How Can We Comprehend the Concept of a Finite Universe?

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Imagining a spatially finite universe poses significant challenges, as it requires conceptualizing dimensions beyond our typical experience. The discussion draws parallels between understanding a finite universe and historical misconceptions about Earth's shape, emphasizing that our brains may struggle with higher-dimensional concepts. Analogies involving lower-dimensional beings illustrate how humans might grasp the idea of a finite universe, such as a "threesphere," where traveling in one direction eventually leads back to the starting point. The conversation also touches on the implications of cosmic inflation, suggesting that while the universe appears flat locally, its true geometry may be more complex. Ultimately, the difficulty lies in visualizing these abstract ideas within the limitations of human cognition.
  • #31
string querry said:
the surface of the balloon is 2D, yes, but why do the theorist always use the surface of the ballon.
It is only a model to help people conceptualize the idea of spherical space.

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
Garth said:
It is only a model to help people conceptualize the idea of spherical space.

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...
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

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
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
Cossmology needs occams razor, not pandoras box.:smile:
 
  • #35
wolram said:
How do you imagine a finite universe ? i find it very difficult.
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.

Bend it, twist it, tie it in a knot, a finite Universe is hogwash.
 
  • #36
Thor said:
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.

Not if that point is itself moving! Think again about the expanding balloon analogy. Any two points on the surface of the balloon are receding from one another as the balloon expands.
 
  • #37
The FRW model pretty much excludes that concept, Thor. I do not understand your point. Are you conserving energy, or ignoring it? What I do see is an effort to introduce an Arpian twist into this discussion.
 
  • #38
Thor said:
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.

Bend it, twist it, tie it in a knot, a finite Universe is hogwash.
Are you considering spherical space?

In which case your two points would be each other's antipodes.
In a static universe your statement would be true, just as on the Earth's surface any direction moved from the South Pole takes you closer to the North Pole, what is hogwash about that?

In an expanding universe these distances would be increasing, but still the distance between the two antipodean points would be a maximum of all distances in the universe at anyone cosmological epoch.

Garth
 
  • #39
SpaceTiger 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.
Your absolutly right, it doesn't have to be something. It could be nothing, empty space, going on infinitly. Our observations are limited by our finite knowledge.
 
  • #40
scarecrow said:
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.
Please define higher dimension. I know the proper definition of dimension is: A measure of spatial extent, expecially width, heigth, or length. Its not feasible for their to be any further dimensions, unless you count time, which isn't spatial but has a relationship to distance none the less. As from what I've learned of many of the theories of extra dimensions, the extra dimensions are mathimatical fillers for theory equations that did not make sense. (string theory for example) Like me saying two plus two equals five because of the other dimension. Also how is an infinite universe religion? Higher dimensional universes sounds much more religious. Wheres occams razer when you need it?
 
  • #41
Balence said:
Your absolutly right, it doesn't have to be something. It could be nothing, empty space, going on infinitly.

In GR and QFT, "empty space" is something. I'm saying that there need not be anything other than the universe we observe and that this universe could be finite in size.
 
  • #42
SpaceTiger said:
In GR and QFT, "empty space" is something. I'm saying that there need not be anything other than the universe we observe and that this universe could be finite in size.
There either has to be something or nothing out side the observable universe, if there's nothing, it stretches on infinitly having the potential to be filled by something. Also nothing must have the potential to produce something, or we will never find a complete answer to the beggining of the universe, thus the nothing out side our obserable universe has or will give way to new matter or energy. As nothing stretches on infinitly given infinite time mean that probally there's "stuff" out side our observable universe and its impossible to know what because its unubservable. Much like trying to see beyond the horizon.
 
  • #43
Balence said:
There either has to be something or nothing out side the observable universe, if there's nothing, it stretches on infinitly having the potential to be filled by something.

Nothing is just nothing, it doesn't stretch out infinitely and it's not the same as empty space. The concept of "outside" isn't even necessary here. The universe, by definition is all that there is. It doesn't make sense to talk about anything outside of it and there's no reason that it can't be finite.


As nothing stretches on infinitly given infinite time mean that probally there's "stuff" out side our observable universe and its impossible to know what because its unubservable.

Most current theories do suggest that there is stuff outside of our observable universe, but when we talk about a finite vs. infinite universe, we're usually talking about the entire universe, even that which is unobservable.

This will be hard for you to understand without a little background in general relativity. You might want to browse the "Special and General Relativity" forum a bit.
 
  • #44
Anything that is finite has boundries. It would seem logicaly that this conflicts with the universe being all there is, as that definition should include what's inside, outside, and the boundries themselves. Even with the curvature of space creating a finite boundry for humans or any other form of matter or energy to travel, does not make the universe finite. Perhaps the limitations due spacecurvature is what's ment by the term universe, and I am taking it a bit literally. Though I still believe an "outside" would be more than relevant and logical.
 
  • #45
Balence said:
Anything that is finite has boundries.
Not true - otherwise sailors would still be worried about 'falling off the end of the world'.

Garth
 
  • #46
Garth said:
Not true - otherwise sailors would still be worried about 'falling off the end of the world'.

Garth
Sailors never were astronauts though, "the world" is still finite and still has its boundries which have been crossed.
 
  • #47
ultimately I think that the very idea of a universe finite or infinite with a 'boundary' is wrong-headed- a thing like a universe emerges from the relationships of a causal network- the metrics of distance/duration are established by the relationships of the elements in the network- a boundary is only an arbitrary concept of where one can fit the abstract map of such a causal set in an imaginary mathematical space- but there is no reason for that map-space to exist in any physical way- the elements and events that arise in a causal network don't connect to any kind of outside boundary- causality and the metrics of space and time that emerge from it propagate locally through the elements/events in the network ONLY- there is no spatial/temporal analog of a 'boundary' to be fenced-in by-

given this- my thinking is that emergent systems of relationships that arise form causal networks -like universes [whether they are infinite or finite]- are boundary invariant
 
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  • #48
In the paper "Philosophical Implications of Inflationary Cosmology" by Joshua Knobe, Ken D. Olum and Alexander Vilenkin, there is a theory saying that the universe actually is infinite (see ch 2.2). I am no cosmologist, but the way I understand it, this is somehow a consequence of the inflation theory. I don't quite understand this, because I thought it almost was a "proven fact" that our universe is finite, and not infinite...? :confused:

Anyway, here is the paper:
http://arxiv.org/pdf/physics/0302071
 
  • #49
VikingF said:
In the paper "Philosophical Implications of Inflationary Cosmology" by Joshua Knobe, Ken D. Olum and Alexander Vilenkin, there is a theory saying that the universe actually is infinite (see ch 2.2).

You might want to check out this paper by Linde (a big name in inflationary theory):

http://arxiv.org/abs/hep-th/0408164"

People often assume, for simplicity, that the universe would have trivial topology. If this is not the case (and Linde's paper suggests that it shouldn't be), then an inflationary universe can be finite.

Keep in mind that much of this stuff is a long way from experimental testing -- science is probably a long way from providing a definitive answer to the finite/infinite question.
 
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  • #50
  • #51
setAI said:
ultimately I think that the very idea of a universe finite or infinite with a 'boundary' is wrong-headed- a thing like a universe emerges from the relationships of a causal network- the metrics of distance/duration are established by the relationships of the elements in the network- a boundary is only an arbitrary concept of where one can fit the abstract map of such a causal set in an imaginary mathematical space- but there is no reason for that map-space to exist in any physical way- the elements and events that arise in a causal network don't connect to any kind of outside boundary- causality and the metrics of space and time that emerge from it propagate locally through the elements/events in the network ONLY- there is no spatial/temporal analog of a 'boundary' to be fenced-in by-

given this- my thinking is that emergent systems of relationships that arise form causal networks -like universes [whether they are infinite or finite]- are boundary invariant
Theories for finite univeres I've researched have a shape whether its a hypersphere or a dodecahedron and a way for it to seem boundless whether its mirrors or traveling so far you return to where you started. A good example I feel is a pac man game (no offense). It has a shape and is boundless for pac man. As pac man travels he notices he always returns to his starting point even if traveling in a strait line, he correctly concludes that the curvature of digital space must be the cause. He also assumes the universe must be finite. However one day he tries an experiment. He finds a large dot and specialy marks it then travels in a strait line counting all the small dots till he returns to his large dot. He counted 1000 dots so he can rightfully assume that the distance across his universe is 1000 dots. He then repeats the experiment with other large dots and compares his finding thus being able to pin point where the warp occurs, or where the boundry of his possible travels. He can then do a thought experiment in which he travels 10,000 dots from the large one without traveling through the warped space. He then can consider the possibility of an infinite universe. My point is that a finite universe by nature has boundries. In the end I come to the same conclusion of universes being boundry invairiable and since a finite universe must have a boundry I personaly conclude that the universe must be infinite. Additionaly the hyperspere uses multiple dimensions to prove it correct. For one pac man is not 2D he is made of pixels which are 3D, they have length width and height regardless of how small. Second its impossible to conceive these dimensions because we are 3D (the theories own argument) therefore it seems scientificly unsound.
 
  • #52
VikingF said:
I don't quite understand this, because I thought it almost was a "proven fact" that our universe is finite, and not infinite...? :confused:
Finite universes is taught as almost proven fact by many teachers and professers. The idea of a finite universe is very comforting vs an infinite one because we can fully understand (over time) a finite universe. A infinite universe can have a large number of possible contradicting laws and is very chaotic thus limiting what we can hope to understand. Though I personaly believe over time we will find laws to explain the chaos. Additionaly history has shown man prefers to be as important as can be, an infinite universe makes us even smaller and more insignificant.
 
  • #53
SpaceTiger said:
Keep in mind that much of this stuff is a long way from experimental testing -- science is probably a long way from providing a definitive answer to the finite/infinite question.
I agree, only time will tell for sure. Hopefully though it will be rather soon so I can start my victory dance.
 
  • #54
Balence said:
...He counted 1000 dots so he can rightfully assume that the distance across his universe is 1000 dots. He then repeats the experiment with other large dots and compares his finding thus being able to pin point where the warp occurs, or where the boundry of his possible travels.

Care to explain how Mr. Pac-Man made this last deduction?
 
  • #55
Balence said:
I agree, only time will tell for sure. Hopefully though it will be rather soon so I can start my victory dance.

Your ideas are not falsifiable and can't really be called science. Basically, it sounds like you're asserting that any self-contained finite universe must be embedded in a larger space (as per the "boundaries" you speak of). I disagree with you on philosophical grounds, but we can never disprove your assertions any more than we can disprove the existence of a "creator". If this infinite space you speak of is out of causal contact with our universe, then there's nothing we can do to detect it.
 
  • #56
Teecher said:
Care to explain how Mr. Pac-Man made this last deduction?
He conveniently has a living space in which every straight line of dots going horizontaly have 1000. Conveniently each big dot is one small dot down and to the right of the first big dot. Conveniently the horizontal dots are equal to the vertical so both dimensions are 1000. Using the big dots as markers packman can create a map that would show a declining line of big dots slanting through the center of his finite space. From this he can conclude where the warp is. You can also try drawing it out on graph paper. If this doesn't work then he kept getting digispace sick and figured it must be that warped space. I really wanted to get to the point and wanted to get off pac man so I skiped how he might figure this out.
 
  • #57
SpaceTiger said:
Your ideas are not falsifiable and can't really be called science. Basically, it sounds like you're asserting that any self-contained finite universe must be embedded in a larger space (as per the "boundaries" you speak of). I disagree with you on philosophical grounds, but we can never disprove your assertions any more than we can disprove the existence of a "creator". If this infinite space you speak of is out of causal contact with our universe, then there's nothing we can do to detect it.
At this point my theory does loose scientific value due to the fact we can not currently detect this infinite space. However, many current finite theories have even less scientific value and are widely accepted as known truth despite the inability to properly test them thus making them even more unscientific. According to occams razor an infinite universe is more feasible than a finite one. I only assume one thing that is rational, and keep it simple. Finite theories assume alot, much of which is "inconcievable" to us, (irrational) have simular instances in history, (earth being in the center, spontaneous generation) finnaly, and coinciding with my last point, the idea is very alluring as the universe is more predictable if its finite. Additionaly there are several different finite universe theories out there. My point is that while infinite universe theory can be compared to theories of a "creator" its much more closer to compare "creator" with finite theories.
 
  • #58
Balence said:
He conveniently has a living space in which every straight line of dots going horizontaly have 1000. Conveniently each big dot is one small dot down and to the right of the first big dot. Conveniently the horizontal dots are equal to the vertical so both dimensions are 1000. Using the big dots as markers packman can create a map that would show a declining line of big dots slanting through the center of his finite space. From this he can conclude where the warp is.

How does he know where to put the big dots such that they pass through the center?

Let's try a simpler example to ensure that we're on the same page. Suppose Pac-Man is confined to one dimension (a line). You see him on the screen, moving along the line. From your point of view, he keeps moving to the edge of your screen until he reaches the "warp" point and then comes out the other side. But does this warp point have any significance to Pac-Man? On an initially unmarked line, is there any point along the line that is different from the other? No, from his point of view, it's just a line seeming to extend off infinitely in either direction. He can determine the size of his finite universe by simply marking a point and seeing how long it takes to come back to it. However, there's way for him to know if that point is on the edge or the center of your screen.

The situation is similar in 2-D. The initially unmarked landscape is just a plane seeming to go off inifinitely in all directions. He can mark any set of points that he likes, but there's no way for him to know where these points lie in relation to the center of your screen or the "warp", as you put it.
 
  • #59
Balence said:
At this point my theory does loose scientific value due to the fact we can not currently detect this infinite space.

We could never detect infinity to start with, but what's worse is that there is no hypothetical observation that could prove your theory wrong. You could always just say that we're out of causal contact with this extra universe.


However, many current finite theories have even less scientific value and are widely accepted as known truth despite the inability to properly test them thus making them even more unscientific.

All current scientific theories are hypothetically testable, but many are beyond the reach of current technology. Your theory is not falsifiable even in principle.


According to occams razor an infinite universe is more feasible than a finite one.

Actually, occam's razor says nothing about an infinite versus a finite universe. If, however, we discovered that the universe was finite, one could invoke occam's razor to support the case for a universe with no boundaries.


My point is that while infinite universe theory can be compared to theories of a "creator" its much more closer to compare "creator" with finite theories.

I think you've misunderstood. I'm not comparing infinite theories to theories of a creator, I'm comparing your "universe with boundaries" idea to that of a creator. Infinite universes are commonplace in mainstream science.
 
  • #60
an odd thing- you can in principle prove the universe is finite- if it is- but can you EVER prove or even know if it is infinite? I would think that locality makes it impossible even in principle-
 

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