Where Is The Center Of The Big Bang Universe?

[sol invictus]

Sol Invictus,

What evidence suggests that if the universe imploded into a big crunch existence would end and there would be nothing?

The entire universe and everything in it has just crunched down into a tiny region. That region will be extremely hot, dense, and inhomogeneous. What happens next no one knows, but any real system put into such a state will NOT bounce and begin expanding nicely and smoothly. Its entropy should increase, which probably means it stays small and hot.

However nothing can be said for sure, because we don't have a theory which applies in this case.

 

[sol invictus]

In the cosmological constant case the universe continues to expand ever faster, and you get what happens in your heat death description except that the rate doesn't slow, it speeds up.

With one caveat - universes dominated by positive cosmological constant have a Hawking temperature associated with their event horizon. So there is never a real heat death - that component of the temperature does not decrease with expansion (it's constant). Very rarely, thermal fluctuations in that bath of particles may conspire to form interesting structures.

 

[Skeptic Ginger]

OK, I'm having more genius Universe contemplating thoughts on this one which I shall post even though no one here is paying attention to me.

When we peer out into space, we can only see the time dimension at great distances. We can see 3D, but we can't really see current space time more than a relatively short distance. That's like the people of flatland being unable to see anything not on their 2D surface.

And science has drawn all these conclusions about no center and no edge based on an imperfect view of the actual Universe.

If we are going to use the balloon surface model to describe the Universe, that model curves back on itself. We don't know if that is true for the Universe or not because we cannot see the Universe in real time.

I propose that if you were to take off in a straight line and you could cross the Universe with the time dimension frozen, IE a snapshot of the whole Universe as it is at this moment, you either have to reach the edge, implying a center, or you have to return to where you started. Or, the third option is the Universe is infinitely large. But infinitely large excludes expansion.

There may be nothing beyond the edge, there may be something the Universe is expanding into. The current model says nothing being expanded into.

In my cosmological ignorance I am going to say the emperor has no clothes. We accept this 'Universe expanding, that's all there is, no center, no edge' because it fits what we observe. I have no objection to that.

But, there is still a Universe we do not see. That is the actual Universe in real time. It is there. That is unless the thing died out and the absence of light hasn't reached us yet. And it started out one size and expanded. Regardless of the concept of there being nothing outside of the Universe, it still expanded in 3 dimensions plus time. And 3 dimensional things have centers and edges. Either that expansion curves back on itself, or it doesn't. And it is hard to imagine how a 3D object curves back on itself like a 2 D surface can.

So there is a center and an edge of the Universe. But we are unable to see the Universe in real time, so we cannot see it. And the speed of the expansion or the size of the Universe and our location within it plus the constraints of light speed, makes it impossible for us to detect the center or edge. And my evidence for calling the no clothes here, if the Universe were a singularity, it would have a center and an edge. Of the 3 dimensions in the Universe, there is a middle and edge. It is only when you add the 4th time dimension that you can have your no edge, no center model. But we have 3 dimensions over short distances where time does not impact our observations as it does over large distances. And by the same token, there are the 3D components to the larger Universe which exist when time is frozen.

 

[Skeptic Ginger]

And here is someone else who sees what I see.

Universe Measured: We're 156 Billion Light-years Wide!

The universe is at least 156 billion light-years wide.

In the new study, researchers examined primordial radiation imprinted on the cosmos. Among their conclusions is that it is less likely that there is some crazy cosmic "hall of mirrors" that would cause one object to be visible in two locations. And they've ruled out the idea that we could peer deep into space and time and see our own planet in its youth.

First, let's see why the size is a number you've never heard of before.

Stretching reality

The universe is about 13.7 billion years old. Light reaching us from the earliest known galaxies has been travelling, therefore, for more than 13 billion years. So one might assume that the radius of the universe is 13.7 billion light-years and that the whole shebang is double that, or 27.4 billion light-years wide.

But the universe has been expanding ever since the beginning of time, when theorists believe it all sprang forth from an infinitely dense point in a Big Bang.

"All the distance covered by the light in the early universe gets increased by the expansion of the universe," explains Neil Cornish, an astrophysicist at Montana State University. "Think of it like compound interest."

Expansion of the Universe along with the consequences of special relativity still leaves us with the 3D properties of the Universe in real time.

That means there is an edge and a center. The emperor has no clothes and common sense returns to cosmological contemplating.

This article generated quite a few e-mails from readers who were perplexed or flat out could not believe the universe was just 13.7 billion years old yet 158 billion light-years wide. That suggests the speed of light has been exceeded, they argue. So SPACE.com asked Neil Cornish to explain further. Here is his response:

"The problem is that funny things happen in general relativity which appear to violate special relativity (nothing traveling faster than the speed of light and all that).

"Let's go back to Hubble's observation that distant galaxies appear to be moving away from us, and the more distant the galaxy, the faster it appears to move away. The constant of proportionality in that relationship is known as Hubble's constant.

"One seemingly paradoxical consequence of Hubble's observation is that galaxies sufficiently far away will be receding from us at a velocity faster than the speed of light. This distance is called the Hubble radius, and is commonly referred to as the horizon in analogy with a black hole horizon.

"In terms of special relativity, Hubble's law appears to be a paradox. But in general relativity we interpret the apparent recession as being due to space expanding (the old raisins in a rising fruit loaf analogy). The galaxies themselves are not moving through space (at least not very much), but the space itself is growing so they appear to be moving apart. There is nothing in special or general relativity to prevent this apparent velocity from exceeding the speed of light. No faster-than-light signals can be sent via this mechanism, and it does not lead to any paradoxes.

 

[RecoveringYuppy]

That means there is an edge and a center.

Don't see how. I think this just means the unverse we occupy at any point in time is a spherical intersection of the 4 dimensional hypersphere some of us have been discussing (as opposed to it being the entire surface of the hypersphere).

It does raise an issue for those of us asking if it's appropriate to view time as the radius of that hypersphere, with all of the universe's history being the interior of that hypersphere. The radius can't be time, but it may be a function of time. And I think that may be true for other reasons because I don't think the "volume" of the universe is linearly proportional to time.

 

[Fredrik]

But infinitely large excludes expansion.

Actually it doesn't. Expansion in this case would mean that the distances between galaxies are increasing relative to e.g. the size of the galaxies themselves (and that the geometry in an arbitrary region of space, e.g. a cluster of galaxies, keeps getting flatter with time).

And 3 dimensional things have centers and edges. Either that expansion curves back on itself, or it doesn't. And it is hard to imagine how a 3D object curves back on itself like a 2 D surface can.

They are hard to visualize, but not difficult to represent mathematically. For example, the set of points (x,y,z,w), such that x²+y²+z²+w²=R² is a 3-sphere with radius R. But even this 3-sphere is embedded in a 4-dimensional Euclidean space (the set of all the (x,y,z,w)), so there is definitely something "surrounding" it.

It's not easy to see how an n-dimensional "object" can be curved without being embedded in a Euclidean n+1-dimensional space, but it is possible. The branch of mathematics that explains this is called differential geometry.

 

[Fredrik]

I think this just means the unverse we occupy at any point in time is a spherical intersection of the 4 dimensional hypersphere some of us have been discussing (as opposed to it being the entire surface of the hypersphere).

I don't think the term "hypersphere" is correct. A "hypersurface" is usually an n-dimensional subset of an n+1-dimensional surface. E.g. there are some 3-dimensional hypersurfaces of space-time that it makes sense to think of as "space, at a certain time".

Also, space-time is not a 4-sphere in the model we've been talking about. It's a one-parameter family of 3-spheres (and it is such that it makes sense to think of each 3-sphere as representing space at a certain time).

It does raise an issue for those of us asking if it's appropriate to view time as the radius of that hypersphere, with all of the universe's history being the interior of that hypersphere. The radius can't be time, but it may be a function of time. And I think that may be true for other reasons because I don't think the "volume" of the universe is linearly proportional to time.

Yes, it's a function of time and it's not linear.

 

[RecoveringYuppy]

@Fredrik,

Is the distinction between a 4-sphere whose radius is a function of time and one-parameter family of 3-spheres really meaningful in our particular universe? I can see an important difference in a universe that is expected to "crunch".

 

[sol invictus]

I propose that if you were to take off in a straight line and you could cross the Universe with the time dimension frozen, IE a snapshot of the whole Universe as it is at this moment, you either have to reach the edge, implying a center, or you have to return to where you started. Or, the third option is the Universe is infinitely large. But infinitely large excludes expansion.

This is your mistake - infinitely large does not exclude expansion. If you can imagine a balloon stretching, go close to the surface and consider a little patch. That little patch doesn't care that it's part of a spherical balloon, and not part of an infinite rubber sheet - it stretches the same way in either case.

There are three options in standard cosmology, which (if the world were one dimensional) correspond to circle, line, and hyperbola. The second two are both infinite; none has a center or an edge.

 

[Fredrik]

Is the distinction between a 4-sphere whose radius is a function of time and one-parameter family of 3-spheres really meaningful in our particular universe?

A 3-sphere (not 4-sphere) with a radius that's a function of time is a one-parameter family of 3-spheres. Time is the parameter.

There's no solution of Einstein's equation that describes space-time as a 4-sphere. There's a minus sign in a crucial place in the mathematics that guarantees that.

 

[articulett]

For some reason I was expecting that page to be very interesting because it would all be explained in folk songs.

I misread it as "Joan Baez" myself the first time.

 

[edd]

I misread it as "Joan Baez" myself the first time.

Joan's his cousin actually.

 

[RecoveringYuppy]

There's no solution of Einstein's equation that describes space-time as a 4-sphere. There's a minus sign in a crucial place in the mathematics that guarantees that.

OK. Where?

 

[Skeptic Ginger]

This is your mistake - infinitely large does not exclude expansion. If you can imagine a balloon stretching, go close to the surface and consider a little patch. That little patch doesn't care that it's part of a spherical balloon, and not part of an infinite rubber sheet - it stretches the same way in either case.

There are three options in standard cosmology, which (if the world were one dimensional) correspond to circle, line, and hyperbola. The second two are both infinite; none has a center or an edge.

It's not a mistake, infinity plus one is an oxymoron.

Look, I understand all about the expanding Universe. If you read my posts, hopefully that was clear. Are you saying the singularity was infinitely large?

Oh, and you seem to have ignored the link.

 

[RecoveringYuppy]

A 3-sphere (not 4-sphere) with a radius that's a function of time is a one-parameter family of 3-spheres. Time is the parameter.

Am I using the terminolgy incorrectly? I would have thought that a family of 3-spheres with a radius that is a function of time could also be described as a 4 sphere where 1 of the 4 dimensions is a function of time.

 

[Gate2501]

It's not a mistake, infinity plus one is an oxymoron.

Look, I understand all about the expanding Universe. If you read my posts, hopefully that was clear. Are you saying the singularity was infinitely large?

Oh, and you seem to have ignored the link.

I have seen people refer to it as " infinitely dense ". I really have no comment on how it is possible for anything to be infinite tho

 

[sol invictus]

It's not a mistake, infinity plus one is an oxymoron.

I'm sorry, but I don't know how to parse that sentence.

Look, I understand all about the expanding Universe. If you read my posts, hopefully that was clear.

No, it wasn't.

Are you saying the singularity was infinitely large?

In a flat or open universe, yes, there is a sense in which the singularity is infinitely large. For example, you'd have to wait an infinite amount of time for the light from the most distant parts of it to reach you. However there is also a sense in which it was a point - if you take any finite sized region of space some time after the big bang and trace it back, it will be of zero size at the bang. The real problem is that our intuition about space and time is a little bit wrong, and very wrong in this case.

Oh, and you seem to have ignored the link.

I didn't ignore it. The size they're talking about is not the distance to a real edge - it's the distance to the edge of what we can see today. It's related to that fact I mentioned above, that it will take infinite time for light from all along the singularity to reach us. Someone 156 billion light years away (by the way, that number is much too big - I think it's an error) would see precisely what we see.

EDIT - that number is definitely wrong. See here, under misconceptions: http://en.wikipedia.org/wiki/Observable_universe

 

[MattusMaximus]

It's not a mistake, infinity plus one is an oxymoron.

Uhhh, not necessarily. There is a branch of mathematics by George Cantor that actually shows that not all infinities are alike. Strange, but true... read more about it here:

http://en.wikipedia.org/wiki/Transfinite_number

Btw, Sol is right about our Hubble Limit not being the edge of the universe. It's best to say that is the edge of our observable universe. So long as the rate of expansion of spacetime doesn't out pace light-speed, as time goes on we should be able to observe more and more of the universe.

 

[MattusMaximus]

There are three options in standard cosmology, which (if the world were one dimensional) correspond to circle, line, and hyperbola. The second two are both infinite; none has a center or an edge.

For the lurkers on the thread, a great example of a one-dimensional situation which is finite but not bound (in the sense that it has no 1D "edge" - I hope I got that right) is the Moebius strip.

Try making one and trace it - there's only one side

 

[sol invictus]

Am I using the terminolgy incorrectly? I would have thought that a family of 3-spheres with a radius that is a function of time could also be described as a 4 sphere where 1 of the 4 dimensions is a function of time.

A 4-sphere is a 4-dimensional Riemannian manifold. It has 4 space directions and 0 time directions. We can speak about the topology of such a manifold; mathematicians have classified and studied them extensively.

A spacetime is a 4 dimensional Lorentzian manifold with 3 space directions and 1 time direction. I'm not sure if there's really a good notion of Lorentzian topology - certainly I don't see how to give a meaning to "Lorentzian 4-sphere".

To make this a little more vivid, go down by two dimensions and imagine a small circle (a 1-sphere) which, as a function of time, expands out to a maximum size and then shrinks back to a point. If the circle is also moving upwards in some third direction, the shape it traces out might be a 2-sphere. But the motion of the circle is not a 2-sphere - it's a motion, which is something else entirely. If you lived on that circle, you'd never be able to visit the south pole (because it would be in your past).