# Infitine Space

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The bounded infinite spaces I proposed are metric spaces that are only bounded according to a different metric. I don't think they can be called bounded metric spaces. Pure imbecility!, sorry about that.

I think we should stop talking about boundaries, because that only answers the question about whether or not space is infinite, if there IS a boundary. Since no one is arguing for the existence of a boundary, we may as well assume there is no boundary.

For a metric space to be finite and have no boundary, does this mean that no spatial dimension has a bound, yet the distance metric has an upper bound?

Is it a confusion of spatial dimensions and the distance metric that is causing all the trouble?

"Bounded" as a metric space and having a boundary as a manifold are two completely different things.

An ordinary sphere is a 2-manifold without boundary, but it is certainly bounded as a metric space.

The right-half plane, including the y-axis, is an unbounded metric space, but it is a 2-manifold with boundary.

I would stop worrying so much about metric spaces. The space-like slices of spacetime are metric spaces using the inherited metric, because it happens to be a Riemannian metric. But the Lorentzian metric of the full spacetime does not induce a topological metric on all of spacetime (because it is not positive-definite). Note that the word "metric" is being used in two different ways here -- a metric tensor need not be related to a topological metric (It does in Riemannian geometry, but not in pseudo-Riemannian geometry).

You can, if you wish think about "finite" space as being a bounded metric space, but I think it is easier to think of it as compact. That is more natural and depends only on the topology and not the specific choice of metric.

Unless you are very precise in your use of terminology, you are headed for a semantic morass. The only cure is to understand the mathematics in some depth.

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The bounded infinite spaces I proposed are metric spaces that are only bounded according to a different metric. I don't think they can be called bounded metric spaces. Pure imbecility!, sorry about that.

I think we should stop talking about boundaries, because that only answers the question about whether or not space is infinite, if there IS a boundary. Since no one is arguing for the existence of a boundary, we may as well assume there is no boundary.

For a metric space to be finite and have no boundary, does this mean that no spatial dimension has a bound, yet the distance metric has an upper bound?

Is it a confusion of spatial dimensions and the distance metric that is causing all the trouble?

Right. Owl actually quoted a good definition for a bounded metric:

A finite universe is a bounded metric space, where there is some distance d such that all points are within distance d of each other. The smallest such d is called the diameter of the universe, in which case the universe has a well-defined "volume" or "scale."

IOW, there is a bound on the distance between any two points. This article -- The Possibility of a "Finite" and yet "Unbounded" Universe -- and this statement:

Logically, if space is finite it has an end or boundary or wall... a limit of some kind.

refer to the kind of boundary that you might run into in moving around the space. That is the meaning I was intending as well. Sorry for any confusion.

Logically, what confines the above arbitrary "diameter of the universe" to "d?" (What prevents "d+1" of whatever units of distance?) You seem incapable of thinking about what would lie beyond such a well defined (finite) volume. If "something," what?... if nothing... more empty space, ad infinitum.

In a closed spherical space with a diameter of 1 km, anything that travels 2 km in a straight line will end up back where it started. I really think this would help: The Possibility of a "Finite" and yet "Unbounded" Universe.

Edited by Iggy
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Owl, you're getting hung up on definitions and misunderstandings.

One typical one that you posted:

"So "closed" in this context has a special, counter- intuitive meaning. One usually thinks of closed as having an inside and an outside, and in the context of this thread, the space outside of a closed cosmos (I will not say "universe" in this context) has no end or boundary, so is therefore infinite. "

No! The manifold is the cosmos, or universe, and it is closed or compact because it curves back on itself. It is not the inside ( or outside ) of the manifold. The inside or the outside, are inconsequential and have no meaning. Why are you trying to give them a meaning?

You seem well read on the philosophical implications of the finite and infinite. Maybe you should read an elementary text on topology, or even a popularization. I seem to remember a book called The Poincaire Conjecture which did an adequate job of describing higher dimensional curved spaces. I think you would then comprehend the meaning of finite but unbounded manifolds.

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I think steevey answered the title question well in post #3:

There are no observed boundaries for the universe. Also, as far as scientific consensus is concerned, the universe also has no observed center, even though the universe is said to exist in denser and hotter states previously in time.

As far as I see it though, I don't see how the universe couldn't be infinite. Why would space itself, something not proven or disproven to exist, wouldn't go on infinitely, or why there wouldn't be infinite room for matter to expand into. What would be stopping the existence of infinite space?

There's also something else too, since the fabric of space itself is not proven to exist, even though the universe is said to be filled with virtual particles, there could still be space of nothingness between those, which if thats the case and true space is nothing, there could be infinite "nothing", since there would be no amount of something to run out of, and there wouldn't be a "something" that needs to travel distances.

Math and "higher dimensional geometry" by itself does not confer understanding, and all the technical concepts discussed in this thread (mostly without "real world" observable referents) do not answer the simple questions, "How big is the universe... and, Is there an end of space?"

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You want real references ? Very well. Look up quasi-crystals. You will find that their crystalline structure is not regular at all like all other crystals. However it turns out their structure is a projection ( which see ) of a 5-dimensional structure, ie their structure is only regular in FIVE dimensions.

You are confused as to the meaning of dimensions in physics. For the mathematical meaning DrR has already explaned several times but in physics an extra dimension is not another direction beyond the known three, but another degree of freedom. In effect another 'way' to estabilish a relation. Take for example Siberian Mongol peoples and North American Inuit people, how are the two rlated ? We can establish a connection between the two only by considering another dimension. We realise that the dimension of time estabilishes a connection between the two about 15000 yrs ago ( the Bearing Strait land bridge ).

This is the 'real',' physical' meaning of extra dimensions, you should try to wrap you head around it as a curved space/time is not a big stretch from these examples. We build models of reality using mathematical tools such as extra dimensions. Sometimes these dimensions are so small ( 10^-33 ) and compact ( ie curve in on themselves like a straw ) and two gentlemen named Kaluza and Klein managed to use this ffth compacted dimension to relate and unite Maxwell's theory of electomagnetism with Einstein's general relativity. Current string theories involve 10 or 11 dimensions to relate and unify all four known forces.

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Current string theories involve 10 or 11 dimensions to relate and unify all four known forces.

Some say up to 26. The 11th "dimension" was first supposedly 'debunked' and then, years later, praised as the way to unite the various (five or six) versions of what a "string" is supposed to be.

Please explain each of the string theory dimensions beyond the 3-D axes of volume/space and "time," (if we must call event duration a "dimension.")

Or maybe it's still all in the very imaginative minds of M-theory's history of creators (read "theorists.")

How does such unobservable speculation become such "popular science?"

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Some say up to 26. The 11th "dimension" was first supposedly 'debunked' and then, years later, praised as the way to unite the various (five or six) versions of what a "string" is supposed to be.

Please explain each of the string theory dimensions beyond the 3-D axes of volume/space and "time," (if we must call event duration a "dimension.")

Or maybe it's still all in the very imaginative minds of M-theory's history of creators (read "theorists.")

How does such unobservable speculation become such "popular science?"

1. String theory is still speculative. It is not "popular science".

2. In general relativity you do NOT have 3-spatial axes and one time axis, except locally for a chosen observer.

2a. In special relativity you have flat Minkowski spacetime, a 4-dimensional spacetime with a metric of signature (+,-,-,-) or equivalently (-,+,+,+). Neither "time" nor "space" are uniquely defined, A vector x is "timelike" if ,x,x> < 0 and ANY timelike vector give the "direction" for time for some observer. The orthogonal directions are the "space" for that observer.

2b. In general relativity the situation of special relativity is seen to be only local -- special relativity applies to the tangent space at a point, and is accurate only as a local approximation. There is NO global notion of either time or space. Time and space are "mixed together" by the curvature of the spacetime manifold. On other words there is no such thing as a "time axis" or three "space axes" except as local approximations.

2c. You may find this counter-intuitive but that is irrelevant. There is a mountain of empirical data supporting special and general relativity.

3. The idea of extra dimensions arose with the observation of Kaluza and Klein that electromagnetic theory and gravitation arose naturally from a theory like general relativity if one postulated a fifth spatial dimension. Kaluza Klein theory runs into difficulties with particle physics and has given rise to a more general approach -- Yang-Mills gauge theories. There are still unresolved issues. The point is that "extra" spatial dimensions are postulated in these theories in order to explain empirical facts -- the existence of known particles and forces -- in a unified manner.

4. It is very obvious that in our ordinary experience, locally, there are three spatial dimensions, not 5 or 11 or whatever. But as Klein observed, if extra spatial dimensions are compactified -- realized in a geometrically small compact manifold -- they would go unnoticed. This is of course speculative, but that is consistent with physics being a vibrant area of research -- there is a lot that is not understood.

5. String theories add another layer of research and speculation. There is much work needed to even clearly define in mathematical terms just what string theory is. Nevertheless it appears that additional spatial dimensions, in the form of Calabi-Yau manifolds, are needed to make string theories internally consistent, and to determine the laws of physics that come with each candidate string theory. Here spacetime is the Cartesian product of ordinary spacetime with a compact Calabi-Yau manifold, so again the existence of additional compactified dimensions can be made plausible if the Calabi-Yau manifold is sufficiently small.

Yes, this came from imaginative minds -- both imaginative and disciplined. No, it is not established -- it is representative of cutting-edge and therefore speculative research. Yes, there is a body of supporting empirical evidence for some of it, and laboratory investigations continue unabated. No, it is not fantasy.

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This is piecemeal. I hope to get back to more in-depth replies later, after reading some of the recently suggested links. But the following simply addresses MigL's mistaking my "referents" above for "references."

Me:

Math and "higher dimensional geometry" by itself does not confer understanding, and all the technical concepts discussed in this thread (mostly without "real world" observable referents) do not answer the simple questions, "How big is the universe... and, Is there an end of space?"

MigL:

You want real references ?

Referents definition (from my computer dictionary):

referent:

the thing that a word or phrase denotes or stands for : “the Morning Star” and “the Evening Star” have the same referent (the planet Venus).

ORIGIN mid 19th cent.: from Latin referent- ‘bringing back,’ from the verb referre (see refer ).

DrRocket is very fluent in math and the "higher dimensional" non-Euclidean geometries, for instance, while my forte' is in the philosophy of science, specifically the ontology of such "dimensions." The two realms of expertise are obviously not in communication in this thread, and DrR seems to believe that ontology is irrelevant to this discussion. (Correct me if I'm wrong.)

So when he or anyone speaks of the various theoretical properties/descriptions of different theoretical manifolds and "higher dimensions" or of "spacelike slices of spacetime" as what science means by "space" and I refer to the ongoing investigation of what "spacetime" actually is if anything (see multiple references to the International Society for the Advanced Study of Spacetime)... to the point here... "Is space infinite?"... we talk past each other from different worlds.

The "slices" in "spacelike slices of spacetime" are mental concepts in the abstract world of math and non-Euclidean geometry. "They" have no real world referents. Space is not that complicated in the sense queried in this thread i.e., whether or not space is infinite, i.e., does it have an end or boundary or not? If one is proposed, then the ontological questions remain, what is the nature of such a boundary or end, and then, of course, beyond that... what?

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DrRocket is very fluent in math and the "higher dimensional" non-Euclidean geometries, for instance, while my forte' is in the philosophy of science, specifically the ontology of such "dimensions." The two realms of expertise are obviously not in communication in this thread, and DrR seems to believe that ontology is irrelevant to this discussion. (Correct me if I'm wrong.)

But you are giving a philosophical answer to a question that pertains to General Relativity, in a Sciences > Physics > Relativity forum, not a philosophy forum.

You could very well be right, but you can't prove it in terms of relativity, science, or math. The reasoning in what you considered the best answer is this: "I don't see how the universe couldn't be infinite." That's simply not acceptable. I think it does a disservice to anyone who comes here trying to understand relativity (and not the philosophy of science), to find answers that are based on not being able to see how some potential implications of GR can be real.

The question remains an open problem (whether considered from a scientific perspective, or a philosophical one).

If you had reasoning that addressed why closed (curved) space should be considered impossible, in terms of GR, that would be interesting.

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DrR seems to believe that ontology is irrelevant to this discussion. (Correct me if I'm wrong.)

Ontology as practiced by scientists is relevant. As practiced by philosophers in its most benign form it is merely irrelevant -- see essay by Steven Weinberg. Note quote from Wittgenstein on lack of relevance of philosophy to the practicing scientist.

http://depts.washington.edu/ssnet/Weinberg_SSN_1_14.pdf

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Ontology as practiced by scientists is relevant. As practiced by philosophers in its most benign form it is merely irrelevant -- see essay by Steven Weinberg. Note quote from Wittgenstein on lack of relevance of philosophy to the practicing scientist.

http://depts.washington.edu/ssnet/Weinberg_SSN_1_14.pdf

Thanks. I'll check it out. Meanwhile you've inspired me to dig up my reply earlier in this thread to the proposition that philosophers are "dopey" and that the only reason to tolerate philosophy on a campus is to broaden sophistication in the humanities of the real students and teachers, the people that matter, the scientists. (I saw this, and still do, as the ultimate scholastic bigotry and arrogance... I'll find it.)

Iggy, You wrote:

Finite space does not necessitate or imply a boundary.

Here are selected quotes and my commentaries:

The development of non-Euclidean geometry led to the recognition of the fact that we can cast doubt on the infiniteness of our space without coming into conflict with the laws of thought or with experience (Riemann, Helmholtz).
(My bold.)

I am astounded that the development of non-Euclidean geometry and the named references (however well respected) make a fact out of (and legitimized) our ability to “cast doubt” on a previously obvious fact... there is no possible end of space. (See the several absurdity scenarios I have already presented about walls and beyond.) There is still a place for reason in science.

In the first place, we imagine an existence in two dimensional space. Flat beings with flat implements, and in particular flat rigid measuring-rods, are free to move in a plane. For them nothing exists outside of this plane:

We can imagine whatever strikes our fancy. Unicorns are cute too. But the analogy, inter-dimensional (2-D to 3-D) relevance is limited. In the real world, we are 3-D creatures in a 3-D universe... (add time if you like, for motion, which “takes time.”)

Recall my earlier posts on the transition beyond Euclidean geometry. (Warning: It involves ontology!)

A curved line actually exists on a plane; A curved plane exists as a 3-D form, regardless of shape. A “curved volume” is, so far, just an act of imagination (4-D space.) I’ll dig up the link for the whole ontology piece again if you are interested.

With increasing values of r, F increases from zero up to a maximum value which is determined by the " world-radius," but for still further increasing values of r, the area gradually diminishes to zero.

...For no particular reason presented but the whim of the author... but of course it is his thought experiment.

At first, the straight lines which radiate from the starting point diverge farther and farther from one another, but later they approach each other, and finally they run together again at a "counter-point" to the starting point.

What causes this to happen, and how did a counter point develop?

Under such conditions they have traversed the whole spherical space. It is easily seen that the three-dimensional spherical space is quite analogous to the two-dimensional spherical surface. It is finite (i.e. of finite volume), and has no bounds.

“Quite analogous” is not “the same as.” A plane remains 2-D and a sphere remains 3-D

It follows from what has been said, that closed spaces without limits are conceivable.

They are conceived as analogies to actual unlimited space, infinite space. Yet in reality there is always more space beyond what the finite mind conceives as a “form, a closed space.”

In other words (same meaning), no limit to surface travel on a sphere is this analogy’s version of limitless. But any closed space (defined form) exists in the real 3-D universe, and the surface of any sphere is its limit/boundary as measured from its center outward (toward, expanding into, actual universal 3-D space), and beyond that surface must always be more space, as I’ve said a dozen times or more.

I'm done saying it now. I think that one must abandon his/her faculty of reason to believe that there is an end of space, that the universe is a "finite form." But of course relativity theory encourages that (abandonment of reason... even for all the good theory it provides for predicting the finer points of gravity... with the magical fabric "spacetime" and the amazing mystery of constant lightspeed proven by SR.) Seriously.

Edited by owl
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My apologies, owl, I assumed a spelling mistake where there was none. I was ( always seem to be ) in a bit of a hurry.

My only point was that extra dimensions are a useful tool, whether real or imagined. If they have predictive effects then they may as well be real. There are a lot of things which cannot be seen or proved directly, only by their effects ( black holes, dark matter, sub-atomic particles, radiation, even air ). Yet I'm sure you have no problem accepting them.

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MD65536:

If you had reasoning that addressed why closed (curved) space should be considered impossible, in terms of GR, that would be interesting.

GR assumes that space is an entity which is curved by mass as a theory of gravity. Quantum mechanics has an alternative theory, as I understand it. Anyway the status of space as a malleable medium/entity is not a given fact, and ontology asks "What is it, if anything besides empty volume?" This is a very relevant question for science, even if it is ontology, another bastard child of the philosophy of science.

Forms made of cosmic "stuff" may be "compact" or closed (even the visible cosmos but the question this thread asks is still about what lies beyond any such form, not to assert as a given that space has form, but rather that stuff in space has form... with no end of space beyond any conceivable form.

Btw, DrRocket, I've read about half of the paper, "Against Philosophy" by Weinberg, and I'm working on commentary in reply.

A correction to my post 86 (too late to edit it), re:

"A curved plane exists as a 3-D form, regardless of shape."

I should have said "a curved surface." A plane is flat, not curved. (And "flat space" as describing Euclidean 3-D space is a misnomer, though it looks like we are stuck with it as ubiquitous usage would have it.)

I have decided not to post my reply to the Weinberg essay in this thread, as it belongs in the philosophy section. Maybe I'll start a new thread there on the relevance of philosophy to science... "Are epistemology and ontology relevant to science?" (or... "Who cares what it is as long as the math works? )

Edited by owl
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Still trying to catch up with replies to previous posts, specifically parts of DrRocket's May 11 post.

There is NO global notion of either time or space. Time and space are "mixed together" by the curvature of the spacetime manifold. On other words there is no such thing as a "time axis" or three "space axes" except as local approximations.

I have a global notion of space as unlimited, i.e., without end. What would an end look like? And beyond that?

Also one can reasonably "imagine" that beyond focus on local "time environments" (duration of local events) the present is present and ongoing everywhere, universally. (See intro to Deiks' volumes cited below.)

Time and space are "mixed together" by the curvature of the spacetime manifold"... On other words there is no such thing as a "time axis" or three "space axes" except as local approximations.
...

Have you read either of the two volumes of papers compiled by Dennis Deiks on The Ontology of Spacetime as presented at the international conferences on same? It's not as cut and dried (matter of fact) as you present it. But of course, you may not be interested in what "curvature of the spacetime manifold" means in the real world of observable phenomena. Yes, objects effected by gravity often have curved trajectories. But do you care if the phrase "curvature of the spacetime manifold" has a referent in the real world, or is a working abstract concept enough without a referent? (An ontological question?)

It is very obvious that in our ordinary experience, locally, there are three spatial dimensions, not 5 or 11 or whatever. But as Klein observed, if extra spatial dimensions are compactified -- realized in a geometrically small compact manifold -- they would go unnoticed.

Of course there must be many things in the cosmos that "go unnoticed." But how would small forms (speaking of real entities, not just concepts) or defined spaces with boundaries existing in real 3-D space make the whole universe or endless space finite? It is a "reasonable" question, and directly to the point of this thread's inquiry.

And since three axes describe space as volume (defined with specific size or infinite), to what would a fourth (or fifth or eleventh) spatial axis possibly refer?

The point is that "extra" spatial dimensions are postulated in these theories in order to explain empirical facts -- the existence of known particles and forces -- in a unified manner.

What empirical facts? What distinguishes the many extra "dimensions" in M-Theory from metaphysical "dimensions", as "spiritual realms" beyond the "merely mundane" world of science?

Ps: Still not finished with Weinberg's philosophy bashing paper, but any reply will be posted in the philosophy section. But this post has again addressed the ontology of spacetime, so your reply to the above may be sufficient.

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Still trying to catch up with replies to previous posts, specifically parts of DrRocket's May 11 post.

I have a global notion of space as unlimited, i.e., without end. What would an end look like? And beyond that?

Therein lies the problem. Your notion is very obviously based on the everyday experience, Euclidean geometry. What Einstein discovered is that the model of your everyday experience is wrong. And that is what should be relevant to ontology.

Also one can reasonably "imagine" that beyond focus on local "time environments" (duration of local events) the present is present and ongoing everywhere, universally. (See intro to Deiks' volumes cited below.)

You can imagine all sorts of things that are wrong. This is just one of them. You seem to be insisting on an ontological study of erroneous ideas.

...

Have you read either of the two volumes of papers compiled by Dennis Deiks on The Ontology of Spacetime as presented at the international conferences on same? It's not as cut and dried (matter of fact) as you present it. But of course, you may not be interested in what "curvature of the spacetime manifold" means in the real world of observable phenomena. Yes, objects effected by gravity often have curved trajectories. But do you care if the phrase "curvature of the spacetime manifold" has a referent in the real world, or is a working abstract concept enough without a referent? (An ontological question?)

I have zero interest in the opinion of someone who is clueless regarding the mathematical meaning of curvature on the subject of what curvature "really means". I know what curvature really means.

Of course there must be many things in the cosmos that "go unnoticed." But how would small forms (speaking of real entities, not just concepts) or defined spaces with boundaries existing in real 3-D space make the whole universe or endless space finite? It is a "reasonable" question, and directly to the point of this thread's inquiry.

And since three axes describe space as volume (defined with specific size or infinite), to what would a fourth (or fifth or eleventh) spatial axis possibly refer?

Your question is not the least bit reasonable. It is in fact ridiculous. ridiculous

The Calabi-Yau manifolds occur as one term in a Cartesian product, and they are WITHOUT BOUNDARY. They are also compact and are therefore completely irrelevant to the discussion of whether space is compact (aka finite) or open (aka infinite).

A fourth or fifth spatial dimension quite obviously refers to a fourth or fifth spatial dimension -- what else could possibly be the referent ?

What empirical facts? What distinguishes the many extra "dimensions" in M-Theory from metaphysical "dimensions", as "spiritual realms" beyond the "merely mundane" world of science?

Empirical facts -- the existence of the known list of elementary particles.

The extra dimensions of string theories are required for the mathematical consistency of those theories. Whether they are valid theories that describe nature remains unknown.

Ps: Still not finished with Weinberg's philosophy bashing paper, but any reply will be posted in the philosophy section. But this post has again addressed the ontology of spacetime, so your reply to the above may be sufficient.

It is amusing to watch you attempt to address the ontology of spacetime when you have no idea what spacetime is and harbor so many gross misconceptions regarding general relativity. It is rather like a critique of French poetry by someone who speaks and reads only Swahili.

Edited by DrRocket
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DrRocket:

It is amusing to watch you attempt to address the ontology of spacetime when you have no idea what spacetime is and harbor so many gross misconceptions regarding general relativity. It is rather like a critique of French poetry by someone speaks and reads only Swahili.

But would you mind answering a few sincere questions?... starting with my last post would be very much appreciated.

Also, before you declare victory for the established fact of spacetime, please do the required* research into what the International Society for the Advanced Study of Spacetime (ISASS) has been debating for most of the last decade.

*(If you care about what spacetime is)

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It is amusing to watch you attempt to address the ontology of spacetime when you have no idea what spacetime is and harbor so many gross misconceptions regarding general relativity. It is rather like a critique of French poetry by someone speaks and reads only Swahili.

But would you mind answering a few sincere questions?...

A recent post of yours reminded me of Family Guy - Speaking Italian, so maybe there is something to Dr. Rocket's comment and it shouldn't be rejected as insincere.

You say very definite things about concepts that you don't seem to understand at all. Like Peter not realizing that he doesn't speak Italian, I don't think you realize that you don't know what relativity is or what a closed space is.

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DrRocket:

But would you mind answering a few sincere questions?... starting with my last post would be very much appreciated.

Also, before you declare victory for the established fact of spacetime, please do the required* research into what the International Society for the Advanced Study of Spacetime (ISASS) has been debating for most of the last decade.

*(If you care about what spacetime is)

http://www.isass.org/

Apparently Google has better things to do with its resources also.

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...what "curvature of the spacetime manifold" means in the real world of observable phenomena. Yes, objects effected by gravity often have curved trajectories. But do you care if the phrase "curvature of the spacetime manifold" has a referent in the real world, or is a working abstract concept enough without a referent? (An ontological question?)...

I just don't understand what you're trying to get at here. As I understand it, "referent" is defined as: "The specific entity in the world that a word or phrase identifies or denotes."

The inertial path of objects effected by gravity always have curved trajectories. In the real world of observable phenomenon this is the referent of the phrase "curvature of the spacetime manifold".

Are you saying that it's something different?

Chris

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I just don't understand what you're trying to get at here. As I understand it, "referent" is defined as: "The specific entity in the world that a word or phrase identifies or denotes."

The inertial path of objects effected by gravity always have curved trajectories. In the real world of observable phenomenon this is the referent of the phrase "curvature of the spacetime manifold".

Are you saying that it's something different?

Chris

Those curved trajectories are a bit misleading.

An object in freefall, such as an orbit, has a trajectory that is a geodesicc in spacetime. But, for instance, an elliptical orbit is obviously not a geodesic in space. Neither is the familiar parabolic trajectory of an artillery shell. A geodesic in spacetime is quite different from a geodesic in space and the curvature in question is spacetime curvature, not just curvature of "space". In fact there is no clear separation of space and time, except locally. Spacetime is not space and time, but an intertwined amalgamation of both. In this regard special relativity can be misleading.

The "referent" is the spacetime trajectory, the world line. The world line is also the source of time. The length of the world line (divided by c), a timelike path, is the tme experienced by the body associated with that world line. Time is not a universal, but rather is associated with each world line and two bodies with different world lines may experience very different times -- this is the essence of the "twin paradox".

Owl is indeed saying something very different. He and Einstein are on completely different pages.

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DrRocket:

Apparently Google has better things to do with its resources also.

I just got Deiks' volumes by Googling "Deiks Spacetime Ontology" and the International Society for the Advanced Study of Spacetime with "Spacetime Society"... both in less than a minute... not that difficult to find... just requires a smidgen of interest in the ontology of spacetime.

csmyth3025:

The inertial path of objects effected by gravity always have curved trajectories. In the real world of observable phenomenon this is the referent of the phrase "curvature of the spacetime manifold".

Are you saying that it's something different?

I am saying that the obviously curved trajectories of objects effected by gravity does not verify the actual existence of an entity "the spacetime manifold." There is a lively ongoing debate among well credentialed scientists and philosophers of science about what "spacetime" is (if anything.) See key word references above.

Also, regarding "curved spacetime" as the established fact for how gravity works, what about the quantum theory of gravity? I don't know the technical/math details, but I think it is a whole different theory of gravity, no?

Btw, presentism is another study which inquires beyond local frames of reference and "time environments" and the usual "who sees what and when" of relativity. It can be ignored, but it will not go away. The most simple and obvious illustration of presentism is that now is now for both earth and sun even though it obviously takes over eight minutes for sunlight to travel to earth.

Then, this "now" can be extended to "now everywhere," that the universal present is not limited by lightspeed.

Calling it wrong doesn't make it wrong.

Finally, to this exchange:

me:

I have a global notion of space as unlimited, i.e., without end. What would an end look like? And beyond that?

DrR:

Therein lies the problem. Your notion is very obviously based on the everyday experience, Euclidean geometry. What Einstein discovered is that the model of your everyday experience is wrong. And that is what should be relevant to ontology.

Do you think Einstein and GR have answered the the two fundamental questions above, the focus of this thread? GR obviously "works well" locally, but this thread is a global/universal focus, which you refuse to address.

Edited by owl
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GR assumes that space is an entity

Citation? I don't think that's true.

You've stated in this thread that you don't consider space to be an entity. Would you then conclude that GR is based on false assumptions? Would you also say that because of this, GR can be safely ignored, and that an understanding of GR is irrelevant to this discussion?

Also, before you declare victory for the established fact of spacetime, please do the required* research into what the International Society for the Advanced Study of Spacetime (ISASS) has been debating for most of the last decade.

*(If you care about what spacetime is)

On the website that you are referencing, they have the question "Is Space Infinite?" on their Open Questions page: http://www.spacetime...nquestions.html

Your source does not seem to agree that the question has been answered.

Others in this thread accept that it remains an open question. So how is it that their minds are made up while yours is not?

It is amusing to watch you attempt to address the ontology of spacetime when you have no idea what spacetime is and harbor so many gross misconceptions regarding general relativity.

I also find it amusing, but at the same time it is really bothersome to see the same misinformation repeatedly posted. As someone who doesn't have a firm grasp of relativity, I find it harmful to my attempts to understand relativity, and I think it does not belong in a relativity forum.

I also think it's sad that what is claimed to be an expertise in the ontology of spacetime, seems to me to be based not only on a lack of understanding of relativity, but also some confusion about the very meaning of ontology (due to the apparent assumptions that for spacetime to have properties implies that it is an entity). I am not an expert on the philosophy of science, but to me this seems naive.

Btw, presentism is another study which inquires beyond local frames of reference and "time environments" and the usual "who sees what and when" of relativity. It can be ignored, but it will not go away. The most simple and obvious illustration of presentism is that now is now for both earth and sun even though it obviously takes over eight minutes for sunlight to travel to earth.

Then, this "now" can be extended to "now everywhere," that the universal present is not limited by lightspeed.

Now this is an interesting topic relevant to my interests. But I think discussion of it is off topic and probably belongs in the Speculations forum anyway.

Edited by md65536
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...I am saying that the obviously curved trajectories of objects effected by gravity does not verify the actual existence of an entity "the spacetime manifold." There is a lively ongoing debate among well credentialed scientists and philosophers of science about what "spacetime" is (if anything.)...

The spacetime manifold (as DrRocket points out) refers to the world line (the path, if you will) of an object or event through space and time. To avoid misleading you, I again quote Dr. Rocket's post: "...In fact there is no clear separation of space and time, except locally. Spacetime is not space and time, but an intertwined amalgamation of both..."

This is the specific entity in the world of observational phenomenon that the phrase denotes. The formulas of General Relativity have successfully predicted the motion of celestial bodies as varied as the tiny planet Mercury to multi-stellar-mass orbiting neutron stars based on this thing that scientists call spacetime.

What more do you want in the way of a definition or "meaning"?

Chris

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I will try to keep this topic relevant, but GR based theory in answer to the topic requires discussion of spacetime, including what it is.

First, to back up a bit...

csmyth:

I just don't understand what you're trying to get at here. As I understand it,

"referent" is defined as: "The specific entity in the world that a word or phrase

identifies or denotes."

The inertial path of objects effected by gravity always have curved trajectories. In

the real world of observable phenomenon this is the referent of the phrase

"curvature of the spacetime manifold".

Are you saying that it's something different?

Repeating, " I am saying that the obviously curved trajectories of objects effected by gravity does not verify the actual existence of an entity "the spacetime manifold."

Also, from a previous but as yet unanswered question, is quantum theory of gravity not an alternative to GR's curved spacetime theory?

Since all GR texts and websites assume "curved spacetime" as central to understanding the theory, how is it that the ontology thereof (see recent references) is not relevant to this discussion of the shape and size of the universe?

md65536, replying to my, "GR assumes that space is an entity."...

I should have said... "that spacetime is an entity," in that "it" is said to be curved by gravity. (Objects' trajectories are obviously curved by gravity, but the theoretical 'malleable medium' begs for ontological inquiry. As for "space itself," mainstream cosmology posits that space is an entity which "expands." )

Citation? I don't think that's true.

You've stated in this thread that you don't consider space to be an entity. Would you then conclude that GR is based on false assumptions? Would you also say that because of this, GR can be safely ignored, and that an understanding of GR is irrelevant to this discussion?

Yes, not an entity. It is reasonable to assume that space is empty volume, no-thing-ness. If "it" is considered to be some "thing" then ontology asks, "What?"

No, GR has "a mountain of evidence" for predicting local gravitational effects. (It's forte', not global cosmology, this thread's focus.) 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.

On the website that you are referencing, they have the question "Is Space Infinite?"

on their Open Questions page: http://www.spacetimesociety.org/openquestions.html

Your source does not seem to agree that the question has been answered.

Others in this thread accept that it remains an open question. So how is it that

their minds are made up while yours is not?

I rely on reason, that "and end of space" is an absurd concept in the real cosmos/universe, regardless of what kinds of "shape and size" we can conceive of as models or how complicated the many varieties of theoretical "manifolds" can be, whether compact or not, open or closed, based on metaphysical "higher dimensions," etc... etc.

Even the three standard varieties of possible "shapes of cosmic space" beg the question, what lies beyond any conceivable shape?

The reason an end of space is absurd is that all such boundaries are just concepts, not some kind of "wall out there." And then of course there is the further absurdity of ignoring the question, "What is beyond this wall?"

The human mind has a tough time with infinity, but this does not mean that, therefore the universe must be finite, just because are minds and concepts are.

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Why is it reasonable to asume that space is an empty volume ???

Maybe 'ontology' cannot explain virtual pair creation and all the effects attributed to this phenonenon, but GR/QM can.

There is an energy associated with 'empty' space/time. This energy accounts for various effects ( such as the above pair creation and Casimir effect ) and predictions which are still being worked on ( possibly even the origin of the universe and its expansion ). So yes space/time is an entity, and it has many measurable quantities. Because philosophy and ontology do not bother with measurable quantities and experiment doesn't mean space/time is not an 'entity'.

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