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Is the Universe a Hall of Mirrors?
PhysicsWeb is running an article by one of the researchers who has developed the theory that the universe may be finite, rather small, and soccer-ball shaped. The question is still open; it's one theory that fits cosmic microwave data from the Wilkinson Microwave Anisotropy Probe (WMAP). Apparently testing the theory by looking in the indicated way through the WMAP data would so far be computationally prohibitive. From the article: "The Poincaré dodecahedral space can be described as the interior of a 'sphere' made from 12 slightly curved pentagons. However, there is one big difference between this shape and a football [soccer ball] because when one goes out from a pentagonal face, one immediately comes back inside the ball from the opposite face after a 36 degree rotation. Such a multiply connected space can therefore generate multiple images of the same object, such as a planet or a photon. Other such well-proportioned, spherical spaces that fit the WMAP data are the tetrahedron and the octahedron."
The article mentioned is well over a year old. The outstanding analysis of data due in 2004 has been completed. The validity of the information is being questioned Although it would be fun living inside a football.
Of course it can, and the universe is expanding in exactly this way.
The steady-state theory proposed that new matter was being created all the time, at a very slow rate. This was disproved by the cosmic microwave background, that instead agrees exactly with the preductions of the big-bang theory. I think, the inflation theories allow new material to enter at any time, but the idea there is that the initial expansion of the universe was so fast, that any other matter (say, from another big-bang) would be so far away that it would not ever be possible to detect it. But if the universe is finite, and it is possible to see the periodic boundaries, then surely it disproves inflation? cosmologists out there?
http://www.simulation-argument.com/
it's in my head
Err... the edges are shared, so there are less than 30. I'm trying to figure out the exact number but my maths is too stale.
No, the exact number would in fact be 30. The edges are indeed shared, which is why there are less than 60 (5 * 12) edges.
"Convictions are more dangerous enemies of truth than lies."
"Who's Moriarty?"
:P
That's probably what the person who modded my parent post down was asking themselves, too, I'd guess. Shame on those of you who missed the ST:TNG reference!
Please see the Wikipedia page for Professor Moriarty and on that page, scroll down to where it says "Moriarty in pop culture" where it includes the bit about the ST:TNG episode where "the three trapped crewmembers programmed the holodeck inside the holodeck to create a holographic simulation of the outside world, leaving Moriarty and the Countess safely stored in a databank aboard the Enterprise." At the end of the episode, Picard mentions something about how we all may simply be inside such a device sitting on someone's desk somewhere.
No, that is completely incorrect. The whole point of Relativity is that nothing can exceed the speed of light, in any frame of reference. The situation that you describe, where Newton's laws of motion would imply the relative speed of the two observers is greater than the speed of light, never occurs because instead the passage of time is affected by the motion. If you had a clock, and were transmitting to me what the current time was, your clock would appear to me to be running too slow. And vice versa, you would think that my clock was running too slow.
The only situation in which the photons can never catch up, is if they pass the event horizon of a black hole ;)
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'The Road to Reality' (Roger Penrose) http://www.amazon.com/Road-Reality-Complete-Guide- Universe/dp/0679454438/
Great discussion about physics laws and math, one of the bests titles of Mr Penrose, and yes, the ' dodecahedral/tetrahedral/octahedral space' possibilities are also explained from the ground up.
What's in a sig?
You're essentially correct, under this model you end up with a continuous space. Perhaps the easier way to see how it works is with a simpler example like a torus: you can make a torus (donut shape) from a flat piece of paper by first rolling it up into a tube (identifying the top edge with the bottom edge) and then looping the tube around (identifying the two ends of the tube with each other). Thus you can think of the flat piece of paper as a torus by imagining that when you pass off the top edge you appear at the bottom edge, and when you pass off of one side you appear on the other. Now, what happens at the corner (the equivalent of an edge of the dodecahedron)? A quick check and you'll see it all works out: in some sense you might be "broken up" with half of yourself on one side of the paper, and half on the other, but remember those sides are connected together, so so are you.
The same trick works with the dodecahedron, you just have to get the identification of faces right. On passing out through a fae you'll appear on the opposite face, rotated. Take a quick look at a dodecahedron (here's an example that is translucent and rotatable so you can look around) and you'll get the idea. Looking through the dodecahedron from one face you can see the opposite face doesn't align: it's at an angle - hence the rotation. Visualsing where you'll come out as you approach an edge (and where the other face of that edge will result in you appearing) you'll see that the whole thing in indeed continuous; the edges present no problems.
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That is not quite true. Quantum mechanics technically still holds at the macroscopic level. However, Newtonian physics is an "approximation" that is incredibly good in intermediate scales (i.e. not relativistic or quantum).
Of course the universe isn't truly Newtonian. That said, Newtonian is how we perceive it in our day to day lives. Sure, there are electrons and atoms bouncing all around me, but the only thing I see is a flat desk with gravity pointed straight down.
I can guarantee you that the dog is not doing newtonian physics in his head; neither is he hardwired to do it that way. If you throw a ball at a puppy, he will not be able to catch it right away. Just like a little kid can't. We aren't hardwired to "think Newtonian." As it is, Newtonian physics are a representation of the world we live in, not the world itself.
Do you truly and honestly believe that in the millions of years of evolution in a world that looks like a teenagers physic books opening lessons that nothing has been hardwired to deal with a Newtonian outlook on the world?
Take a gazelle. Drop it out of its mothers womb, and watch as within an hour it is performing a balancing act in modern robots struggle to mimic. This stuff is hardwired in.
Take a baby. Try and teach it calculus. Spend every single day trying to teach it calculus, and see how successful you are. The baby is going to find this utterly impossible because calculus is something we have absolutely zero evolutionary adaptation for. When we learn calculus, we learn it through blood, sweat, and tears. Now take a baby and try and teach it English. Spend every single day talking to the baby and trying to teach it English. You will probably take the better part of year before you start to see any success. It will probably take the child until he is in high school before the child has mastered the language. Language comes quicker then math because we have entire centers of the brain that have been devoted to learning it. It is still a new evolutionary adaptation on the grand scheme of things, but there has been some time for it to get a foothold in our brains.
Now, try and teach a baby how a Newtonian world works. The baby is going to understand that something coming towards its face is going to hit, that objects are solid, and that things fall in parabolas long before it even has the beginnings of muscle control do anything about it. A baby will start making sense out of the photons bouncing around in a deeply intuitive way almost instantly.
A young child is significantly faster and more accurate then Ph.D. in physics can ever be without the aid of a computer when trying to predict a trajectory or what happens when an object is struck. This stuff is so hardwired into us that we don't even think about it. Hell, we CAN'T think about it because it is so hardwired into us. Acting in a Newtonian world comes easier then breathing.
However, if you have never experienced something (even Newtonian physics), then you have no intuition about it because it is not something hardwired. Examples: on this very site a while back, there was a heated discussion about what would happen if there were a a tunnel bored completely through the Earth and you fell it in. What would happen? People disagreed. Also, Total Internal Reflection.
Of course we don't have an intuitive understanding of what happens when gravity is doing anything other then pulling us down or any we are bouncing things through a fiber optic cable. Why in the hell would any species evolve to understand such things? When I say that we understand Newtonian physics, I don't mean every single rule and law that falls under "Newtonian physics". I mean that we perceive the world like the first few chapters of a high school physics book.
Further, the intuitive jump for understanding complex but still Newtonian things is a small jump compared to trying understand quantum mechanics or general relativity. After a
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