Where is the center of the universe?

[marcus]

Tex,
here is a free 9 page article by a world-class academic James Hartle:
http://arxiv.org/abs/gr-qc/0506075
click on PDF

He gives his thoughts about teaching Gen Rel to undergraduates. How to motivate it, make it real, not abstract.
He lists a bunch of APPLICATIONS of GR that will make it interesting to undergrads. And other people I think.

Hartle has a textbook called "Gravity" that sells for $70. It would be at a local college library in the math or physics section. I'm getting curious. Does he use his own philosophy about applications to make his textbook interesting?

Another essay by a reputable guy that i personally find less interesting, Robert Wald, giving his thoughts about teaching Gen Rel:http://arxiv.org/abs/gr-qc/0511073
He lists and evaluates the available textbooks and gives high marks to Geroch, General Relativity from A to B. This is only $9.50 and has no math. I didn't like what I saw of it. But Wald is a reputable guy and said it is an excellent introduction. He could be right and I wrong. Wald himself also has a GR textbook.

Personally I think Hartle is more creative and has more interesting ideas about how to motivate and explain. I would say forget the Wald article, and forget his Geroch recommendation and I would read the Hartle article and I'm actually tempted (not to buy but) to track down his textbook at some library. I'm curious. Just my personal attitude.

There is a free online textbook by Sean Carroll that some people I've talked to like. I'll get a link.
http://relativity.livingreviews.org/Articles/lrr-2001-1/
This is a short clearly written online COSMOLOGY text. It was written 2001 but has been updated until around 2008, a lot of simple math formulas. Mathy but nothing terribly hard. And anyway its free. You can read it online in HTML or download it PDF. No pictures.
Here is a "no nonsense" short intro to GR and cosmology in 24 pages by Carroll:
http://preposterousuniverse.com/grnotes/grtinypdf.pdf
Here is a 230 page set of lecture notes by Carroll written in 1997
http://arxiv.org/abs/gr-qc/9712019
basically a free GR textbook! He is a talented communicator.

But my mind keeps going back to that 9 page article by Hartle

 

[Chronos]

We have reached the point where it appears new physics is required to answer the remaining 'big questions', IMO. Scientists have never widely accepted the idea that existing knowledge is a 'horizon' on our ability to understand the universe, AFAIK. To paraphrase Sherlock Holmes - the mission of science is to eliminate the impossible. Whatever remains, however improbable, includes the truth - The universe is a cruel, yet irresistable mistress.

 

[Flatland]

If our universe has to have a center it would exist in a higher dimension and not in our 3d space.

Well, I don't want to get folks mad or in an argument. I think I still cling to what seems to me to be logical explanations. Clearly, it's gone well beyond intuitive. What I need is a good book that takes a layman and brings into the current theory with something I can understand. I don't think I am illiterate since I have taught college advanced computer programming and and am an air traffic control instructor as well as a former commercial pilot.

So I guess I need help understanding. And I do want to learn this stuff. So thanks for your all's help in advance.

tex

What exactly are you having trouble understanding?

First, guys this is my first post. I have been reading on here for awhile and the pure amount of information on this website has blown me away. Thank you to all of you for teaching me so much already.

I have a question or two that goes along with Tex's questions so I hope you don't mind me jumping in here.

So I understand the 2D balloon analogy is just a comparison to the universe and not a theory to explain the universe. But I heard on this forum that some study was done (I don't remember the acronym) that showed that the universe was either nearly flat or exactly flat.

If the universe is not flat and had some curve does that mean if you traveled in one direction would you eventually end up in the same place? For example the surface of the balloon can kinda be considered infinite because if you start in one direction you will continue on forever. Even though you will pass over your starting point many times. Is this how an infinite universe can be considered? Or am I way off base here?

If there is no curve to the universe and what I said above is not true (which I suspect it's not) I have a hard time understanding how there can be an infinite universe without a boundary.

Also, could someone try to explain the difference between a positive curve and a negative curve? I've seen that referenced a couple of times but I have no idea what the difference is. Thank you.

Positive curvature would be like the outside surface of a sphere and negative curvature would be like the inside. The angles of a triangle would add up to more than 180º under positive curvature and less than 180º under negative curvature.

 

[marcus]

Positive curvature would be like the outside surface of a sphere and negative curvature would be like the inside. The angles of a triangle would add up to more than 180º under positive curvature and less than 180º under negative curvature.

The bolded thing is not quite right.
The blue thing is right.

 

[Flustered]

I feel like you cannot compare the expansion of the universe to ants on a balloon. Ants can only move across the surface of the balloon. While we can move in 3D in our universe, now if ants could go inside the balloon and travel to the other side (surface). This analogy would fit perfectly. If you blow a balloon up and tie a knot. The center of the balloon will be inside where all the air is. So the balloon analogy doesn't work at all. If there is a center to the balloon that is expanding, there has to be a center to the universe?

Is there any kind of model or video that shows the big bang in very slow motion. Showing how it expanded? If not, why not?
Why can't scientist make a video showing how space doubled in size so many times in so little time?

How can so many people be convinced that nothing existed before the universe? There is absolutely no proof of this at all, but yet so many followers..

 

[Chalnoth]

Positive curvature would be like the outside surface of a sphere and negative curvature would be like the inside. The angles of a triangle would add up to more than 180º under positive curvature and less than 180º under negative curvature.

Just to clarify Marcus' statement, the inside of a sphere has the exact same curvature as the outside. Negative curvature has a different shape entirely: it's more like a saddle.

 

[Chalnoth]

I feel like you cannot compare the expansion of the universe to ants on a balloon. Ants can only move across the surface of the balloon.

Yes, and we can only move in our three dimensions of space.

Anyway, the main point here is that a center is a point of symmetry. It's a unique point in the space where stuff is the same in basically every direction from it. The Sun, for example, is a reasonable center for our solar system because if we choose it as our center, the rest of the solar system moves around it. If you're near the Earth, then the center of the Earth makes for a good center for most things. If you're talking about our galaxy, well, that's got a center too: Sagittarius A*.

What makes all of these important is they are points of symmetry: the galaxy, or the solar system, or the Earth all look very similar if you rotate those respective systems around those centers. The universe as a whole has no such unique point of symmetry. Instead, you can rotate the entire universe all you like around any point and it will, more or less, look the same. There simply isn't any unique point of symmetry for the whole universe.

 

[Flustered]

Yes, and we can only move in our three dimensions of space.

Anyway, the main point here is that a center is a point of symmetry. It's a unique point in the space where stuff is the same in basically every direction from it. The Sun, for example, is a reasonable center for our solar system because if we choose it as our center, the rest of the solar system moves around it. If you're near the Earth, then the center of the Earth makes for a good center for most things. If you're talking about our galaxy, well, that's got a center too: Sagittarius A*.

What makes all of these important is they are points of symmetry: the galaxy, or the solar system, or the Earth all look very similar if you rotate those respective systems around those centers. The universe as a whole has no such unique point of symmetry. Instead, you can rotate the entire universe all you like around any point and it will, more or less, look the same. There simply isn't any unique point of symmetry for the whole universe.

Yes we can move in 3d, a balloon is 3d. Ants are moving 2d on a 3d object. How does that correspond to our 3d universe? Unless you are implying that our 3d is on a face of a 4d object. I'm not talking about time.

 

[minio]

But our universe is at least 4d object. And I am talking about time.

 

[Chalnoth]

Yes we can move in 3d, a balloon is 3d. Ants are moving 2d on a 3d object. How does that correspond to our 3d universe? Unless you are implying that our 3d is on a face of a 4d object. I'm not talking about time.

Obviously the analogy isn't perfect. No analogy is. That's why they're called analogies. But it works if you note that the ants are moving in two dimensions on a two dimensional surface. It's a two-dimensional analogy for a three-dimensional phenomenon. If you try to talk about the third dimension in the balloon analogy, you're focusing in on the point where the analogy breaks down: it only works if you only consider it as a two-dimensional analogy and nothing more than that, with the third dimension only there for visualization purposes.

 

[Flatland]

Yes we can move in 3d, a balloon is 3d. Ants are moving 2d on a 3d object. How does that correspond to our 3d universe? Unless you are implying that our 3d is on a face of a 4d object. I'm not talking about time.

You can think of our universe as the 3d "surface" of a 4d sphere. That's what the balloon analogy is trying to convey.

 

[DaveC426913]

You can think of our universe as the 3d "surface" of a 4d sphere. That's what the balloon analogy is trying to convey.

It is important to recognize though that it is just an analogy. It does not require the existence of a 4th dimension in order for the 3D universe to have this curvature. i.e. the curvature we see is not evidence of the existence of a 4th dimension.

 

[thetexan]

It seems that my sticking point is going from the 'common sense' idea of the universe being a big loaf of baked bread to only a surface of a sphere or a flat or near flat surface. If I just accept the surface idea then I have no problem understanding the other points. Maybe someone can help me to understand that model. Or better stated, at one point decades ago the big 3 dimensional loaf of bread idea must have been the popular idea. Then, at some point, scientists said 'no, even though that seems common sensical, here is some evidence that points to the idea that the universe is curved...or flat...or whatever' and then that seemed correct. Please help me understand that transition and maybe it will help me see all of this.

tex

 

[marcus]

In cosmology when people say "flat" they mean zero curvature. This can be with 3D space as well as the more familier 2D examples.
What would be an example of UN-flat in the 3D case? Well you would know that you were living in an Un-flat region of 3D space if when you measured the angles of a triangle you kept getting different from 180 degrees.

In a NON-flat 3D region, the bigger the triangle the more noticeable the discrepancy.The bread analogy came into use as a picture of expansion. Popular science writers would talk about RAISIN BREAD DOUGH RISING. The raisins were the galaxies and they were getting farther apart.

An important part of that picture was that the dough was infinitely big. The loaf had no boundary. If you didn't get that detail then you missed an important part of the story.

The rising unbaked bread-dough analogy is still used in popular accounts. We sometimes use it here. You seem to have gotten the notion that things have changed because you used to hear the bread dough analogy and now you hear the word "flat". That doesn't represent a change---the messages are consistent.

The raisin bread-dough analogy actually depicts the case we call "flat". That is infinite volume 3D space with zero curvature where, for example, the angles of a triangle always add up to 180.

 

[voxilla]

If a 2D balloon surface makes sense for a 3D thing, wouldn't make an explosion make even more sense ?

 

[Chalnoth]

If a 2D balloon surface makes sense for a 3D thing, wouldn't make an explosion make even more sense ?

The problem is that explosions are messy. Really messy. Here's some cool high-speed videos of some explosions:


By contrast, the early universe was extraordinarily smooth and uniform, only becoming more clumpy much later on due to the gravitational attraction of matter.

 

[voxilla]

No need to tell me about explosions see my site

 

[Flustered]

Can someone post a picture of a geometric shape that they believe the universe most likely resembles. I heard some cosmologist say that they think the universe is like a soccer ball, and it's looped in on its self.

 

[Chalnoth]

Can someone post a picture of a geometric shape that they believe the universe most likely resembles. I heard some cosmologist say that they think the universe is like a soccer ball, and it's looped in on its self.

Unfortunately, there really isn't any way to say.

Imagine the soccer ball, for example. If our universe happens to be of that shape, then the part of it that we can see is only a teeny tiny fraction of one of the little sections of the ball. So even if the overall shape is rather like a soccer ball, the fact that we can only see this itsy bitsy bit of it means that it would be extremely hard, if not impossible, to ever actually show that it genuinely is that shape.

Our best bet of finding the overall shape, if it is possible at all, is to demonstrate that the start of our universe had to happen in a certain way. It may be (but it is absolutely not guaranteed!) that this kind of start tends to occur with a particular shape. So we may be able to indirectly deduce that our universe is probably of that shape, though we're not anywhere close to that kind of indirect deduction yet. Even then, finding direct evidence will always be hard if not impossible.

 

[Flustered]

Unfortunately, there really isn't any way to say.

Imagine the soccer ball, for example. If our universe happens to be of that shape, then the part of it that we can see is only a teeny tiny fraction of one of the little sections of the ball. So even if the overall shape is rather like a soccer ball, the fact that we can only see this itsy bitsy bit of it means that it would be extremely hard, if not impossible, to ever actually show that it genuinely is that shape.

Our best bet of finding the overall shape, if it is possible at all, is to demonstrate that the start of our universe had to happen in a certain way. It may be (but it is absolutely not guaranteed!) that this kind of start tends to occur with a particular shape. So we may be able to indirectly deduce that our universe is probably of that shape, though we're not anywhere close to that kind of indirect deduction yet. Even then, finding direct evidence will always be hard if not impossible.

Why is it a forgone conclusion that the universe has no edge to it, when we cannot see outside our own observable section? To say there is no edge is absurd in my opinion because our vision it limited.

 

[Flatland]

Why is it a forgone conclusion that the universe has no edge to it, when we cannot see outside our own observable section? To say there is no edge is absurd in my opinion because our vision it limited.

Because if would violate some of the fundamental laws of physics for the universe to have a physical edge.

 

[voxilla]

Because if would violate some of the fundamental laws of physics for the universe to have a physical edge.

Proof your point.

 

[DaveC426913]

Proof your point.

It's not his point, it is generally accepted cosmology.

There's a fair bit of reading, but you could start with the Cosmological principle and the Principle of Mediocrity, though they are not compelling.

 

[Drakkith]

Why is it a forgone conclusion that the universe has no edge to it, when we cannot see outside our own observable section? To say there is no edge is absurd in my opinion because our vision it limited.

They don't say there isn't an edge. They say that the model doesn't require there to be an edge for it to work. As far as I know at least.

 

[marcus]

They don't say there isn't an edge. They say that the model doesn't require there to be an edge for it to work. As far as I know at least.

There is some truth to that! You can put it in terms of Occam Razor commandment---Thou shalt not make thy models unnecessarily complicated.

We see no evidence of a boundary, so why put it in the model? Plus it would be a mathematical headache. If there is a boundary forces would be unbalanced and expansion would appear asymmetrical unless you put the Earth at center. But putting Earth at center is "Un-Copernican"

The thing a lot of newcomers don't realize is that cosmology is a mathematical science that is primarily concerned with a math MODEL of the universe and that model runs according to the 1915 GR equation (Einstein Field Equation) which is our current law of gravity. If you have a model which must run according to an equation you don't have a lot of freedom to mess around.

The GR equation describes the evolving geometry of all space. We know it changes and the law of gravity describes how. On page one of the book you are given a manifold which is all space thru all time, and a metric or distance function that describes the geometry---what paths are straight and how distances relate to areas and volumes and how distances change thru time etc.

Personally I find the idea of a boundary UNINTUITIVE. The universe is supposed to be ALL SPACE. So what would a boundary be separating space from?

The GR equation is by far the most accurate law of gravity we've ever had---it gives more precise numbers than the older Newton law. It has been tested repeatedly and checks out every time. And it is a law both of gravity and evolving geometry because they are the same thing (how massive objects influence geometry).
So there is a COMMON SENSE reason to base models of the universe's geometry on the GR equation. Its a no-brainer in fact.

So if you accept to base your model cosmo on the accepted law of gravity/geometry, then the idea of a boundary has no standing. How to implement? Maybe by having the average density of galaxies gradually peter out so that our region is surrounded by a large "void". But then expansion would most likely be decelerating so let's fix that with a larger cosmological constant, and so on. It is not naturally a part of the picture. Just giving the idea of a boundary a meaning seems likely to lead to headaches and a more complex picture.

The discussion gets over into talking about what's called the "cosmological principle". On large scale the universe seems on average uniform. Matter seems uniformly distributed throughout space, at anyone time. So we infer looking back in time. At each epoch matter was uniformly distributed at some average density that prevailed at that time.

So people say "homogeneous and isotropic" which basically just means evenly distributed on largescale average.

That makes the model simple and we see no evidence to the contrary so since the job is to get the simplest model with the best fit, and no evidence to contrary, evenness is assumed.

Maybe, as Drakkith suggests, it is at heart an Occam thing--the ancient tradition in mathematical sciences of keeping the model simple.

 

[Rob D]

Personally I find the idea of a boundary UNINTUITIVE. The universe is supposed to be ALL SPACE. So what would a boundary be separating space from?

Precisely. "Bubble theory" as a model for the uber-universe, does not require any membranes around the bubbles but rather they may simply be viewed as cosmological villages in the vast darkness, collections of local activity activated by some localized phenomenon such as a big bang and separated from any other such areas of activity by lots and lots of nothing, or something or what have you. And, of course, the mass and energy making up the village are reorganized every 14 billion years or so, at least in this mind model. It's always been there and always will be there following the various conservation laws.

But, no boundary or membrane encapsulating the universe or universes is needed since the vastness of infinite space pretty much takes care of the isolation question on its own.


RD

 

[voxilla]

So if you accept to base your model cosmo on the accepted law of gravity/geometry, then the idea of a boundary has no standing. How to implement? Maybe by having the average density of galaxies gradually peter out so that our region is surrounded by a large "void". But then expansion would most likely be decelerating so let's fix that with a larger cosmological constant, and so on. It is not naturally a part of the picture. Just giving the idea of a boundary a meaning seems likely to lead to headaches and a more complex picture.

Right, and what about this 'bounded' universe to be surrounded by similar universes ?

 

[marcus]

it gets into semantics and I lose interest. most "other universe" talk seems vacuous, devoid of empirical content. I try to keep language simple and consistent with professional usage---universe is all space and all physical existence.

That seems to be how it is used in 99% of the cosmology research papers that come out daily on the preprint archive.

Have a look for yourself. http://arxiv.org/list/astro-ph.CO/recent
Essentially nothing about "multiverse" in the run of mill professional literature.
More confined to popular media where they stimulate the imagination in order to sell books. Talk about string theory and God and multiverses and stuff.

 

[voxilla]

You obviously don't get my point.
Call our accelerated expaning bubble of galaxies 'A', picture it in space and surround it with 'A2', 'A3', ...

 

[Drakkith]

You obviously don't get my point.
Call our accelerated expaning bubble of galaxies 'A', picture it in space and surround it with 'A2', 'A3', ...

What about it? Even if it's possible, there's no way for us to know at the moment. Our current theory is difficult enough as it is without trying to complicate it with unknowable stuff.