Is the Universe Finite or Infinite?

[Deveno]

i understand very little of cosmology. i am given to understand that the conclusion that "the fabric of the universe is stetching apart" is based on the cosmic microwave background, which is (as far as we know so far), "too uniform" to support the notion that space existed first, and that just the stuff expanded later into it. better data collection efforts may substantiate, or revise this idea.

but as a mathematician, i feel i must point out that there is a difference between "infinite" and "unbounded". a circle is bounded, but i don't think anyone would claim it consists of only a finite number of points.

if space is a continuum, then it is infinite, even if it is embedded in a bounded manifold in some n-dimensional ambient space. it is not possible for us to tell, at the moment, if this bound is just very large (compared to us), or non-existent. it is my understanding that the basic assumption in cosmology is that the universe is (relatively) uniform, so "local" measurements of curvature should tell us about the universe in general, but of course, this assumption may be wrong (the energy content of "our corner of the park" may somehow influence its geometry).

on the other hand, if space itself is quantized in some manner, then it's conceivable our universe is "absolutely" finite (it is a discrete structure). i think this unlikely, but some have suggested that a finite-dimensional lattice could propagate instructions in such a way as to create the illusion of states evolving over time (the universe itself could be some form of complex-behavior automaton).

it is difficult to tell how many dimensions we "need" for our (perceived) space to exist inside "a larger one". if certain algebraic relationships hold, the choices are not entirely free, as some numbers work better than other ones (4, for example, is a better choice than 3, and 8 is better than 7...there are good reasons for believing it should be an even number).

of course, the very idea of our universe existing in some larger structure, sounds very much like saying: "the universe isn't the (whole) universe", but it's still possible that the "enveloping universe" somehow leaves evidence in our discoverable universe that tells us it's there (or rather; if we hypothesize such a universe, we may be able to "explain" things that have predictable value, that might be borne out by experiment. this isn't really "proof" per se, but if it works in practice, we are likely to adopt this view).

there isn't any pure logical reason, that i know of, for thinking the universe is finite, or non-finite. my guess is, is that since the universe exhibits similar levels of complexity across all the scales of resolution we have; it is infinite in depth, as well as breadth. it's possible this question may never be answered, due to our limitations.

 

[josewrivera]

if the universe is expanding, it must be expanding into something, isn't that something also part of the universe, if it is expanding how come we keep the same distance from the sun, the big bang was just one more explosion in the universe, one of billions and billions of explosions happening as we speak, if we are moving or expanding we are just looking to occupy a different location in the infinite universe, there is no beggining or end because there is no beggining to time, and if there is no beggining to time, there is no beggining to the universe, and if there was no beggining. there was no creation, no matter how you diced or sliced, by the way I am no scientist and forgive my spelling

 

[Chalnoth]

if the universe is expanding, it must be expanding into something,

Not at all. The expansion simply means stuff within the universe is getting further apart. It is, in a very real sense, just a change of shape of the universe. There is no reason whatsoever for there to be any "outside" at all. In fact, in General Relativity, the very concept of an outside doesn't work very well.

if it is expanding how come we keep the same distance from the sun,

Because the expansion is a large-scale, average phenomenon. Overdense regions, such as our own galaxy or solar system, are quite stable within an expanding universe.

 

[skydivephil]

if it is expanding how come we keep the same distance from the sun,

I think this impression is created by poor explanation of what the expansion means. We measure disatnt galaxies as receeding away from us at a speed proprtional to their distance. The important point to note is that this only applies to distant galaxies. Why only distant galaxies?
Becuase for nearby obejct they are gravitationally bound and the expansion of the universe is not strong enough to unbind them. It might be in the future, google "big Rip" for this possibility, but it is not now.
Hence gravitationally bound strucutres do not see any expansion. The solar system is grvaitiationally bound, so is our galaxy and so are nearby galaxies. For example Andromeda is on a collision course with the Milky Way. If everything felt the expansion this could not be the case.
Bottom line: for local structures, think nearby galaxies and closer , the expansion of the universe is irrelevant.

 

[skydivephil]

, if we are moving or expanding we are just looking to occupy a different location in the infinite universe, there is no beggining or end because there is no beggining to time, and if there is no beggining to time, there is no beggining to the universe, and if there was no beggining. there was no creation, no matter how you diced or sliced, by the way I am no scientist and forgive my spelling

We don't know whether or not the universe is infinite. We do know there was a big bang event, but whether there were others and how far back they go back is currently unknown. Perhaps you are referring to certainly interesting models such as eternal inflation, CCC, ekpyrotic and bounce cosmologies that imply our big bang was not a unique event. But we have to be honest and say none of these models have been experimentally veirified yet. So I think a "we don't know" attitude is best. We should wait for the data to tell us the answeres and until that happens we should not presume anything.

 

[Deuterium2H]

if the universe is expanding, it must be expanding into something, isn't that something also part of the universe, if it is expanding how come we keep the same distance from the sun, the big bang was just one more explosion in the universe, one of billions and billions of explosions happening as we speak, if we are moving or expanding we are just looking to occupy a different location in the infinite universe, there is no beggining or end because there is no beggining to time, and if there is no beggining to time, there is no beggining to the universe, and if there was no beggining. there was no creation, no matter how you diced or sliced, by the way I am no scientist and forgive my spelling

Jose, I encourage you to read the FAQ section of this forum (listed at the very top of this section). Many of your questions are answered in descriptive, non-rigourous and very accesible explanations.

As has already been explained (e.g. Chalnoth), the known physics of our Universe does not require an additional "dimension" within which to expand. The shape/curvature of our Universe is an intrinsic geometric property, and does not require a higher dimension in which it is embedded. That is to say, our Universe can be infinite, open, and expanding...but it is not expanding into any "external" pre-existing volume. This fact is precisely why thinking of the Big Bang as a single "explosion" IN Space is misleading and incorrect. The correct concept is to understand the Big Bang as occurring everywhere, and to imagine it is an explosion OF space. The Big Bang occurred simultaneously in the space now occupied by the current position of your belly-button, as well as any (and all) arbitrary points in the Andromeda galaxy.

According to the Standard model of Cosmology, there was a definite beginning of "time", which was the instant of the Big Bang. The Big Bang created our Universe which contains space and time, and our Universe does not exist "in" space and time. This is part of the "Containment Principle", which is an integral aspect of modern Cosmology.

 

[skydivephil]

Jose, I encourage you to read the FAQ section of this forum (listed at the very top of this section). Many of your questions are answered in descriptive, non-rigourous and very accesible explanations.

As has already been explained (e.g. Chalnoth), the known physics of our Universe does not require an additional "dimension" within which to expand. The shape/curvature of our Universe is an intrinsic geometric property, and does not require a higher dimension in which it is embedded. That is to say, our Universe can be infinite, open, and expanding...but it is not expanding into any "external" pre-existing volume. This fact is precisely why thinking of the Big Bang as a single "explosion" IN Space is misleading and incorrect. The correct concept is to understand the Big Bang as occurring everywhere, and to imagine it is an explosion OF space. The Big Bang occurred simultaneously in the space now occupied by the current position of your belly-button, as well as any (and all) arbitrary points in the Andromeda galaxy.

According to the Standard model of Cosmology, there was a definite beginning of "time", which was the instant of the Big Bang. The Big Bang created our Universe which contains space and time, and our Universe does not exist "in" space and time. This is part of the "Containment Principle", which is an integral aspect of modern Cosmology.

Everything you say may be true but I think the picture is more nuanced than that. I think most comslogigst that work on the very early universe would agree that "The Standard Model" is not to be trusted as we get v close to the Planck scale. Hell all of my textbooks say that too, so this is nothing new. In order to say there was a beginning of time at the big bang we need to trust the mdoel all the way to the Planck scale which i think very few people would say is wise.

 

[josewrivera]

we have trouble undestanding events that ocurred only a couple thousand years ago, but we think we have the answer to what happened 5 billion years ago, the big bang didnt create the universe nothing no matter how big can affect a infinite universe in its totallity some time in the future humanity is going to come to this conclusion no beggining no end and there was time before the big bang, and is not possible to reach the beggining because there is always a second before, and a minute and an hour.

 

[phinds]

we have trouble undestanding events that ocurred only a couple thousand years ago, but we think we have the answer to what happened 5 billion years ago, the big bang didnt create the universe nothing no matter how big can affect a infinite universe in its totallity some time in the future humanity is going to come to this conclusion no beggining no end and there was time before the big bang, and is not possible to reach the beggining because there is always a second before, and a minute and an hour.

You really need to read some basic cosmology before posting such nonsense on a forum where people take science seriously.

"big bang" has two meanings

1) the singularity / t=0 and nobody pretends to know what this was all about, it's just the place where the models break down.

2) everything since one Plank time after the singularity. This is remarkably well understood, although there are still puzzles. I recommend you read "The First Three Minutes" by Weinberg.

 

[Chalnoth]

we have trouble undestanding events that ocurred only a couple thousand years ago, but we think we have the answer to what happened 5 billion years ago,

This is really sad. Why not try learning a little bit about how we have learned these things before throwing out blanket condemnations of science you know nothing about?

 

[jay.yoon314]

I think the universe is infinite in space and time, but finite in energy and mass.

 

[phinds]

I think the universe is infinite in space and time, but finite in energy and mass.

Do you have any SCIENCE to back up this statement or is it merely unsupported, and unsupportable, personal opinion?

 

[jay.yoon314]

Everything you say may be true but I think the picture is more nuanced than that. I think most comslogigst that work on the very early universe would agree that "The Standard Model" is not to be trusted as we get v close to the Planck scale. Hell all of my textbooks say that too, so this is nothing new. In order to say there was a beginning of time at the big bang we need to trust the mdoel all the way to the Planck scale which i think very few people would say is wise.

Why is it that it is necessary to explain the creation of space-time, on one hand, and mass-energy, on the other hand, as having occurred simultaneously? I argue that there is no contradiction in an alternative mechanism of a Big Bang occurring in such a way that the creation of space-time precedes the creation of mass-energy.

I also mention another point as follows: Is there any way to "see" empty space? I postulate that the limits of our observable universe may merely be the limits at which space-time truly becomes empty. Not only empty in a sense that Object A is located 5 billion light years away, and that there is nothing in that line of sight until 12 billion light years away, but rather empty in that there simply hasn't elapsed enough time for something to be 80 billion light years away.

We cannot assume that the only kind of empty space that there could be is empty space that is between two other "things" (such as galaxies). It is possible for empty space to mean that there is literally nothing out there beyond some distance away from some position (such as ours).

A region of the universe that we cannot see presently because it has undergone metric expansion beyond our "horizon" greater than the speed of light, and a region of the universe that we cannot see because it is empty space, are indistinguishable, I believe.

 

[jay.yoon314]

Do you have any SCIENCE to back up this statement or is it merely unsupported, and unsupportable, personal opinion?

Sorry about that, it was a bad first post.

The reason why I believe that is because space-time will continue to exist is specifically because of the time dimension of space-time. Assuming that time will continue to exist no matter how much "time" passes, it is unbounded. In the language of limits, there is no finite time interval starting from any initial time not t = 0 such that space-time itself will not exist at the end of that interval.

In the case of matter and energy, on the other hand, we know of no law that states that the mass-energy as a whole can be created or destroyed, nor have we ever observed such a process. Therefore, the amount of mass-energy that exists now will be the amount of mass-energy that exists at any time in the future.

The distinction between space-time and mass-energy is clear in the sense that space-time has the capacity to become unboundedly large whereas mass-energy clearly does not, according to presently known physical laws. I argue that a quantity that has the capacity to become infinitely large is actually infinite. If this were not the case, how is the following paradox resolved?

Space-time can grow without bound, and probably will. Let us define two variables:
P (present) := presently existing space-time
F (future):= potentially available but not currently existing space-time
S (sum) := P + F

We cannot, with perfect confidence, know F. We cannot even know P, since we do not know exactly how large our whole universe is.

But if the universe is accelerating in its expansion rate, then we know that F is unbounded. Then even if P is finite, S is unbounded. The universe will exist for a lot longer than it exists now. Therefore, I argue that F, being the "long run supply curve" of space-time versus P, being the "short run supply curve" of space-time, is the most faithful representation of space-time's true nature.

However, if the metric expansion of space involves the conversion of space-time into mass-energy specifically in the form of dark energy, then my claim cannot stand. But this would involve having to define an additional conservation law between not only energy and mass, but between mass-energy and space-time, and there isn't a shadow of a hope for that to work.

 

[Chronos]

The observable universe ends abruptly 13.7 billion years ago. This 'boundary' is called the CMB, or surface of last scattering. There are no galaxies, stars, etc. lurking behind the CMB waiting to be discovered, and precious little spacetime. Only about 400,000 years separates the CMB from the Big Bang.

 

[Chalnoth]

I think the universe is infinite in space and time, but finite in energy and mass.

Pretty sure that is fundamentally impossible.

 

[phinds]

However, if the metric expansion of space involves the conversion of space-time into mass-energy specifically in the form of dark energy, then my claim cannot stand. But this would involve having to define an additional conservation law between not only energy and mass, but between mass-energy and space-time, and there isn't a shadow of a hope for that to work.

Possibly I am misunderstanding what you are saying here, but it seems to imply that you believe in conservation of energy on cosmological scales, but there is no such thing.

 

[jay.yoon314]

Possibly I am misunderstanding what you are saying here, but it seems to imply that you believe in conservation of energy on cosmological scales, but there is no such thing.

If there is indeed no such thing, at what scale does the law of conservation of mass-energy break down? It breaks down neither at the atomic nor at the level of the galaxy. If it breaks down at the level of the observable universe as a whole, shouldn't this breakdown be observed at the level of the galaxy (or galaxy clusters?)?

A conservation law that is so general cannot go from being obeyed in all instances at all scales that are smaller than some arbitrary scale, but then transition abruptly into there being existing "no such thing" as you said. In any case, the burden of proof is on your part. We both agree that there is a possibility that the universe's properties at the cosmological scale are different, even in extremely surprising ways, from the universe at smaller scales. But this doesn't eliminate the fact that such differences need to be quantified, or precisely stated. How is saying that there is no such thing as a conservation of energy on cosmological scales any different, in its radicalism, than me saying that there is a finite amount of mass-energy? At least, in my view, the law of conservation of mass-energy is obeyed, which is not at all a triviality.

 

[phinds]

If there is indeed no such thing, at what scale does the law of conservation of mass-energy break down? It breaks down neither at the atomic nor at the level of the galaxy. If it breaks down at the level of the observable universe as a whole, shouldn't this breakdown be observed at the level of the galaxy (or galaxy clusters?)?

A conservation law that is so general cannot go from being obeyed in all instances at all scales that are smaller than some arbitrary scale, but then transition abruptly into there being existing "no such thing" as you said. In any case, the burden of proof is on your part. We both agree that there is a possibility that the universe's properties at the cosmological scale are different, even in extremely surprising ways, from the universe at smaller scales. But this doesn't eliminate the fact that such differences need to be quantified, or precisely stated. How is saying that there is no such thing as a conservation of energy on cosmological scales any different, in its radicalism, than me saying that there is a finite amount of mass-energy? At least, in my view, the law of conservation of mass-energy is obeyed, which is not at all a triviality.

Unfortunately I'm not knowledgeable enought to explain it adequately, but it has been discussed numerous times here on the forum and I assure you it is true, however non-intuitive it is. I too found it quite disagreeable when I first heard it. I suggest a forum search if you want a decent explanation.

 

[salvestrom]

Unfortunately I'm not knowledgeable enought to explain it adequately, but it has been discussed numerous times here on the forum and I assure you it is true, however non-intuitive it is. I too found it quite disagreeable when I first heard it. I suggest a forum search if you want a decent explanation.

spacetime has non-zero vacuum energy. infinite spacetime automatically leads to infinite energy. it should also be kept in mind that current theory says all the mass/energy in the observable universe that isn't dark energy was created out of the vacuum energy during reheat. so again, infinite spacetime would lead to reheat that occurred everywhere (in all areas of space at least equal in size to the observable universe) creating infinite mass/energy.

 

[Drakkith]

If there is indeed no such thing, at what scale does the law of conservation of mass-energy break down? It breaks down neither at the atomic nor at the level of the galaxy. If it breaks down at the level of the observable universe as a whole, shouldn't this breakdown be observed at the level of the galaxy (or galaxy clusters?)?

I could be wrong on this, but I'll go out on a limb and try to explain part of what I think is the reason for this.

Think about the expansion of space and the resulting redshift of light. If all galaxies outside our cluster are receding from us, and those galaxies in their cluster see all other galaxies receding from them as well, that means that we are losing energy. Normally redshift from a moving object is countered by the fact that the light emitted in the opposite direction is blueshifted the same amount. The galaxies at redshift z=2 or whatever are moving away from us but they are not moving towards anything else, meaning there is no blueshift, only redshift. So, since expansion doesn't happen on the galaxy cluster scale, the conservation of energy still applies. It is only above this scale that it breaks down. However this could simply be a lack of understanding about dark energy, expansion, or any number of things.

Now, think about the following. You look at a proton traveling at 10% c. How much energy does it have? Well obviously it would have a certain energy we can find by doing the math with the right equations. But wait...that energy is only for one particular frame of reference. If you were moving at 5% c in the same direction then the proton would NOT have the same energy as it did in the stationary frame. So how much energy does it "really" have? I don't think that's answerable. (This may not be relevant to conservation of energy, but I wanted to point out that some types of energy are relative)

Also, as has been explained to me, energy is ill defined in General Relativity, so it's hard to say whether it's conserved or not. I had a link to a page that explained some of it, but I don't know where it is at the moment. Even the page itself states something along the lines of "Is energy in GR conserved? Well, that depends on what you mean by energy...and what you mean by conserved...", so I really don't know for sure.

If I've made a mistake somewhere someone let me knwo.

 

[Chalnoth]

If there is indeed no such thing, at what scale does the law of conservation of mass-energy break down?

It breaks down the moment that the expansion of the universe becomes a non-negligible component to the behavior of the system. For smaller systems, you can define energy in such a way that it is conserved.

In any case, the burden of proof is on your part. We both agree that there is a possibility that the universe's properties at the cosmological scale are different, even in extremely surprising ways, from the universe at smaller scales.

What you don't seem to be getting is that this fact is derived directly from physics we observe here in our own solar system. First of all, energy conservation is now understood to not be a fundamental fact of nature, but instead a consequence of a particular sort of symmetry. In fact, all conservation laws are now understood to be consequences of symmetry.

Conservation of momentum is honored whenever you have a system that is unchanged when you move the system from place to place.

Conservation of angular momentum is honored whenever you have a system that is unchanged when you rotate it through some angle.

Conservation of energy is honored whenever you have a system that is unchanged when you move the system forward or backward in time.

This fact comes directly from Noether's theorem. And the actual statement is a bit more subtle (in reality, some things can change). If you imagine our own solar system, for example, it is a periodic system: if you wait some amount of time, the planets will all be back in their previous positions. So energy is a conserved quantity for planetary motion. You can build similar arguments for most anything we do here on Earth.

In fact, for most of our laws of physics, those laws remain unchanged at all times. The specific system may change, but the laws do not. This means that energy has to be conserved for Newtonian gravity, electricity and magnetism, and quantum mechanics. However, General Relativity throws a wrench into this whole system, because there is no absolute time coordinate any longer. Time itself becomes a parameter in the theory, and this symmetry is lost. No longer can you change time without changing the laws of motion in General Relativity, and so you can't define a conserved energy.

However, General Relativity doesn't get rid of conservation of energy entirely. Instead of conserving energy, it conserves the stress-energy tensor. This tensor has ten independent components, including energy density, pressure, momentum density, and twisting forces. Conservation of the stress-energy tensor will sometimes force energy to change because the other components of the tensor change. So GR doesn't say, "anything at all can happen," but rather that we now have a new conservation law which is more correct: conservation of stress-energy. And conservation of stress-energy doesn't allow energy to be conserved in all cases.

Finally, I'd just point out that the conservation of mass is trivially disproven by the fact that we can create higher-mass particles in particle accelerators, and do so very often.

 

[Drakkith]

Thanks Chalnoth! That's the first explanation of conservation of energy in GR that I've actually understood and learned something from.

 

[bill alsept]

It would seem that you guys do not use the accepted definition for the word "universe".
Universe: The totality of everything that exists.

It cannot be in something, or located. It is everything.

Compared to solar systems, galaxies, clusters and super clusters we can call everything else the universe only because we are inside of it. But that doesn't mean there are not many other universes just like it all lined up forever. I believe they use to call the Milky Way the universe.

 

[phinds]

Compared to solar systems, galaxies, clusters and super clusters we can call everything else the universe only because we are inside of it. But that doesn't mean there are not many other universes just like it all lined up forever. I believe they use to call the Milky Way the universe.

Yes, and they used to call the Earth flat. What's your point? Previous ignorance should require current ignorance?

You don't get to decide what you want the definition to be even though you seem to think you can.

 

[bill alsept]

Yes, and they used to call the Earth flat. What's your point? Previous ignorance should require current ignorance?

You don't get to decide what you want the definition to be even though you seem to think you can.

WOW, nice input