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Some have said they don't really know how big the universe is. My question is this. If the density of the universe is a certain amount, do we reach a certain point where the universe is a black hole and thus limiting its size. I'm thinking this would be the size of the Hubble sphere. What are the arguments for and against. In my opinion, the Hubble Sphere must be the size of the universe.
Order of Kilopi
No and this is why. You need 2 conditions for a black hole. You need a certain amount of mass within a given radius and you need a sufficient differential of in the space outside of that radius. For example if you had a sphere of water 9au in radius it would have enough mass to be a black hole but the only way you'll get the black hole to form is if the space outside that sphere is lower density.Originally Posted by Copernicus
black holes have a counter intuitive property that the larger the black hole the lower the average density it has inside its horizon to an outside observer and if you calculate out you'll find that a given volume of space can very easily have enough mass within it to qualify as a black hole but this ignores other factors like the fact that since the universe seems to be homogeneous at the large scale there is no place where an EH can form. There is no where that the gradient of gravity or better put the curvature of space causes an event horizon. It also ignores dark energy which you can think of as an outward push preventing the mass from collapsing in on itself.
If dark energy was weaker then we'd expect the universe to start collapsing back on itself but this still isn't limiting the size of the universe. The universe could still be infinitely large and be collapsing just as it can be infinitely large and still be expanding.
I'm sure others will come and put what I've said in much more eloquent words.
The basics is that while there might be some properties that are found in the formation of a black hole there are others that are missing. This is why in the early universe we didn't just end up with a bunch of black holes because the energy density of the universe was so high.
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The following article, http://phys.org/news/2012-05-black-h...-solution.html, "A Universe in every blackhole" seems to imply our universe would be a black hole. What are thoughts about this?
Administrator
My thought is this: We can't know yet. With some handwaving the idea makes sense, but for now we should just leave it as a possible explanation for the beginning... where it has been for decades.
Forming opinions as we speak
Order of Kilopi
There are many problems with saying our universe is the inside of a black hole.
For one our cosmic event horizon behaves itself very differently then the EH of a black hole. Another problem is that inside a black hole the dimension heading radially towards the singularity becomes less space like and more time like.
I'd like to see some of the "science" behind this claim because the popular science article you linked is nothing more then unsupported hand waving.
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I agree that it is totally unsubstantiated in the article, but I don't see how a singularity, for a black hole, is substantiated either. Not that I am opposed to super high density either.
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The problem with the Hubble sphere is that it is earth based. If the universe is everything in our Hubble sphere, then we are the very center of it, by definition. It just seems so incredibly convenient. Wouldn't the center of a black hole be its singularity? Doesn't that imply that earth is the singularity of the black hole universe? I think not.
Also, that would mean that inflation initially acted on something smaller than a grain of sand. I personally think the universe, even at that time, held more than the 'singularity' of the big bang. Who knows how much spacetime there was when inflation cut us off from seeing it.
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Okay, so wouldn't it be interesting if we were near the center of the universe, just by accident. When the age of the universe is calculated from the CMB, it is about 13.62 - 13.88 billion light years. What if our spot was within that variation of 0.13 billion light years of the center? Does the CMB measure a slight difference in age of the universe in different directions?
Order of Kilopi
Here you go: http://arxiv.org/abs/0902.1994
(Published in Physics Letters B, Volume 687, Issues 2–3, 12 April 2010, Pages 110-113)
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Now this is awesome, is this against the mainstream, that we could be living in a black hole, that is not a point particle?
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It is a speculative idea that is consistent with the mainstream - it has been proposed many times, often as a solution as to why the constants we observe have the values they do. By suggesting that each budding off of a new universe allows the constants to change slightly you can posit a sort evolutionary universe where the probability of black hole formation acts like a selection parameter to make universes somewhat like ours the most common.
Once you get beyond a certain point in a black hole their structure is not well understood. GR predicts a point, but it is pretty commonly thought that this is more an indication that we need a consistent quantum gravity theory to understand what is going on.
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This is nice to know, that a point prediction, means the theory needs developing. I really wish this would be emphasized.
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It is - until you get to popular science pieces where they tend to leave out the caveats. Scientists know that the current theories are not complete and it is rare you would find one saying stuff like "everything at the centre of a BH is definitely crunched into a single, zero size point because GR says so".This is nice to know, that a point prediction, means the theory needs developing. I really wish this would be emphasized.
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I guess what you are saying about a homogeneous universe is true, but I am thinking that any discontinuities would have to lead to universes of equal size over a long period of time.
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So from what I am understanding, the reason the universe is not a black hole, is because stuff outside of our hubble sphere perfectly pulls on the stuff inside so it cannot form a black hole. However we wonder why we have solar systems and galaxies, and unequal CMB out of this perfect balance inside and outside of our hubble sphere.
Just a question
Order of Kilopi
I wouldn't say it is perfect for one. To have a EH of a black hole you need a large shift in gravity. The EH for a black hole are fairly close to its centre from the view of an external observer. Our sun's EH would be just 2.95km in radius. Its hard to picture in 3d but here is the way I think of it some times in a 2d view.
gravity.png
The vector field for gravity works in way where the amount of gravitational pull you feel at a give point can be represented a line tangent to the surface of the well. In 2d this is easy to demonstrate. A & B have horizontal lines and the point that they touch the well there is essentially no significant gravitational pull in any one direction. If you where there you would feel "weight less" Now as a whole this seems to be about what any average point in space would be like since most points in space are far from any significant amount of mass.
As that line tilts more and more the observer would feel more and more gravity.
A black holes event horizon is essentially where that line is rotated 90 degrees from "flat space" to get a slope you have to have a difference in gravity from one point to another. And at the large scale there is not enough of a difference.
This means while you can find points in space that have zero gravitational pull you'll not find any area with zero pull because gravity range is infinite. It is just that it is an inverse square law and you can for most purposes treat many areas in space having almost no gravitational influence.
Order of Kilopi
My understanding is that if space and time are shown at
the same scale on your graph, the curve of gravitational
field strength has a 45-degree angle at the event horizon
of a black hole. It approaches a 90-degree angle as it
approaches the black hole's center. The curves for bodies
like the Earth and Sun have dished bottoms as you show.
-- Jeff, in Minneapolis
http://www.FreeMars.org/jeff/
"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"
"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves
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The hubble sphere is identical to an inside out (negative curvature) black hole with a linear 'attractive' force, i.e. the 'center' of the black hole is Earth. Since space is moving away at light speed at that radius, there is an event horizon, with all of the usual phenoma; Hawking radiation, complimentarity, everything. Objects approach the horizon from inside, and the area 'past the horizon' (wich doesn't exist in the spacetime of an 'inside' observer) is outside. Tommac suggested it a while back, everyone disagreed. I asked Leonard Susskind and he said Tommac was right. I'm not joking.
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Andrew, I was wondering if you could elaborate more.
Order of Kilopi
Note that is a lot of differences from a black hole. Negative curvature as opposed to positive. Linear attractive force as opposed to an inverse square and note that we are still on the outside of that "object". I fully admit they share traits as they are both types of event horizons. I'm not sure what your conversation with Susskind was like but he does have a tendency to go "Ya ya, you are right" about concepts he isn't very interested in getting into the nitty gritty details of. So again I'll point out that our universe while having SOME similarities to an inside out black hole it is very different to being inside a black hole that is the size of our visible universe.
Also if expansion stops or reverses then you'll see that event horizon change drastically. Where only hawking radiation can "escape" a black hole whole galaxies would be able to pass through the cosmological event horizon. Or more precisely there ceases to be a cosmological event horizon.
If you get the chance ask him "could our visible universe be inside a black hole with physics as we understand it". I imagine you'll get a much different answer.
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What is meant by positive or negative curvature?
Order of Kilopi
I don't know what negative curvature is, but positive
curvature is the curvature of spacetime around gravitating
masses. The more strongly curved spacetime is in the
positive direction, the greater the gravitational field
strength at that place.
It would also be the overall curvature of spacetime of a
finite, closed universe.
-- Jeff, in Minneapolis
http://www.FreeMars.org/jeff/
"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"
"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves
Order of Kilopi
Susskind also concludes that since there are 10500 possible Calabi Yau manifolds, and hence 10500 different superstring solutions, then there must be a "landscape" of universes, i.e., 10500 actual, different universes beyond our own, never to be observed. I am therefore a little leery of Susskind's authority.
Everyone is entitled to his own opinion, but not his own facts.
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I'm not really asking about string theory, but I suppose it is related. If one could figure out what the mathamatical principle is that creates a stable universe, one could calculate the number of universes based off of that mathematical principle. The Calabi Yau manifolds only remind me of the wrong variables in the wrong places of an equation, but there must be some kernel of truth to the idea. My feeling is that the equations are so complicated that almost everybody knows the emperor is wearing no clothes, but they think there is a possiblity that their glasses are an invisibilty cloak.
Last edited by Copernicus; 2012-May-31 at 08:38 PM. Reason: mispelled their
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A position you come to without understanding the equations yourself... There are plenty of good reasons people like or dislike String theory, a gut feeling driven by the fact that the maths is hard is not a useful addition to the debate. After all, GR is not that easy either.My feeling is that the equations are so complicated that almost everybody knows the emperor is wearing no clothes, but they think there is a possiblity that their glasses are an invisibilty cloak.
Positive curvature is basically what you get on the surface of a sphere (although intrinsic curvature does not require the surface to be curved in higher dimension), negative curvature is the curvature you'd get in a saddle shape.
Order of Kilopi
This is the way I understand it. Curvature is the warping of space time. Positive energy/mass causes positive curvature.
if we look at a torus, like this
torus.png
The green area represents positive curvature. This is much like the surface of a globe. If you try making a triangle in a region of space that has positive then the total of the angles will end up > 180 degrees.
In negatively curved space, represented by red, the shape is more like a saddle. If you try making a triangle there then the total angles will end up < 180 degrees.
Funny enough if you do an integral of the curvature over a torus then you end up with zero curvature and it doesn't matter if the torus is very symmetrical like the one above or highly irregular like a tea cup with a handle. Now apparently a 3 torus is mathematically flat too.
Order of Kilopi
Wayne,
Positive curvature of space is gravity.
Does negative curvature of space exist? Can it?
Since you use the term, what is a "3 torus"?
-- Jeff, in Minneapolis
http://www.FreeMars.org/jeff/
"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"
"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves
Order of Kilopi
Yes positive curvature of space time locally is equivalent to gravity.
Have we observed it? There are papers that say it is required for the voids that we see in our universe.
Well as I understand it yes. That is why manifolds like a 3 torus are considered for valid topologies of the a closed universe.
it is like a 3 sphere except being spherical its torus like. The 3 torus is a manifold that allows for omega to equal 1 causing the universe to be flat on the whole but also finite. So if you want a flat but finite universe then you need the universe to be something like a 3 torus. A 3 sphere can give the illusion of the universe being flat but if it is a 3 sphere then the size of the universe has a lower bound of something on the order of 250 times the visible universe.
Order of Kilopi
Just to avoid any confusion, it may be worth noting that a "normal" (three dimensional) sphere (or torus) is a 2-sphere (2-torus). I assume this because mathematicians are only concerned with the two-dimensional surface of such an object. Which is also related to previous discussions here about a circle being a one dimensional object.
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Just a side note on negative curvature. I've seen it more as a mathematical tool to find the maximum and minimum of a function. If the function 'flatlines' at point A, that could be the maximum or minimum of the function. The easiest way to do that is to look at the curvature. For a function of multiple variables, positive curvature would correspond to said max/min. Negative curvature is called a saddle point.
For example, if y=x2 , we all know from experience that there is no maximum, but a minimum at the point (x,y)=(0,0).
Now try y=x3. Its derivative for x=0 is the same, 0, However, that is a type of saddle point. It is neither the maximum or minimum of the function. As you approach the origin from the left, the curvature is 'downwards'. As you approach the origin from the right, it curves 'upwards'.
An easy way to visualize it is to tell yourself, x2 keeps wanting to curve downwards. Since it always curves in the same direction, it is positive curvature. However, x3 changes from curving 'downwards' to curving 'upwards'. This flip in curvature, combined with a derivative property(italic so I have ammo when someone jumps on that even though I haven't omitted it) is negative curvature. In 3D, you have the basic saddle which curves say, upwards in the x direction, and downwards in the y direction. That's not important right now.
Things like sine waves obvious flip between 'upwards' and 'downwards' curvature, but the derivative must 0 to qualify as a saddle point. That derivative property is called being a 'stationary point'. If the function represents a force, there would be no force at that point, the object would remain stationary.
All signs point to a flat universe, so there's no point in working with a negative curvature spacetime for the universe.
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