“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?
Lol
Freakier yet are the problems with the disk accretion theory of planetary formation, which, if disproved, leave us with impossible odds of a planet capable of supporting life, to the point that it may well take an infinite universe to create not only a planet with life, but a planet with sentient life. We may, in fact, be the only life out there. What this does to theology or our sense of purpose is anyone’s guess. My take is that we simply don’t have the smarts to suss this and similar questions yet. I’m hoping that we have the smarts now that could get us to where we can figure out the conundrums of existence. If we don’t, game over.
Only good cops.
The universe may have inflated from the size of a mote of dust to the size of today's observable universe, all during the first few moments of the Big Bang.
Personally, I don't like the term 'inflation' because to me it implies movement, making me erroneously, so many times in the past, wonder how anything could go faster than the speed of light. I'm not a physicist, but I like to think what really happened during the first few moments of the Big Bang was that space itself was actually being created everywhere at a tremendous rate -- including between all the bits of debris in the Big Bang, thereby increasing the distance between those bits (if I'm wrong on this point would some physicist please chime in and correct me? thx).
The expansion continues to this day, but not as rapidly (though it is accelerating).
You can read a little about inflation here.
Ok- Lets blow up a balloon and lets say our galaxy as we know it and all we know is inside that balloon— then whats beyond the ballon (or whats holding up the balloon)and beyond the next— it must keep going forever— there is no beginning of space and no end to it.
God leaves clues of the unknown when he gets angry with Job and demands answers-(JOB chapter 38 thu 42.)- In gen. chapter 1 he states that the earth was built upon water
What is beyond the balloon (universe)?......Nothing.....Aristotle, when asked what is nothing,....he replied...."Nothing...is what rocks dream of...No thing. Space is a thing...there is no space beyond the spacial boundary....dimentionally speaking. It is a very hard concept. Think of it this way...the universe began at a moment and at that moment time, space, energy, matter....all came to be. The explosion of creation was a release of energy on a scale which we simply cannot comprehend, and from that there came to be 10 to the 80th atomic particles. Also space came to be. We know that at the pressures and temperature the character of matter was unlike anything we know of now and that the rate of expansion at Plank time was unimaginable. But it expanded at a rate. Then 2 minutes later the expansion continued at an incredible rate, creating space. And that has been occurring since the explosion....and space has been being created. That barrier continues to expand at a rate faster than the speed of light. Matter and energy are fixed (2nd thermal law). So as we speak ther is not a condition where space goes on forever. There is a barrier (constantly expanding).
Will it go on forever....No.....eventually, without intervention, will die a cold death, with all atoms, subatomic particles, being washed out into a cosmic ocean of near nothingness, approaching absolute zero....entropy will have completed its mission. But it will titrate to an end, and space will cease to expland(or nearly so).
If you want to read more on the subject look at Kaalams Cosmological Arguemnt, The Cosmological Arguements (both of these arguements are families of arguements explaining these matters)
It cant be nothing— our planet earth sits in a galaxy, the galaxy sits in the known universe— well, whats the known universe setting in? then what that setting in, and so forth?
But, there is NO THING.....nothing. What is logic made of? What is love made of? What is the physical makeup of consciounsess, or the number 3, or any abstract entity? Nothing...that is the physical makeup of that beyond the time/space barrier. It is, I will agree, a very difficult concept....but that is it.
OK- i can understand how a planet would have a beginning- But how does a universe start? does it have a beginning or birth? or has space always been there with no birth? were did the void come from before stars and planets?
And yet, after all that, Adams takes us to the Restaurant at the End of the Universe.
2. The Universe had a beginning.
3. The Universe had a cause.
Think of this. All of time, matter, energy, matter came to be at a moment. Just prior to that singularity, there was no universe. Then,...there was. Einstein profered the General theory of relatity, Eddington proved it with care calculations and photography of the a complete Solar eclipse. Hubble proved the theory with his discovery of the Red Shift. Penzias and Wilson recorded the vanishing remnant of the sound of the initial explosion, George Smoot was the overseer of NASAs COBE probe which proved what had been predicted 40 years prior by photoghaphing the residual heat 'ripples' of that initial explosion, and the WMAP probe reconfirmed Smoots findings.
So, in accordance with the Priniciple of Causality, you ask, what caused it. That is the age-old question. Things which begin (or come to be) have a cause. So from the afforementioned scientists we find that all of physics indicate that there was a cause. What is this cause. We do know that all of causality falling int one of two groups, either an abstract concept, but abstract concepts do not stand in a causal relationship to physical 'things', or the cause is personal (as Mind). So Mind does stand in causal relationship to the physical. So this cause, along the order of Mind, seems to be characterized by the following: unimagninably powerful to have created the masssiveness of the universe, timeless (in that time did not exist prior to the moment of creation), unimaginably intelligent (to ordered the universe out of the entropy of the creation explosion, Personal (in that a decision was made to create everything out of nothing (creatio ex nihlo). Self-existant (as that cause existed outside of the universe). These are the characteristics of First Cause which science, by induction, we can know of this cause. You already know who that is.
So I will ask you this one question, originally put by Leibnez, "If there is no God, why is there anything at all?"
That could be.
Or he plays Basketball - which would explain why we get the Hiccups.
And one last clue: every 'thing' composed of atoms is therefore composed of a pinch of space, a grain of time, and energy, all expressed as a wave function; but that wave function is non-distinct until the function collapses to be expressed in 'linear' temporal expression. Before collapse the wave function is a volumetric expression of time. That's where the notion of quantum non-locality arises.
IIRC, it was DeBroglie who told the Copenhagen gaggle that everything these is is an expression of wave function.
And one last clue: every 'thing' composed of atoms is therefore composed of a pinch of space, a grain of time, and energy, all expressed as a wave function; but that wave function is non-distinct until the function collapses to be expressed in 'linear' temporal expression. Before collapse the wave function is a volumetric expression of time. That's where the notion of quantum non-locality arises.
IIRC, it was DeBroglie who told the Copenhagen gaggle that everything there is is an expression of wave function.
Thanks for taking the time to post this. Food for thought.
It’s big.
It goes to eleven.
Hiccups? Dang.... Never thought of it that way... But wow, a new theory is born that might explain a few things.
You ought to apply for a grant.
I am being sidetracked in reading this neat article by the photos, especially the fourth, discussing “curvature”.
I am almost certain that the “curvature” in that photo is caused by “Fisheye Lens Effect”, not “atmospheric distortion”.
In addition, I know that it is nevertheless possible to directly observe Earth’s curvature without going into orbit.
As a pilot, I definitely noted Earth’s curvature (as well as darkening zenith) when flying near 50,000ft, by viewing the horizon.
At lower altitudes in the 30,000 ft range on very clear days, it is amusing to observe “section lines” while flying over the great MidWest of our country. Looking North/South, they appear straight. Looking East/West, they clearly appear “bent” toward the North. This is the case due to their being laid out by compass. Think about it a bit if this effect baffles you; it really is quite interesting demonstration that Earth is curved, even though at those lower altitudes the curvature of the horizon was not noticeable.
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