- #1
wolram
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How do you imagine a finite universe ? i find it very difficult.
Exploring a Finite Universe: Understanding its Challenges
In summary, a finite universe is difficult to imagine because it is like thinking of the surface of a balloon being only 2D and you have to think of what would be the 3D analog of that. It is easier to imagine what it must have been like to live in a time before it was known that the Earth was round and that gravity kept us all from falling off the surface. After all, we can see that the surface extends to the horizon in all directions. If we walk towards the horizon then the limit of the horizon moves with us and we can see how the surface extends further. So surely there can be only two
- #2
marcus
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wolram said:
remember we are just talking SPATIAL finite
timewise it can still go on forever
what is the problem imagining a spatially finite universe?
it is the old "surface of a balloon" thing except the surface of a balloon is only 2D and you have to think of what would be the 3D analog of that.
- #3
wolram
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marcus said:
Hi Marcus, i do not want to go into the philosophy, it is just that i can not
imagine, (get a picture in my mind) of a finite universe, this is a problem i
encounter, i need a picture to make it real.
- #4
Distant
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Indeed it is difficult to imagine a finite Universe. It is much easier to imagine what it must have been like to live in a time before it was known that the Earth was round and that gravity kept us all from falling off the surface. In such a time a similar question to the one of the finite Universe was posed about the surface of the Earth. After all, we can see that the surface extends to the horizon in all directions. If we walk towards the horizon then the limit of the horizon moves with us and we can see how the surface extends further. So surely there can be only two possibilities. Either the surface extends on, forever, and if we carried on walking towards the horizon we would forever encounter new lands, or the surface if somehow ‘bounded’. Maybe we would reach some solid impenetrable wall through which we cannot pass – or maybe we would fall off the edge! (to where exactly wasn’t clear!). Of course, sea voyages set out to investigate the truth of the matter and I am not aware of them encountering either of these problems.
Although we may now view such thoughts in a rather patronising manner, without an understanding of the concepts of gravity and the spherical planet they are natural and logical questions. The spherical shape of the Earth ‘squares the circle’. It does not have a bounded edge to its surface, but it is not infinite – magic! (of a sort).
It required new (rather none intuitive) concepts to understand this problem. We are generally not aware of the curvature of the Earth. The planet is too big and we move too slowly to notice it. It would have been hard to convince to old “flat Earthists” that people living in a far off continent were, in effect, “upside-down” relative us!
Now, back to the Universe. Physicists tell me that the 3 dimensions of space are not the whole story. Time itself can be treated as another dimensions to describe something they call “spacetime”. Just as we once had an inability to notice (or comprehend) the curvature of the Earth (nowadays we can view photos from space easily portraying this) we ‘similarly’ have an inability to notice or comprehend the curvature of this spacetime. Trying not be be a modern day equivalent of a “flat Earthist” we may choose to accept the word (and mathematics and experimental evidence!) of the physicists on this point. The point being is that it is postulated that spacetime if also curved, like the Earth is in 3 dimensions in order to produce a 4 dimensional spacetime Universe that is neither bounded nor infinite.
I fear that a more ‘natural’ understanding of such a ‘closed’ Universe, in the same way as we understand and experience a 3 dimensional ‘closed’ sphere, may not be possible. Maybe because our brains are not set up to work in 4 dimensional spacetime.
However unsatisfying this explanation maybe to the none physicist like myself, it surely surpasses the cosmological equivalent of the brick wall at the edge of the Universe, or indeed ‘falling over the edge’!
Ahhhhhhhh!…………
Although we may now view such thoughts in a rather patronising manner, without an understanding of the concepts of gravity and the spherical planet they are natural and logical questions. The spherical shape of the Earth ‘squares the circle’. It does not have a bounded edge to its surface, but it is not infinite – magic! (of a sort).
It required new (rather none intuitive) concepts to understand this problem. We are generally not aware of the curvature of the Earth. The planet is too big and we move too slowly to notice it. It would have been hard to convince to old “flat Earthists” that people living in a far off continent were, in effect, “upside-down” relative us!
Now, back to the Universe. Physicists tell me that the 3 dimensions of space are not the whole story. Time itself can be treated as another dimensions to describe something they call “spacetime”. Just as we once had an inability to notice (or comprehend) the curvature of the Earth (nowadays we can view photos from space easily portraying this) we ‘similarly’ have an inability to notice or comprehend the curvature of this spacetime. Trying not be be a modern day equivalent of a “flat Earthist” we may choose to accept the word (and mathematics and experimental evidence!) of the physicists on this point. The point being is that it is postulated that spacetime if also curved, like the Earth is in 3 dimensions in order to produce a 4 dimensional spacetime Universe that is neither bounded nor infinite.
I fear that a more ‘natural’ understanding of such a ‘closed’ Universe, in the same way as we understand and experience a 3 dimensional ‘closed’ sphere, may not be possible. Maybe because our brains are not set up to work in 4 dimensional spacetime.
However unsatisfying this explanation maybe to the none physicist like myself, it surely surpasses the cosmological equivalent of the brick wall at the edge of the Universe, or indeed ‘falling over the edge’!
Ahhhhhhhh!…………
- #5
wolram
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A warm welcomb Distant, it all ways gives me a glow inside when people
answer my some times inane questions, your anology with the flat earthers
is good, but when it comes down to all there is, my mind just can not cope,
i try to understand, but some times these theories are just so unintuitive.
answer my some times inane questions, your anology with the flat earthers
is good, but when it comes down to all there is, my mind just can not cope,
i try to understand, but some times these theories are just so unintuitive.
- #6
marcus
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if you keep telling yourself it is unintuitive you will make it worse.
do a series of "analogy pushups"
start by thinking of yourself as a 1D being living on a straight line
who imagines adding a "point at infinity" to his world, an extra point that fills the gap between + oo and - oo
so that if he goes faster and faster to the east he eventually comes whizzing in from the west
and he doesn't believe this is real, it is just an abstract mathematical idea for him
he has INVENTED THE CIRCLE, never having seen one, as a mathematical idea.
then 1000 years later the 1D astronomers uncover evidence in the CMB that their actually is a circularity of the universe. they discover that what was just a math idea is actually REAL and they are left scratching their onedimensional heads.
====================
push up to the next level analogy, think that you are a 2D being living in a flat plane, or one that looks flat to you. being an abstract thinker you imagine that there is a "point at infinity" so that if you go racing off in a straight line in any direction you will eventually come zooming in from the opposite direction
you have INVENTED THE MATHEMATICAL IDEA OF THE SPHERE as best as you can imagine it with your limited 2D wits.
it is like you are at the south pole and of the Earth and it seems like an infinite flat plane, and the point at infinity is the north pole. so any direction you go in, departing from south pole, you eventully return from the opposite direction.
and maybe years later they discover that this idea of a sphere is REAL and actually how nature is.
=====================
push up to the next level analogy, now you are a 3D being living in a regular square-angle normal euclidean 3D space, analogous to the 2D flat plane...and you imagine a "point at infinity" is added to your 3D space so that if you go off in a straight line in any direction then eventually after a long enough time you come back from the opposite direction...
you have done something mathematically creative: you have INVENTED THE SOCALLED "THREESPHERE"
and maybe after hundreds of years the astronomers could supply evidence that what you thought was regular 3D space actually was a threesphere all along. All that time you were living in a threesphere, which you thought was a mere abstract concept.
========================
technically the ordinary sphere----the surface of a balloon---can be called a TWOSPHERE because the local neighborhood of a point looks like a normal flat 2D plane
and a circle or a ring could be called a ONESPHERE because the local nbd of a point looks like a bit of an approximately straight line
so all we are doing is imagining this kind of thing with the dimension jacked up, to get a threesphere
and anyway, Wolram, there are SEVERAL kinds of finite 3D spaces possible------the threesphere is not the only one. there are a whole bunch, just like in the 2D situation you can have donut shapes with more than one hole. But this does not matter. It is enough to just imagine one possible spatially finite 3D thing----and the threesphere is good enough.
Before falling asleep every night, try to imagine that you live in a threesphere, and if you shine a light off in one direction then that same beam of light will eventually get back to you from the opposite. (unless the poor lightbeam has been frustrated by having the space go and expand faster than it can cope with but expansion is another business, ignore that for the while)
do a series of "analogy pushups"
start by thinking of yourself as a 1D being living on a straight line
who imagines adding a "point at infinity" to his world, an extra point that fills the gap between + oo and - oo
so that if he goes faster and faster to the east he eventually comes whizzing in from the west
and he doesn't believe this is real, it is just an abstract mathematical idea for him
he has INVENTED THE CIRCLE, never having seen one, as a mathematical idea.
then 1000 years later the 1D astronomers uncover evidence in the CMB that their actually is a circularity of the universe. they discover that what was just a math idea is actually REAL and they are left scratching their onedimensional heads.
====================
push up to the next level analogy, think that you are a 2D being living in a flat plane, or one that looks flat to you. being an abstract thinker you imagine that there is a "point at infinity" so that if you go racing off in a straight line in any direction you will eventually come zooming in from the opposite direction
you have INVENTED THE MATHEMATICAL IDEA OF THE SPHERE as best as you can imagine it with your limited 2D wits.
it is like you are at the south pole and of the Earth and it seems like an infinite flat plane, and the point at infinity is the north pole. so any direction you go in, departing from south pole, you eventully return from the opposite direction.
and maybe years later they discover that this idea of a sphere is REAL and actually how nature is.
=====================
push up to the next level analogy, now you are a 3D being living in a regular square-angle normal euclidean 3D space, analogous to the 2D flat plane...and you imagine a "point at infinity" is added to your 3D space so that if you go off in a straight line in any direction then eventually after a long enough time you come back from the opposite direction...
you have done something mathematically creative: you have INVENTED THE SOCALLED "THREESPHERE"
and maybe after hundreds of years the astronomers could supply evidence that what you thought was regular 3D space actually was a threesphere all along. All that time you were living in a threesphere, which you thought was a mere abstract concept.
========================
technically the ordinary sphere----the surface of a balloon---can be called a TWOSPHERE because the local neighborhood of a point looks like a normal flat 2D plane
and a circle or a ring could be called a ONESPHERE because the local nbd of a point looks like a bit of an approximately straight line
so all we are doing is imagining this kind of thing with the dimension jacked up, to get a threesphere
and anyway, Wolram, there are SEVERAL kinds of finite 3D spaces possible------the threesphere is not the only one. there are a whole bunch, just like in the 2D situation you can have donut shapes with more than one hole. But this does not matter. It is enough to just imagine one possible spatially finite 3D thing----and the threesphere is good enough.
Before falling asleep every night, try to imagine that you live in a threesphere, and if you shine a light off in one direction then that same beam of light will eventually get back to you from the opposite. (unless the poor lightbeam has been frustrated by having the space go and expand faster than it can cope with but expansion is another business, ignore that for the while)
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- #7
wolram
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Thankyou very much Marcus, what you say in words makes perfect sense,
but to form an image in ones mind is much harder, maybe i am to stupid, i wish i could understand.
but to form an image in ones mind is much harder, maybe i am to stupid, i wish i could understand.
- #8
marcus
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it makes it worse to keep supposing that one is stupid---one is a human and that involves certain brain limitations which one tries cheerfully to overcome.
try to imagine what it would be like to BE IN a certain space
don't try to imagine what it would look like to a God who is somehow on the outside of it.
we are not asked to imagine what it would look like to an higherdimensional being outside of space
just get a feel for what to expect if you are a 3D creature, which we all are, living in a threesphere
all it means, really, is that if you send a lite-beam off in some direction out in front eventually it will come back from behind you
as 2D creatures living on a Twosphere (the surface of the earth) we are ALREADY USED TO THAT kind of behavior-----of being able to head off in some direction and eventually get back to the same place having gone around
so the analog (3D "flat" space with a point at infinity added) can't be so hard to imagine what it would be like to live in
(forget about God's point of view, just imagine living in it)
try to imagine what it would be like to BE IN a certain space
don't try to imagine what it would look like to a God who is somehow on the outside of it.
we are not asked to imagine what it would look like to an higherdimensional being outside of space
just get a feel for what to expect if you are a 3D creature, which we all are, living in a threesphere
all it means, really, is that if you send a lite-beam off in some direction out in front eventually it will come back from behind you
as 2D creatures living on a Twosphere (the surface of the earth) we are ALREADY USED TO THAT kind of behavior-----of being able to head off in some direction and eventually get back to the same place having gone around
so the analog (3D "flat" space with a point at infinity added) can't be so hard to imagine what it would be like to live in
(forget about God's point of view, just imagine living in it)
- #9
Chronos
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While a spatial finite universe is difficult to imagine, a temporally finite universe is less difficult. It is, for me, easy to picture a universe where you are both at the center and the edge due to the finite speed of light.
- #10
wolram
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Thanks Marcus, i do have a picture now, it may be a little fuzzy, almost
abstract, but at least i can think about it now.
abstract, but at least i can think about it now.
- #11
Silverbackman
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Hmmm, so I guess it is impossible to imagine looking a threesphere like we look at a balloon or a ball. Damn I hate being human.
Then again I know more than a being from a dot, circle, and twosphere world. Is it possible for a foursphere, fivesphere, ect. ect. till infinite? Of course we can't imagine these other spatial dimensions, similar to how a 2D being wouldn't be able to imagine a 3D world or twospere.
But doesn't the known curvature of the universe suggest that we live in a flat universe and not a saddle or sphere universe? If so then how can we be living in a threespere?
Then again I know more than a being from a dot, circle, and twosphere world. Is it possible for a foursphere, fivesphere, ect. ect. till infinite? Of course we can't imagine these other spatial dimensions, similar to how a 2D being wouldn't be able to imagine a 3D world or twospere.
But doesn't the known curvature of the universe suggest that we live in a flat universe and not a saddle or sphere universe? If so then how can we be living in a threespere?
- #12
SpaceTiger
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Silverbackman said:
I don't understand the question...
Measurements of flatness are local. If inflation occurred, then the universe will be much, much larger than the region of space we can observe and, regardless of its true large-scale geometry, it will appear flat to our instruments. It's basically the same reason the ancients thought the Earth was flat -- they could only see a very small part of it.
If inflation had not occurred, however, this wouldn't be the case and we should, in principle, be able to measure the curvature of the entire universe.
- #13
wolram
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I have an idea to call my image the, ( frustrated boomerang), curved space
with expasion.
with expasion.
- #14
VikingF
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SpaceTiger said:
I think he wondered how many dimensions that can possibly exist. If there may be "infinitely many" dimensions... (1D,2D,3D,4D,...,?D).
- #15
-Job-
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One second though. The possibility that we live in continuous unbounded universe, the equivalent of a 4D sphere follows rationally and is more plausible than a finite universe or an infinite universe that does not "wrap-around". But regardless, if we live in a 4D sphere, then this 4D sphere is in 4D space. How is this 4D space then bounded? Is it infinite or finite? Does it wrap around? The alternative is that we live in a 4D sphere which does not reside in space, but then the notion of dimensions should not apply, and it's not a 4D surface at all.
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- #16
Silverbackman
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wolram said:
You mean torus?
Yea, I wonder what a eightsphere universe would look like.
Or how about a 1,678,489,986sphere?- #17
Flatland
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I actually have a problem imagining an infinite universe. And a universe with an infinite dimensions? you wouldn't be able to go anywhere.
- #18
setAI
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I conjecture that it is possible for a finite AND flat universe without the topology of a torus or similar form- in fact it can have ANY arbitrary topology as long as it is closed-
how? it is a natural result of computational /category theories and some forms of LQG where the metric of spacetime itself emerges from relationships- for instance the universe can be decribed as a 2-dimensional lattice of 2in/2out quantum logic gates- one could construct such a lattice of quantum logic gates on the surface of a sphere- or any other closed shape- yet the topology of the emergent spacetime metric could compute a FLAT spacetime that wraps around-
consider a classical computational analog: the game Asteroids- where the ship flies straight but wraps around when it hits the edge of the screen- the virtual space of the ship is flat- but the edges are connected in the software- so the virtual space is finite yet unbounded
how? it is a natural result of computational /category theories and some forms of LQG where the metric of spacetime itself emerges from relationships- for instance the universe can be decribed as a 2-dimensional lattice of 2in/2out quantum logic gates- one could construct such a lattice of quantum logic gates on the surface of a sphere- or any other closed shape- yet the topology of the emergent spacetime metric could compute a FLAT spacetime that wraps around-
consider a classical computational analog: the game Asteroids- where the ship flies straight but wraps around when it hits the edge of the screen- the virtual space of the ship is flat- but the edges are connected in the software- so the virtual space is finite yet unbounded
- #19
VikingF
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Silverbackman said:Yea, I wonder what a eightsphere universe would look like.
Yeah... Me too!
:tongue: According to String theory, there exist 10 dimensions, and M-theory says that there exist 11.
- #20
Silverbackman
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VikingF said:Yeah... Me too!
According to String theory, there exist 10 dimensions, and M-theory says that there exist 11.
Yea but they say those dimensions may just exist. It doesn't have anything to do with the universe being a tensphere or elevensphere I think. Or does it?
Actually it probably does because I assume 10 or 11 dimensions cannot exist unless is within some sort of nsphere (or something like an nsphere).If we do live in a threesphere only that would mean there are four spatial dimensions and one dimension of time. That sounds pretty aesthetically perfect considering 5 is a "perfect" number. Both 5 and 10 seem like aesthetically perfect because of their place on the number line. Why an omnipotent God or even randomness of Nature would pick 4, 7, or 11 as the "official" number of one of the most important aspects of our universe is beyond me.:uhh:
- #21
Garth
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There is an anthroopic argument as to why we are living in a 3D + time universe.Silverbackman said:
Time is necessary for process, we exist and evolution of complex beings requires process, therefore time.
In a 1D or 2D spatial universe there is not enough topological freedom for complex organic molecules to operate, the 3D geometry is important for proteins etc. to 'do their stuff'. Hence we cannot exist in a spatial 1D or 2D universe.
Keplerian orbits are unstable in a spatially 4D or higher universe. The Newtonian law of gravity becomes [itex]F = GMm/r^3[/itex] in a 4D universe for example and the Earth would spiral into or away from the Sun. Hence we cannot exist in a spatial 4D or higher universe.
We exist: therefore our universe has 3 space D + time.
Garth
- #22
VikingF
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Silverbackman said:Yea but they say those dimensions may just exist. It doesn't have anything to do with the universe being a tensphere or elevensphere I think. Or does it?
No, if I have not misunderstood it completely, String theory says that our universe is one of infinitely many three dimensional (or four with time) universes in an infinite ten- or eleven dimensional multiverse.
It's like the drawing on the piece of paper in front of me is two dimensional in a four dimensional universe.
- #23
Garth
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The normal understanding is to ask: "If there are more than 3 spatial dimensions why do we not observe them?" The answer given in string theory is that the extra dimensions are 'rolled' up like a 2D sheet of paper rolled up into a 'straw' with length and very little width. The extra widths are too small to observe normally, and do not affect dynamics such as Keplerian orbits as in my post #21 above, but may be observed microscopically, such as by minute changes in Newtonian gravity at very small ranges.
Garth
Garth
- #24
Silverbackman
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Garth said:There is an anthroopic argument as to why we are living in a 3D + time universe.
Time is necessary for process, we exist and evolution of complex beings requires process, therefore time.
In a 1D or 2D spatial universe there is not enough topological freedom for complex organic molecules to operate, the 3D geometry is important for proteins etc. to 'do their stuff'. Hence we cannot exist in a spatial 1D or 2D universe.
Keplerian orbits are unstable in a spatially 4D or higher universe. The Newtonian law of gravity becomes [itex]F = GMm/r^3[/itex] in a 4D universe for example and the Earth would spiral into or away from the Sun. Hence we cannot exist in a spatial 4D or higher universe.
We exist: therefore our universe has 3 space D + time.
Garth
This maybe true for our universe but I'm sure a 1D or 2D universe may have different laws of nature. In these universes organic molecules may not be needed to create matter that can become conscious. So anything maybe possible even if it is beyond our current reasoning. As human beings we can't imagine how it would be to live in a 2D or 6D universe. But this all sort of enters the realm of philosophy. There is no proof either way one whether conscious beings can evolve in a 1D or 2D universe. We can't exist in these universes but perhaps in another universe matter can adapt to whatever dimension limitations it may have.
If our universe cannot be spatially 4D, how can we live in a finite threesphere? Wouldn't an extra dimension be needed in order for our 3D universe to curve into a round shape where if you go in one direction that you will come back in another direction?
It is similar to the notion of a 1D being living in a round universe. To him reality is only on the X-axis but if his universe is round then his universe is actually a circle. Circles are 2D. Perhaps the some total of our 3 known spatial dimensions add up to a 4th spatial dimension when curving.
Yea but how can other universes exist in these other dimensions that are rolled up. And how do we there is an infinite amount in only a 10D or 11D universe.
- #25
Balence
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Any shape still has space out side of it, therefore the universe is still infinite. As far as extra dimensions most were created because the mathematics in a theory did not add up so they made alternet dimensions to prove their theory right, they have no proof for these dimensions (besides the faulty equations that gave birth to them) and there are 3 spatial dimensions, all of which are abstract. The dimension of time isn't a dimension on dictionary terms but since it is used to measure can be qualified as a dimension. Any thing that exsists must have and can only have length, width, height, and a place in time. Time is also abstract.
- #26
SpaceTiger
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Balence said:
There's no necessity for something "outside" of a finite universe. It need not be embedded in another space to reproduce what we observe.
- #27
Aki
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marcus said:
So does the shape of our universe has anything to do with the Calabi-Yau theory?
- #28
string querry
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the surface of the balloon is 2D
the surface of the balloon is 2D, yes, but why do the theorist always use the surface of the ballon. Why not the volume of the ballon, such as a balloon fuill of gel. Something in the volume of the balloon wil still expand away from anything else in the volume, assuming the the balloon is filled with more gel from a central point of origin, and also discounting gravity/and velocity ie: filling the balloon in a zero-G environment.
marcus said:
the surface of the balloon is 2D, yes, but why do the theorist always use the surface of the ballon. Why not the volume of the ballon, such as a balloon fuill of gel. Something in the volume of the balloon wil still expand away from anything else in the volume, assuming the the balloon is filled with more gel from a central point of origin, and also discounting gravity/and velocity ie: filling the balloon in a zero-G environment.
- #29
string querry
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Yep
Exaclty what I've been thinking for years, but nobody on any of the plethora of Education programs every metnions it. I think the closest I've come to finding that idea was a rather bogus documentary where the "expert" decide that were are all living in a "Matrix" virtual universe. Maybe his right, but that's more of a religion than science...but the basic idea of any point in a curvature having flat properties relative to other points if the properties with the curvature are natural to that state--i agree that is possible, but I don't have the math skills to prove it, and the people that do have the skills can't agree with each other and call each other morons, so such ideas are far ahead of their time and currently trapped in science fiction.
setAI said:
Exaclty what I've been thinking for years, but nobody on any of the plethora of Education programs every metnions it. I think the closest I've come to finding that idea was a rather bogus documentary where the "expert" decide that were are all living in a "Matrix" virtual universe. Maybe his right, but that's more of a religion than science...but the basic idea of any point in a curvature having flat properties relative to other points if the properties with the curvature are natural to that state--i agree that is possible, but I don't have the math skills to prove it, and the people that do have the skills can't agree with each other and call each other morons, so such ideas are far ahead of their time and currently trapped in science fiction.
- #30
marcus
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string querry said:
hello querry,
this is a question you should ask directly to cosmology theorists!
fortunately we have some here at PF. Garth is an active cosmologist (I think with a different day job). SpaceTiger is a PhD student in Cosmology at princeton. He could already have his PhD now, since it is Summer and the semester is over.
I forget who else. Anyway I expect they would be happy to tell you why working cosmologists always use the surface of the balloon (notice that the "sphere" has no edges, no boundary, a creature living in it would never need to encounter a barrier or a higher dimension region, which might have some relevance to your question)
but I ALSO expect that they would be happy for you to believe whatever you want about the universe!
You can believe it is a balloon full of gel if that is what you like. I personally see no reason why you should feel obliged to get in contact with the mainstream professional cosmologist picture.
I guess I will pass on this question and let someone else explain the theorist's preference.
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- #31
Garth
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It is only a model to help people conceptualize the idea of spherical space.string querry said:
3D space is a 'space-like' slice or 'foliation' of 4D space-time.
We cannot visualize 4 dimensions - at least I cannot - and therefore in order to get the idea across, and for students to 'see' what we are talking about, it is helpful to reduce the number of dimensions and suppress one of the space dimensions.
Thus a 3D spherical surface becomes the 2D surface of a sphere - i.e. its surface and not its interior.
Reduce one more space dimension and the 2D spherical surface becomes the 1D line of a circle.
In each case 1D, 2D or 3D these hypersurfaces share the common property of being finite in extent yet unbounded.
Theorists do not always use the surface of a balloon, which is a model of spherical space.
Space can also be flat (the surface of a flat sheet of paper) or hyperbolic (the saddle point of a saddle). These spaces share the common property of being infinite in extent yet unbounded.
Although we visualize these spaces 'from outside' it is also possible to test to see what kind of space we are living in by its intrinsic geometry. Euclidean geometry only holds for a flat space. A triangle's interior angles sum to 1800. In a spherical space a triangle's interior angles sum to > 1800, and in a hyperbolic space they sum to < 1800, for example.
I hope this helps.
Garth
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- #32
string querry
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Garth said:
THanks! Incredible explanation!
One question, from another thread with no asnwer yet:
Am I stretching the accuracy of the illustration if I infer from it that the "shape" of space/time is spherical (I do not mean in terms of three dimensional space, I know that the universe is not an orb, but in the sense that the furthest point from any given point has the same differential as the differntial between any other given point and the point furthest from it--is that making any sense? I'm trying to define the shape with as little 3Dness as possible) Is that extracting something from the illustration after the point that it breaks down. The reason I ask is that, if so, regardless of any expansion or contraction of the universe, the "shape" would not change and wouldn't all points of space time maintain the same ratios of distance/differencial from each other. Also, would this mean that the universe would have no end, center or edges, just as the surface of a sphere has no center, end or edges?
- #33
scarecrow
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The universe we live in is probably like a membrane (finite of course, but expanding nonetheless)...like an expanding balloon. But then you ask, "what's outside the membrane?" Well, my answer would be the higher dimensional universes. Overall, it would seem that it would be infinite, but then we'd have to go into religion.
- #34
wolram
Gold Member
Dearly Missed
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Cossmology needs occams razor, not pandoras box.
- #35
Thor
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If the universe was finite then for any given point there must exist another point within a finite distance at which motion in any direction will not increase the distance between the two.wolram said:
Bend it, twist it, tie it in a knot, a finite Universe is hogwash.
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