and this is a possibility in some speculative theories) then objects outside of the current observable universe could re-enter the observable universe in the future.

 

When you get down to it, as a practical matter nothing outside the galaxy is likely to affect us any time soon, and everything outside the solar system is out of our ability to exert any meaningful influence. Nevertheless, scientific curiosity dictates that we try to understand it.

 

Science is not engineering. Many benefits have come from science, but the fundamental goal of science is understanding, not application. Attempts to understand the topology and geometry of space may yield insights affecting our understanding of the implications of general relativity or of a successor theory.

[csmyth3025]

The "observable universe" is time-dependent and location-dependent.. If the universe continues to expand at a non-decreasing rate then anything outside of our Earth-bound observable universe "now" will forever be causally disconnected from us. This scenario is dependent on what "dark energy" really is and how it behaves in the future.

 

If the rate of expansion were to decrease, or if expansion were to reverse (and this is a possibility in some speculative theories) then objects outside of the current observable universe could re-enter the observable universe in the future.

 

When you get down to it, as a practical matter nothing outside the galaxy is likely to affect us any time soon, and everything outside the solar system is out of our ability to exert any meaningful influence. Nevertheless, scientific curiosity dictates that we try to understand it.

 

Science is not engineering. Many benefits have come from science, but the fundamental goal of science is understanding, not application. Attempts to understand the topology and geometry of space may yield insights affecting our understanding of the implications of general relativity or of a successor theory.

My question is mainly directed to whether the hypothesis that the universe is infinite (or not) is testable in any way - now or in the forseeable future.

 

As I understand it the current estimates are that that the universe is "very nearly" spatially flat:

Analysis of data from WMAP implies that on the scale to the surface of last scattering, the density parameter of the Universe is within about 2% of the value representing spatial flatness.

(ref. http://en.wikipedia....verse#Detection )

 

Also, as I understand it, the topology of the universe doesn't necessarily dictate whether the universe is finite or infinite:

When cosmologists speak of the universe as being "open" or "closed", they most commonly are referring to whether the curvature is negative or positive. These meanings of open and closed, and the mathematical meanings, give rise to ambiguity because the terms can also refer to a closed manifold i.e. compact without boundary, not to be confused with a closed set. With the former definition, an "open universe" may either be an open manifold, i.e. one that is not compact and without boundary,^[8] or a closed manifold, while a "closed universe" is necessarily a closed manifold.

 

In the Friedmann-Lemaître-Robertson-Walker (FLRW) model the universe is considered to be without boundaries, in which case "compact universe" could describe a universe that is a closed manifold.

 

The latest research shows that even the most powerful future experiments (like SKA, Planck..) will not be able to distinguish between flat, open and closed universe if the true value of cosmological curvature parameter is smaller than 10⁻⁴. If the true value of the cosmological curvature parameter is larger than 10⁻³ we will be able to distinguish between these three models even now.

(ref. http://en.wikipedia....#Open_or_closed )

 

From this I take it that it might be possible to determine at some future point in time whether the topology of the universe is flat, open, or closed. If this measurement is obtained, will any of these three possibilities require (or rule out) an infinite universe?

 

Chris

[DrRocket]

My question is mainly directed to whether the hypothesis that the universe is infinite (or not) is testable in any way - now or in the forseeable future.

 

As I understand it the current estimates are that that the universe is "very nearly" spatially flat:

 

(ref. http://en.wikipedia....verse#Detection )

 

Also, as I understand it, the topology of the universe doesn't necessarily dictate whether the universe is finite or infinite:

 

(ref. http://en.wikipedia....#Open_or_closed )

 

From this I take it that it might be possible to determine at some future point in time whether the topology of the universe is flat, open, or closed. If this measurement is obtained, will any of these three possibilities require (or rule out) an infinite universe?

 

Chris

 

1. The question as to whether the universe is finite (compact) or infinite (non-compact) is a question of topology. Compactness is a topological property. Geometry and topology are different things. Sometimes they can be related and sometimes not.

 

2. The question of flatness is geometric, not topological. The relationship between curvature and topology in cosmology is based on questionable assumptions. If one assumes that the universe is homogeneous and isotropic then it can be shown that "space" is a Riemannian manifold of constant curvature and there are classification theorems that then relate curvature to topology. This is the source of the often seen correspondence: flat --- Euclidean 3-space; positive curvature --- 3-sphere ; negative curvature -- hyperbolic 3-space. This is legitimate only so long as one keeps in mind the assumptions that go with it.

3. There are flat spaces that are also compact. A flat torus is one such space. There are serious proposals that space could actually be a flat 3-torus. It is not isotropic in the technical sense, but a large flat torus could very well present itself observationally as being "the same in all directions".

 

4. "Flat, open, or closed" is not the set of options. "Closed" means compact without boundary in the terminology of manifold theory. "Open" means non-compact without boundary. "Flat" is a geometric property which is peripheral to the question.

 

5. Be careful with the physics literature. There are many misconceptions, particularly in older literature, regarding the connection between curvature and topology. Many physicists are unaware of the existence of compact manifolds having negative curvature (I know of at least one very well-known relativist who had not heard of them until I told him about them.) Thurston showed that there are lots of them. Not all are aware of flat compact manifolds either (The relativist knew about the flat torus.)

 

6. Even with the assumption of strict homogeneity and isotropy experimental determination of curvature is a problem. Topologically there is all the difference in the world among scalar curvature of 0 , -0.0000000000000000000000000000000001 and 0.000000000000000000000000000000000001

 

 

7. I doubt that any direct test of compactness will occur in the foreseeable future, but it may eventually be deducible from some aspect of a theory that is testable. No guarantees.

 

 

BTW if you want to see some consideration of the flat torus see Brian Greene's new book The Hidden Reality. While I do not like the book, and it has some questionable mathematical reasoning, he does discuss the possibility of a "Pac Man space" and that is a flat torus.

[csmyth3025]

Thanks for the reply DrRocket. Topology and the subject of manifolds remains a real head-scratcher for me.

 

I'll try Brian Greene's "Hidden Reality" and hope that I don't get lost after page three.

 

Chris

 

-----------------------------------------------------------------------------------------------------

 

I'm happy to report that I've not only gotten past page 3 without getting lost, I'm all the way to chapter 3 and I haven't gotten lost - nor have I found any part of "The Hidden Reality" boring or "slow-going" (yet).

 

I was all set to go to the bookstore to get a copy of this book and I figured I'd check Amazon.com to see what sort of price range I could expect (about $15, as it turns out). Then I disovered that they have this nifty thing called Kindle - a sort of electronic book. More importantly, I found that they also have a Kindle app. for computers.

 

I do most of my reading hunched over my computer late at night on my "off days" (I work nights). My wife, bless her heart, has tolerated my odd habits for 40 years with just a little bit of complaining. So, I thought I'd give this new (to me) technology a try. The next thing I know, there I am with the whole book on my computer and I didn't even have to get out of my chair!

 

Isn't the internet an amazing thing!

 

Chris

 

Edit: The first part of this reply was actually written about 2AM. I forgot to hit the "add reply" button.

Edited May 18, 2011 by csmyth3025

[owl]

Can anything outside our obsevrable universe have any effect on events within our observable universe?

 

If not, then does it make any difference whether it's infinite or not?

 

Chris

Believe it or not, I actually agree with DrRocket's general answer to the above!, regardless of his technical exposition, which still doesn't address the 'challenge of the wall... and beyond.'

However good one is at technical circumlocution it still doesn't answer this thread's question. Again, as I requested yesterday "Somebody tell me about the end of the universe." Otherwise it will remain, as is, without end, which is what infinite means in this context.

 

Iggy:

In euclidean space you would be correct. Space is either infinite and unbounded or finite and bounded. All you know is Euclidean space so you no doubt assume that what is true for Euclid is true in general.

 

Your error is in failing to conceptualize non-euclidean space and assuming that such a space is impossible.

 

Now we are getting somewhere. You have no idea what I know about "non-Euclidean space" and what ontological assumptions it requires.

 

I have studied the transition from Euclidean to non-Euclidean geometry in depth and have often repeated quotes from my favorite paper on the subject, The Ontology and Cosmology of Non-Euclidean Geometry, by Kelley Ross. Seems that you still have not read it.

Here again is the link.

http://www.friesian.com/curved-1.htm

[Iggy]

I have studied the transition from Euclidean to non-Euclidean geometry in depth

No. You haven't.

 

and have often repeated quotes from my favorite paper on the subject, The Ontology and Cosmology of Non-Euclidean Geometry, by Kelley Ross.

You have already shown that you don't understand that paper. I can quote the paper too,

On the other hand, it may be that intrinsically curved spaces can exist in reality without extrinsic curvature and so without being embedded in a higher dimension. This could be called the axiom of hetero-curvature, and it would make true non-Euclidean geometry possible

Your favorite paper that you keep quoting is trying to tell you the same thing we are... you're just not going to get it.

[owl]

View Postowl, on 18 May 2011 - 11:50 AM, said:

I have studied the transition from Euclidean to non-Euclidean geometry in depth

Iggy:

No. You haven't.

 

I haven't studied what I just said that I've studied? I didn't know that you were such a "seer" that you know me (and what I've studied) better than I know myself!

 

View Postowl, on 18 May 2011 - 11:50 AM, said:

and have often repeated quotes from my favorite paper on the subject, The Ontology and Cosmology of Non-Euclidean Geometry, by Kelley Ross.

 

You have already shown that you don't understand that paper. I can quote the paper too,

I have no need to show you that I understand the paper... to pass your test, I do not agree with all of it... your wrong assumption.

 

Iggy quoting Ross:

On the other hand, it may be that intrinsically curved spaces can exist in reality without extrinsic curvature and so without being embedded in a higher dimension. This could be called the axiom of hetero-curvature, and it would make true non-Euclidean geometry possible

Iggy:

Your favorite paper that you keep quoting is trying to tell you the same thing we are... you're just not going to get it.

 

"It may be" quite a few variations (did you read the whole paper or just cherry picking?), including that concepts may exist in the human mind without a referent in the real world that can be observed and verified.(Read his ontology on this.)

Now, what was the whole paper telling me again that I missed? I have run down every reference he mentions and understand all of it very well.

 

(Incidentally, I must now set you straight about your constant insistence on how stupid you think I am. I am hoping you tell the truth, as I do. Please tell me your IQ by PM and I will tell you mine.)

 

As you know, I have no qualms about questioning the ontological assumptions central to GR's "spacetime, but what you don't know is that the "cause" (you know, "cause and effect") of this confidence is that I was born at the high end of the scale, and never lost interest in open scientific inquiry... including the "questioning authority" thing which many textbook scientists here obviously despise.

[Iggy]

I haven't studied what I just said that I've studied? I didn't know that you were such a "seer" that you know me (and what I've studied) better than I know myself!

Dr. Rocket said to you some time back "the problem is that you don't know that you don't know". I'm sorry, but it's clearly true.

 

I have no need to show you that I understand the paper...

That train sailed.

 

"It may be" quite a few variations (did you read the whole paper or just cherry picking?), including that concepts may exist in the human mind without a referent in the real world that can be observed and verified.(Read his ontology on this.)

The quote I gave said "exist in reality" and you interpret that "without a referent in the real world". Hopeless I'm afraid.

 

Please tell me your IQ by PM and I will tell you mine.

 

And with that, I formally abandon this hopeless conversation. Thank you for your time.

 

Indeed.

[DrRocket]

While the topic if this thread is not creationism, I think the analogy is clear:

 

Debating creationists on the topic of evolution is rather like trying to play chess with a pigeon -- it knocks the pieces over, craps on the board, and flies back to its flock to claim victory." - Scott D. Weitzenhoffer

 

 

[MigL]

Tried to play chess with my cat once. Other than the crap all over the board, same result. Knocked all the pieces over and continuously licked my fingers when I tied to make a move.

[owl]

So... no replies at all on the substance of the transition beyond Euclid or on Ross' quite intelligent examination of how we got to the "curved space" of non-Euclidean geometry... as applied to "Is space infinite?"

Rather just slurs like painting me as a creationist (Yikes!... now how was that relevant again?) or a bird brained pigeon trying to play chess with you real people, but just crapping all over the board.

 

This kind of "crap" you are purveying is not worthy of science.

 

Btw, Ross said, "it may be that intrinsically curved spaces can exist in reality..." not that they do in fact exist.

Likewise 4-D space "may exist" but no one has clue what it would mean or be in the real world... Just a mind game like, "a curved line requires a plane;... a curved surface requires volume;... so, therefore a "curved volume" (space) must exist in a 4th spacial dimension. (Forget whether "it" exists at all or not.)

And how about those curved line orbits of planets and such "actually" being straight lines in curved space. Very "sophisticated", this concept of curvature being intrinsic to one manifold but extrinsic to another (mental) manifold... but nonsense!

And how about those parallel lines finally intersecting "in infinity" as a math concept (without real world referent?)How "real" is that "infinity"... or does anyone give a hoot about what is real in the actual world ( the focus of ontology.)

But enough on this already! What, still no 'wall out there' as the end of space?) How does it end, again, if its not infinite?

Edited May 19, 2011 by owl

[MigL]

Wasn't calling you names, just having some fun.

 

But again, these GR models of space/time, with 3 spatial dimensions and 1 of time, do make a lot of verifiable predictions, like the bending of light around massive objects, and are certainly more accurate than Newton's model of ( flat , Euclidian ) gravity, which cannot explain the orbit of Mercury.

So whether 4-dimensional space exists or not, is academic, but as a model of physical reality , it is pretty darn accurate.

 

And you'd be a fool to argue with that.

[owl]

Wasn't calling you names, just having some fun.

 

But again, these GR models of space/time, with 3 spatial dimensions and 1 of time, do make a lot of verifiable predictions, like the bending of light around massive objects, and are certainly more accurate than Newton's model of ( flat , Euclidian ) gravity, which cannot explain the orbit of Mercury.

So whether 4-dimensional space exists or not, is academic, but as a model of physical reality , it is pretty darn accurate.

 

And you'd be a fool to argue with that.

I have never disputed those verifiable predictions, nor the three spatial dimensions and the time factor (movement from A to B or event duration.)

 

"Flat" Euclidean space is an unfortunate use of the word flat, which applied only to planes before the mental/conceptual transition to non-Euclidean and all "higher dimensional" geometry.

Space is most reasonably described and denoted as 3-D volume, not a "flat" plane. Volume/space is not "flat" except via a new invention for the meaning of "flat" by non-Euclidean mental/conceptual exercises and subsequent theories of "shaped space."

 

Consider the possibility that gravity bends light around massive objects without the theoretical existence of malleable, curved "spacetime."

Light acts as if it has an infinitesimal amount of mass in other experiments and situations too. Like the "box of mirrors" which gains inertia as if gaining mass with the intro of light bouncing around inside. Or the recoil when lasers are fired. It's not all set in concrete that light is absolutely mass-less, so the deals are not yet done on why light is curved by gravity/mass.

(Oops!, this is way off subject again. Sorry.)

Edited May 20, 2011 by owl

[csmyth3025]

But enough on this already! What, still no 'wall out there' as the end of space?) How does it end, again, if its not infinite?

I have to stick with DrRocket's May 18,12:22 AM reply which reads, in part:

 

1. The question as to whether the universe is finite (compact) or infinite (non-compact) is a question of topology.

....................

7. I doubt that any direct test of compactness will occur in the foreseeable future, but it may eventually be deducible from some aspect of a theory that is testable. No guarantees.

 

Until such time as the compactness (or non-compactness) of the universe can be deduced "...from some aspect of a theory that is testable..." I consider this an open (and unanswerable) question.

 

For your question: "...How does it end...if it is not infinite?..." there have been many replies that have attempted to explain the theoretical and mathematical concept of manifolds in general. I doubt that I have any deeper understanding of these concepts than do you.

 

My own lack of understanding is only compounded by explanations such as:

 

Compact manifolds are, in an intuitive sense, finite. By the basic properties of compactness, a closed manifold is the disjoint union of a finite number of connected closed manifolds. One of the most basic objectives of geometric topology is to understand what the supply of possible closed manifolds is.

(ref. http://en.wikipedia....ompact_manifold )

 

Nevertheless, if the universe is shown to be a compact manifold as a consequence of a testable theory, I'm inclined to work harder at trying to understand what, exactly, this means rather than insist that the scientific community must be wrong because I can't imagine what it means.

 

Chris

[DrRocket]

Space is most reasonably described and denoted as 3-D volume, not a "flat" plane. Volume/space is not "flat" except via a new invention for the meaning of "flat" by non-Euclidean mental/conceptual exercises and subsequent theories of "shaped space."

 

 

What you fail to realize is that Gauss's concept of curvature, extended to higher dimensions by Riemann lies at the heart of Riemannian geometry. In turn Einstein utilized the work of Riemann in formulatng general relativity as a generally covariant theory of gravitation. Cosmology is based on general relativity. So the ONLY notion of curvature or of flatness that is germane to cosmology is that which comes from Riemannian geometry.

 

You have two choices: 1). Learn and understand the concepts on which the theory is built. 2) Continue to babble incoherently making inane, irrelevant and nonsensical comments..

[michel123456]

You have two choices: 1). Learn and understand the concepts on which the theory is built. 2) Continue to babble incoherently making inane, irrelevant and nonsensical comments..

 

Incoherent, inane, irrelevant, maybe.

But certainly not nonsensical.

If one remain to his actual experience and sensitivity and refuses to embark into concepts like "curved space" or "expanding space" while the word "space" represents [insert here what you think], then there is no hope for common understanding.

[MigL]

I haven't done the math myself, but I seem to remember that if you consider the bending of light around a massive object as due to the rest mass of the photon, you end up with bending which is half of that predicted by GR and curved space/time. Which happens to be half of what was actually observed by Eddington during the eclipse of 1919.

 

So GR is accurate, newtonian gravitational attraction of the photon's rest mass is not !!!