The universe's boundaries and origins

1. Jul 18, 2008

thomasxc

If the entire universe expands from a single point in spacetime, and expands in a uniform manner, then the universe has a boundary, regardless how fast or whether or not it’s still expanding. If it has boundaries, then what’s on the other side? One might say that the big bang was/is only the expansion of matter into nothingness. But then the question arises: if, the universe has borders, how did something come to exist in the infinity of nothingness? This gives rise to another question: how do we differentiate nothingness from the near absolute vacuum of deep space? So by deduction, there must be more to empty space if it is to be different from nothingness-if there is nothingness on the outside. i cant make much sens of it. can anyone else?!

2. Jul 18, 2008

mathman

Not so - you are implicitly assuming the universe geometry is Euclidean. It isn't.

3. Jul 18, 2008

marcus

Mathman is quite right, Thomas. Your reasoning is incorrect from the word go, because of the pre-1850 way you imagine space.

People who can't get past 1850 hold up progress. Please get past that blockage---it really isn't hard---and start helping rather than hindering.

here's the story.

the best theory of gravity we have----the only one that predicts everything to high precision and really works---is vintage 1915 General Rel. People have tried to find better for generations and failed---and they have tried for 90 years to catch it out, in disagreement with some observational test, and it passes every test.

this theory of gravity requires the mathematics of manifolds developed around 1850 by Riemann.
Using that mathematical language one can (just to take an example) easily imagine and describe and calculate with a boundaryless 3D continuum analogous to the 2D surface of a sphere, and which is not immersed in any higher dimension surroundings.*

So here's the deal: your reasoning is wrong unless you take us back to the pre-1850 geometry of infinite 3D right-angle graph paper such as Newton or Descartes might have imagined----the Euclidean idea of space. If you want to eliminate the progress in mathematics made since 1850, and go back there, then it is incumbent on you to provide us with a theory of gravity which works as well for precision calculation as Einstein Gen Rel, but which uses the rigid foursquare Euclidean space instead of the continuum that mathematicians have been using since 1850 thanks to Riemann.

*that is just one of the many 3D geometries you get as a reward for switching over to the post-1850 continuum. I'm not saying it is the particular one the universe uses---it is just an example of a boundaryless manifold---a 3D continuum without edges. General Relativity is not dependent on any one particular geometric setup---it uses the formalism in a general way.
===================

Also look at this:
Thomas, as far as I know there is no astronomer who says this. Maybe I'm wrong. Can you give us an example of some professional writing where a real scientist says "the entire universe expands from a point in spacetime"? If you can, please give a link to click on. It would be interesting to see.

A common mainstream science view is that the universe IS all of spacetime together with whatever matter fields.
No surround need be assumed, no boundary needs to be imagined. The mathematical model allows space (in the sense of distances) to contract (in the sense of distances decreasing systematically) and likewise to re-expand.
So one version we are hearing a lot about recently has a socalled bounce. there is contraction to a point where the density becomes so high that quantum effects make gravity repel and then contraction reverses and the usual bigbang expansion story begins.

that contraction and expansion involves the whole of space----it is not something that happens IN space.
the bounce is something space and matter do together---as one organic unity.
it is not something that matter does, Newton-style, in the midst of a static empty space (that would have been the pre-1850 attempt at a description)

Also please keep in mind that there are several different pictures currently being studied besides the bounce picture. There is a book coming out next year with chapters by a dozen or more authors, laying out the different ideas. I wont waste time trying to list all of them that I can remember. The bounce picture has plenty of competition. But all the approaches are grounded in post-1850 kind of geometry. Keep an eye out for the book. Here is the amazon page

http://www.amazon.co.uk/Beyond-Big-Bang-Prospects-Collection/dp/3540714227

https://www.amazon.com/Beyond-Big-Bang-Prospects-Collection/dp/3540714227

Last edited: Jul 18, 2008
4. Jul 18, 2008

Peter (IMC)

The way I understand it, thomas is that what you consider to be the whole universe now, is, in a way, just as big (infinite even) now as it was at the moment of the big bang. It never was a point in space that started to grow and became bigger from one side to the other. It's more like that everything that you consider to be space was the same place because time didn't exist in the exact moment of the big bang. And without time, our perception of distance doesn't exist. Then distances between matter started to grow, not because they were moving away from each other but because space it self was expanding and what ever is inside that space, moved with it. But there isn't an actual force pulling objects away from each other.

In fact, the way I understand it, 2 objects are actually attracting each other, it's just that the further away they are from each other, the less strong that attraction is, so over big enough distances, they are moving away from each other with space, faster than they can attract each other. So locally matter atracted itself into big bubbles of matter and in between were created big voids of empty space, where the expansion of space is just making them go further appart.

5. Jul 19, 2008

jonmtkisco

Hi Thomasxc,
Take a look at https://www.physicsforums.com/showthread.php?t=235035" thread where the model of a universe with a possible center and edges is discussed.

I have yet to read any serious explanation for why this model is ruled out by GR or current observations. Based on everything I've read, the model is not at all ruled out.

A scientific approach to this topic would benefit from more thoughtful analysis and less dismissiveness. Cosmology doesn't need more crackpots, but it also ought not to be treated as a popularity contest.

Morever, scientific demonstration of the physical reality of a 4th spacial dimension, which is crucial to the physical reality of GR mathematical prediction of spatial curvature, is utterly lacking. I find it distressing that mainstream cosmology has skipped over this huge missing link in the physical theory. There is a fundamental distinction to be drawn between the accurate mathematical predictions of GR, and the exotic physical reality popularly associated with that math by mainstream cosmology. The physical reality may eventually be demonstrated to be quite a bit more mundane. Like (prepare to be shocked!) the universe may be discovered one day to have only the 3 spatial dimensions we know and love (along with the time dimension if you want to think of it that way) and the underlying geometry might indeed be Euclidean. Even if that turns out to be so I expect the mathematical predictions GR makes about gravitational action will be reaffirmed.

Jon

Last edited by a moderator: Apr 23, 2017
6. Jul 20, 2008

jonmtkisco

Here's a relevant excerpt from James B. Hartle's excellent textbook "Gravity - An Introduction to Einstein's General relativity" (2003) p. 368:

Emphasis added. So, a Euclidean universe with a center and an edge would not alter GR's observational predictions. Note the key bolded word "assume". It's a bit startling to see it stated that a centerless and edgeless universe is merely an assumption. Yes there's no evidence against it, but Hartle in effect admits there's no specific evidence for it either, other than the obvious point that if there is an edge, we are too far away from it to observe (at least so far) any phenomena that specifically reveal its existence to us.

Reading between the lines a bit, it seems that mainstream cosmology has opted for the mathematical elegance of a theory based on a "strong" cosmological principle that requires 4 spatial dimensions, over a supposedly messier (I question that) theory based on a "weak" cosmological principle that requires only our tried-and-true 3 spatial dimensions.

Jon

Last edited: Jul 20, 2008
7. Jul 20, 2008

marcus

?

never heard anyone say that it requires a 4th spatial dimension in order for a 3D surface to be curved---or to mathematically define curvature

in GR an extra spatial dimension is not required----curvature is defined intrinsically just fine.

any differential geometry textbook or GR text should set you straight on this, Jon.

See if you can find an online GR text where an extra spatial direction is needed to define curvature and show us the reference.
============

Basic reasoning by analogy is that flatlanders have no need of an extra spatial dimension in order to discover if their world is curved.. They can find out just by measuring distances and angles. If their 2D world happens to be embedded in some 3D space, fine---the curvature will show up externally there. But if their flatland DOESN'T happen to be immersed in some surrounding space that is fine too. As long as the distances and angles are what they measured before, their flatland still has the same intrinsic geometry, same curvature etc. No physical need for an extra dimension exists.
=============

Sean Carroll has an online GR textbook. You might look there and see if an extra spatial dimension is ever invoked.
Good luck

Last edited: Jul 20, 2008
8. Jul 20, 2008

Wallace

Good point Marcus, the balloon analogy often confuses people who wrongly assume that there must 'really' exist a 4th spatial dimension playing the analogous role of the 3rd dimension of the Balloon. It's an analogy, nothing more. Like all analogies, it is folly to try and push the analogy to ask any question that the analogy was not specifically designed to demonstrate. The balloon analogy just demonstrate how a homogeneous expansion looks at every point to be expansion away from that point. That is it. Nothing else should be attempted to be learned from that analogy and this kind of confusion it was follows from trying to do so.

The closed, finite, FRW universe does not imply the existence of any more than the regular 3 spatial and one temporal dimensions.

9. Jul 20, 2008

jonmtkisco

Hi Wallace,

Of course the FRW metric itself does not imply the existence of more than the regular 3 spatial dimensions -- for example, the case where the universe is expanding from a single origin point is easy to portray as a solid FRW model in 3 dimensions.

But 4 spatial dimensions are indeed required in order for an FLRW universe to expand "from every individual point in the universe, in all directions simultaneously," where, by definition, there is no single origin or center point. Try to build a solid model of that... Better textbooks feel obliged to mention that it can't be done in 3 dimensions.

Hi Marcus,

Sorry to hear that you've never read that it is impossible to construct a 3 dimensional solid object which exhibits 3 dimensional surface curvature. CompuChip and I recently wrote about this very subject on https://www.physicsforums.com/showthread.php?t=243442".

Please explain how you would go about constructing a 3 dimensional solid object which exhibits 3 dimensional surface curvature. Sure, that's a rhetorical invitation, because we all know it's impossible. The fact that a 3 dimensional surface is capable of being embedded mathematically into a 3 dimensional manifold does not mean it is capable of physical embodiment in 3 dimensions. All of us should be frustrated that the advanced geometry textbooks you perhaps have in mind aren't more clear about that distinction.

It's pretty obvious to anyone who is thinking rather than reciting, that mathematical/geometrical theory and tangible, locally touchable physical reality are two very separate things, which may or may not coincide on any give topic.

Jon

Last edited by a moderator: Apr 23, 2017
10. Jul 21, 2008

Wallace

GR is a 4D theory, 3 spatial and one temporal. That's it. Nothing that comes from GR can possibly suggest that any more dimensions exist (that's not to say they don't, just that GR does not describe there effects if they do).

In Euclidean space you need extra dimensions to define curvature, because the space itself is not curved. In general, metric spaces, such as those found in GR, do have curvature. A curved N dimensional manifold can either be described as a curved N dimensional manifold, or a curved surface within a higher dimensional space. What you can do is shift the intrinsic curvature of the space into curvature of the surface in higher dimension. The maths looks different but the reality is the same. Don't mistake co-ordinates for reality!

Have a look at section 3.1 of Peacock (page 69 in my copy, maybe different in other editions?). It describes how a constant time slice of an isotropic, homogeneous, closed Universe can be defined as equivalent to a Euclidean 4 sphere by a suitable transformation. This is interesting, but it does not really mean that if the Universe is finite it has 5 dimensions and 4 if not.

People have played around with non 4D GR like theories, the conservation laws and then all different and you get strange results. For instance in 2D, gravity is repulsive, and for other dimensions gravity no longer goes to 1/r^2 for the Newtonian limit. Therefore the physics, which is what is real, is intimately connected to the number of true spatial co-ordinates. You can't just add extra ones in and think it won't change everything.

11. Jul 21, 2008

jonmtkisco

Hi Wallace,

I have no objection to most of what you say. But it is quite straightforward to demonstrate that a model of 3-dimensionally curved space or "centerless space" cannot be physically constructed in 3 dimensions.

An isotropically expanding sphere with a unique center is easy to model in 3 dimensions -- just start with a sphere of arbitrary size and add on nesting shells of ever increasing size - like Russian dolls. The existence of a unique "center" or coordinate origin is never in doubt, at least until infinite size is attained.

Now try constructing a solid model (in incremental pieces) of an isotropically expanding sphere with no center. It can't be built. It certainly isn't modeled by an expanding loaf with raisins, which has an obvious center in 3 dimensions. It's extremely difficult to even imagine it in 3 dimensions let alone to construct it. At best it can be constructed only as a 2-dimensional model of such a surface on a 3-dimensional manifold, e.g the surface of an expanding balloon.

It's just not physically real, in 3 dimensions. It's real only in people's heads -- as a mathematical/geometrical construct. And it can be physically real, but only if there are 4 spatial dimensions.

Jon

Last edited: Jul 21, 2008
12. Jul 21, 2008

Wallace

Your reasoning is correct, if all spaces are Euclidean. General Relativity is founded on the idea that in general the space-time of our Universe is non-Euclidean. You can take the view that only Euclidean spaces can be 'real' but then you are forced to use a theory of gravity other than GR. What you cannot do is use GR to make a prediction and then violate an assumption of the theory that made that prediction in order to derive a physical interpretation! You can't use the GR result for an closed Universe, then pretend that aspects of GR don't exist when making an interpretation!

The FRW metric can describe a closed, finite, homogenous and isotropic universe and that metric contains only 3 spatial dimensions, and was derived from a theory relying on there being only 3 spatial dimensions.

I didn't make the Universe so I can't apologise for relativity being difficult to understand, but that's just how it is.

13. Jul 21, 2008

Haelfix

Jon distinguish between the topology of spacetime and the metric of spacetime. The two are related but not necessarily restrictive.

So for instance you CAN have a big bang occuring at one point, just like you can have a big bang occuring everywhere.

For instance in the closed FRW universe, from the point of view of the metric, you can just as easily make the topology a flat plane(s), as well as a sphere as well as various other multiple connected topologies. In the case of a sphere, all homotopic curves contract to a point, so in that case you have a unique origin point.

But for the case of a flat plane (identify the boundaries), you have no such thing, all points feel the big bang, even though the distance between them (even arbitrarily far apart) shrinks to zero. All this is the same exact metric, but what occurs at the boundaries differs physically (and presumably its observable in principle).

Other than that, spacetime does not need to be embedded in a higher space. In general, you actually need twice the amount of dimensions to embed an arbitrarily complicated geometry (Nash embedding theorem).

14. Jul 21, 2008

jonmtkisco

Hi Wallace and Haelfix,

Any geometry can be "physically real" in 3 dimensions if, and only if, we can build a solid 3 dimensional model of it in our real world. That is a very straightforward criterion of what "physically real" means; no subjective judgment is involved. If space can be curved in 3 dimensions, then we should be able to construct a solid physical model of curved space in 3 dimensions. Alas, we can't. And we certainly can't build a solid model of a "centerless" 3-dimensional manifold. If we had 4 spatial dimensions to play with, we could do both. GR may specify only 3-dimensional manifolds, but they simply can't be physically constructed unless we have 4 spatial dimensions available to work in.

The precise mathematical predictions of GR can be physically interpreted in more than one way. It is widely recognized in GR technical literature that the physical interpretation of the individual components of the Einstein Field Equations are ambiguous.

I submit that a physical interpretation is possible, consistent with the precise mathematical predictions of GR, which explains the so-called spatial curvature as substantively representing an integration across an infinite series of local SR reference frames immersed in a homogeneous cosmic gravitational field, over which the length of our physical rulers is affected by a series of Lorentz Transformations. Eliminate those Lorentz Transformations, and the manifestation of spatial curvature vanishes.

Jon

Last edited: Jul 21, 2008
15. Jul 21, 2008

Haelfix

"Any geometry can be "physically real" in 3 dimensions if, and only if, we can build a solid 3 dimensional model of it in our real world."

Last I checked, GR is (3+1) dimensional. And I suppose that depends what you mean by physically real. Physically real to me, means it gives values for all experiments in its domain that I can measure and that are accurate.

"And we certainly can't build a solid model of a "centerless" 3-dimensional manifold"

Umm, sure you can. A 3 dimensional flat plane (R^3) is a manifold and centerless..

Also you cannot embed GR by adding an extra spatial coordinate. As I mentioned you actually need 8 dimensions (6 + 2) for the most general (torsionless) geometry.

16. Jul 21, 2008

thomasxc

excuse me for being an idiot. im only a 10th grader trying to understand this stuff or the first time.

17. Jul 21, 2008

marcus

Heh heh. You're fine. You are asking questions. No excuse needed! There is a problem when people start declaring unfounded stuff as if it were God's truth. But that's not you.

I wish more highschool students would get some exposure to cosmology (and not just by reading some popularization). What kind of library resources do you have?

18. Jul 21, 2008

marcus

Interesting conversation. I think the nub of it is that Jon wished to persuade Thomas (a 10th grader new to the forum) that General Relativity is physically unreal because we cannot build a solid model of curved 3D space in our normal Euclidean 3D laboratory space.

This is an unusual viewpoint to say the least (and may involve private non-standard definitions of terminology). I replied that I had never heard of GR needing a 4th spatial dimension and invited Jon to find a passage in an online GR text, e.g. Carroll's, that we could look at. Wallace also responded to Jon, very helpfully I think, as follows:

Jon responded by giving his what seems to be his own private definition of what it means to be physically real---namely that you can build a solid model of it in ordinary 3D space.

Haelfix took issue with Jon's idea of what is physically real (which indeed does seem peculiar in the context of physics---although it might seem reasonable to general audience.)

It is an interesting stand-off. Let's stay tuned and see what we can learn, if the discussion continues.

19. Jul 21, 2008

marcus

Jon, I see you have given your own coinage of two other technical-sounding terms:

strong cosmological principle

and

weak cosmological principle

These sound like they might be accepted cosmology terms. But in fact I don't believe they are. Here is how you introduce and use the terms:

In fact mainstream cosmology is based on Gen Rel which does not require a 4th spatial dimension. Haelfix and Wallace have spoken to that.

I don't know where the quote-marks come from, around "strong" and "weak". Who, if anyone, is being quoted? I tend to be dubious of posts with a lot of quote-marks unless there is a link that allows me to easily locate the source.

Anyway, my question is this: Jon, what exactly is the strong cosmological principle and what exactly is the weak cosmological principle?

The cosmological principle I am used to has to do with assuming uniformity---the premise that the world looks pretty much the same from different standpoints and in all directions.

Last edited: Jul 21, 2008
20. Jul 21, 2008

shamrock5585

you should understand the entire universe by tenth grade thomas... shame on you... study up haha