Proving the universe is infinite
Let`s imagine a library from one cylindrical chamber and suppose it`s a finite universe; every book must contain a part from the existing information and images so that all the data is contained; also the information and the images of them – of their covers, of their files and of the ensemble cover-pages/ exterior- interior- must be contained. From here we distinguish two possible cases: the data about the books can be divided and shared between them or we have another book which contains the data and the images about the others. In any of the cases, there still remains data not included: case 1.the image of the book containing solely the information about others and 2.the images of the ``new books``, the old books containing now more information, which asserts a new form and more space.
If we try to incorporate them in: a bigger book, there still remains free data about that book or in the same volumes, adding files, we still have this second generation of containers to be added to The Library.
So, whatever we do, we always have the newest forms/containers not contained. The essence: if we try to have all the information we need a place to put it and for the information about that place we need another space and so on, ad infinitum.
As an universe needs to contain everything, it needs to contain his actual form and, as he can`t do this as a limited universe or as a ``possibly infinite`` universe (because in order to contain himself it needs to update so the ``newest`` form is never contained even if grows progressively and becomes a ``possibly infinite`` universe*) we can have only an ``actually infinite`` universe.
Finally, I can`t make suppositions in the domain of physics but I can say only that it will never prove the universe if limited: it will prove only that a part of our universe is limited. And, why not, if the universe is infinite, then there can`t be more universes or multiverses, because they would juxtapose. There can be only places outside the ``bubble`` of matter we live in/ places that don`t respect the laws of physics, if the ``bubble`` of matter is actually infinite.
Note: here are the definitions of the universe: ``the universe: all of space and everything in it`` Merriam Webster; ``The Universe is all of time and space and its contents`` Wikipedia;
`` The sum of everything that exists in the cosmos, including time and space itself`` Wiktionary.
*The assumption that no finite universe ever reaches infinity doesn`t assume it`s still finite, because it grows continuously and progressively and can`t be measured.
If we try to incorporate them in: a bigger book, there still remains free data about that book or in the same volumes, adding files, we still have this second generation of containers to be added to The Library.
So, whatever we do, we always have the newest forms/containers not contained. The essence: if we try to have all the information we need a place to put it and for the information about that place we need another space and so on, ad infinitum.
As an universe needs to contain everything, it needs to contain his actual form and, as he can`t do this as a limited universe or as a ``possibly infinite`` universe (because in order to contain himself it needs to update so the ``newest`` form is never contained even if grows progressively and becomes a ``possibly infinite`` universe*) we can have only an ``actually infinite`` universe.
Finally, I can`t make suppositions in the domain of physics but I can say only that it will never prove the universe if limited: it will prove only that a part of our universe is limited. And, why not, if the universe is infinite, then there can`t be more universes or multiverses, because they would juxtapose. There can be only places outside the ``bubble`` of matter we live in/ places that don`t respect the laws of physics, if the ``bubble`` of matter is actually infinite.
Note: here are the definitions of the universe: ``the universe: all of space and everything in it`` Merriam Webster; ``The Universe is all of time and space and its contents`` Wikipedia;
`` The sum of everything that exists in the cosmos, including time and space itself`` Wiktionary.
*The assumption that no finite universe ever reaches infinity doesn`t assume it`s still finite, because it grows continuously and progressively and can`t be measured.
Comments (48)
"The only constant is change."
Science makes a pretty good case that the universe we inhabit is finite, so one could speculate that there has to be something outside of our universe, something different. But it is impossible, so far, for science to see what that might be, or the extent of it, so currently the topic is moot.
EDIT: I buy the Big Bang theory. That is only a theory, but it makes more sense to me than the theory that the universe has no beginning or end, that it was always here and will always remain as it is for all eternity.
You just didn`t understand what I have said there and my point: to prove this model of universe including everything within can`t be limited.
Then can we have a limited universe containing everything we know of? The known universe, meaning everything we can see.
Quoting Asktheshadow
I'm really trying hard to follow you here. In order to contain everything, there has to be something that does the containing, and that something falsifies the definition of everything?
Quoting Asktheshadow
The definitions should say "everything in the known universe. Everything we can see."
Quoting Asktheshadow
Again you are personifying something, God, all of creation? That is a different argument. And I don't follow the "newest form" If all of creation stepped outside itself to contain itself, there would be another him?
Quoting Asktheshadow
But there is a limit to the known universe. Everything, as you say, also includes what might or might not be outside of the known universe, beyond the limit. There is no way we can know what is there. Science ignores it altogether. There is no way to prove that Everything that exists is without limit.
His library is finite but the number of books (all possible combinations of letters) would exceed the number of estimated atoms in our universe by a tremendous magnitude. You could travel among recognizable copies of Moby Dick for your lifetime.
One of the imaginary librarians speculates that all is needed to reproduce this finite library is a single volume, since all books are limited to 26 letters and whatever the repeating format is.
I wonder what silly number the permuted arrangement of periodic elements would give us, given the amount of atoms there are in the universe.
Infinity has no meaning if we are finite creatures. Infinity also has no meaning if we are infinite creatures, because it's all relative to the scope of what we experience, whether we agree upon finity or infinity as a qualitative description.
In an infinite world maybe contradictions are permitted. The meaningless is meaningful. Infinity is finity, et cetera.
Now think at Laplace`s point: if we would live everything in universe at a point in time and if the universe is infinite, and we are infinite, then we should have lived all the possibilities, all the scenes of the movie without scrolling them. Here is the first contradiction in what you say: how can a infinite consciousness experience infinity from a relative point, if it experiences all the points?Quoting Nils Loc
Maybe, but in one part of it. Nobody says things have to repeat in an actually infinite world. In a limited world that begins a process of growing to infinity by repeating, maybe this rule of canceling would repeat in more parts of the universe, but this still doesn`t means this permitted contradictions would overlap other rules. Thinking at this, if ``Infinity is finity`` maybe finity could be infinity, and we only changed the positions( finity becomes infinity, infinity becomes finity and nothing changed).
Yes, I`ve read his stories and others and I loved them!
Depending upon which unit we use to measure the coastline of England, the kilometer, meter, the centimeter, the femtometer with respect for accuracy and precision, the end values change. At some point it is impractical and useless to choose a unit that isn't useful. No one could ever measure the coastline by planck length, but it it were possible the length coastline of England would contradict its practical length.
I struggle to make this coherent but maybe when dealing with infinity, things need not be coherent (maybe infinity's semantic neighborhood includes words like contradiction, incoherence, impossibility, unlimitedness, endlessness, et cetera).
I borrow this idea from Borges story. Most of the information library is incoherent relative to the finity (limit, end, terminus) that is the reader. In the absence of a reader, or being, there is nothing (infinity or noumenon). Even if we are to concede that the universe exists without observers, so what, it is only meaningful relative to the what imposes or receives meaning upon it.
The library has all possible configurations of letters which code information but it's all relative to ciphers or interpretive agents.
When presented with a book or cipher you would always say that it is finite relative to your function or its function but that goes without saying. Actual infinity is just as incomprehensible as super humongous giant universal size sets of whatever.
There is too much to count some in some finite set but there is always more to count in another finite set, and there is always more to count in another finite set, et cetera.. ad finitum.
Who is counting? Who is measuring? Surely these agents are infinite? .....
:s
It is folly to entertain the notion that ideas can prove something about existence*. For at least two reasons, firstly ideas are abstract constructs entertained by something in existence. Something the existence of which is not understood. Secondly that which entertains the ideas is demonstrably limited in all facets of its action and its existence.
There are problems in attempting to circumscribe, nail down, existence.
*by existence I am refering to the very existence of existence itself and any processes involved.
?To question upon the concept of limit, that is the original question – this is the way Heidegger would formulate our idea. It speaks about an essence. It might be the very essentiality of our existence in this world.
?But what would it be possible that limit mean firstly? No doubt you think the same: this is our attitude, our way of defining our human condition, guided by wonder and question ...
?... We try, for instance, to understand time: did it begin with the universe? How could mind comprehend that the speed of light is invariably in the case in which an object moves towards the beam of light with a certain speed (Einstein)? Finitude limit I would call the first questioning, limit simply undone, in the other case.
~In the first case we might have the classical thinking boundaries in thinking the infinitude. Alright, but before the Big Bang, if Universe did not yet exist, what exist there? So, time-born with the universe- was not? How do you think this thing - if time defines thinking?
I concur with what you say before the above quote,but this sentence I find hard to digest.
When you say that they "subsist in a non-physical state'',in what sense do they ''subsist''?And of what nature is the realm of their subsistence?
How can such an existence contain the logical possibility that there is no existence or that the instantiation of one logical possibility excludes the instantiation of all other logical possibilities? The semantic sophistry of 'subsist in a non-physical state' does not get you off the hook here. The word "contain" is meaningless if it does not require instantiation, at least in the context of "existence". All you are saying is that all logical possibilities exist as logical possibilities a trivial truth of no ontological significance whatever.
The infinite universe may be theorised endlessly but it simply falls apart in science. If the Universe is infinite then there is no entropy. Barring a complete overturning of every basic concept of astrophysics there is entropy in our Universe and so it must be finite. Incomprehensibly vast but finite.
Now when a physicist talks about expanding space they don't mean that the universe is getting bigger. They just mean that galaxies are getting farther apart. That can happen in either a finite or an infinite universe.
There is currently no conclusive evidence as to whether the universe is finite or infinite.
Neither statement captures the full, precise meaning of the equations. If it did, there would be no need for the equations.
Say that you have a library that consists of one book, with a cover that's simply a picture of an elephant, and it has one page containing the letter "E," then a back cover.
Every book in that library contains part of the existing information and images so that all the data in that library is contained. Namely, all the data is the cover with the picture of the elephant, and the letter "E" on that one page.
There's no need for anything more than that. There's no other information and no other images in that library.
Likewise, for every book we add in the library, the information and images are exhausted by those being the books in that library.
Now, maybe you're not stating your idea that clearly, and what you're wanting to get at is something like, "All possible information and images," but (a) you'd be assuming that "all possible information and images" is an infinite set, which would make your argument question-begging, and (b) you'd be assuming that information and images exist, including information like meta information about the books in the library, without anyone thinking as much (or codifying a representation of that thinking in a book, say), which you'd then need to argue for; we can't just assume that this is so, because some of us disagree that it is.
Of course, you might have something different in mind, too. Maybe this is pertinent to some problem in computer science or something. I don't know. But as expressed, I don't see why the books in the library wouldn't do the job simply by being the books in the library in question.
The equations are capable of making definitive statements about whether the universe is finite or infinite, based on observations. Observations have not been made to date that can determine which it is, but it is possible that there may be in the future, in which case the finitude or otherwise of the universe will become definitively and scientifically settled one way or the other.
I should add that the equations only relate to this spacetime. Proving that this spacetime is finite would not rule out the possibility of additional, possibly inaccessible spacetimes, of which there could be infinitely many. In that case we need to be more precise about whether by 'universe' we mean 'this spacetime' or 'everything that exists'.
Exactly. The "stream of experience" or the "totality" or "everything" simply includes the scientific image and is itself much richer. Talk about the image is often treated as talk about the larger reality in which the image is dependently embedded.
I have given this a lot of thought over the years and the only logically consistent answer I could come up with is that it is the finite which doesn't exist and everything is infinite. But that we are in a state of delusion in which we experience a kind of finite existence.
Unfortunately in this thought experiment there are new loose ends, for example infinity and existence are inconceivable from our deluded perspective.
Seems you might think that Hilbert's Hotel can't take any more guests?
If the universe is finite, then what's outside it? What does it expand into?
Put differently, the length of the shortest straight-line trip around the universe (analogous to circumnavigating the Earth along the equator or another Great Circle) increases.
Certainly expansion of a finite spacetime can create room for more guests if by room we just mean 'empty space'. Where the hotel & guest analogy breaks down then is with the question 'where are the extra guests going to come from?' If they were in the spacetime all along then there's no need to make room for them. On the other hand if they somehow come from outside the spacetime then the spacetime is not a closed system and we'd need a whole lot more info about what sort of system it is to begin to analyse the question.
What is the shape of a finite, flat, homogeneous, isotropic universe with dark energy?
According to current cosmological theories there cannot be such a spacetime. If it is flat it must be infinite.
Both of these are objects that are embedded in 3D space - hence the three coordinates x, y and z.
Since space is 3D, to get something like a sphere for our universe we would need to be referring to the analog of these that are objects embedded in 4D space, which we would call 'hyperspheres' because they have one extra dimension. These would be the spaces whose coordinates satisfy the equations
The second is not possible because it has a boundary, and can be dismissed by Aristotle's ancient argument about going to the boundary and then poking my spear through it.
However the first has no boundary because it IS a boundary. It is a 3D space inhabited by 3D creatures, so they cannot point their spears in a direction perpendicular to their space. So that space is possible, and is one of the three models that is possible for the shape of the universe under current cosmological theories. Those models are elliptic, flat and hyperbolic, and the hypersphere is elliptic.
Which of the three models is the case depends on whether the overall global average spacetime curvature is positive, negative or zero. Zero corresponds to flat. We could never prove that curvature is zero because there will always be an accuracy limit to our measurements, so we can only ever determine that the curvature is less than some number. On the other hand, it IS conceivable that we could prove that curvature is positive or negative, in which case we would know the universe is elliptic (hyperspherical) or hyperbolic.
So in answer to your specific question, a (hyper)sphere is possible, but it is not flat. A spacetime that is both flat and finite would have to have a boundary, and that possibility can be dismissed by a variety of arguments, including Aristotle's, and the observation that such a space is not homogeneous (because some points are nearer the boundary than others).
Technical point. Although we always visualise a 2D sphere boundary as embedded in 3D space, it is not necessary for that to be the case. One can construct such an object without using three dimensions. Similarly, there is no need for a 3D hypersphere (which mathematicians call a '3-sphere' or just S^3) to be embedded in 4D space. I mention this otherwise pedantic-seeming point just to head off comments that then there must be something for the universe to 'expand into'.
That's a great post. Thanks.
But I do have a little point. We have these mathematical models, almost like "video games" or simulates that spit out the right predictions (they agree with observations). So we trust them, as we should, given the success so far of that approach.
But it's almost as if we have a little prediction box in some corner of the intersection of our "total" human realities and we point to that box as the real universe. I'm not saying that it's not wise to act-as-if for certain purposes, but from one perspective it looks like a little prediction machine. This is just a "map is not the territory" sort of comment, I suppose.
"If the universe is finite, then what's outside it? What does it expand into?"
You might be in a state of delusion, or an artificial construct in a more subtle reality etc.
If by "subtle" you mean "assuming a cognitive ability in your reader", then perhaps.
I'll try to be less subtle:
The density parameter of the universe has been measured. If the parameter = 1, the universe is flat. The result obtained is: ? = 1.000 +/- 0.004 . The universe is flat.
We also know (via similar measurements) that the universe is homogeneous and isotropic, and expanding at an accelerating rate.
The notion that the universe is not simply connected doesn't seem to attract much attention. I suspect that if it were not, evidence would be found in CMB, and it's a strange idea anyway. The universe is not a Klein bottle or a torus.
Given that we know the universe possesses this geometry, we may now address the question of finiteness.
Quoting andrewk
Now while andrewk's statement is true, it is not logically correct. There is no logic that prevents you from ad-hoc modifying GR to create a finite universe with a boundary, which is precisely what you are forced to do if you value finiteness more than reason. And, if you choose that course, you will be asked "what such a universe is expanding into" by someone.
This being the case we can't with certainty know what finite entails, or that there is anything finite external to our perception. It's worse than this regarding infinity, because it is entirely a figment of the human imagination.
* I am working from the observation that the only thing we can know with any certainty is that we have being and experience and that all else is secondary to this fact.
We don't know any of those things. I'll consider them one by one.
Flat? The density parameter has been measured to be very close to 1, but it has to be EXACTLY 1 for the universe to be flat. But if it is exactly one there will always be values greater than and less than 1 within the error bounds of any unbiased measurement. We can never know the exact value of any measurement. If the universe is in fact flat we will never be able to tell whether that is the case or whether it is elliptic or hyperbolic with a parameter very close to 1. In the flat and hyperbolic cases the universe would be infinite. In the elliptic case it would be finite but unimaginably large.
Homogeneous and isotropic? We know these do not hold at the usual scale. The cosmological principle states that these must hold 'at the large scale' but no formal definition is given of what that means. One of my current projects is to develop a formalisation of that definition, but it keeps getting interrupted by other things. Most cosmology tends to just assume the universe is isotropic and homogeneous.
Spherical? It depends what is meant by that. Certainly we can mark out a sphere in space, and develop a spherical system of coordinates for it - indeed Spherical Coordinates is a standard type of representation of 3D Euclidean space. But that tells us nothing about the shape of the universe as a whole. The three shapes envisaged by current theories are Elliptic, Flat and Hyperbolic, corresponding to density parameters greater than, equal to and less than 1. It is conceivable we could prove the shape is elliptic or hyperbolic, because it's possible to get a confident reading about an inequality. But we could never prove it is flat because that would require a reliable measurement of an EXACT equality. The best we could say is that it is very nearly flat, but that doesn't help at all with the crucial question of whether it is finite.
Under current theories and methods, the only way to conclude the universe is finite (infinite) would be to get a measurement that shows the parameter is greater than (less than) 1, beyond the limits of experimental error.
The wiki article on the shape of the universe covers these issues and I think is rather good.
I hear you. Lots of math has some kind of intuitive reality for me, but it's a big step from that more or less inter-subjective intuition to metaphysical statements. We also understand the "manifest image" and measurements of length and time. So science can earn our trust as a prediction machine. To me the scientific universe is a mathematical image. We place ourselves in that image, but that image is also within the much richer totality of our lives. From this perspective, any sort of reduction of all of experience to some facet of experience is nakedly absurd. It completely reason to talk about whether the universe of the scientific image is infinite or not. I'm just saying that there doesn't have to be any metaphysical investment in the question. What I'm getting at could apply to any sort of reduction, not just to the scientific image. Every metaphysical or physical theory of the totality is still just an idea in the still-untamed totality that exceeds and contains it. Every map is part of and smaller than the territory. Yet the utility of statements may depend exactly on talking and acting as if the totality has been tamed and mapped. So I'm just poking a breathing hole in the paper sky, perhaps.