What is "spacetime" really?

[Michael Mooney]

From the "new thread" on th "absolute now"... a piece more appropriate back here:

 

Likewise the assumption that space is something that expands, contracts, assumes shape, etc. is the the assumption all "spacetime" theorists make as a given... that ontologically space *is something* that has the above properties. Non-Euclidean "space" is assumed as a fact or given, so well established as to preclude argument. It is not.

 

(See again the piece on "The Ontology and Cosmology of Non-Euclidean Geometry" at

The Ontology and Cosmology of Non-Euclidean Geometry

See also the several links given previously on the "ontology of spacetime" "It" is not, in fact, and established and "proven" entity.

 

I am really tired of hearing that I simply don't understand relativity. I have made my criticisms of it and my acceptance of parts of it very clear many times... yet in such a long thread as "spacetime" late comers keep repeating the SOS for criticism that Modest and others have hammered on for 80 some pages.

 

From the git-go, page one Tormod started with a reply **assuming** "spacetime" as an established reality, and no one yet has addressed the ontological question "what is it, really? Everyone has simply "followed the leader" and ignored the question."

 

(So... are you going to shift the latter point back to the original thread or what? Or should I transcribe the ontology stuff back to "spacetime?")

Michael

[modest]

(See again the piece on "The Ontology and Cosmology of Non-Euclidean Geometry" at

The Ontology and Cosmology of Non-Euclidean Geometry

See also the several links given previously on the "ontology of spacetime" "It" is not, in fact, and established and "proven" entity.

 

The article you link says:

Einstein's general theory of relativity proposes that the "force" of gravity actually results from an intrinsic curvature of spacetime, not from Newtonian action-at-a-distance or from a quantum mechanical exchange of virtual particles. If we view Einstein's philosophical project as an answer to Kant's Antinomy of Space--to explain how straight lines in space can be finite but unbounded--the introduction of time reckoned as the fourth dimension suggests that we may separate the intrinsic curvature of spacetime into curvature based on the relationship between space and time: we can think of Einstein's theory as one that satisfies the axiom of open ortho-curvature, with the peculiarity that it is indeed time, rather than a higher dimension of space, that is posited beyond our familiar three spatial dimensions. This is a metaphysically elegant theory, since is gives us the mathematical use of a higher dimension without the need to postulate a real spatial dimension beyond our experience or our existence.

I fail to see why you are linking an article which claims Einstein's spacetime is "a metaphysically elegant theory" and interprets spacetime curvature in a very classical way (mostly focusing on intrinsic vs. extrinsic). Do you agree with this article? For example, where it says:

When we are not in free fall, e.g. standing on the surface of the earth, we feel weight, just as according to the equivalence principle when we are being accelerated by a force (e.g. a rocket engine) in the absence of a gravitational field. These are indeed equivalent because in each case we are moving relative to space according to our own frame of reference. When we are accelerated by a rocket we say that we move in the stationary reference of external space; but when we are accelerated standing on the surface of the earth, it is space itself that is displaced (by time) relative to us. Either we move through space, or space moves through us. That is the experience of weight.

Is this an interpretation you advocate? If not, why are you linking this article?

 

~modest

[Michael Mooney]

Modest,

The article covers a lot of ground, both pro and con on all sides of the topic. You picked the parts you like which support your bias.

 

Here are some of mine (please consult text for context);

 

"It is amazing that such things need to be said, and it is particularly revealing that the responses Agassi got to his questions reminded him of the intolerance of religious dogmatism.

 

Nevertheless, there is still rarely a public word spoken about the philosophical intelligibility of Einstein's own theory: the Relativistic theory of gravitation. That theory rests on the use of non-Euclidean geometry. There are still many good questions to ask about non-Euclidean geometry; but in treatment after treatment in both popular expositions and in philosophical discussion, the questions consistently seem pointedly not to get asked."

 

M: I have been asking the ones which reflect my challenge to spacetime in particular and non-Euclidean space/cosmology in general.

 

" On the other hand, in March of 1976, Scientific American also published an article by J. Richard Gott III (et al.), "Will the Universe Expand Forever?" This article detailed the evidence then available indicating that the universe was not positively curved, finite and unbounded, as Einstein, and everyone since, has wished. Instead, the universe is more likely to be infinite, either with a Lobachevskian non-Euclidean geometry, or even with a Euclidean(!) geometry after all.

(bold the latter)

 

My problem is that the philosophical implications of the likelihood that observation will continue to reveal an infinite universe (despite "missing mass," "dark matter," etc.) have not been explored.

 

M: Contradicting what you said earlier, the more "missing mass" that is found, the more likely it will be that a cyclical model is accurate. But "my model" is both cyclical and a very minute part of "infinite space" in which "zillions" of cosmi, like ours might exist.I like his openness to "an infinite universe."

 

"In what follows I will attempt to ask questions about non-Euclidean geometry that I do not often, or ever, see asked. In section three I will then briefly attempt to suggest how the philosophical implications Einstein's application of geometry in his theory of gravitation may be reconsidered....

§2. Curved Space and Non-Euclidean Geometry "

 

M: Please review this whole section on how non-Euclidean geometry came out of (to my observation) 'forcing' parallell lines to converge by sheer fore of creative imagination.

 

"This happened because non-Euclidean planes can be modeled as extrinsically curved surfaces within Euclidean space. Thus the surface of a sphere is the classic model of a two-dimensional, positively curved Riemannian space; but while great circles are the straight lines (geodesics) according to the intrinsic properties of that surface, we see the surface as itself curved into the third dimension of Euclidean space. A sphere is such a good representation of a non-Euclidean surface, and spherical trigonometry was so well developed at the time, that it now is a little surprising that it was not the basis of the first non-Euclidean geometry developed [cf. Gray ibid. p.171]. However, as noted, such a geometry does contradict other axioms that can easily be posited for geometry. Accepting positively curved spaces means that those axioms must be rejected. Also, and more importantly, these models in Euclidean space are not always successful. The biggest problem is with Lobachevskian space."

 

M: Please review that problem.

"This raises two questions: 1) what can we spatially visualize? (a question of psychology) And 2) what can exist in reality? (a question of ontology).................... The formulas gave meaningfulness to non-Euclidean geometry as common sense never could."

 

"The Euclidean nature of our imagination led Kant to say that although the denial of the axioms of Euclid could be conceived without contradiction, our intuition is limited by the form of space imposed by our own minds on the world. While it is not uncommon to find claims that the very existence of non-Euclidean geometry refutes Kant's theory, such a view fails to take into account the meaning of the term "synthetic," which is that a synthetic proposition can be denied without contradiction."

 

"If we are unable to visualize non-Euclidean geometries without using extrinsically curved lines, however, the intelligibility of Kant's theory is not hard to find.......................... Non-Euclidean geometry did not change our spatial imagination, it only proved what Kant had already implicitly claimed: the synthetic and axiomatically independent character of the first principles of geometry. "

 

"In light of the distinction between intrinsic and extrinsic curvature, we must consider all the kinds of ontological axioms that will cover all the possible spaces that Euclidean and non-Euclidean geometries can describe.......................... This could be called the axiom of hetero-curvature, and it would make true non-Euclidean geometry possible, since lines with non-Euclidean relations to each other would be straight in the common meaning of the term understood by Euclid or Kant. "

 

"A further ontological distinction can be made. Even if the ortho-curvature axiom is true, a functionally non-Euclidean geometry would be possible if a higher dimension that allows for extrinsic curvature exists but is hidden from us................................ This gives us three possibilities:

 

 

That, with the axiom of closed ortho-curvature, there are no true non-Euclidean geometries (and no spatial dimensions beyond three), but only pseudo-geometries consisting of curves in Euclidean space;

 

That, with the axiom of open ortho-curvature, there are no true non-Euclidean geometries but we may be faced with a functional non-Euclidean geometry in Euclidean space whose external curvature is concealed from us in dimensions (more than the three familiar spatial dimensions) not available to our inspection--this is an apparent hetero-curvature;

 

And that, with the axiom of hetero-curvature, there are real non-Euclidean geometries whose intrinsic properties do not ontologically presuppose higher dimensions (whether or not there are more than three spatial dimensions)."

 

M: I've got to go now. I'll continue with comments on the rest next time.

I don't ordinarily like to quote so much, but i doubt if anyone besides you has read this piece, so in- depth detail as it was written is important.

As You know, I especially liked the stuff toward the end on the more "humble" place of mathematics in the context of what it actually refers to in the real world... if anything!

 

Next time...

 

Michael

[watcher]

That, with the axiom of closed ortho-curvature, there are no true non-Euclidean geometries (and no spatial dimensions beyond three), but only pseudo-geometries consisting of curves in Euclidean space;

 

"it is hard to follow what the article wanted to conclude. which is to imagine that there are two kinds of space. a non-euclidean space overlayed in the euclidean space. its a bit absurd.

it is easier to imagine that there is only one kind of space that flexed to become flat or curved.

iow, the real space defines itself to become euclidean or non so that curvature, emptiness, flatness are its properties.

 

That, with the axiom of open ortho-curvature, there are no true non-Euclidean geometries but we may be faced with a functional non-Euclidean geometry in Euclidean space whose external curvature is concealed from us in dimensions (more than the three familiar spatial dimensions) not available to our inspection--this is an apparent hetero-curvature.

 

And that, with the axiom of hetero-curvature, there are real non-Euclidean geometries whose intrinsic properties do not ontologically presuppose higher dimensions (whether or not there are more than three spatial dimensions)

 

concealed dimensions and non-euclidean geometries imply/require that there are higher dimensions.

[lawcat]

There is only one thing I agree with in that article: There are no spatial dimensions beyond three, for all practical purposes.

[watcher]

well im an electrical engineer and i only need ohm's law to make a living. LOL

[modest]

Modest,

The article covers a lot of ground, both pro and con on all sides of the topic. You picked the parts you like which support your bias.

This doesn't answer my question nor do I believe you're capable of doing so. You are linking an article which supports a philosophy of relativistic curved spacetime while you claim such a thing doesn't exist. There is simply no logical explanation you could give. The article is investigating the ontology of non-Euclidean geometry and you're saying non-Euclidean geometry doesn't exist. If you can't see the difference between those two things.... :hyper:

 

I don't ordinarily like to quote so much

and you should not according to the site rules and fair use copyright laws, so... not a good idea for future reference.

 

~modest

[Michael Mooney]

This doesn't answer my question nor do I believe you're capable of doing so. You are linking an article which supports a philosophy of relativistic curved spacetime while you claim such a thing doesn't exist. There is simply no logical explanation you could give. The article is investigating the ontology of non-Euclidean geometry and you're saying non-Euclidean geometry doesn't exist. If you can't see the difference between those two things.... :hyper:...

 

This: ..."nor do I believe you're capable of doing so"... is as rude and insulting as it gets. I hereby issue you a common citizen's citation.

It has no "teeth" but your very nasty insult will be obvious to everyone.

You continue:

'The article is investigating the ontology of non-Euclidean geometry and you're saying non-Euclidean geometry doesn't exist. If you can't see the difference between those two things.... ;)

 

I'm agreeing with the article that non-Euclidean geometry is "synthetic." Do you grasp the difference... the ontological meaning of non-Euclidean as synthetic... or the difference between intrinsic and extrinsic curvature... as to which is "synthetic" and which is Euclidean? Apparently not.

 

You are mistaken that "this supports a philosophy of relativistic curved spacetime..." and the above quote is totally false.

 

It is actually a quite well balanced inquiry into both sides of the issue... which is why I have repeatedly bumped it and quoted it in this thread.

I was in the process of quoting and commenting on parts of it which allowed the possibility of a legitimate Euclidean space/cosmology, and there was lots more to come.... until...

 

and you should not according to the site rules and fair use copyright laws, so... not a good idea for future reference.

 

... in reply to my, "I don't ordinarily like to quote so much"...

 

So now I'm gagged against further quoting, not knowing how much is too much. Apparently your quotes were OK, so how many words do I get to quote before the quote police give me another "citation" as I struggle to quote just enough to show that this article looks fairly at both sides... and is not...as you insist, a blanket endorsement of the non-Euclidean camp, i.e., a full vindication of the established ontological reality of "spacetime" as Einstein and Minkowski presented it.

 

I see no fairness in this kind of "moderation." And You have consistently condescended upon me in the manner of this post throughout this thread.

 

You only see what you want to see in this article.

 

Maybe if I just cite short quotes and give commentaries to this point... or maybe I should wait for your word limit per quote. Hopefully that will also give the total word limit for all quotes so I will not be violating any copyright laws.

 

This is ridiculous.

 

Michael

[modest]

not knowing how much is too much.

It's actually quite complicated:

 

Fair use - Wikipedia, the free encyclopedia

 

Use your best judgment, I'm sure it'll be fine.

 

~modest

[maddog]

(See again the piece on "The Ontology and Cosmology of Non-Euclidean Geometry" at

The Ontology and Cosmology of Non-Euclidean Geometry

I am fascinated why you keep pointing to this paper... Except for the following points

with supporting quotes.

1. This paper is more about dismissing Non-Euclidean Geometry than any discussion of

Ontology or Cosmology

A further ontological distinction can be made. Even if the ortho-curvature axiom is true, a functionally non-Euclidean geometry would be possible if a higher dimension that allows for extrinsic curvature exists but is hidden from us. We must consider whether only the three dimensions of space exist or whether there may be additional dimensions which somehow we do not experience but which can produce an intrinsic curvature whose extrinsic properties cannot be visualized or imaginatively inspected by us. Thus we should distinguish between an axiom of closed ortho-curvature, which says that three dimensional space is all there is, and an axiom of open ortho-curvature, which says that higher dimensions can exist. This gives us three possibilities:

1. That, with the axiom of closed ortho-curvature, there are no true non-Euclidean geometries (and no spatial dimensions beyond three), but only pseudo-geometries consisting of curves in Euclidean space;
   
2. That, with the axiom of open ortho-curvature, there are no true non-Euclidean geometries but we may be faced with a functional non-Euclidean geometry in Euclidean space whose external curvature is concealed from us in dimensions (more than the three familiar spatial dimensions) not available to our inspection--this is an apparent hetero-curvature;
   
3. And that, with the axiom of hetero-curvature, there are real non-Euclidean geometries whose intrinsic properties do not ontologically presuppose higher dimensions (whether or not there are more than three spatial dimensions).
   

It is necessary to keep in mind that these axioms are answers to questions concerning reality that would be asked in physics or metaphysics and are logically entirely separate from the status of geometry in logic or mathematics or from our psychological powers of visual imagination. The second axiom leaves open the question whether "hidden" dimensions are just hidden from our perception or actually separate from our own dimensional existence. With these ontological alternatives in mind, we can now examine the philosophical implications of Einstein's use of non-Euclidean geometry.

So even the paper does not prevent Non-Euclidean Geometries itself, maybe an attempt

to marginalize to only Case 3. Funny thing that Case 3 being the most general case

is "everything else".

 

See also the several links given previously on the "ontology of spacetime" "It" is not, in fact, and established and "proven" entity.

I never claimed an "entity" attribute to "spacetime" -- you have. ;)

From the git-go, page one Tormod started with a reply **assuming** "spacetime" as an established reality, and no one yet has addressed the ontological question "what is it, really? Everyone has simply "followed the leader" and ignored the question."

This was likely that Tormod (like myself) had attempted to "answer" you in the "vein of"

"what is the spacetime, really" -- like you didn't know and would like to "know". Not like

you already had an opinion and wanting to "catch" us "in the act". :thumbs_do:thumbs_up

 

maddog

[modest]

So even the paper does not prevent Non-Euclidean Geometries itself

 

In fact, if you read further you'll see it gives Einstein's General Relativity as an example of such a *truly* non-Euclidean geometry—calling it elegant for how it has no need for embedded curvature in a higher Euclidean dimension. :thumbs_up

 

~modest

[Pyrotex]

This: ..."nor do I believe you're capable of doing so"... is as rude and insulting as it gets. I hereby issue you a common citizen's citation.

It has no "teeth" but your very nasty insult will be obvious to everyone....

It is NOT obvious that he was insulting you. If, as he says, you have quoted a text that assumes the existance of something that you have been consistently denying, then you might be unable to bridge the gap between the quoted text and your stand -- and this would not reflect on you or your judgement at all. It would not be an "insult", just a reflection that the two POVs are incompatible. He could just as well have said: "nor do I believe anyone is capable of doing so".

:thumbs_up

[Michael Mooney]

Modest,

Rather than continue with long quotes and commentaries on the article in question, I will re-focus on the very core of the ontological comparison of Euclidean vs non-Euclidean space/cosmology.

(Maddog too picked up on this section as central to the viability of the Euclidean model... which is the main reason I like this article so much)... Thanks again for originally providing the link.

I ask you to reply to the following before I proceed further into the essay... and the place of Math in the overview of "it all.'.. and into the "synthetic" nature of non-Euclidean as compared with Euclidean.

 

Thus we should distinguish between an axiom of closed ortho-curvature, which says that three dimensional space is all there is, and an axiom of open ortho-curvature, which says that higher dimensions can exist. This gives us three possibilities:

 

1. That, with the axiom of closed ortho-curvature, there are no true non-Euclidean geometries (and no spatial dimensions beyond three), but only pseudo-geometries consisting of curves in Euclidean space;

2. That, with the axiom of open ortho-curvature, there are no true non-Euclidean geometries but we may be faced with a functional non-Euclidean geometry in Euclidean space whose external curvature is concealed from us in dimensions (more than the three familiar spatial dimensions) not available to our inspection--this is an apparent hetero-curvature;

3. And that, with the axiom of hetero-curvature, there are real non-Euclidean geometries whose intrinsic properties do not ontologically presuppose higher dimensions (whether or not there are more than three spatial dimensions).

 

For openers, two out of three possibilities that " there are no true non-Euclidean geometries" ain't bad. And the possibility that non-Euclidean models are "only pseudo-geometries consisting of curves in Euclidean space"... hits the nail right on the head for me.

See why I like this essay so much?

 

I'll leave it there for now and await your reply. But I really "dug deep" into the rest of the essay and would welcome further dialogue on it.

 

Michael

[modest]

The article lists three possibilities. Throughout this thread you have consistently rejected the possibility of the third. The article doesn't do that. You clearly need to reassess your assumption that the universe must be Euclidean.

 

I don't know what else there is to say.

 

~modest

[maddog]

For openers, two out of three possibilities that " there are no true non-Euclidean geometries" ain't bad. And the possibility that non-Euclidean models are "only pseudo-geometries consisting of curves in Euclidean space"... hits the nail right on the head for me. See why I like this essay so much?

I'll leave it there for now and await your reply. But I really "dug deep" into the rest of the essay and would welcome further dialogue on it.

As Modest says below there were three (equally valued) possibilities {1, 2, 3} from this

website. So this is not probabilities, so "2 out of 3" means nothing.

The article lists three possibilities. Throughout this thread you have consistently rejected the possibility of the third. The article doesn't do that. You clearly need to reassess your assumption that the universe must be Euclidean.

 

I don't know what else there is to say.

IMHO I think your disdain for the third possibility derives from you "shun" as you call "maths".

You simply do not understand and so proselytize for renunciation of "three". This

practice of "ignorance" was often used in the "burning of witches" too.

 

:omg::shrug:

 

maddog

[lawcat]

Eucledian Space is perfect for us as a tool for defining position. No more, no less is necessary. Eucledian geometry is sufficient, universally.

When we introduce time as a dimension, we automatically introduce motion and relativity. Then, we make an ontological judgment that everything moves, or changes, in time; and therefore we must define position by an additional parameter--time.

For this reason Eucledian space is practically decribed in terms of polar system, where position is decribed in terms of a vector r, and the angle(s). This is particularly convenient for all types of motions--linear or oscilatory, or a combination.

 

Now, there can be infinately many axis, or dimensions. But if we do that, then we choose not have the axis be orthogonal, but less than orthogonal. (we choose to have the angle between axis less than 90). If the angle chosen between the axis approaches 0, then the number of dimensions--axis--approaches infinity. This approach can be adopted, but it is not practicial by any stretch of imagination.

If we say that a plane--or a frame--is an area bound by two or more axis--however you want to envision it--then there can be infinately many planes minus 1, with respect to number of axis. Again, this serves no practical purpose, other than visualisation of vector possibilities.

[watcher]

If we say that a plane--or a frame--is an area bound by a two or more axis--however you want to evnision it--than there can be infinately many planes. Again, this serves no practical purpose, other than for visualisation of vector possibilities.

 

no practical purposes?

am i to believed that the employment of higher dimensions in our equations are just a whim? and were not solutions that reflect to the physical behaviors on our scientific experiments?