20220801, 20:11  #67 
"Curtis"
Feb 2005
Riverside, CA
1010101100001_{2} Posts 
If uniform density, centre of mass of a finite sphere is at the center of the sphere; or, why isn't it the same for a circle, sphere, and 3sphere? I suppose I'm missing a subtlety when addressing a 4th spatial dimension, but I don't know what it is.
Edit: Aha! The center of a sphere is not *on* the sphere. I struggle to conceive of a 3torus, even after perusing the wiki blurb about one. However, a standard torus has center of mass outside the object, which makes my "mass would accumulate at the center of mass" a bit tricky... Last fiddled with by VBCurtis on 20220801 at 20:16 
20220801, 20:25  #68 
Apr 2020
3^{2}·5·19 Posts 
Indeed!
In order for it to make sense to talk about the centre of mass of a 3sphere or a 3torus, you need to embed it in 4dimensional space. But hypothetically, if the universe has one of these shapes, that doesn't mean there's some actual 4dimensional space that it's embedded in; it just tells you how geometry works on a large scale. For example, the universe being a 3sphere would mean that going far enough in any direction would eventually lead back to the place you started, and that the angles of a very large triangle would add up to more than 180 degrees. 
20220801, 20:34  #69  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
3^{2}·1,277 Posts 
Got it in one.
Quote:
Take a onedimensional line and join its ends together, without letting the line cross itself. You have a closed simple loop, a 1torus, embedded in a twodimensional space. Take a two dimensional square and join two opposite edges together, again without letting anything intersect. You have a tube embedded in a threedimensional space. Now join the ends of the tube together, again without intersection, to produce 2torus which looks like a car wheel's inner tube. Again, a simple closed surface. Now take a threedimensional cube and join its opposite faces together, three times. You need to embed it in a 4d space or it will intersect itself. (Try making a 2torus solely within the plane of the square to see why.) 

20220802, 01:18  #70  
Feb 2017
Nowhere
3×1,993 Posts 
Quote:


20220802, 04:10  #71  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
19C7_{16} Posts 
Quote:
To me there is not enough data to extrapolate a pattern. Especially as we have no understanding of what the force is, then I think it is folly to try to predict that it will simply keep getting stronger and give us the bigrip. It is also possible the giant turtle that is currently blowing into the 4balloon to expand it will soon have to stop and catch its breath. Perhaps it will fumble with the stopper and the 4balloon will deflate again, collapsing us back into a big crunch. 

20220803, 13:44  #72  
Feb 2017
Nowhere
13533_{8} Posts 
Quote:
The "accelerating expansion" theory is currently fashionable due to work which was the subject of the 2011 Nobel Prize in Physics, which was shared: one half was awarded to Saul Perlmutter, the other half jointly to Brian P. Schmidt and Adam G. Riess "for the discovery of the accelerating expansion of the Universe through observations of distant supernovae." The supernovae were what are called "type 1a supernovae." As I understand it, type 1a supernovae are a sort of "standard candle." They occur when a white dwarf in a binary system accretes matter from its companion. Basically, when it accretes enough matter, bang. And, according to the theory of such things, it's always the same amount of matter, hence the same size bang. Now, of course, not knowing about such things, I wonder how well we really know what we think we know about type 1a supernovae. I also wonder whether, in the ancient universe, there might have been some other kind of supernova which we might be mistaking for type 1a. And I wonder whether there might be some reason we haven't thought of that the light from ancient, faraway type 1a supernovae might be dimmer than we expect it to be. I have a vague recollection that, not terribly long after the size of the universe was first estimated using Cepheid variable stars as "standard candles," the size estimate had to be doubled fairly abruptly, because a new type of variable star had been discovered, and its properties were different from the originallydiscovered Cepheid variables. The press had a field day. Sorry, I don't remember the details. The situation in cosmology now is really weird. The posited early "inflationary period" which somehow also ended early, is pretty bizarre. And in the presentlyobservable universe there is thought to be "dark matter," more specifically "cold dark mater," which we haven't figured out how to detect directly. But the way stars in the arms of galaxies orbit around the galaxy's center  period essentially independent of distance from the center  says that either gravity doesn't work the way we think it does, or else there is a very large amount of mass present that we can't see. It is well known that the periods of planets orbiting Mr. Sun vary with period, the period being longer the further out the orbit is. This was stated formulaically by Kepler in the early Seventeenth Century as R^{3} โ T^{2} where R is the semimajor axis of the elliptical orbit, and T is the orbital period. So stars at different distances from the center of a galaxy having the same orbital period is difficult to explain. And so, it seems that we can't see most of the matter in the universe. We can see "baryonic matter" (atoms and many subatomic particles), and know about neutrinos, which are sometimes referred to as "hot dark matter" because they interact so weakly with baryonic matter they can zoom out from stellar cores practically unimpeded, and seem only to exist on their own moving at a large fraction of the speed of light. The only ways they get slowed down or stopped that we know of, involve being absorbed, which is how we detect them. Now, with the accelerating expansion, it seems that we can't detect most of the energy in the universe, either. 

20220804, 12:51  #73 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
6,599 Posts 
Perhaps. This is another thing we don't know; whether the inflationary force is the same as the the "dark energy" force we see in the data today. We don't have any data from the inflationary era to compare to.
If inflation was caused by the same thing we call "dark energy" today, then it was briefly very strong in the past. 
20220805, 04:30  #74 
Romulan Interpreter
"name field"
Jun 2011
Thailand
10011101111001_{2} Posts 
Who was the FED boss at the time when that inflation happened?
Now seriously, joking apart, what "contradictions with black holes" (current title of the thread, I guess it won't survive like that for long) do you guys have? I have no contradiction with them, they never contradict me. Every time I tell them something, they don't reply anything back to me. Neither to agree, nor disagree. They just keep quiet behind the horizon... As I am an optimistic guy, I assume they agree... So, no contradiction. Last fiddled with by LaurV on 20220805 at 04:34 
20220805, 04:45  #75 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
14707_{8} Posts 
Contradiction confirmed
Me: Hi BH. Do you agree that the internal angles of triangles add up to 180ยฐ? If not then say nothing.
BH: 
20220805, 05:10  #76 
Romulan Interpreter
"name field"
Jun 2011
Thailand
5×43×47 Posts 
Nope... On the surface of the sphere, they don't.
Inside of the back hole, who knows? .... (you started it ) 
20220805, 06:13  #77 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
1100111000111_{2} Posts 

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