# Singularity, Infinity, Edge, Expansion

1. Jan 17, 2012

### Flustered

First post in the Physic forum, the thread title are the words that really get on my nerves. I have the following questions.

a) Cosmologists say the universe started at a singularity, there for there is a point where the universe started to expand from, if you could look at the singularity after 1.0 X 10-34 sec after big bang, you could see a point where everything is moving away from, how come now we cannot find this point?

b) Hubbles law says farther galaxies are moving away faster relative to us? Does this mean we are not expanding and that everything else is expanding away form us? See diagram below

A B C D Milky way is galaxy A, after a few billionths of a sec
A ---------->B----------> C-----------> D all the other galaxies have moved away from us, and this is how I was taught the universe is expanding. In this diagram galaxy A has not moved at all, but everything else has moved away. Which leaves me wondering why are we not expanding and if we are and I could put a galaxy X into the diagram so it looks like this, we are only moving away from galaxy X, and even though BCD are expanding away from us we are also expanding in their same direction. This is why 2D models of universal expansion will never make sense to me and I need someone to really help me grasp this
X------------>A---------->B------------>C----------->D

Physcists talk about a Multiverse, few questions, if thee is a multiverse would all these "verses" make on big UNIVERSE? also if there is a multiverse, anyone who says the universe is everything and it cannot be expanding into anything is WRONG! if there are other universes like ours, that would mean there is something outside of our universe that we are expanding into.

Why cant there be an edge to the universe, if the universe is a sphere and is expanding in all directions, like the earth is a sphere. Than there would have to be an edge, just like on earth the atmosphere is the edge, where gravity stops and astronauts experience 0 gravity.

Last edited: Jan 17, 2012
2. Jan 17, 2012

### Simon Bridge

(a) that is because we are inside the Universe. If we were outside the universe in some meta-space, then we'd be able to see the point.

Anyway - a singularity is just what the best current models tell us: the Universe looks very much like it expanded from a small very dense state and our math has a singularity. There is a general feeling that this singualrity represents a flaw in our math and models like Hartle-Hawking do away with it.

We cannot see the center of the Universe from the inside for the same reason we cannot see a center for the surface of the Earth.

(b) it means that everything is moving away from everything else. Wherever you are in the universe, you will see distant galaxies moving away from you at a speed that depends on their distance from you.

eg. here's a mini-universe at two times, you'll see it is expanding.
the -- represents empty space and the 0,o,x are places in it.
t1: 0---o---x---o---0
t2: 0----o----x----o----0

put the observer on the x to start with: in T=t2-t1, the 0 has moved away from the x by 2 units, while the o has moved 1.
so you see everyting moves away from the x with a speed that depends on the distance?

shift the observer to the o on the right: the right 0 has moved 1 unit one way and the x has moved 1 unit the other way. the left o has moved 2 and the left 0 has moved 3.
so that observer sees the same thing.

(c) If the Universe had an edge, then there would have to be an outside for there to be an edge to, but by definition, the Universe is all that there is. If we flew off in one direction and ran into some sort of edge, that would just tell us that what we currently know is not all there is to the Universe. That's mostly semantics but gives you an idea of the problems with this sort of discussion.

We can see quite a long way, and no edge. Furthermore, the math that best describes what we can see is consistent with a Universe without an edge.
This is not the same as being without bounds though ... we expect the Universe to have a finite life for example - though language is difficult here since we only have words to talk about beginnings and endings within time, not of time. The usual analogy is that the surface of the earth does not have an edge ... travel as far as you like and you won't fall off. It is still finite though.

Of course the Earth has an edge - you just have to travel up or down to find it. In other words, you need to travel in a direction orthogonal to the two surface dimensions to find the edge of the surface of the Earth. Continuing this analogy - to find the edge to the Universe, you have to find a fourth space-like dimension to travel in.

Aside:
These topics are quite well covered in introductory books to cosmology.
To cover them well would take much more than an online forum post ... so I'd suggest going and getting some.

Start here:
http://www.cfa.harvard.edu/seuforum/faq.htm

Last edited: Jan 17, 2012
3. Jan 17, 2012

### Flustered

Yes but X seems to be stationary and not moving at all. Everything else is moving away from it. Also the galaxies that are closer to the outer limits of the universe must see something different? What about the outer most points in the universe, the points that are close to the actual big bang horizon. Galaxies formed here must see something different.
put the observer on the x to start with: in T=t2-t1, the 0 has moved away from the x by 2 units, while the o has moved 1.
so you see everyting moves away from the x with a speed that depends on the distance?

4. Jan 17, 2012

### marcus

I didn't see Simon Bridge's post when I was writing this. He may have covered all these points, or otherwise answered your question. I will post this anyway.
That is not what they say, if you listen carefully.

What they say is that the beautiful otherwise very successful theory of geometry on which cosmology is based BREAKS DOWN as you approach the start of expansion.

This is considered to be a sign that the theory needs to be improved or replaced by a more rugged durable one which will not break down at high density.

In math, when a man-made theory or model breaks down the breakdown is called a singularity. We do not think singularities exist in nature. They occur in math models of nature and normally are gotten rid of by improving the models. So this is being worked on in the case of cosmology. People are working on a new theory of geometry and how it interacts with matter.

But you could say (somewhat misleadingly) that because our current successful model of geometry, called GR, breaks down as you go back in time and approach start of expansion---that therefore, in our current model, "the universe starts with a singularity".

This gives laymen the wrong idea that a singularity is something real that was sitting at some point in space.

That is a totally wrong picture. What "the universe starts with a singularity" really means is that the current math model of the U expanding geometry works beautifully back as far as 13.7 billion years ago and then in conditions of extreme high temperature and density it blows up, so "to go back before that we need a better model."

The other way you can refine your picture is to reflect that a uniform pattern of expansion where all distances increase is not like ordinary motion because nobody gets anywhere by it. It is just a change in geometry (which GR says is "live" and interacts with matter). So relativity allows the distances between things to increase, if necessary at rates that are many times the speed of light. It's not ordinary motion that would be restricted by "special"relativity.
Two things that the universe thinks are both sitting still can have the distance between them be increasing. This is what happens when you have a dynamical theory of geometry like what Albert E. gave us in 1915.

Welcome. Have fun here

Last edited: Jan 17, 2012
5. Jan 17, 2012

### Simon Bridge

Only from the POV of someone sitting on x.
Someone sitting on either of the o's would think their o is stationary and everyone is moving away from them. Don't believe me? redraw the pic with the x in any of the other positions.

In my little pocket Universe yes - since I drew it with an edge that our Universe does not have ... that is a limitation of the analogy.
There are others; my pocket universe also only has one dimension, for instance, while space has 3.

I could have drawn a closed pocket universe easily enough by looping it back on itself. In that case, the circumference of the circle increases while the number of points on it stay the same. However, it is hard to draw a circle in text. Just imagine that the left and right-most 0 are actually the same place like 0 and 360 degrees are the same place on a protractor and see if your question still makes sence.

Anyone so far away from us would see their own big-bang horizon just as far away from them as ours is from us. The "horizon" is formed by the amount of time it took for light from there to get here. It is what was there billions of years ago - it looks quite different now. To anyone out there, we are sitting in the big-bang horizon.

6. Jan 17, 2012

### Simon Bridge

refining my model for a closed-space 1+1 universe - no edges.
let c be our observer:
t1: 0--a--b--c--d--e--0
t2: 0---a---b---c---d---e---0
t3: 0----a----b----c----d----e----0

the clue to c that the motion of the other letters is due to an expansion in their space and not just ordinary motion is that the speed is proportional to the distance. How do the other letters know how far from c they are to regulate their speeds accordingly?

(It could be that it's because there's someone outside the Universe typing extra spaces into a computer somewhere ... but that amounts to the same thing: the Universe is expanding.)

now: lets see what this looks like from the POV of the observer at a:
t1: d--e--0--a--b--c--d
t2: d---e---0---a---b---c---d
t3: d----e----0----a----b----c----d

notice that the endpoints are now "d" that means I can still get to d by going right from c or left from e. I have rotated the Universe to put a in the middle. I can rotate the universe to put "a" anywhere in the diagram I like because it is circular. This also works if the universe is infinite.

The upshot is that all the observers will see themselves at the center of an expanding Universe.

If you extrapolate backwards, you'll find the time to the big bang in this universe would be 2 time intervals. If you set the time interval to, say, seconds, and two distance units are 1 light-second, then you can have fun working out what is seen by any observer at different times. Pick 0 for the observer, and give each letter an age from the big bang so you can record when 0 sees which letter at what age.

7. Jan 17, 2012

### Flustered

t1: 0--a--b--c--d--e--0
t2: 0---a---b---c---d---e---0
t3: 0----a----b----c----d----e----0

If we are POV C would b and d appear to be red shifting?
If so, would c appear to be red shifting to them?
In your model it appears that in each direction that the galaxies are moving away, the galaxies to the right are moving to the right and the ones to the left are moving left. In which direction is our galaxy moving? It appears to be staying still while everything expands around it, which is a contradiction because from POV b, c would appear to be moving away. I guess the hardest thing for me to wrap my mind around is, how can our galaxy appear to be still but from another galaxy it appears to be red shifting. If this is the case which way are we expanding, because the model shows galaxies expanding in 2D. If space is a sphere that wraps in in it's self. Then light from early galaxies we see could also be the same exact galaxy in a different direction,but this galaxy is more matured. Also the 3d infinity sphere doesn't explain observable and non observable universe.

8. Jan 18, 2012

### Simon Bridge

yes
yes
nowhere - that's where we are. the observer is always stationary from the POV of the observer.
but from the POV of b, b is going nowhere. From the POV of a different galactic cluster to our own, our galaxy is red-shifted.

I know what you mean. But that is normal relativity, nothing to do with the redshift. Everybody is stationary from their own POV.

The reason you think you can tell if you are moving or not is because you look and see that the ground is moving - you realize that the ground is usually still and so deduce that you are moving instead. Stuff like that. In intergalactic space - what can stand-in for the ground?

Actually, my model was only 1D ... a closed universe could be a hypersphere - all 3 dimensions of space eventually wrap around on themselves.

If the universe were small enough we could confirm this directly since we could look out as see ourselves, much younger, some distance away. You get that in the little model too ... remember it is a circle?

---0---a---b---c---d---e---0---a'---b'---c'---d'---e'---0'---

... here I have primed the repeats because c' is just c only younger (provided this universe is not expanding: expansion changes things). if the gap "---" is a light-year then c would see c' (itself at that distance), but from 6 years ago.

If you imagine that this universe expands one "-" a year, then it started 3 years ago. That means anything more than 3ly away from c looks like the primal universe ... same with everyone else: they all see the primal universe 3ly away. Nobody gets to see the whole universe for a while. What's more, if this universe were bigger, then parts of it will be retreating from the observer faster than light - and so will never be seen. (This last one took me a while.)

If the stars only started shining 2 years ago, then nobody will even get to see to the start of Everything.

What with all this, if the curve of the universe is shallow enough then it will appear flat ... just like the Earth looks flat to people on it's surface. We have to detect the curvature of the Earth indirectly - or leave the surface. But we cannot leave the Universe so indirect is the best we got.

What some people suggest is thinking of the galaxies as currents in a pudding - the pudding starts out as a dense dough and expands as it is cooking. The expanding pudding is space.

The trouble with this is that the pudding, having edges, has a well-defined center to measure expansion from. But if you imagine an infinite pudding, then there is no place which can be called the "center" (and it is the same for the "closed" pudding - but harder to imagine) and you end up with something quite close to the Universe.

9. Jan 19, 2012

### Flustered

Your post helped a lot, say there are only 3 galaxies in this universe.

A-B-C

If I'm understanding what you are saying, this would mean that.
A----B----C, galaxy C would than see A in the following A-----B-----C-----A
Galaxy C would see A in two directions? If this is true than you are proposing that space is a sphere. That wraps in on its self, so you should be able to travel in one direction long enough and end up at the same point eventually?

If my first paragraph was false with the diagram, than what would galaxy C see at this moment in time. A-----B-----C if C was to look ----> that direction, would they see the "edge" or would they see A galaxy again? If there were only 3 galaxies in the universe?

10. Jan 19, 2012

### Flatland

Scientists believe that the universe is either open and infinite or closed but unbounded.

If the universe is infinite then there is no center or edge; it just goes on forever. Pretty self explanatory.

If the universe is closed but unbounded, that just means that if you travel in a particular direction long enough you will come back out through the other side. The universe loops back onto itself in all 3 directions so to speak. In either scenario there is no center.

Last edited: Jan 19, 2012
11. Jan 19, 2012

### Simon Bridge

@Flustered:
In that last picture yep - C would see (urk) an old A to the right and a young one to the left. If those were people's heads, then C would eventually see the back of his own head. Travel long enough in one direction you end up back where you started.

As it is we have not observed any of these repeated galaxies so the Universe is big enough that they must be on the other side of the observable limit however, we know that space-time can curve like that because we observe related effects from more local curvature. The effect is called gravitational lensing.

Note - if it takes T for light to go between 2 galaxies, then the light from each galaxy emmitted at the exact time that the universe had the configuration shown would arrive at C at different times in C's history. The light from the RHS of A will arrive at C 2T later, while the light from the LHS of A takes only T to get there. During that time, the universe will have expanded so the exact configuration that C can observe is not the actual distribution of mass at that time. Which can complicate things no end.

Your first picture is not much use, I'm afraid discussing it further will only confuse things more. These 1D models are limited enough as they are.

In practise, we do our calculations in space-time - which simplifies things, and extrapolate to the kinds of things we can measure in space at a particular time.
We are kinds hitting the edge of the kinds of things we can easily talk about without a specialized language. Beware.

Hopefully you are now more comfy with the idea that there is no center? To put it (philosophically) more precisely: we do not need to postulate a center to account for our observations, and Occam's Vorpal sword goes snickity snack.

Of course, we don't have to passively wait around for an observation that does require the postulate, we can actively go look for one by figuring out what having a center means and watching for the signs. Nobody has ever found the slightest sign there may be one, but it can be a fun exercise for a postgrad cosmology student.

@Flatland: - I'd like to direct your attention to the short answer to the same question in the link in post #2. Seems there is a possibility of "both". However, in terms of post #1, afaik nobody seriously thinks that the universe is finite and bounded.

Last edited: Jan 19, 2012
12. Jan 19, 2012

### Flustered

Thats impossible it cannot go on forever, say someone could travel at 100 times the speed of light.. What if scenario, they blast off in one direction, eventually they would to come to a point where space has not yet expanded into. The edge.? Where is my logic wrong, I feel like this is common sense, but cosmologist feel different.

What would this shape look like?

13. Jan 19, 2012

### Simon Bridge

Remember this: "common sense" is what tells you the Earth is flat.
The place where you logic fails is in thinking that space expands into something. Same as before.

Space can be infinite and expanding ... it is the gaps between things that is getting bigger. When you go back in time the (infinite) Universe does not get smaller, the matter and energy in it gets denser. The maths still works out for infinite space - however, there is a tendency to favor finite models of the Universe.

An infinite version of those 1D model universes would just run off the edge of the screen in both directions and keep going on and on for ever.
In the past, more letters/galaxies could fit on the screen. In the simple expansion model I used, you'd still get a time when there was zero separation between letters/galaxies.

Tha is a subject of continuing research and speculation. Pretty much every 4+D shape you can think of has been considered. The simplest would have spherical symmetry in 4D but that does not account for time being special. Most of the common ones give time it's own geometry while 3D space has spherical symmetry. Remember, we have to try and describe the shape of space-time from the inside - that requires a specialized language. What you'd intuitively think of as "shape" does not make sense in this context.

Hawking's work on this, for instance, focuses on the nature of time (as the "problem child" of the dimensions) so his models have 1D of space represented as a circular loop - just like my universe-ette above - and he puts time as perpendicular to that. Since the loop expands with positive time, and the expansion seems to be accelerating, this produces a trumpet shape on the page.

We don't know what will happen to the expansion in the future - maybe it will slow down and reverse? So these pictures tend to leave the open end of the trumpet open.
Going back in time, it would converge to a point ... which is the singularity that is viewed as a flaw in the model. That would be a boundary - we tend to like theories of time which are finite to the past, and boundless, for reasons that have already been gone into. Basically it neatly avoids hard problems. Hawking found a solution (actually a set of them) where, at a particular minimum circumference time bend around into a circle so the time-space surface forms a hemisphere. Problem solved.

This kinda means if it were possible to go back in time far enough, you'd end up going forward again on the opposite side of the universe.

Careful though: that is not the only geometry available. It is a simple one which shows what sort of thing is possible: like a proof of concept.
We like to use the simplest one we can get away with because of Occam's razor.

You are having a hard enough time with 1D and expansion: take it slow huh?

Last edited: Jan 19, 2012
14. Jan 19, 2012

### Flustered

Disagree, why would people think the world is flat, but at the same time say the sun is orbiting around the earth? How can the sun orbit a flat piece of paper like the earth? It seems like a contradiction to me.

Trying to relate 1D expansion to a 4D universe expansion is difficult, if I had a smart board and a marker I could write out my thoughts more thoroughly.

15. Jan 19, 2012

### Flatland

There wouldn't be a place "where space has not yet expanded into" if space was infinite. It just means that you can travel through space forever and never reach an edge or loop back around. Infinity can still expand.

No one truly knows.

16. Jan 19, 2012

### voxilla

With the same logic infinity can shrink to 0, so infinity == 0.

17. Jan 19, 2012

### Simon Bridge

"Common sense is what tells you the World is flat."
-- Bertrand Russel [1]

Also see: Shadewald R. J. The Flat Out Truth

That's not "common sense" - you seem to be one of those (us) who are cursed with the knee-jerk reaction of actually thinking about statements you read and hear:) When people go through their normal lives, they do not even think to account for the curvature of the earth ... that is what the statement means. That is what is "common" about common sense. It is quite uncommon for someone to wonder about the problems about this without prompting. These days we rely on education to do the prompting - which is why flat-earthers still exist.

Common sense shows you that you basically go down as much as you go up in your travels - ergo: flat World. The Sun crosses the sky from horizon to horizon - common sense says the sky is a big blue bowl upturned over us and the sun is a light that slides over it - why can't it go down to the horizon someplace past the seas? Maybe the flat Earth has an edge for the Sun to go past? Maybe is enters the surface of the World through a huge hole or cataract?

However - this is the sort [the questioning/skeptical sort] of thinking that leads to the Curved Universe theories that we have today - same sort of problems but on a very big scale.

Nope - that only follows if you think it is the universe expanding in size.
That only works for a finite universe - a particular total volume say. In an infinite universe has no sensible size and it's volume is always infinite ... so the compressed beginning is still an infinite universe with a much higher energy density because all the points are closer together.

You can almost get the idea by thinking in terms of a coordinate density - i an infinite expanding universe, the coordinate density decreases over time ... the number of discrete space-points in a unit volume decreases. Before you object: I said, "almost".

In an infinite universe it makes no sense to talk about expansion in terms of the size of the Universe ... it is the geometry that is expanding.

-------------------------

[1]...as quoted in: A History of Modern Western Philosophy [1945] - I'd like a better reference, anybody?
The problem with quotes on the internet is they are so unreliable. --- Abraham Lincoln

Last edited: Jan 19, 2012
18. Jan 19, 2012

### supermarina

Well, just for fun, no. Earth-bound perspective tells you that World is flat. Change perspective, and common sense works just fine.

19. Jan 19, 2012

### Simon Bridge

That would be accurate - common sense is from the common perspective. Read the Flat Out Truth link for a very sad failure of common sense linked with the concept of finding the truth then believing it to the end.

IT's not just the Earth-bound perspective that does it though - you can figure out the Earth is not flat from Earth-bound observations - to the extent that no "educated person" seriously believed that the Earth was flat well before sputnik changed the perspective.

20. Jan 19, 2012

### supermarina

I read it, and that is not the kind of common sense I was referring to. What will we believe in, if not in our ability to understand? Change of perspective is very powerful, not necessarily physical change, but rather mental. Nice posts in this thread, by the way.

21. Jan 19, 2012

### Simon Bridge

Ah well - epistomology.
I think Russell (it's a quote remember) was referring to the naive application of reason, or "intuition", rather than it's systematic and disciplined application. It is the latter we need in order to reliably advance our understanding. But this is not a philosophy thesis and Russell was being glib not rigorous. (His works are in the Gutenberg project btw).

Dragging this back to context: appealing to common sense notions about expansion as a guide to figuring out GR is probably not reliable.

Note to say our intuitions cannot be useful - just see how creepy the red room sequences in Twin Peaks are.

22. Jan 19, 2012

### Flustered

If the sun entered the earth, and came out the other side. Would the sun actually be going around the earth?

Egyptians lined pyramids up with the cosmos, Columbus thought we would fall of the face of the earth... Disconnect.

23. Jan 19, 2012

### phinds

You would do well to study the math of infinity. You are trying to apply finite math to infinity and is just does not work. n x infinity = infinity, regardless of the value of n. It just isn't like "normal" math.

24. Jan 19, 2012

### marcus

==quote Flustered==
Thats impossible it cannot go on forever, say someone could travel at 100 times the speed of light.. What if scenario, they blast off in one direction, eventually they would to come to a point where space has not yet expanded into. The edge.? Where is my logic wrong, I feel like this is common sense, but cosmologist feel different.
==endquote==

The two most common models AFAIK are basically two cases of the standard LCDM (lambda cold dark matter picture).
1. infinite space case: U was infinite at start of expansion. distances have been expanding as per usual equation. U is of course still infinite. You can continue forever at 100 times speed of light.

2. positive curvature "hypersphere" case: U was finite volume at start. distances have been expanding as per usual equation. U is of course still finite volume. If you travel in same direction at 100 time speed of light you will get back here.

Probably, unless the thing is just too damn big so that even the slowly accelerating expansion that we now witness is enough to defeat you. But then by going faster you could still circumnavigate. Like 1000 times speed of light. We don't yet have a good estimate of how big it is (in the finite case) so I can't say just how fast you would have to go in order to circumnavigate.

25. Jan 19, 2012

### Simon Bridge

Well I said "World" for a reason here - maybe the Earth is only part of the flat World, the Sun can go around the Earth part without going all the way around the whole World.

Fun, isn't it.
But off-topic.

I believe the original questions have been answered :)