“The greatest enemy of knowledge is not ignorance, it is the illusion of knowledge.” -Stephen Hawking
Millenium simulation from Volker Springel et al., from the Max Planck Institute for Astrophysics.
Posted on 07/21/2012 12:57:15 AM PDT by LibWhacker
“The greatest enemy of knowledge is not ignorance, it is the illusion of knowledge.” -Stephen Hawking
The Universe is a vast, seemingly unending marvel of existence. Over the past century, we’ve learned that the Universe stretches out beyond the billions of stars in our Milky Way, out across billions of light years, containing close to a trillion galaxies all told.
Image credit: NASA, ESA, S. Beckwith (STScI) and the HUDF Team.
And yet, that’s just the observable Universe! There are good reasons to believe that the Universe continues on and on beyond the limits of what we can see; the question is, how far does it go on? Forever? Or does it close back upon itself at some point?
To help us better understand this question, let’s turn to something more familiar (and smaller) that we know how to measure the size of: the Earth.
Image credit: Tom of http://apacificview.blogspot.com/.
From the top of a tall mountain, like Mauna Kea, shown here, you might hope to measure the Earth’s curvature, but your efforts would be in vain. From even 14,000 feet up, the curvature of the Earth is totally indistinguishable from flat.
There are images out there where the Earth appears curved when you look out at the water, and indeed, they’re not hard to find. But is that because of the Earth’s curvature?
Image credit: James Elders of Flatwoods and Lighterknots.
Not at all; it’s because of atmospheric distortion. If you were to try and calculate the circumference of the Earth from a photo like this, you’d get a world that was smaller than even the Moon is; you cannot measure the curvature of the Earth from any known location on the surface of the planet.
What’s more than that is that, over land, the Universe isn’t perfectly smooth. Some places are curved upwards, others downwards, and any small region visible to you is unlikely to be a fair representation of the entire planet.
Image credit: Stefan Zenker atop Weisshorn, 1974.
There is a way that you’d be able to tell, though, what the shape and size of the planet actually is. All you’d have to do is take the appropriate measurements and use geometry.
It’s as simple as going to three separate locations on Earth and drawing a triangle to connect those three points.
Image credit: John D. Norton from the University of Pittsburgh.
On a flat sheet of paper, the three angles of any triangle will always add up to 180°, as you well know. But if you’re on the surface of a sphere (or, mathematically, any surface of positive curvature), those angles will add up to more than 180°. Knowing the distance between each of those three points and the measure of all three angles allows you to calculate what the circumference of the Earth is.
And, of course, the farther away your three points are from one another, the less important the mountains, valleys and oceans are, and the more important the overall shape of the Earth is to your measurement. The converse would have been true if the Earth were shaped with negative curvature, like a saddle, as shown below.
Image credit: John D. Norton from the University of Pittsburgh.
A surface of negative curvature has any three points form a triangle whose three angles sum to less than 180°, and again, knowing the distances and measurements of all three angles allows you to calculate the radius of curvature.
In practice, the very first calculation of the circumference of the Earth — dating to the 3rd Century B.C. — used a very similar method, again reliant on simple geometry.
Image credit: NOAA Ocean Service Education's history of geodesy.
It would not be until the 20th Century that we were actually able to achieve altitudes capable of measuring the curvature of the Earth from space, something we are only able to do because we can step off of the two-dimensional surface of the Earth and look at it from afar.
Image credit: Johns Hopkins University & the U.S. Navy.
By 1948, we were creating mosaics of the Earth by stitching together multiple images of the Earth from space, and there could no longer be any doubt as to its circumference.
Image credit: Johns Hopkins / U.S. Navy, from the Smithsonian Air & Space Museum.
But space itself is a little trickier. Yes, it is just a geometric construct (albeit a slightly more complicated one), but it also has an inherent curvature to it. The amount that the space of our Universe is curved is directly related to the amount of matter and energy that we have in it.
Image credit: Francesco Iacopino of Learning is Beautiful.
Dense, heavy masses like the Sun cause very large amounts of curvature in very small spaces, significant enough to bend starlight by amounts significant enough you could notice it with 1919′s technology. But that’s local curvature, the same way mountains, valleys and oceans are local curvature here on Earth; what we’re interested in is whether the entire Universe ever closes back in on itself, and if so, how big it is. In other words, these local sources of curvature are things we need to not be fooled by.
The Earth, too, curves the spacetime around it. Remember that we use two dimensions as an illustration, but unlike measuring the curvature of Earth, where we can fly “up” and observe the planet below, there is no extra dimension to move through to step back from the curvature of space.
Image credit: Christopher Vitale of Networkologies and the Pratt Institute.
All of the spatial dimensions are curved. Since stepping back from the Universe and observing it from afar isn’t an option, the only way to get a good handle on its curvature is to examine it on its largest scales, and try to infer its geometry.
Image credit: V. Springel et al., MPA Garching, and the Millenium Simulation.
In principle, this is pretty straightforward. Just as any three points on a surface can help you calculate that surface’s curvature, you can do the exact same thing with the Universe! Take any three points that are far enough apart, measure the distances between those points and the relative angles between them as well, and you’ll be able to figure out not only how your spacetime is curved, but also what the radius of curvature is!
Image credit: Dave Goldberg and Jeff Blomquist.
You can imagine three possible cases, of course. One is where the Universe is positively curved, like a higher-dimensional sphere, one is where the Universe is totally flat, like a higher-dimensional grid, and one where the Universe is negatively curved, like a higher-dimensional saddle. In the context of general relativity, it’s the energy density — the amount of matter and all other forms of energy — that determine this curvature.
Image credit: NASA / WMAP science team / Gary Hinshaw.
In real life, we don’t have man-made objects far enough away to communicate with us across the necessary distances to measure curvature. Even if we did, it would take billions of years to do it, which is a disheartening way to attempt to do science. But we have light signals from when the Universe was just 380,000 years old, that tell us what the Universe is like 46 billion light years away.
The fluctuations in the cosmic microwave background — the leftover glow from the big bang — provide a window allowing us to see how our Universe is curved.
Image credit: Smoot Cosmology Group / Lawrence Berkeley Labs.
The first robust measurements of this came from the BOOMERanG experiment in the late 1990s (hearing Paolo de Bernardis talk about this in 2004 was a highlight for me during the early stages of my scientific career), where they first determined that rather than having significant positive or negative curvature, the Universe was indistinguishable from flat.
Image credit: A.E. Lange and P. de Bernardis et al. for the Boomerang collaboration.
That doesn’t mean that it is flat, of course. If you walked outside and tried to measure the curvature of the Earth right now, but only within 5 km (or 3 miles) of your current location, you would find that the Earth is consistent with being flat, but it could also be positively or negatively curved on a larger scale than you’re currently measuring.
So it goes with the Universe as well. We were able to measure that the Universe, if it is curved, has a much larger radius of curvature than that of our observable Universe, which is about 46 billion light years. But if we could make that measurement more precise, we could conceivably measure a much smaller curvature than even that. Thanks to the WMAP satellite, we now have the temperature fluctuations over the entire sky measured at a very narrow, less-than-half-a-degree resolution.
Image credit: NASA / WMAP science team.
And what they teach us is that not only is the Universe consistent with being flat, it’s really, really, REALLY flat! If the Universe does curve back and close on itself, its radius of curvature is at least 150 times as large as the part that’s observable to us! Meaning that — even without speculative physics like cosmic inflation — we know that the entire Universe extends for at least 14 trillion light years in diameter, including the part that’s unobservable to us today.
Image credit: Ned Wright's cosmology tutorial.
Just because the part of it we can see is indistinguishable from flat doesn’t mean it’s intrinsically flat in its entirety. But it does mean that the Universe is far larger than we’ll ever see. Even taking the minimum allowable estimate for the size of the Universe means that, at most, less than 0.0001% of the volume of the Universe is presently or will ever be observable to us. Once you put our knowledge about dark matter and dark energy in there, you’ll realize that we’ll never see more of the Universe than we can right now.
So all that we see — the billions of stars in our galaxy, the hundreds of billions of galaxies lighting up the observable Universe — is just a teeny-tiny fraction of what’s actually out there, beyond what we can see. And yet, we can know that it’s there. Isn’t science wonderful?
The Universe pisses me off.
I don’t believe in physical matter. We are all imagining this together within the confines of God’s laws.
Not big enough for Obama, Michelle and myself. I think they should leave.
This photo shouldn't be possible. By all rights it should be all black or at best a foggy glow. The density of the Universe must be set to a knife edge in order to see any visible structure across 10 billion light years. Yet we see spectacular galaxies more than halfway across the Universe.
It's as if God wants us to see his creation and marvel at it.
When i was in high school, our science teacher told the class that space has no end.. The girl next to me stood up and said, “ thats impossible for space to have no end, there has to be a wall out there..” -— I looked at the girl and said, “ well, whats on the other side of the wall?”.. ——I guess the human mind can’t process something thats eternal and has no end..
It’s a great big universe
And we’re all really puny
We’re just tiny little specks
About the size of Mickey Rooney.
(Animaniacs)
Thinking about what’s beyond that wall freaks me out more than anything else.
Ha Ha — i know when you think about it - it gets freaky.. something that doesnt end is strange to us because we have a beginning and a end— Only God has stated he had no beginning and has no end— God wasnt born, he was always there— thats stange to the human mind, and hard to process—lol
"It is known that there are an infinite number of worlds, simply because there is an infinite amount of space for them to be in. However, not every one of them is inhabited. Therefore, there must be a finite number of inhabited worlds. Any finite number divided by infinity is as near to nothing as makes no odds, so the average population of all the planets in the Universe can be said to be zero. From this it follows that the population of the whole Universe is also zero, and that any people you may meet from time to time are merely the products of a deranged imagination. ---Douglas Adams
How are astrophysicists supposed to maintain any dignity if it turns out the universe is shaped like a donut?
Yes it is truly awesome to comprehend the incredible scope of the heavens but remember this......those heavens themselves comprehend nothing.
Whatever size the universe is, it’s not enough.
Thanks martin_fierro. I think this has been the best couple of weeks for the X-Planets and String Theory lists in quite some time.
Thanks martin_fierro. I think this has been the best couple of weeks for the X-Planets and String Theory lists in quite some time.
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The introduction begins like this:
Space is big. Really big. You just won't believe how vastly hugely mind-boggling big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space. Listen… and so on.
(After awhile the style settles down a bit and it begins to tell you things you really need to know, like the fact that the fabulously beautiful planet Bethselamin is now so worried about the cumulative erosion by ten billion visiting tourists a year that any net imbalance between the amount you eat and the amount you excrete while on the planet is surgically removed from your body weight when you leave: so every time you go to the lavatory there it is vitally important to get a receipt.)
To be fair though, when confronted by the sheer enormity of the distances between the stars, better minds than the one responsible for the Guide's introduction have faltered. Some invite you to consider for a moment a peanut in Reading and a small walnut in Johannesburg, and other such dizzying concepts.
The simple truth is that interstellar distances will not fit into the human imagination.
Even light, which travels so fast that it takes most races thousands of years to realize that it travels at all, takes time to journey between the stars. It takes eight minutes to journey from the star Sol to the place where the Earth used to be, and four years more to arrive at Sol's nearest stellar neighbor, Alpha Proxima.
For light to reach the other side of the Galaxy, for it to reach Damogran, for instance, takes rather longer: five hundred thousand years.
The record for hitchhiking this distance is just under five years, but you don't get to see much on the way.
The Hitchhiker's Guide to the Galaxy says that if you hold a lungful of air you can survive in the total vacuum of space for about thirty seconds. However, it does go on to say that what with space being the mind-boggling size it is the chances of getting picked up by another ship within those thirty seconds are two to the power of two hundred and seventy-six thousand, seven hundred and nine to one against.
-Douglas Adams
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