What Is the Universe Expanding Into?

[Ulnarian]

I realize this topic has probably been beaten to death on here but I've never had the fortune of coming across it so I made my own.

Now, if you believe the whole Big Bang theory, the universe is exanding. In order for anything to expand, there must be something for it to expand into. Now, if we define the universe as "everything", just what the heck is the universe exanding out into, nothing??

Any thoughts?

 

[Chronos]

Hi Ulnarian. Your question is often asked. We say the universe is expanding because, in this universe, objects move away from each other over time. The volume occupied by galaxies and such are otherwise meaningless. There is no space outside of space. Space can only be described in terms of the distance between physical objects.

 

[Math Is Hard]

ok, I'm a complete dum-dum at cosmology (among other things), but I always had trouble with the use of the word "expanding" in this context. In my ordinary, simplistic, everyday use of the English language, I have certain ideas that I associate with the word "expanding". For instance, if I think of a balloon expanding, one of the things I immediately think of is that it is increasing in volume and taking up more space.
But this doesn't quite work with the idea of an expanding universe, because what "space" is it "taking up" even though the objects move farther and farther apart?
What I'd really like to know is: how do you conceptualize such a thing? Or is it impossible to "picture" because it is too abstract?

 

[JesseM]

According to the Big Bang theory, the Big Bang was not an explosion in a preexisting 3-dimensional space, with matter and light expanding out into empty space from some central point--instead, matter and energy are understood to fill all of 3D space, and what's expanding is space itself. The key is to understand that the Big Bang theory is based on Einstein's theory of general relativity, which explains gravity in terms of matter/energy causing spacetime to become curved--depending on the average density of matter/energy throughout the universe, a consequence of this is that the universe as a whole can be curved, with either positive curvature, zero curvature, or negative curvature. For a closed universe with positive curvature, you can visualize it if you drop the dimensions by one--instead of curved 3-dimensional space, which is impossible for us to visualize, picture a 2D universe a la Flatland in which 2D space is actually curved into a sphere, and "expanding space" means that the sphere is blowing up like a balloon while the bits of 2D matter on the surface do not change in size. You can see that if you pasted a bunch of bits of paper on a balloon and then blew it up, each bit would see the other bits receding from it, just like what we see with other galaxies. If you play the movie backwards so that the size of the sphere approaches zero, you can seen that all the bits of matter throughout the universe get more and more squished together, approaching infinite density as the size approaches zero--this is what the big bang is supposed to be. Of course, this analogy forces you to picture the 2-dimensional surface of the sphere expanding in a higher 3rd dimension, and while it is possible that our curved 3D space is expanding in some kind of higher 4D space, mathematically there is no need for such a thing--instead of describing the curvature of a surface with reference to a higher-dimensional "embedding space", it is possible to describe curvature using purely intrinsic features that could be observed by a being confined to the surface (like whether the sum of angles of a triangle drawn on the surface is more, less, or equal to 180 degrees), and general relativity uses only such intrinsic features to describe what it means for space to be curved (see this page on differential geometry, the mathematical basis for general relativity, which talks about the difference between intrinsic and extrinsic descriptions of curvature).

For a universe with zero curvature, picture an infinite chessboard in which all the squares are growing at the same rate, while the pieces at the center of each square remain unchanged in size. If you play the movie backwards, the distance between any two squares approaches zero as you approach the moment of the big bang, which means the density of the matter on the squares (represented by the chess pieces) approaches infinity as it gets smushed together more and more tightly. A universe with negative curvature would be something like an infinite saddle-shape which is a little harder to picture expanding, but if you can picture the other two you get the basic idea. From Ned Wright's Cosmology Tutorial, a graphic showing the 2D analogues of the three types of spatial curvature, negative, zero, and positive:

 

[Chronos]

Not abstract, it is really fairly simple. Things only expand with respect to your reference frame. For example, if LA gets more distant from all other places on planet earth, over time, it suggests Earth is expanding. Much the same with the universe. We can only see a finite part of the universe. All the parts of it appear to be moving away from each other.

 

[Math Is Hard]

I think my only quibble is an issue with semantics. In my immediate world, "expanding" would mean things (inside of a contained thing) moving farther and farther apart - but also, to accommodate this, this contained thing would be increasing in volume. So things in the universe can move farther and farther apart from each other while the universe itself does not increase in any kind of volume that we could measure? Only the first part of my conception of "expanding" holds.
I hope that makes sense. I am speaking only in my immediate and known 3D sensibilities.

 

[Garth]

Hi Ulnarian welcome to these Forums - if you haven't been welcomed already!

Now, if we define the universe as "everything", just what the heck is the universe exanding out into, nothing??
Any thoughts?

That's a very interesting question that is often not taken seriously in GR circles. It might be argued philosophically that if the universe is all that there is, then logically there cannot be a 'container' in which it is situated and into which it is expanding. Relativists would argue that such a philosophical argument is ignorant of the dynamic nature of space-time itself; for not only is space-time 'curved' by the presence of matter and energy, but also it must expand or contract; a space-time that is held static by a cosmological constant is found to be unstable.

However we can ask, "If the universe is expanding, and we are part of that universe, 'inside it', how do we measure the expansion? Might it be that our rulers expand with the universe, for they are embedded within that expanding space-time, and therefore this would render the expansion undetectable?"

One answer to this is, "In fact we do observe Hubble Red shift, the relative abundances of the elements agree with Big Bang nucleosynthesis, and the Cosmic Microwave Background (CMB) is an observation of a time when the universe was much smaller and full of hot plasma, therefore the expansion of the universe definitely has been detected.”

Consequentially we can argue that the universe has expanded relative to physical (i.e. atomic) rulers, however the wavelength of a photon is red shifted and expands with the universe, therefore measured relative to the wavelength of a photon from the CMB the universe has not expanded! Instead atoms have shrunk within a static universe.

So it comes down to, "How do you measure the expansion?" Define an atom to provide your unit of length and the universe has expanded, define the wavelength of a representative photon sampled from the CMB, say at the wavelength of its peak intensity, to be your unit of length measurement and the universe is static!

A final thought, map the 4D of a finite universe space-time onto a 3D hyper-surface and define a time by the hyper-sphere's radius. The passage of time and the expansion of the universe now become two different experiences of the same mysterious phenomenon, but now if we ask "What is the universe expanding into?" we find the answer "Its future!"

Just a thought or two..

Garth

 

[JesseM]

I think my only quibble is an issue with semantics. In my immediate world, "expanding" would mean things (inside of a contained thing) moving farther and farther apart - but also, to accommodate this, this contained thing would be increasing in volume. So things in the universe can move farther and farther apart from each other while the universe itself does not increase in any kind of volume that we could measure? Only the first part of my conception of "expanding" holds.
I hope that makes sense. I am speaking only in my immediate and known 3D sensibilities.

If the universe has finite volume then sure, you can think of the volume increasing, just like the 2D surface area of a balloon increases as you blow it up. In an infinite universe, the volume is infinite at all times--see my analogy above about the infinite chessboard where every square is growing while the pieces stay the same size.

 

[Entropy]

Nothing exists outside the universe because by definition the universe is everything.

 

[Math Is Hard]

If the universe has finite volume then sure, you can think of the volume increasing, just like the 2D surface area of a balloon increases as you blow it up. In an infinite universe, the volume is infinite at all times--see my analogy above about the infinite chessboard where every square is growing while the pieces stay the same size.

I felt overwhelmed by your first post, JesseM, but now reading this one - something actually seems to have clicked. This particular statement "the volume is infinite at all times" makes it clearer for me. Thanks.

 

[Chronos]

I resist the notion of an infinite universe because it is unphysical. The universe is not observationally infinite. It has a finite size called the particle horizon - which envelopes us in a sphere with a radius of around 13.5 billion light years. It is the only volume of space that is, or ever will be, causally connected to our reference frame, hence, the only one physically meaningful.

 

[setAI]

I resist the notion of an infinite universe because it is unphysical.

I resist the notion of physical infinities- instead I embrace the original and central meaning of the concept of infinity as limitlessness-as INDEFINITE- so that Infinity really implies limitless finite forms [which strongly reinforces the idea of an emergent Multiverse]- only finity is physically real:

"...many feel that the concept of infinity is fully paradoxical and absurd in-an-of itself- but it’s only their erroneous DEFINITION of infinity- as an impossibly “large” amount of something that “goes on forever”- or a never ending counting process- but this is not the case- Infinity is a concept of LIMITLESSNESS- to understand Infinity we should look to the origins of the concept- the oldest idea of Infinity found in human culture- the six thousand year old Qabbalistic concept of AIN SOPH- got it right from the start- the Hebrew AIN SOPH was the second of a trinity of absolute concepts that crown Kether- the first sephiroth of the Tree of Life- this crown begins with AIN- which is usually translated as NOTHINGNESS- but literally means NOT- then AIN SOPH- translated as INFINITY- but literally translated it means NOT LIMIT- no limits! then finally AIN SOPH AUR- which is Infinite Light: NOT LIMIT LIGHT-

so from the very beginning of human culture we had a proper concept of infinity as a limitlessness that allows FINITE forms to be- and those finite forms are limitless- thus finity can extend INDEFINITELY- that is the crucial understanding of infinity- not a forever arching hugeness of something- but the absence of absolute limits- so really Infinity is a statement DENYING an absolute [final limit/ nothingness]- not claiming to be an absolute-"

The universe is not observationally infinite. It has a finite size called the particle horizon - which envelopes us in a sphere with a radius of around 13.5 billion light years. It is the only volume of space that is, or ever will be, causally connected to our reference frame, hence, the only one physically meaningful.

I never understand this attitude that "we are isolated" when there is simply no evidence to support the idea that we now posess the full understanding of how our universe exists and works and evolves over trillions of years- absurd! there is simply no honest way to say that the universe we can see is causally closed to anything beyond it- it is certainly very possible- and in some models very likely that regions of spacetime are totally closed to themselves- but cannot be stated with any great certainty or confidence at all- there are so many ways in which our theories suggest possible influence of other space-time regions- from gravitons and other forces passing through higher spatial dimensions between branes to colliding branes to many-worlds QM parallel interactions to black holes/ wormholes connecting universes or even spawning them as in Smolin's CNS-

 

[whatzzupboy]

If there was a second universe what is in between us and them? Heaven? Hell? Ect?

 

[wimms]

I resist the notion of an infinite universe because it is unphysical. The universe is not observationally infinite. It has a finite size called the particle horizon - which envelopes us in a sphere with a radius of around 13.5 billion light years. It is the only volume of space that is, or ever will be, causally connected to our reference frame, hence, the only one physically meaningful.

There are 2 concepts: infinity and infinite. They are all the time confused. What you seem to refer to is observational infinity beyond which we have no means to observe, today. Despite having finite volume, which seemingly is causing your resisting, it is not real bounds. Any point at 6billion lightyears from us has exactly the same sphere of 13 billion light years around it, us included. Ad infinitum. Thats what Big Bang is all about, isn't it.

13billion years ago, that "horison" was so much closer that things beyond it had causal relations with our frame. Similarily, its quite fatalistic to deny possibility that signal emitted somewhere beyond our horison won't ever reach our frame sometime in distant future, or even now.

 

[wolram]

My take is that space is infinite, as in, if i get in my spaceship and
head in one direction i will go on forever, without returning to the
same starting point, our universe may be governed by set rules,
but why should that preclude an infinite background? what for
instance rules out other universes existing in the same time and
background as our own, separated only by distance.

 

[ohwilleke]

The axiom that "everything that exists" and that "everything that came out of the big bang" are identical is not based upon any solid empirical evidence to my knowledge and is not in my opinion compelled by general relativity. It is an axiom about whose truth I am agnostic. The truth of this proposition is unknowable.

Suppose that 700 billion light years from Earth that there is another "universe" billions of light years across and of a corrosponding age with its own big bang. If special relativity is correct, and gravity indeed propogates at the speed of light as the consensus view holds, there would be no way we could know that this is the case. In much the same way, there is no way that a Dolphin in the Mediterranean Sea could know that Lake Victoria in Africa exists.

(Note that this is not the same as the "many worlds" intepretatio of QM which suggests that there might be multiple Earths out there, e.g.).

 

[selfAdjoint]

The axiom that "everything that exists" and that "everything that came out of the big bang" are identical is not based upon any solid empirical evidence to my knowledge and is not in my opinion compelled by general relativity. It is an axiom about whose truth I am agnostic. The truth of this proposition is unknowable.

Suppose that 700 billion light years from Earth that there is another "universe" billions of light years across and of a corrosponding age with its own big bang. If special relativity is correct, and gravity indeed propogates at the speed of light as the consensus view holds, there would be no way we could know that this is the case. In much the same way, there is no way that a Dolphin in the Mediterranean Sea could know that Lake Victoria in Africa exists.

(Note that this is not the same as the "many worlds" intepretatio of QM which suggests that there might be multiple Earths out there, e.g.).

Perfectly correct. And just because we can know nothing about any such addenda, we have nothing whatever to say about them. And in that case, as Witgenstein advised, we should shut up about them.

 

[wolram]

Itis a perpetual argument that nothing exisits outsde our universe, and
that our universe has the only background to support existence, how
do you give support to this prepostious assupution

 

[JesseM]

Itis a perpetual argument that nothing exisits outsde our universe, and
that our universe has the only background to support existence, how
do you give support to this prepostious assupution

That is not the argument. The argument is just that there is no need for an external higher-dimensional space to hold the curved 4D spacetime of our universe--you can have a perfectly self-contained description of curved spacetime and an expanding universe without referring to any such external space. That doesn't mean such a space might not exist, it just means that there is no compelling reason we must believe in such a space, and if GR is correct the existence of such a space would have no testable consequences.

 

[turbo]

I resist the notion of an infinite universe because it is unphysical. The universe is not observationally infinite. It has a finite size called the particle horizon - which envelopes us in a sphere with a radius of around 13.5 billion light years. It is the only volume of space that is, or ever will be, causally connected to our reference frame, hence, the only one physically meaningful.

You may resist the notion of an infinite universe, but consider this: If the Big Bang model is real, the most distant things we can see in EVERY direction are at about 13.5Gy back in time, just after the surface of last scattering. Since the Big Bang supposedly does not have a physical origin and began everywhere at once, you must consider that these most distant galaxies/quasars that we see in all directions are each at the very center of their own "observable universes" each with a unique sphere of observable space 27Gy in diameter. Every galaxy that is observable just inside the surface of last scattering of each of these spheres is also in the center of its own sphere. We can carry this model out forever, increasing the size of the universe with each iteration.

If the universe is flat or open (as most BB theorists claim), you are therefore faced with the absolute certainty that the BB universe is infinite in extent. The only way to avoid this is to stipulate that the Big Bang universe is NOT homogeneous and isotropic, and that there has to be an edge or border somewhere. That stipulation would put you on a slippery slope, indeed.

 

[Ulnarian]

If there was a second universe what is in between us and them? Heaven? Hell? Ect?

A cheezy Star Trek movie.

 

[JesseM]

If the universe is flat or open (as most BB theorists claim), you are therefore faced with the absolute certainty that the BB universe is infinite in extent. The only way to avoid this is to stipulate that the Big Bang universe is NOT homogeneous and isotropic, and that there has to be an edge or border somewhere. That stipulation would put you on a slippery slope, indeed.

You can have a flat/open universe of finite volume without the need for an edge--the condition is that the universe would have to have a nontrivial topology, like the topology of a torus. See http://astro.uchicago.edu/home/web/olinto/courses/A18200/nbower.htm , for example.

 

[cronxeh]

Didnt you watch Men In Black?

They explained everything at the end

 

[Gold Barz]

This question has been asked many many times, there is no answer to this question...It could be nothing, could be other universes, could be a void, pondering the unponderable

 

[ohwilleke]

You may resist the notion of an infinite universe, but consider this: If the Big Bang model is real, the most distant things we can see in EVERY direction are at about 13.5Gy back in time, just after the surface of last scattering. Since the Big Bang supposedly does not have a physical origin and began everywhere at once, you must consider that these most distant galaxies/quasars that we see in all directions are each at the very center of their own "observable universes" each with a unique sphere of observable space 27Gy in diameter. Every galaxy that is observable just inside the surface of last scattering of each of these spheres is also in the center of its own sphere. We can carry this model out forever, increasing the size of the universe with each iteration.

If the universe is flat or open (as most BB theorists claim), you are therefore faced with the absolute certainty that the BB universe is infinite in extent. The only way to avoid this is to stipulate that the Big Bang universe is NOT homogeneous and isotropic, and that there has to be an edge or border somewhere. That stipulation would put you on a slippery slope, indeed.

This line of reasoning doesn't follow from current Big Bang theory. What you are doing is similar to the impression you get when you are walking or driving that the moon is following you. If the Big Bang theory is correct, it turns out to be difficult beyond the scope of our measurement ability to figure out just where the middle from which the expansion originated is, in part because all the visual input we receive is time delayed, but neither current "norm" in cosmology nor most variations of it that are Big Bang accepting propose an infinite universe.

 

[JesseM]

This line of reasoning doesn't follow from current Big Bang theory. What you are doing is similar to the impression you get when you are walking or driving that the moon is following you. If the Big Bang theory is correct, it turns out to be difficult beyond the scope of our measurement ability to figure out just where the middle from which the expansion originated is, in part because all the visual input we receive is time delayed, but neither current "norm" in cosmology nor most variations of it that are Big Bang accepting propose an infinite universe.

I thought that in the standard Friedmann-Robertson-Walker model, the universe would indeed be spatially infinite if it is flat or open, and that there would be no "middle from which the expansion originated".

 

[turbo]

You can have a flat/open universe of finite volume without the need for an edge--the condition is that the universe would have to have a nontrivial topology, like the topology of a torus. See http://astro.uchicago.edu/home/web/olinto/courses/A18200/nbower.htm , for example.

I have trouble imagining warping three-dimensional space into a hyper-dimensional torus in such a way that geometry of the universe remains Euclidean, while allowing the closure that can permit motion in any particular direction to bring you back to your starting location. Is there another way to explain how a flat universe can be closed, because that website didn't do it for me...

 

[turbo]

This line of reasoning doesn't follow from current Big Bang theory. What you are doing is similar to the impression you get when you are walking or driving that the moon is following you. If the Big Bang theory is correct, it turns out to be difficult beyond the scope of our measurement ability to figure out just where the middle from which the expansion originated is, in part because all the visual input we receive is time delayed, but neither current "norm" in cosmology nor most variations of it that are Big Bang accepting propose an infinite universe.

It is my understanding (and I stand to be corrected) that the BB theory does not posit ANY center from which the expansion originated. The entire universe began expanding everywhere at once, and although extrapolating back to the Big Bang leads us apparently to a mathematical singularity, the singularity cannot be thought of as a discrete point that existed at some "place". Furthermore the model of a homogenous and isotropic Universe forbids us to exist in a "special location" or "special frame of reference" from which such a center could be sensed or from which the direction of such a center could be deduced. In the BB universe, every observer (regardless of location) is at the most mature spot in the Universe, looking out (and back) toward more distant (and younger) galaxies in every direction.

 

[JesseM]

I have trouble imagining warping three-dimensional space into a hyper-dimensional torus in such a way that geometry of the universe remains Euclidean, while allowing the closure that can permit motion in any particular direction to bring you back to your starting location. Is there another way to explain how a flat universe can be closed, because that website didn't do it for me...

To say a space has the topology of a torus doesn't mean you have to "warp" its curvature in any way--think of the video game asteroids, where if you fly off the top of the screen you reappear at the same spot on the bottom of the screen, and if you fly off the right side of the screen you reappear at the same spot on the left side. This is an example of a flat space with the topology of a torus--see the diagrams and additional explanation on this page for help understanding this.

 

[Chronos]

Itis a perpetual argument that nothing exisits outsde our universe, and
that our universe has the only background to support existence, how
do you give support to this prepostious assupution

No one assumes that nothing exists outside our universe. You can, however, assume it is irrelevant. There are two schools of thought in this thread - one physical and the other metaphysical. The observable universe is the only one that is testable, hence scientifically meaningful. Perhaps some links would help:

http://en.wikipedia.org/wiki/Universe
The reader should be warned that both popular and professional research articles in cosmology often use the term "Universe" when they really mean "observable universe". This is because unobservable physical phenomena are scientifically irrelevant (i.e., they cannot affect any events that we can perceive, and therefore effectively do not exist.

http://xxx.arxiv.cornell.edu/abs/astro-ph/0406099
In a universe dominated by a small cosmological constant or by eternal dark energy with equation of state w < -1/3, observers are surrounded by event horizons. The horizons limit how much of the universe the observers can ever access. We argue that this implies a bound N~60 on the number of e-folds of inflation that will ever be observable in our universe if the scale of the dark energy today is ~(10^{-3} eV)^4. This bound is independent of how long inflation lasted, or for how long we continue to observe the sky. The bound arises because the imprints of the inflationary perturbations thermalize during the late acceleration of the universe. They "inflate away" just like the initial inhomogeneities during ordinary inflation. Thus the current CMB data may be looking as far back in the history of the universe as will ever be possible, making our era a most opportune time to study cosmology.

http://xxx.arxiv.cornell.edu/abs/gr-qc/0108043
Nature abhors an infinity. The limits of general relativity are often signaled by infinities: infinite curvature as in the center of a black hole, the infinite energy of the singular big bang. We might be inclined to add an infinite universe to the list of intolerable infinities. Theories that move beyond general relativity naturally treat space as finite. In this review we discuss the mathematics of finite spaces and our aspirations to observe the finite extent of the universe in the cosmic background radiation.

 

[Chronos]

...Since the Big Bang supposedly does not have a physical origin and began everywhere at once, you must consider that these most distant galaxies/quasars that we see in all directions are each at the very center of their own "observable universes" each with a unique sphere of observable space 27Gy in diameter. Every galaxy that is observable just inside the surface of last scattering of each of these spheres is also in the center of its own sphere. We can carry this model out forever, increasing the size of the universe with each iteration...

ohwilleke answered this nicely, I just wanted to add this. Suppose the light from a galaxy 12 billion light years distant included a map of the universe made by an ancient astronomer. How big do you think they observed the universe to be? I would guess 1.5 billion light years in all directions.

 

[turbo]

ohwilleke answered this nicely, I just wanted to add this.

Please read my post above carefully, taking into account the validity of the point of view of an observer in the distant galaxy today, then read his reply. There is a disconnect that I believe you have missed. Then read below:

Suppose the light from a galaxy 12 billion light years distant included a map of the universe made by an ancient astronomer. How big do you think they observed the universe to be? I would guess 1.5 billion light years in all directions.

Look at a galaxy 12Gly distant. We see it as it was 12Gy ago. If that galaxy still exists, today, what would an observer in such a galaxy see? He or she (or it or "the hive mind" or whatever) would look around themselves and see a Universe of apparent diameter 27Gly, just like we do. In addition, 'WAY off near their surface of last scattering, they would see our galactic neighborhood (if it were recognizable as such) as it appeared 12Gy ago.

We are forbidden by the finite speed of light from seeing the distant galaxy in "real time". We only get 12G-y-old EM waves to work with. The trick is, if you believe in the BB theory, you also have to accept a homogenous, isotropic Universe with NO preferred location. That galaxy on the edge of our Universe occupies a reference frame just as valid as our own. And since (by the BB model's extrapolation of redshift = cosmological expansion) we believe that we see that galaxy as it was 12Gy ago, we must believe that an observer in that galaxy today sees himself at the most mature location (center) of the Universe, surrounded by a 27Gly sphere of observable Universe, which he interprets as "younger" with increasing distance, due to the finite speed of light. There will be many objects in his observable sphere surrounding that galaxy (about half of them, in fact) that are not observable from ours, because they are beyond our particular "surface of last scattering". The fact that they are NOT observable from our location in no way negates their existence. In fact, if you wish to deny the existence of galaxies beyond our surface of last scattering or plead agnosticism to their existence, you must either deny the validity of the frame of reference of the observer on the 12Gly-distant galaxy (which violates the "no special location" concept), or you must amend your acceptance of "homogenous and isotropic" as definitions of our Universe, and establish some arbitrary boundaries on the Universe to enforce this.

JesseM pointed out a third possibility - that the Universe can be locally flat/Euclidean, but have a non-trivial topology that allows it to curve back on itself. The website he links uses a torus as an example, but others use Klein bottles, teacups, manifolds with multiple interconnedctions, etc, etc. Other than the possibility of seeing self-similar constructs on opposite sides of the Universe (which has never been done, even in the WMAP data) I am not aware of any testable predictions by which these mathematical curiosities might be falsified. In science, something that cannot be falsified (for instance a statement like "angels are pushing the Universe apart, causing expansion") has no standing. Just because it is mathematically possible to do geometry in a topologically non-trivial frame, that does not make the chance that our Universe has assumed that topology likely, nor even possible.

Using Occam's Razor (apparently flat universe, without assuming a complex non-trivial topology) I believe that you will have to accept a spacially infinite Universe with no center from which it all began, as JesseM stated earlier.

 

[Chronos]

Please read my post above carefully, taking into account the validity of the point of view of an observer in the distant galaxy today, then read his reply. There is a disconnect that I believe you have missed.

I don't think I missed a thing, except the 12 billion years it took me to get there [at near light speed] and hear his explanation of how the universe, to him, appears to be 24 billion years older than it was when he first sent the message.

 

[ohwilleke]

It is my understanding (and I stand to be corrected) that the BB theory does not posit ANY center from which the expansion originated.

I'd disagree. BB theory may not precisely require a "point source", probably a better analogy would be a compact glob of silly puddy that rapidly gets pulled apart in all directions with a "center" fuzzed out over time, but the whole point of BB theory is that the universe starts at a particular time in a relatively small geometric region.

Furthermore the model of a homogenous and isotropic Universe forbids us to exist in a "special location" or "special frame of reference" from which such a center could be sensed or from which the direction of such a center could be deduced.

I agree that there would be nothing special about a "center" of the universe (unless you get very Machian). In the same way, the only thing that makes "Four Corners" (CO, UT, AZ, NM) in the U.S.A. special is a little monument. Absent that there is nothing about the place that is significant.

In the BB universe, every observer (regardless of location) is at the most mature spot in the Universe, looking out (and back) toward more distant (and younger) galaxies in every direction.

Of course, every spot is equally "mature", it has just been stretched (imagine, e.g. mapping the rational number line onto the real number line) and of course, everything we see happened in the past. This doesn't however, make the Universe infinitely wide.

 

[ohwilleke]

we must believe that an observer in that galaxy today sees himself at the most mature location (center) of the Universe,

Nope. As you yourself explained, there is no such most mature place, identifying "most mature" with "center" doesn't make sense. Every location is equally mature, just "stretched". For example, a "spherical" region with a path from Earth to Alpha Centuri as a diameter (in round numbers 3 light years long), currently has a volume of perhaps 113 cubic light years. If you map that "spherical" region back 12.3 billion light years, the "source" region has a volume of 0.11 cubic light years. But, every point in the current region has an analogous point in the prior region, and hence every point in the current region is at least 12.3 billion light years old. This can be carried back all the way to the singularity.

 

[JesseM]

JesseM pointed out a third possibility - that the Universe can be locally flat/Euclidean, but have a non-trivial topology that allows it to curve back on itself. The website he links uses a torus as an example, but others use Klein bottles, teacups, manifolds with multiple interconnedctions, etc, etc. Other than the possibility of seeing self-similar constructs on opposite sides of the Universe (which has never been done, even in the WMAP data) I am not aware of any testable predictions by which these mathematical curiosities might be falsified. In science, something that cannot be falsified (for instance a statement like "angels are pushing the Universe apart, causing expansion") has no standing. Just because it is mathematically possible to do geometry in a topologically non-trivial frame, that does not make the chance that our Universe has assumed that topology likely, nor even possible.

Using Occam's Razor (apparently flat universe, without assuming a complex non-trivial topology) I believe that you will have to accept a spacially infinite Universe with no center from which it all began, as JesseM stated earlier.

If neither an infinite universe with the simplest topology nor a finite universe with a nontrivial topology make any distinct predictions, how can it possibly be a scientific question which one is actually true? An argument which uses "Occam's razor" is a purely metaphysical one if it is impossible in principle to test whether your conclusion is correct (unlike, say, the theory that the laws of physics work differently on a single planet in the Andromeda galaxy, an idea which seems very implausible by Occam's razor, but which could in principle be tested directly). Plus, some people might argue that a finite universe is inherently simpler than an infinite one, and is therefore favored by Occam's razor even if it requires a slightly more complicated topology. As it happens, it could actually be possible to find experimental evidence for a finite universe by looking for repeating patterns in the cosmic microwave background radiation (see http://www.hep.upenn.edu/~angelica/topology.html ), but this would only work if the radius of the universe is smaller than the maximum distance we can observe.

 

[JesseM]

I'd disagree. BB theory may not precisely require a "point source", probably a better analogy would be a compact glob of silly puddy that rapidly gets pulled apart in all directions with a "center" fuzzed out over time, but the whole point of BB theory is that the universe starts at a particular time in a relatively small geometric region.

Isn't the whole point just that the density goes to infinity as you approach the big bang, and the distance between any two points in the universe which are today some finite distance apart goes to zero? This isn't the same as saying that "the universe starts at a particular time in a relatively small geometric region", unless you're just talking about the observable universe. Would you agree that in the standard Friedmann-Robertson-Walker cosmological model, if the universe is flat or open then its volume is infinite at all finite times after the big bang?

 

[ohwilleke]

Isn't the whole point just that the density goes to infinity as you approach the big bang, and the distance between any two points in the universe which are today some finite distance apart goes to zero? This isn't the same as saying that "the universe starts at a particular time in a relatively small geometric region", unless you're just talking about the observable universe. Would you agree that in the standard Friedmann-Robertson-Walker cosmological model, if the universe is flat or open then its volume is infinite at all finite times after the big bang?

I think the distinction you are coming to is a semantic one. In other words, how the phrase "volume of the universe" defined determines the answer, and I believe that at least two different definitions of that phrase are being used in this case.

I would intuitively define "volume of the universe" operationally as something on the order of: "(1) select two points at which matter or energy arising from the Big Bang are present, which are as distant or more distant from each other than any other two points in the universe; (2) call the magnitude of the distance between them d; and (3) the volume of the universe in the space-like dimensions is then defined to equal pi*d/6".

In a conventional Big Bang scenario with radiation emitting in all directions from day one and outpacing everything else, one would expect that d would be approximately equal to 2*c*t, or in speed of light units simply 2t, so long as the universe is not contracting. Hence, in a Big Bang scenario, the 3-D volume of the universe, if this definition is adopted, is a function of the time elapsed since the Big Bang (defined as t=0 and hence the volume of the universe overall through point t in four dimensions would be the integral from zero to t of f(t) with respect to t. Hence, this definition would produce a finite 3-D volume of the universe at any given time t, and a 4-D volume of the universe that is infinite or finite depending on the form of f(t) (which depends on the values you put into the Friedman-Robertson-Walker equation in standard GR). (Of course, one would have to be quite clever in defining "t" in the equations above in a way that makes sense).


This isn't quite the same as the "observable universe" (and certainly less elegant) although it is pretty close.

It sounds like the definition of "volume of the universe" you are using is something on the order of V=pi*d/6 for the value of d (defined as above) that is the maxima of the function d(t)= for t between 0 and infinity. This would be infinite given the proper inputs into F-R-W.

The implicit issue that hinges between the two definitions of "what is the universe whose volume we are measuring" is whether empty space should be included when you are defining what the universe is. In a non-aether theory, it would seem to make sense not to include that empty space. In an aether theory, it is vital to do so. General relativity, is basically a non-aether theory that gets a close to an aether theory as it is possible to do, because its geometrical elements are very aether-like.

 

[JesseM]

I think the distinction you are coming to is a semantic one. In other words, how the phrase "volume of the universe" defined determines the answer, and I believe that at least two different definitions of that phrase are being used in this case.

I would intuitively define "volume of the universe" operationally as something on the order of: "(1) select two points at which matter or energy arising from the Big Bang are present, which are as distant or more distant from each other than any other two points in the universe; (2) call the magnitude of the distance between them d; and (3) the volume of the universe in the space-like dimensions is then defined to equal pi*d/6".

But in the Friedmann-Robertson-Walker model of a flat or open universe, there would be no upper limit on d. Matter and energy are distributed evenly throughout all of space in these models, so in a flat or open universe, for any finite distance d you can find two bits of matter/energy which are separated by a distance greater than d (although if the distance is too large there will be no possibility of causal interaction between these points since the big bang).

n a conventional Big Bang scenario with radiation emitting in all directions from day one and outpacing everything else, one would expect that d would be approximately equal to 2*c*t, or in speed of light units simply 2t, so long as the universe is not contracting. Hence, in a Big Bang scenario, the 3-D volume of the universe, if this definition is adopted, is a function of the time elapsed since the Big Bang (defined as t=0 and hence the volume of the universe overall through point t in four dimensions would be the integral from zero to t of f(t) with respect to t. Hence, this definition would produce a finite 3-D volume of the universe at any given time t, and a 4-D volume of the universe that is infinite or finite depending on the form of f(t) (which depends on the values you put into the Friedman-Robertson-Walker equation in standard GR). (Of course, one would have to be quite clever in defining "t" in the equations above in a way that makes sense).

I think you are fundamentally misunderstanding how the "conventional Big Bang scenario" (ie the Friedmann-Roberston-Walker model) actually works. There is no central position in space where the explosion originated, so the notion of radiation "outpacing everything else" doesn't make sense--rather, at all finite times matter and energy are evenly distributed throughout all of space, so there is no empty region where radiation hasn't reached yet.

 

[ohwilleke]

Various Quotations:

One of the most persistently asked questions has been: How was the universe created? Many once believed that the universe had no beginning or end and was truly infinite. Through the inception of the Big Bang theory, however,no longer could the universe be considered infinite. The universe was forced to take on the properties of a finite phenomenon, possessing a history and a beginning.

About 15 billion years ago a tremendous explosion started the expansion of the universe. This explosion is known as the Big Bang. At the point of this event all of the matter and energy of space was contained at one point. What exisisted prior to this event is completely unknown and is a matter of pure speculation. This occurance was not a conventional explosion but rather an event filling all of space with all of the particles of the embryonic universe rushing away from each other. The Big Bang actually consisted of an explosion of space within itself unlike an explosion of a bomb were fragments are thrown outward. The galaxies were not all clumped together, but rather the Big Bang lay the foundations for the universe.

The origin of the Big Bang theory can be credited to Edwin Hubble. Hubble made the observation that the universe is continuously expanding. He discovered that a galaxys velocity is proportional to its distance. Galaxies that are twice as far from us move twice as fast. Another consequence is that the universe is expanding in every direction. This observation means that it has taken every galaxy the same amount of time to move from a common starting position to its current position. Just as the Big Bang provided for the foundation of the universe, Hubbles observations provided for the foundation of the Big Bang theory.

Since the Big Bang, the universe has been continuously expanding and, thus, there has been more and more distance between clusters of galaxies. This phenomenon of galaxies moving farther away from each other is known as the red shift. As light from distant galaxies approach Earth there is an increase of space between Earth and the galaxy, which leads to wavelengths being stretched.

http://www.umich.edu/~gs265/bigbang.htm

What a cosmic can of worms. Turns out even the word "universe" is elusive, having three meanings (two of which depend on whether or not you hit the shift key). So we start with the basics.

What does the word "universe" mean?

The "observable universe," Sweitzer explained, "is the one astrophysicists generally talk about because it's the one open to empirical measurements. In fact it's the only one we can or ever will be able to talk with any certainty about."

He goes on to explain that "universe" (sans the word "observable") is a larger concept that scientists think "conforms to our laws of physics and all the assumptions that go with them." Comprehending this universe, Sweitzer said, "requires a leap of faith into unobservable realms."

Finally, there is "the Universe," which, by virtue of its capital "U," includes "absolutely everything, even possibilities of dimensions, modes and regions that obey laws of physics we don't know or maybe even can't know."

Is the universe finite or infinite?

"The observable universe is finite," Sweitzer said, which is to say that it had boundaries -- physical limits. Sort of. "It's a boundary to the events we can see directly, but not a boundary in the sense that New York State has a boundary."

And in an expanding universe, this boundary is constantly moving, as is everything within it. Cosmologists typically invoke a balloon with spots on its surface, representing galaxies, to explain the expanding universe. As the balloon is inflated, the spots grow farther apart. If you stood within one of these spots, you'd see all the others moving away from you, and the most distant spots would move appear to move the fastest.

Sweitzer goes on to say that the observable universe is probably part of a much larger universe, "which could be finite or infinite. Any global statements about the universe, such as overall extent, are speculative because they require extrapolating local mathematical theories and measurements beyond the observable universe."

So if the observable universe is finite, like the space occupied by a car or a house is finite, then there must be a brick wall or something up there, holding it all together. Right?

Does the observable universe have an edge?

No, said Livio.

Argh. First you guys tell us the universe is expanding. Then you say it is finite. Now you say it has no edge! We need a visual here.

Livio is up to the task. He dredges up the old expanding balloon as his prop. "An ant traveling on the surface of a balloon will never reach an edge," Livio explains. "In the worst case it will return to its starting point."

http://www.space.com/scienceastronomy/astronomy/universe_overview_010605-1.html

Before we discuss which of these three pictures describe our universe (if any) we must make a few disclaimers:

Because the universe has a finite age (~13.7 billion years) we can only see a finite distance out into space: ~13.7 billion light years. This is our so-called horizon. The Big Bang Model does not attempt to describe that region of space significantly beyond our horizon - space-time could well be quite different out there.

http://map.gsfc.nasa.gov/m_uni/uni_101bb2.html

More specifically in response to the statement that:

But in the Friedmann-Robertson-Walker model of a flat or open universe, there would be no upper limit on d.

Because FRW pertains to the "observable universe", there would be a limit on d, because the observable universe is finite, although it does not have an edge. FRW does not model a universe of infinite dimension.

Most cosmologists agree that the observable universe is well approximated by an almost FLRW model, that is, a model which follows the FLRW metric apart from primordial density fluctuations. In a strictly FLRW model, there are no clusters of galaxies, stars or people, since these are objects much denser than a typical part of the universe.

However, for brevity, the almost FLRW model is often referred to simply as the FLRW model (or the FRW model).

http://en.wikipedia.org/wiki/Friedmann-Lema%EEtre-Robertson-Walker

And with regard to this statement:

I think you are fundamentally misunderstanding how the "conventional Big Bang scenario" (ie the Friedmann-Roberston-Walker model) actually works. There is no central position in space where the explosion originated, so the notion of radiation "outpacing everything else" doesn't make sense--rather, at all finite times matter and energy are evenly distributed throughout all of space, so there is no empty region where radiation hasn't reached yet.

While I would agree that there is no "center" where the explosion originated (or more usefully, due to the "stretching of space" we are all still in the center), the speed of radiation does define the distance of the big bang "horizon" which defines the "observable universe" which is the object described by FRW. Put another way, there is no "d" in the universe described by FRW at the present time with a length of 50 billion light years.

See also: http://odin.physastro.mnsu.edu/~eskridge/astr225/week14.html

As I understand it, even in FRW with a flat topology, "stuff" only exists out to the "horizon" even though "stuff" will expand infinitely with the horizon.

Neither FRW, nor any mainstream Big Bang theory makes any statement about the "Universe" as opposed to the "universe".

 

[turbo]

This is a tough crowd, JesseM, with lots of moves. I would like to try one more time with pure logic - stated very simply so questions regarding semantics cannot cloud the issue.

The standard model assumes that the Big Bang occurred ~13.7Gy ago, and it attributes three very basic qualities to the universe, that it is homogeneous and isotropic, and that there is NO privileged or special frame of reference in this universe. These are non-controversial aspects of the standard model, and I will confine the logical proof to these qualities.

Stipulation 1: We observe ourselves and our surroundings, including things beyond Earth. We are Observer "A".

Stipulation 2: Due to the finite speed of light, we see things as they were when light impinging our instruments left those objects. For instance, we see a star 10 Ly distant as it was 10 years ago. If it goes nova NOW, we will not know it for 10 more years. The most mature point in our observable universe is right here, in the very center of our observable universe, 13.7Gy from the surface of last scattering as it appears to us.

Stipulation 3: Judging from their redshifts, we see some distant objects as they were 13Gy ago, less than a billion years after the surface of last scattering.

Now for the logical proof:
Choose a quasar or galaxy at an apparent distance of 13Gly. Given the concordance assumptions of homogeneity, isotropy, and no special frame of reference, what can we say with certainty about a theoretical observer "B" who exists at that distant position right NOW?

We can say:

1. Since the universe is homogeneous and isotropic, and because "B's" frame of reference is no more or less special than ours, our theoretical observer looks out at his universe and sees a universe that is identical in its basic qualities to the one we see. He sees his own neighborhood, and due to the finite speed of light, he sees distant objects as they appeared in the past. Like us, he can only see objects out to about 13 billion light years distant. Anything much further, and he is looking at his surface of last scattering, just like we look out at our own. Just like us, "B" has a visible universe about 27 billion light years in diameter. We are on one edge of his visible universe, just as he is on one edge of our visible universe.

2. Over half of the volume of our visible universe (a ~27Gly diameter sphere) is outside the observer "B's" visible universe and is invisible to him. Over half the volume of "B's" visible universe is outside our visible universe and cannot be detected by us. It may help to imagine these visible universes as a pair of interconnected spheres that overlap one another just a bit more than one radius (~13.7Gy)

3. If observer "B" looks in the direction opposite that of our galaxy, he will be able to see other galaxies ~13Gly distant, and a hypothetical observer "C" in one of those galaxies will be able to look out and see a universe that is identical in its basic properties to the universes that observers "A" and "B" see. This is guaranteed by the three basic properties of the BB universe assumed in the introduction. Except for a very tiny intersecting volume centered on the location of observer "B", no part of the visible universe of observer "C" is in our visible universe (we are at observer position "A"), and except for same that tiny (lenticular, obviously) slice of space, observer "C" can see no part of our visible universe.

4. In a BB universe that is homogeneous, isotropic, and devoid of preferred reference frames, this logical iteration can be carried out forever, projecting to an infinite number of "visible universes" each centered on a unique observer. Therefore, if the BB universe is flat or open (and most adherents of standard cosmology are solidly wedded to flat at a minimum, and perhaps open), it must also be spacially infinite.

This is a logical proof derived from the principles of the standard model. I would attempt to simplify it further, but refrain for fear of loss of coherence.

How could the BB universe possibly be finite? To model a finite BB universe, either at least one the three assumptions made by the standard model about the basic qualities of the universe must be wrong, OR the universe must assume a complex topology that somehow both keeps the universe flat/Euclidean locally AND bends space in such a way that one can set off in one direction and come back upon one's previous location without deviating from a straight path. Such theoretical topologies are apparently not falsifiable by any means, and absent any compelling reason to embrace them (apart from sheer revulsion at the thought of infinities ) there is presently no need to regard them as anything more than mathematical curiosities.

I welcome any logical refutation of this proof. "Carpet-bombing" this post with citations that do not address the logic of the proof and simple nay-saying will be cheerfully ignored. Is there a logical failure in this proof? I would love to see it.

 

[JesseM]

ohwilleke, you are conflating two different issues--one is what the FRW model says about spacetime as a whole, the other is to what extent observational evidence can tell us which model is the best one for the actual universe. The FRW models describe spacetime as a whole, it's just that we can never really be sure which model actually describes the real world. For example, in the FRW model of an open universe with zero cosmological constant, the universe will expand forever (see this page of Ned Wright's cosmology tutorial, for example); however, even if we find that the observable universe has overall negative curvature and zero cosmological constant, that doesn't prove that our universe really will expand forever, because we could just be in a local region that has negative curvature, while most of the rest of the universe has positive curvature, so that the universe will actually collapse at some finite future time. If the FRW models didn't apply to the universe as a whole, you wouldn't be able to say anything for certain about what the models predict about the long-term future of the universe.

On p. 135 of The Large-Scale Structure of Spacetime by Stephen Hawking and George Ellis they explain that the FRW models assume the universe is isotropic at every point in space, so that there is exact spherical symmetry about every point:

It is possible to write down and examine the metrics of all space-times which are spherically symmetric; particular examples are the Schwarzschild and Reissner-Nordstrom solutions (see 5.5); however these are asymptotically flat spaces. In general, there can exist at most two points in a spherically symmetric space from which the space looks spherically symmetric. While these may serve as models of space-time near a massive body, they can only be models of the universe consistent with the isotropy of our observations if we are located near a very special position. The exceptional cases are those in which the universe is isotropic about every point in space time; so we shall interpet the Copernican principle as stating that the universe is approximately spherically symmetric about every point (since it is approximately spherically symmetric about us).

As has been shown by Walker (1944), exact spherical symmetry about every point would imply that the universe is spatially homogeneous and admits a six-parameter group of isometries whose surfaces of transitivity are spacelike three-surfaces of constant curvature. Such a space is called a Robertson-Walker (or Friedmann) space (Minkowski space, de Sitter space and anti-de Sitter space are all special cases of the general Robertson-Walker spaces). Our conclusion, then, is that these spaces are a good approximation to the large scale geometry of space-time in the region that we can observe.

Note that last "in the region that we can observe"--they are making no claim that the real universe matches the model outside the region that we can observe. But the model itself assumes a universe which is spatially homogeneous everywhere, and for a flat or open universe with the simplest topology, this must mean the model is of a spatially infinite universe with matter/energy distributed evenly throughout all of space.

Here are some pages which say that in the FRW model with zero cosmological constant, a universe with zero or negative curvature is spatially infinite:

http://www.phys-astro.sonoma.edu/people/faculty/tenn/FriedmannModels.html
http://tinyurl.com/68beu
http://www.321books.co.uk/encyclopedia/cosmology/standard-models.htm
http://www.jb.man.ac.uk/~jpl/cosmo/RW.html

This is also discussed on pages 724-725 of Gravitation by Misner, Thorne and Wheeler, where they show the metric of each "hypersurface of homogeneity" (a way of slicing spacetime into spacelike hypersurfaces such that the universe is spatially homogeneous in each hypersurface) for a flat and open universe, and conclude in both cases that "the volume of the hypersurface is infinite". They do qualify this with a remark about the topology though:

Warning: Although the demand for homogeneity and isotropy determines completely the local geometric properties of a hypersurface of homogeneity up to the single disposable factor K, it leaves the global topology of the hypersurface undetermined. The above choices of topology are the most straightforward. But other choices are possible.

They then go on to show how a flat universe with the topology of a torus wouldn't have to be infinite in volume.

One final example is Roger Penrose's book The Emperor's New Mind where on p. 321 he writes:

This expanding balloon provides quite a good picture of one of the three standard so-called Friedmann-Robertson-Walker (FRW) models of the universe--namely the spatially closed positively curved FRW-model. In the other two FRW-models (zero or negative curvature), the universe expands in the same sort of way, but instead of having a spatially finite universe, as the surface of the balloon indicates, we have an infinite universe with an infinite number of galaxies.

As I understand it, even in FRW with a flat topology, "stuff" only exists out to the "horizon" even though "stuff" will expand infinitely with the horizon.

Neither FRW, nor any mainstream Big Bang theory makes any statement about the "Universe" as opposed to the "universe".

The models do apply to the "Universe" as a whole. But physicists don't claim there is any scientific evidence to favor the hypothesis that one of these models is actually the correct one for our own "Universe" as a whole, the most we can do is say that our local region (our 'universe') resembles one model or another.

 

[JesseM]

This is a tough crowd, JesseM, with lots of moves. I would like to try one more time with pure logic - stated very simply so questions regarding semantics cannot cloud the issue.

The standard model assumes that the Big Bang occurred ~13.7Gy ago, and it attributes three very basic qualities to the universe, that it is homogeneous and isotropic, and that there is NO privileged or special frame of reference in this universe. These are non-controversial aspects of the standard model, and I will confine the logical proof to these qualities.

Stipulation 1: We observe ourselves and our surroundings, including things beyond Earth. We are Observer "A".

Stipulation 2: Due to the finite speed of light, we see things as they were when light impinging our instruments left those objects. For instance, we see a star 10 Ly distant as it was 10 years ago. If it goes nova NOW, we will not know it for 10 more years. The most mature point in our observable universe is right here, in the very center of our observable universe, 13.7Gy from the surface of last scattering as it appears to us.

Stipulation 3: Judging from their redshifts, we see some distant objects as they were 13Gy ago, less than a billion years after the surface of last scattering.

Now for the logical proof:
Choose a quasar or galaxy at an apparent distance of 13Gly. Given the concordance assumptions of homogeneity, isotropy, and no special frame of reference, what can we say with certainty about a theoretical observer "B" who exists at that distant position right NOW?

We can say:

1. Since the universe is homogeneous and isotropic, and because "B's" frame of reference is no more or less special than ours, our theoretical observer looks out at his universe and sees a universe that is identical in its basic qualities to the one we see. He sees his own neighborhood, and due to the finite speed of light, he sees distant objects as they appeared in the past. Like us, he can only see objects out to about 13 billion light years distant. Anything much further, and he is looking at his surface of last scattering, just like we look out at our own. Just like us, "B" has a visible universe about 27 billion light years in diameter. We are on one edge of his visible universe, just as he is on one edge of our visible universe.

2. Over half of the volume of our visible universe (a ~27Gly diameter sphere) is outside the observer "B's" visible universe and is invisible to him. Over half the volume of "B's" visible universe is outside our visible universe and cannot be detected by us. It may help to imagine these visible universes as a pair of interconnected spheres that overlap one another just a bit more than one radius (~13.7Gy)

This assumption is not necessarily correct, because it may be that due to the topology of the universe, the right edge of B's observable universe overlaps with the left edge of our visible universe. Or it may be that B sees C's galaxy, and C sees D's galaxy, and D sees our galaxy. In the FRW model, if the universe has positive curvature then space must eventually loop around this way (as an analogy, just think of observers on a globe); if the universe has zero or negative curvature, it can still loop around this way if it has a nontrivial topology (think of the video game 'asteroids' which I mentioned earlier).

3. If observer "B" looks in the direction opposite that of our galaxy, he will be able to see other galaxies ~13Gly distant

Yes, but these galaxies may be the same galaxies that we see when we look in the direction opposite to B.

4. In a BB universe that is homogeneous, isotropic, and devoid of preferred reference frames, this logical iteration can be carried out forever, projecting to an infinite number of "visible universes" each centered on a unique observer. Therefore, if the BB universe is flat or open (and most adherents of standard cosmology are solidly wedded to flat at a minimum, and perhaps open), it must also be spacially infinite.

As I explained above, this doesn't logically follow. The universe can be flat, homogeneous, isotropic and devoid of preferred reference frames, but can still only have a finite volume if it has a nontrivial topology.

How could the BB universe possibly be finite? To model a finite BB universe, either at least one the three assumptions made by the standard model about the basic qualities of the universe must be wrong, OR the universe must assume a complex topology that somehow both keeps the universe flat/Euclidean locally AND bends space in such a way that one can set off in one direction and come back upon one's previous location without deviating from a straight path. Such theoretical topologies are apparently not falsifiable by any means

No, but it would be possible to have positive evidence for these topologies, if the radius of the universe is smaller than the radius of the observable universe. Conversely, there is no way to have positive evidence for the simplest topology, and it can only be falsified if we find positive evidence for one of these other topologies.

and absent any compelling reason to embrace them (apart from sheer revulsion at the thought of infinities ) there is presently no need to regard them as anything more than mathematical curiosities.

There is also no need to regard an infinite-volume universe with the simplest topology as anything more than a mathematical curiosity. Only philosophical prejudices should lead us to prefer one over the other, as long as there is no evidence whatsoever for or against either one.

 

[Chronos]

This is a tough crowd, JesseM, with lots of moves. I would like to try one more time with pure logic - stated very simply so questions regarding semantics cannot cloud the issue.

The standard model assumes that the Big Bang occurred ~13.7Gy ago, and it attributes three very basic qualities to the universe, that it is homogeneous and isotropic, and that there is NO privileged or special frame of reference in this universe. These are non-controversial aspects of the standard model, and I will confine the logical proof to these qualities.

Stipulation 1: We observe ourselves and our surroundings, including things beyond Earth. We are Observer "A".

Stipulation 2: Due to the finite speed of light, we see things as they were when light impinging our instruments left those objects. For instance, we see a star 10 Ly distant as it was 10 years ago. If it goes nova NOW, we will not know it for 10 more years. The most mature point in our observable universe is right here, in the very center of our observable universe, 13.7Gy from the surface of last scattering as it appears to us.

Stipulation 3: Judging from their redshifts, we see some distant objects as they were 13Gy ago, less than a billion years after the surface of last scattering.

Now for the logical proof:
Choose a quasar or galaxy at an apparent distance of 13Gly. Given the concordance assumptions of homogeneity, isotropy, and no special frame of reference, what can we say with certainty about a theoretical observer "B" who exists at that distant position right NOW?

We can say that observer B's 'now', is in our future.

1. Since the universe is homogeneous and isotropic, and because "B's" frame of reference is no more or less special than ours, our theoretical observer looks out at his universe and sees a universe that is identical in its basic qualities to the one we see. He sees his own neighborhood, and due to the finite speed of light, he sees distant objects as they appeared in the past.

He sees distant objects as they appeared to be in his past, not ours.

Like us, he can only see objects out to about 13 billion light years distant.

Incorrect. Observer B's universe is younger and smaller

and he is looking at his surface of last scattering, just like we look out at our own. Just like us, "B" has a visible universe about 27 billion light years in diameter.

By the time we receive observer B's report on the size of the universe, it will be 12 billion years older than we perceive it to be.

We are on one edge of his visible universe, just as he is on one edge of our visible universe.

But we are in his future and he is in our past. There is no simulataneity.

2. Over half of the volume of our visible universe (a ~27Gly diameter sphere) is outside the observer "B's" visible universe and is invisible to him.

Not according to his reference frame. You are imposing your reference frame on his reference frame using your 'here and now' coordinate system. That is invalid.

Over half the volume of "B's" visible universe is outside our visible universe and cannot be detected by us. It may help to imagine these visible universes as a pair of interconnected spheres that overlap one another just a bit more than one radius (~13.7Gy)

It will not help. B's visible universe is not observable until I arrive at his planet.

3. If observer "B" looks in the direction opposite that of our galaxy, he will be able to see other galaxies ~13Gly distant, and a hypothetical observer "C" in one of those galaxies will be able to look out and see a universe that is identical in its basic properties to the universes that observers "A" and "B" see. This is guaranteed by the three basic properties of the BB universe assumed in the introduction. Except for a very tiny intersecting volume centered on the location of observer "B", no part of the visible universe of observer "C" is in our visible universe (we are at observer position "A"), and except for same that tiny (lenticular, obviously) slice of space, observer "C" can see no part of our visible universe.

4. In a BB universe that is homogeneous, isotropic, and devoid of preferred reference frames, this logical iteration can be carried out forever, projecting to an infinite number of "visible universes" each centered on a unique observer. Therefore, if the BB universe is flat or open (and most adherents of standard cosmology are solidly wedded to flat at a minimum, and perhaps open), it must also be spacially infinite.

This is a logical proof derived from the principles of the standard model. I would attempt to simplify it further, but refrain for fear of loss of coherence.

How could the BB universe possibly be finite? To model a finite BB universe, either at least one the three assumptions made by the standard model about the basic qualities of the universe must be wrong, OR the universe must assume a complex topology that somehow both keeps the universe flat/Euclidean locally AND bends space in such a way that one can set off in one direction and come back upon one's previous location without deviating from a straight path. Such theoretical topologies are apparently not falsifiable by any means, and absent any compelling reason to embrace them (apart from sheer revulsion at the thought of infinities ) there is presently no need to regard them as anything more than mathematical curiosities.

I welcome any logical refutation of this proof. "Carpet-bombing" this post with citations that do not address the logic of the proof and simple nay-saying will be cheerfully ignored. Is there a logical failure in this proof? I would love to see it.

Your argument is fundamentally flawed. Simultaneity does not exist between our reference frames. By the time observer B travels to Earth to reveal his findings, the universe will be 12 billion years older [not counting inflation].

 

[JesseM]

We can say that observer B's 'now', is in our future.He sees distant objects as they appeared to be in his past, not ours.

His now is not in our future light cone, since there is a spacelike separation between us...do you just mean we won't receive information about his now until the future? Of course, if the universe has negative curvature, we may never receive information about his observations.

Incorrect. Observer B's universe is younger and smaller

If a "hypersurface of homogeneity" (as described in the section of Gravitation I quoted from in my last post to ohwilleke) contains both the event of me making my observation and B making his observation, then each of us should observe the universe to be the same size and age.

 

[Chronos]

His now is not in our future light cone, since there is a spacelike separation between us...do you just mean we won't receive information about his now until the future?

My 'now' will always be in his future light, until we meet. And yes, I do mean I won't receive information from his 'now' until my future.

Of course, if the universe has negative curvature, we may never receive information about his observations. If a "hypersurface of homogeneity" (as described in the section of Gravitation I quoted from in my last post to ohwilleke) contains both the event of me making my observation and B making his observation, then each of us should observe the universe to be the same size and age.

But you will not agree when you made that observation.

 

[JesseM]

My 'now' will always be in his future light, until we meet. And yes, I do mean I won't receive information from his 'now' until my future.

Huh? The event of you making your observation is not in the future light cone of the event of his making his own observation, there is a spacelike separation between these two events. What do you mean by the phrase "My 'now'", anyway? That phrase doesn't seem to refer to a unique event (a unique point in spacetime), since every point along my worldline is called "now" by the version of me at that point.

But you will not agree when you made that observation.

Sure we will, there is only a single unique way to slice up spacetime into a series of "hypersurfaces of homogeneity", and all observers will agree on this unique slicing (foliation). Thus all observers will agree on whether two events occur in the same hypersurface of homogeneity or two different hypersurfaces of homogeneity. And this particular foliation can be used to define a global notion of time (although of course you could also slice up spacetime in such a way that each slice was not spatially homogeneous, and this would define a different global time-coordinate with a different notion of simultaneity).

If you just mean that I won't know about the results of his observation until after I make my observation, and he won't know about the results of my observation until after he makes his, I agree. But in relativity "simultaneity" doesn't have anything to do with when you actually learn about a given pair of events, it just has to do with what time-coordinates you assign the events in retrospect.

 

[turbo]

Only philosophical prejudices should lead us to prefer one over the other, as long as there is no evidence whatsoever for or against either one.

Good science should lead us to prefer a simple topology over a non-trivial (i.e. complex, manifold, etc) one. Alternate topologies cannot be seriously considered unless they can be falsified by some means. If I were to tell you that a "demon" will intervene in your linear path through the universe and bring you back to your original location, you would scoff and dismiss the idea. If I couch the idea in mathematical possibilities, you will likely be a bit more receptive, but good science should prompt you to ask me to predict what effects we might see if the complex topology is real. If I cannot give you testable predictions, you should not waste time pursuing that model. If it cannot be falsified, it is no more scientifically significant than the idea that "demons" intervene.

Mathemeticians may be able to demonstrate Euclidean geometries in complex n-diminesional frames, but that ability does not address the likelihood nor even the possibility that our universe can assume the topologies of their models.

 

[turbo]

This assumption is not necessarily correct, because it may be that due to the topology of the universe, the right edge of B's observable universe overlaps with the left edge of our visible universe. Or it may be that B sees C's galaxy, and C sees D's galaxy, and D sees our galaxy. In the FRW model, if the universe has positive curvature then space must eventually loop around this way (as an analogy, just think of observers on a globe); if the universe has zero or negative curvature, it can still loop around this way if it has a nontrivial topology (think of the video game 'asteroids' which I mentioned earlier). Yes, but these galaxies may be the same galaxies that we see when we look in the direction opposite to B. As I explained above, this doesn't logically follow. The universe can be flat, homogeneous, isotropic and devoid of preferred reference frames, but can still only have a finite volume if it has a nontrivial topology. No, but it would be possible to have positive evidence for these topologies, if the radius of the universe is smaller than the radius of the observable universe. Conversely, there is no way to have positive evidence for the simplest topology, and it can only be falsified if we find positive evidence for one of these other topologies. There is also no need to regard an infinite-volume universe with the simplest topology as anything more than a mathematical curiosity. Only philosophical prejudices should lead us to prefer one over the other, as long as there is no evidence whatsoever for or against either one.

JesseM, each of your objections addresses a possible complex topology that may allow looping. Assume a trivial topology in a flat or open universe and parse the proof in post #41. I do not believe you can find fault with it, although I would be delighted to learn something deeper from this exercise.

 

[turbo]

We can say that observer B's 'now', is in our future.He sees distant objects as they appeared to be in his past, not ours.Incorrect. Observer B's universe is younger and smallerBy the time we receive observer B's report on the size of the universe, it will be 12 billion years older than we perceive it to be.But we are in his future and he is in our past. There is no simulataneity.Not according to his reference frame. You are imposing your reference frame on his reference frame using your 'here and now' coordinate system. That is invalid.It will not help. B's visible universe is not observable until I arrive at his planet.Your argument is fundamentally flawed. Simultaneity does not exist between our reference frames. By the time observer B travels to Earth to reveal his findings, the universe will be 12 billion years older [not counting inflation].

I have lumped all your quotes because they carry a common theme - you have invalidated the reference frames of observers "B" and "C" by imposing the limitiations of our reference frames upon them. This is not acceptable as per the "no special frame of reference".

If we see ourselves as existing at a time 13.7Gy after the BB, then every other presently-existing observer in the BB universe will see themselves as existing at a time 13.7Gy after the BB. The fact that we may not become aware of the existence of such a theoretical observer until we travel to his planet or EM from his location reaches us is irrelevant. EVERY observer presently existing in a BB universe sees himself as existing 13.7Gy after the BB. The fact that our observable universes may or may not intersect is of no consequence to the ultimate validity of the respective reference frames of each of the observers. If every reference frame is equally valid, every presently-existing observer in the BB universe will see essentially what we do, except in the minor details (the homogeneous and isotropic nature of the universe demands it).