The shape of the universe

[Gregorygregg1]

According to Wikipedia, The Wilkenson microwave anisotropy probe has proven that the observable universe is flat, with only an 0.5% margin of error.  See "shape of the universe".
Perhaps this is correct, but my brain cannot fathom it.

My question is: what, besides more dimension can contain dimension?  If the universe has shape, what contains the shape? Doesn't a universe with shape imply a finite universe?

[Watson]

What is the Universe expanding into? Well since we can never know or test any theories we can just except it is the way it is. There will always be limits to what we can know and understand. Where do exotic and virtual particules reside when not briefly detectable within our dimensions? Don't know that either.

[Marshall]

According to Wikipedia, The Wilkenson microwave anisotropy probe has proven that the observable universe is flat, with only an 0.5% margin of error.  See "shape of the universe".
Perhaps this is correct, but my brain cannot fathom it.

My question is: what, besides more dimension can contain dimension?  If the universe has shape, what contains the shape? Doesn't a universe with shape imply a finite universe?

Wikipedia is uneven quality. That "shape of the universe" article is not their best. It cites a badly written NASA public outreach page instead of the real NASA report from the WMAP team

Here are the 2008 and 2010 WMAP reports giving the results relevant to cosmology.

http://arxiv.org/pdf/0803.0547v2.pdf
http://arxiv.org/pdf/1001.4538v3.pdf

If you look at Table 2 on page 3 of the 2010 report you will see a 95% confidence interval for a curvature number.

Don't think of this as the curvature of our space as seen from somebody "outside". In conventional cosmo there is no outside. Space is all of space. So it can have no external shape. BUT curvature can be experienced from within, and measured. By measuring angles for example, or how volumes grow with radius.

WMAP and several other projects managed to measure the curvature and combined results are shown in the last column of Table 2.
They have a number Omega which is ONE if overall average curvature is zero and their confidence interval for Omega is 0.9916 <Omega< 1.0133

[some scratchpad arithmetic: 1 - 0.0084=0.9916]

This is a 95% confidence interval. So it is quite possible that Omega is ONE PERCENT HIGHER than 1.
It could be 1.01 that is still within the confidence interval. That would definitely not be what we'd call a spatially flat universe! It would be a finite volume curved round to itself with a finite circumference analogous to the surface of an ordinary ball: analogous to a sphere. Like the surface of the earth in a way, but in one higher dimension. (technically hypersphere). The surface of the earth is like a flat 2d sheet of paper curved round on itself. This would be full 3D space curved round on itself. Not imaginable from the outside (not easily anyway) but the experience of working inside such a geometry is imaginable.

So I don't know where they got the 0.5% figure. That is only HALF A PERCENT. But if you read the actual NASA document reporting 7 years of WMAP data there is a FIVE PERCENT probability that the curvature is totally outside that interval. AND EVEN WITHIN THAT 95% confidence interval it can be a full ONE PERCENT LARGER than what it would be in the ZERO CURVATURE case.

Remember in the zero curvature case Omega has to be equal to one.

So I would advise not relying on that particular Wikipedia article or the NASA public outreach article (read what the scientists wrote themselves, not the nameless wikipedes and public outreach people.) Just my opinion.

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The main thing is that in this context CURVATURE MEANS SOMETHING EXPERIENCED AND MEASURED FROM THE INSIDE.

If very large triangles add up to slightly more than 180 degrees you are in the positive curved case. If triangles continue to add to exactly 180 no matter how big you make them, then you are in zero curved case. (that is nicknamed "flat" for short, it does not mean that you could get outside the universe and look back at it and something would look flat :-D) It is technical jargon for zero curvature experienced from inside space.

One sign of the sloppiness of those particular Wikipedes and NASA blurb-writers is that they do not make that clear to readers in simple language.
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[Gregorygregg1]

Thank you once again Marshall.

I get the gist, but am still in the dark. Euclidian geometry does not describe the universe.

[Marshall]

Thank you once again Marshall.

I get the gist, but am still in the dark. Euclidian geometry does not describe the universe.

Hi GG, I'm glad you got something, the gist, out of the earlier post. I think you mean this as a question:

Euclidian geometry does not describe the universe?

Thats a good question, we could talk about it sporadically over the course of several posts. I know you have a lot of interests: biology, sculpture, philosophy and much more, so I don't expect you to be constantly involved with this question or anything else in astro/cosmo.

But in fact it's true! and it takes getting used to.

There's quite a lot to the story. You studied biology so you may know the name Konrad Lorenz an Austrian who studied animal behavior.

Well, Euclidian geometry does not include TIME and there was a Dutchman with a similar name Hendrik Lorentz who without even properly realizing what he was doing devised the correct way to include TIME in the Euclidian picture.

LORENTZIAN 4D GEOMETRY IS THE VANILLA GEOMETRY OF THE UNIVERSE. Einstein realized this in 1905 and announced it to the world. But it was Hendrik Lorentz with his pointed beard and nice manners who had actually constructed it. How to set up the coordinates and calculate how things look when they are rotated and how to change perspective from one observer to another. How to do simple calculations in a world uncurved by gravity where no observer can be moving relative to another faster than a certain speed.

Your question really should be Lorentzian geometry does not describe the universe???

because that is the geometry that handles SPACE in an entirely good old Euclid way but adjoins a time coordinate to it in the correct way so that you get vanilla space+time 4d geometry.

The natural thing to expect is that THAT would describe the universe. and it does almost, to an extremely good approximation, as long as there is not too much matter around to bend things. Or as long as the matter that is around is not too DENSE. You know ordinary matter is mostly empty space and from gravity's point of view it is not very dense. So ordinary objects have negligible gravity. You don't feel any gravitational pull from an SUV or an elephant or whatever.

But either some very dense matter or a whole lot of matter actually distorts space+time geometry so that it is not vanilla anymore. That was Einstein's contribution in 1915. He put gravity into the picture.
And according to his 1915 theory the vanilla, or Lorentzian, geometry is just what you get when you throw out all the matter or in some other way neutralize the effect of gravity.

There are other names of people involved in what I'm calling Lorentz geometry: an American named Minkowski, a Frenchman named Poincaré. But just to keep it simple I'm calling it either Lorentzian or Vanilla.

There's more to the story but that ought to do as a first installment.

[Marshall]

When we're talking about the geometry of the universe it's really based on Einstein's 1915 work socalled "general relativity" but there's no reason to rush. The Wikipedia has some nice quotes about Lorentz, who constructed the vanilla version which gets distorted or curved slightly by gravity in the 1915 GR theory. Without the vanilla version we wouldn't have the full GR theory, so I'm going to quote a patch of wikipedia:

==quote from the Hendrik Lorentz article==
Lorentz's publications (of 1895 and 1899) made use of the term local time without giving a detailed interpretation of its physical relevance. In 1900, Henri Poincaré called Lorentz's local time a "wonderful invention" and illustrated it by showing that clocks in moving frames are synchronized by exchanging light signals that are assumed to travel at the same speed against and with the motion of the frame.
In 1899, and again in his paper "Electromagnetic phenomena in a system moving with any velocity smaller than that of light" (1904), Lorentz added time dilation to his transformations and published what Poincaré in 1905 named Lorentz transformations. It was apparently unknown to Lorentz that Joseph Larmor had used identical transformations to describe orbiting electrons in 1897. Larmor's and Lorentz's equations look somewhat unfamiliar, but they are algebraically equivalent to those presented by Poincaré and Einstein in 1905.[2] Lorentz's 1904 paper includes the covariant formulation of electrodynamics, in which electrodynamic phenomena in different reference frames are described by identical equations with well defined transformation properties. The paper clearly recognizes the significance of this formulation, namely that the outcomes of electrodynamic experiments do not depend on the relative motion of the reference frame. The 1904 paper includes a detailed discussion of the increase of the inertial mass of rapidly moving objects. In 1905, Einstein would use many of the concepts, mathematical tools and results discussed to write his paper entitled "On the Electrodynamics of Moving Bodies",[3] known today as the theory of special relativity. Because Lorentz laid the fundamentals for the work by Einstein, this theory was originally called the Lorentz-Einstein theory.

The increase of mass was the first prediction of special relativity to be tested, but the early (1901–1903) experiments by Kaufmann appeared to show a slightly different mass increase; this led Lorentz to the famous remark that he was "at the end of his Latin."[4] The confirmation of his prediction had to wait until 1908. In 1909, Lorentz published "Theory of Electrons" based on a series of lectures in Mathematical Physics he gave at Columbia University.[5]

Assessments
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...
Paul Langevin (1911) said of Lorentz:
It is the great merit of H. A. Lorentz to have seen that the fundamental equations of electromagnetism admit a group of transformations which enables them to have the same form when one passes from one frame of reference to another; this new transformation has the most profound implications for the transformations of space and time
Lorentz and Emil Wiechert (Göttingen) had an interesting correspondence on the topics of electromagnetism and the theory of relativity, and Lorentz explained his ideas in letters to Wiechert. The correspondence between Lorentz and Wiechert has been published by Wilfried Schröder (Arch. ex. hist. Sci, 1984).
Lorentz was chairman of the first Solvay Conference held in Brussels in the autumn of 1911. Shortly after the conference, Poincaré wrote an essay on quantum physics which gives an indication of Lorentz's status at the time:
... at every moment [the twenty physicists from different countries] could be heard talking of the [quantum mechanics] which they contrasted with the old mechanics. Now what was the old mechanics? Was it that of Newton, the one which still reigned uncontested at the close of the nineteenth century? No, it was the mechanics of Lorentz, the one dealing with the principle of relativity; the one which, hardly five years ago, seemed to be the height of boldness.
Albert Einstein (1953) wrote of Lorentz:
For me personally he meant more than all the others I have met on my life's journey.[6]
==end quote==
http://en.wikipedia.org/wiki/Hendrik_Lorentz

[Gregorygregg1]

Marshall,
I appreciate your taking the time to explain things.  indeed, I consider Konrad Lorenz in the same league as Darwin. I have heard of Heinrich Lorenz and poincare', but only in passing.  

It appears that I have been over simplistic in many of my ideas about Cosmology.  Part of the reason I turned my thoughts that direction was that my interest in philosophy seemed directed toward either the physical universe or human behavior, and of the two I found human behavior far more daunting.  Perhaps they are equally so.

The problem with amateur philosophers is that they all think they have the answer to some profound question, and since there is no one to set them straight, they blather on incessantly.
Before I abandon this topic to more accomplished thinkers, I would crave a boon.  Being one of the former ilk, I thought I had a flash of insight about the nature of mater and gravity.  Probably only some bad broccoli I ate, but if you wouldn't mind demolishing it for me, I would be grateful.  

It occurred to me, after reading an article on Black Holes in a popular publication, that mater might be a transition state between space (empty dimension) and the singularity (infinite density), having properties of both.  Might not mater be "the manifestation of the potential energy of the stretch of space as it approaches a singularity, held in existence through the agency of angular momentum?"
This seems to make sense because I interpret GR as implying that mater is potential energy.

[Marshall]

... I thought I had a flash of insight about the nature of mater and gravity.  Probably only some bad broccoli I ate, but if you wouldn't mind demolishing it for me, I would be grateful.  

It occurred to me, after reading an article on Black Holes in a popular publication, that mater might be a transition state between space (empty dimension) and the singularity (infinite density), having properties of both.  Might not mater be "the manifestation of the potential energy of the stretch of space as it approaches a singularity, held in existence through the agency of angular momentum?"
This seems to make sense because I interpret GR as implying that mater is potential energy.

I know it can be very helpful to be shown why an idea doesn't help us understand, or match with observation.

But demolishing ideas is a lot of work and I am lazy and not especially good at it.

I think that PEOPLE DO NOT KNOW WHAT MATTER "IS"

Presumably matter is intimately related to GEOMETRY because they interact. Matter bends or curves geometry (that is what gravity is) and geometry guides matter (objects travel in paths which are shortest distance type curves, geodesics, in the curved landscape that geometry provides---that is what straight means)

so matter curves geometry and geometry guides matter THEY MUST BE FUNDAMENTALLY THE SAME THING at their roots because the interact so intensely and constantly.

that is a vague naive idea I have. I don't know what that common ground of existence of geometry and matter could be. So I do not think about it.

You are a sculptor, you say, so as an artist you have come up with a PICTURESQUE idea of what matter is.
OK.

I will not attempt to demolish because that would just leave a gap. Nothing to put in its place.
Be happy with your idea, it is beautiful (although probably wrong and useless--most physics ideas are) and I can offer nothing better :-D