Relativity and Cosmology Blog

# Relativity and Cosmology

This is a Blog on relativity and cosmology for engineers and the like. My website "Relativity-4-Engineers" has more in-depth stuff.

Comments/questions of a general nature should preferably be posted to the FAQ section of this Blog (http://cr4.globalspec.com/blogentry/316/Relativity-Cosmology-FAQ).

A complete index to the Relativity and Cosmology Blog can be viewed here: http://cr4.globalspec.com/blog/browse/22/Relativity-and-Cosmology"

Regards, Jorrie

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# How BIG is the Cosmos?

Posted July 01, 2008 11:00 PM by Jorrie
Pathfinder Tags: cosmology Size of universe

Having just read Janna Levin's excellent book "How the Universe got its spots", I'm still pondering her statement that the universe probably appears to be infinite, while it is most likely to be quite compact. "Quite compact" she admits, may mean that it is possibly larger than what we can observe, but on the other side of that horizon, it may just repeat itself endlessly, without actually being infinite. Huh?

OK, I don't quite understand all that she wrote about the topology that makes such a scenario possible. What I do understand is that there should be a limit to the size of the universe - infinite things are not really describable by math, science or in words. If the universe is now infinite, it must have started out infinitely large at the Big Bang. Huh? Again!

In principle, something that is finite can never become infinite in size through growing bigger, because then it must have a size and a thing with size cannot be infinite in size, not so? A finite universe is the only one that makes sense.

Fortunately, the best data that we have suggest that the cosmos may be just on the closed side of flat. Closed means it is compact, however big that "compact" may be. It also means that it can be finite without an edge, because it can fold around on itself, much like Earth's surface has no edge because it is folded into a sphere. So how big must such a 'spherical cosmos' be? Here's how big:[1]

This picture suppresses one spatial dimension, so that the universe is portrayed as a two-dimensional surface that is curved into some fictitious hyperspace, hence forming a hypersphere. We have no access to the other dimension (the inside) of the hypersphere. Our observable cosmos is pictured as the small yellow circle on the surface of the hypersphere, around 28 Giga lightyears (Gly) in diameter, with us in the center of course. The observable 'horizon' appears to be 14 Gy from us in light travel time. Actually, it was about a 300 times smaller (~0.045 Gly radius) when the light that we now observe left the horizon. Due to the rapid early expansion, the light took 14 Gy to reach us.

During the 14 Gy that the light was in transit towards us, that region expanded ~1000-fold, from 0.045Gly to around 45 Gly radius today (the white circle, diameter 90 Gly). We will never see the horizon as it "looks" today, because light will take 45 Gy to reach us! This "observable universe" can however not be the total cosmos - observations of the visible part point to more of the same on the other side of that horizon.

Measurements of the overall curvature of space (terribly difficult due to the slight curvature) indicate that a closed universe must be at least 800 GLy in circumference, almost 10 times the present diameter of the observable universe.[2] We use circumference here and not diameter, because we are talking of something similar to the circumference of the Earth. The previous two regions (circles) are characterized by their diameters, because they are situated on the surface of the incredibly large expanding "ball" of hyperspace. So large that on the scale of our human experience, the hypersphere is pretty much "infinite" in circumference.

In the end, it appears as if the cosmos is so big that we don't need to care about its size. Also, the cosmos probably doesn't care much about us either – we are just too insignificant in comparison. We should rather care more about the three-dimensional oblate spheroid that we call home, Earth, Gaia, or whatever. At least we know what size it is and it is surely not big enough to ignore our wrongdoings…

Jorrie

[1] Background artwork is the Cosmic Microwave Background as measured by WMAP. My circles are not quite drawn to scale.

[2] From latest WMAP data by NASA (5-year). I have used rounded values, just to illustrate the points. The 800 Gly minimum circumference comes from the maximum value of the curvature parameter today, Ωk ≤ 0.13. Then circumference today ≥ Observable universe diameter today x Π / 0.13 ≥ 800 Gly.

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#1

### Re: How BIG is the Cosmos?

07/02/2008 11:53 PM

Cosmos is as big as YOU imagine. Your imagination is the limit of the cosmos.

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#2

### Re: How BIG is the Cosmos?

07/03/2008 1:44 AM

Hi gsuhas, you wrote: "Your imagination is the limit of the cosmos."

Right! Science has set the lower limit - you've just set the upper limit!

More seriously, the same data that I've used to calculate the lower limit sets the upper limit of the cosmic circumference to about 2000 Gly. Can you imagine it to be bigger? ;-)

Jorrie

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#3

### Re: How BIG is the Cosmos?

07/03/2008 1:58 AM

Thanks, Jorrie.

[I see your name called upon often, whenever there is a 'far-reaching' topic such as this.]

While I'm not likely to get my tape-measure out anytime soon to 'confirm' your hypothesis, it is interesting and adds to my own feeble imaginings.

What I appreciate most, however, is your conclusion ... speculations and hypothesis are wonderful, but sooner or later (one hopes, sooner), we need to focus a little closer to home ... maybe buy more time to speculate more about the cosmos.

Thanks,

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#9

### Re: How BIG is the Cosmos?

07/03/2008 10:09 AM

Yes, I agree. But I also keep wondering even if we could define the scale of the Universe, what have we achieved? It's nice to know the size, but then what?

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#10

### Re: How BIG is the Cosmos?

07/05/2008 2:43 AM

Hi Guest, you wrote: "It's nice to know the size, but then what?"

As an engineer, I surely can't answer that. However, my view is that one never knows where the accumulation of knowledge will lead us and when that knowledge may become an advantage to humankind (and to us as engineers, specifically!)

Jorrie

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#4

### Re: How BIG is the Cosmos?

07/03/2008 5:08 AM

Hi Jorrie.Just a little question.You said: "...Actually, it was about a 300 times smaller (~0.045 Gly radius) when the light that we now observe left the horizon..." Then you said: "...During the 14 Gy that the light was in transit towards us, that region expanded ~1000-fold, from 0.045Gly to around 45 Gly radius today..." So, the Universe was 300 or 1000 times smaller (14 Gy ago) than it is today???(which of these???... or I didn't understand sth well...)

About the Janna Levin: "..."Quite compact" she admits, may mean that it is possibly larger than what we can observe, but on the other side of that horizon, it may just repeat itself endlessly, without actually being infinite. Huh?..."...

Well, the only way that is possible such a thing is a kind of a "fractal structure". For example, the "Koch snowflake" has a circumference of infinite length while its area is finite (smaller than its perimetric circle). Instead of the 2-d "Koch snowflake", I can imagine a similar 3-d construction with a pyramid (with all triangle faces), as the "basis" of the construction. Then you can add an infinite number of smaller and smaller similar pyramids (in the same way as you create the "Koch snowflake" by adding smaller triangles) in order to built a "thorny" structure (of infinite complexity). The area of its surface is infinite but its volume is finite (smaller than its perimetric sphere). Now imagime that you are on the surface of this "construction" and you are able to walk only on the "flat areas" (and not on the "edges"). Suppose that you try to reach the "end" (one of the apexes) of the "construction" by walking with a constant (any finite) velocity. As you will, always, meet another (smaller) such pyramid on your way, you will never reach the "end" (you will approach the "end" but you will never, actually, reach it). Of course, you consider that the Universe seems to be infinite (but, on the other hand, it is not extended in the space infinitely... it is confined in a finite volume of the space...). Now, go another step further to make this "construction" 4-d.

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#5

### Re: How BIG is the Cosmos?

07/03/2008 5:59 AM

Hi George, you asked: "So, the Universe was 300 or 1000 times smaller (14 Gy ago) than it is today???"

The observable portion was ~1000 times smaller. As I said, the 14 Gly is not really a physical distance of much importance - it is just the distance that light would travel in 14 Gy in a flat, non-expanding space, called one Hubble distance - just a unit of distance, so to speak. I used the "300 times smaller" just to bring home the point that we do not view things as that distance, although it is sometime qualified by saying "light travel distance".

Janna Levin does not favor the fractal idea, but rather that exact copies of the universe repeat (at normal size), much like the dodeahedron idea that I wrote about on this Blog before. You exit the "edge" and enter again from the other side, creating an infinite appearance of a finite space. Your pyramids are closer to her idea, just not smaller and smaller...

Jorrie

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#6

### Re: How BIG is the Cosmos?

07/03/2008 7:39 AM

A question from a by comparrison dim mechanical engineer.

If the univerese is finite, then where is it? and what exists beyond it?

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#7

### Re: How BIG is the Cosmos?

07/03/2008 8:40 AM

Hi exemmet, you asked: "If the univerese is finite, then where is it? and what exists beyond it?"

Why, it's right here. :-)

Beyond it, who knows? Maybe nothing, not even space, time or vacuum. Maybe another dimension that we cannot observe...

Jorrie

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#8

### Re: How BIG is the Cosmos?

07/03/2008 8:51 AM

"If the univerese is finite, then where is it? and what exists beyond it?"

Ah, an easy one! It rests upon the back of a great tortoise (often called the Great Turtle of Creation). And beyond that? It's turtles all the way down.

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#11

### Re: How BIG is the Cosmos?

08/25/2008 9:22 PM

I wonder if quantum holographic principles can be another way to measure the size of the universe. Everything in the universe can be reduced to bits of information. According to quantum holograpy, the information stored within a volume is equal to the information that can be stored on the surface of that volume. Hence, we count up the information inside our volume and we can then calculate the surface area of the universe. Anyways it's big.

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