Black hole universe?

[Jens]

I'm not sure whether this is best posed as a question or in ATM, but anyway I'm posting it here.

Apparently, the Schwarzchild radius of the universe, with a mass of about 3 x 10e53 kg, comes out to just about 17 billion light years, very close to what we believe the radius of the universe to be. I have a question about it, and then a comment.

First, it seems counterintuitive to me. I've read that the Schwarzchild radius of the earth is just a couple of centimeters. So if the density of matter in the universe is so much lower than that of the earth, why is the Schwarzchild radius not much smaller than the matter we can see? I wonder if that makes sense.

The comment is, assuming this is true (I have to admit I haven't done the calculation), isn't it a weird thing? Why would we happen to be at the point in time where the two happen to coincide that way? I would be inclined, in that case, to believe that it is not a coincidence, that there is some reason for it. Implying that the universe is not expanding, at least in the way that we typically understand it. That's why I posed this in ATM.

[antoniseb]

Apparently, the Schwarzchild radius of the universe, with a mass of about 3 x 10e53 kg, comes out to just about 17 billion light years, very close to what we believe the radius of the universe to be.

I've seen this before, but the last time I did this calculation was about 30 years ago, and the numbers were slightly different, but the results were similar. The mass of the universe is about the right amount that light cannot escape from the universe. What does this imply? I bet it implies something, but we have some more things to learn before we can say exactly what.

[Maksutov]

Accepting that the overall density of the Universe is less than that required for a black hole, then perhaps what's happening is a fifth (or more) dimensional black hole (a brane interface?) is pulling at all the matter in the Universe, causing it to accelerate (expansion) and ultimately disappear into said hyper-black hole.

No, I haven't gone over to the Hoagland camp. http://img137.imageshack.us/img137/566/iconwink6tn.gif

[Nereid]

I have to admit I haven't done the calculationHow about we start here? Let's do a calculation (or get a link to where one is done)! the Schwarzchild radius of the universe, with a mass of about 3 x 10e53 kg, comes out to just about 17 billion light years, very close to what we believe the radius of the universe to be Here's where it could get very interesting!

I mean, what is 'the radius of the universe'?

[Jens]

How about we start here? Let's do a calculation (or get a link to where one is done)! Here's where it could get very interesting!

I mean, what is 'the radius of the universe'?

First, I should have said "the radius of the visible universe." I think that's what it means.

Then, for the calculations, these are the figures I've sort of come up with.

Visible radius: about 10^26 m
mass: about 3 x 10^52 kg

Schwarzchild radius: G x M / C^2

The problem I have is that G isn't such an easy formula. According to the article in Wikipedia it's:

G = 6.67 × 10−11 N m2 kg-2

I think it wouldn't be very difficult for someone with a calculator who is used to making such calculations. I could try it, but it may require some effort to get all the terms right!

[GOURDHEAD]

Apparently, the Schwarzchild radius of the universe, with a mass of about 3 x 10e53 kg, comes out to just about 17 billion light years, very close to what we believe the radius of the universe to be.The physical universe is believed by big bangers to be much larger than the observable universe. 75 billion light years is used now and then as a guess for the radius of the physical universe. Since we can't be sure how constant the coefficient of cosmological expansion (aka Hubble's) really is, any number is little more than an ill informed guess.

Although the stuff more than 13.7 billion light years away from wherever we are doesn't affect us with neither light nor gravitational attraction, some of it does affect stuff that affects us. Assuming that stuff now more than 13.7 billion LYs away was near enough to affect us 10 billion years ago (dependent on the actual rate of expansion), how can the effect be quantized?

[Argos]

The universe lacks the density for qualifying as a black hole. If it is a black hole, then everything within the event horizon must be squeezed into a singularity. Reality doesn´t seem to be like that. If the universe is a black hole then we already know what happens beyond the event horizon.

[Nereid]

First, I should have said "the radius of the visible universe." I think that's what it means.I agree, that is an important distinction!

It gets more complicated, as GOURDHEAD mentions in his post (http://www.bautforum.com/showpost.php?p=558833&postcount=6), when you apply GR to the whole universe ... what is the 'ruler' you use to 'measure' this 'radius'?

We can come back to this later.Then, for the calculations, these are the figures I've sort of come up with.

Visible radius: about 10^26 m
mass: about 3 x 10^52 kg

Schwarzchild radius: G x M / C^2

The problem I have is that G isn't such an easy formula. According to the article in Wikipedia it's:

G = 6.67 × 10−11 N m2 kg-2

I think it wouldn't be very difficult for someone with a calculator who is used to making such calculations. I could try it, but it may require some effort to get all the terms right!OK, let's take it step by step.
Schwarzchild radius: if it's a radius, its units should be LENGTH, right?
G: SI units are newton metre^2/kg^2, or MASS LENGTH TIME^-2 LENGTH^2 MASS^-2 -> MASS^-1 LENGTH^3 TIME^-2
M: MASS
c^2: LENGTH^2 TIME^-2

Putting it all together: LENGTH = MASS^-1 LENGTH^3 TIME^-2 MASS LENGTH^-2 TIME^2, or LENGTH (:clap: :dance: ).

So, as long as your input values are all in the same system (SI, in this case), you plug in the numbers, calculate, and voilà!

[bigsplit]

The universe lacks the density for qualifying as a black hole. If it is a black hole, then everything within the event horizon must be squeezed into a singularity. Reality doesn´t seem to be like that. If the universe is a black hole then we already know what happens beyond the event horizon.

Or being squeezed into a "singularity".

[Argos]

What I mean is that a Black Hole is a closed region of the spacetime. The universe is the spacetime itself, and it´s not closed.

[bigsplit]

What I mean is that a Black Hole is a closed region of the spacetime. The universe is the spacetime itself, and it´s not closed.

I understand what you are saying, but if the Universe is closed, what then? I see the universe as a 4 dimensional closed system contained within an infinate 3D singularity (Higg's field). Singularity in the sense that t=0 outside the universe as it is a homogenous infinity field with no partical properties and neutral charge. Since the Universe has a neutral charge on the aggragate their is also no electromagnetic interation between the two.

This is a first guess, I also have recently been considering that the infinate higgs has leaked into and flooded the universe resulting in Higg's theory. The problem I run into here is that such intrusion would generate diffusion outside the "closed" universe, generating dynamics moving outward into infinity in a wave like manner generating differenciation and thus introducing the possibility of measurable time and a vehical for GR. I prefer the former explaination, it is just neater.

[Mosheh Thezion]

We do not have enough data to estimate the amount of mass in the universe.
and so we can not make guestamates about the size of it either.

and as i have proposed, the size of the 3D enviorment, is not limited in anyway by the placement and motions of mass..

space mearly exists as the field enviorments for mass to form and exist.

and its outer limit is at this point pure speculation.
-MT

[Nereid]

We do not have enough data to estimate the amount of mass in the universe.Here's how to make such an estimate, at the OOM level:
- observe the large-scale structure of the universe, out to at least 500 Mpc, from galaxy (etc) surveys
- estimate the mass within rich clusters, the incidence of such (per above); ditto other clusters, non-cluster groups, etc (there are many techniques for this)
- apply Einstein's GR
- turn the handle
... out will pop an estimate of the 'amount of mass in the universe' (OK, purists will assert that it is 'mass-energy', but they're nitpickers, right?).

Do you have a problem with this, MT?

[Mosheh Thezion]

Here's how to make such an estimate, at the OOM level:
- observe the large-scale structure of the universe, out to at least 500 Mpc, from galaxy (etc) surveys
- estimate the mass within rich clusters, the incidence of such (per above); ditto other clusters, non-cluster groups, etc (there are many techniques for this)
- apply Einstein's GR
- turn the handle
... out will pop an estimate of the 'amount of mass in the universe' (OK, purists will assert that it is 'mass-energy', but they're nitpickers, right?).

Do you have a problem with this, MT?
of course i do...

in order to be able to make any real estimate we would need to look at a slice.... but as it is.. we dont know which way is which..

so can we know if 500mpc is enough..? perhaps its twice that far.

we can calculate all day long.. but until we have some real numbers its still conjecture...
-MT

and would your estimates include any dark matter? what about nuetrinos?

seriously.. can anyone point and say.. the edge of space is that way ---->

[Jens]

Putting it all together: LENGTH = MASS^-1 LENGTH^3 TIME^-2 MASS LENGTH^-2 TIME^2, or LENGTH (:clap: :dance: ).


Thanks for the advice. Actually, being a liberal arts major who has been out of schooling for more than a decade, there's a lot I don't know. I use arithmetic and percentages at work, but nothing really beyond that. So I realized at the outset that I wasn't even certain whether the units have to be squared when you square something like C. I.e., should it be 300,000^2 x m / s, or 300,000^2 x m^2 x s^2. Actually, in this case I think it shouldn't matter too much because the units cancel out, right?

In any case, I attempted the math, starting with 10^53 as the mass, and came up with a radius of 10^32. This is too big for what I was hoping to get, i.e. 10^26. If the mass was estimated at 10^51, it would still be 10^30, which is 10,000 times too large, I think. But then again, my math could easily be off somewhere. Basically, cutting out all the small numbers, it's 10^53 (mass) x 10^-11 (from G) x 10^-10 (from C squared).

But still, it seems counterintuitive that the radius would be so large, since in the case of the earth it's much smaller than the actual radius of the visible earth. Does the universe really have a lot more mass / volume (density) than the earth?

[Jens]

Oops. I said my math might be off somewhat. I just discovered that C^2 is about 8.9 x 10^16. So that totally changes the calculation and does come to something like 10^26 meters. Of course, even the mass is a very rough estimate, so I'm not sure how much can be inferred, but it does seem like it could be a very profound fact.

[Sock puppet]

Thanks for the advice. Actually, being a liberal arts major who has been out of schooling for more than a decade, there's a lot I don't know. I use arithmetic and percentages at work, but nothing really beyond that. So I realized at the outset that I wasn't even certain whether the units have to be squared when you square something like C. I.e., should it be 300,000^2 x m / s, or 300,000^2 x m^2 x s^2. Actually, in this case I think it shouldn't matter too much because the units cancel out, right?

In any case, I attempted the math, starting with 10^53 as the mass, and came up with a radius of 10^32. This is too big for what I was hoping to get, i.e. 10^26. If the mass was estimated at 10^51, it would still be 10^30, which is 10,000 times too large, I think. But then again, my math could easily be off somewhere. Basically, cutting out all the small numbers, it's 10^53 (mass) x 10^-11 (from G) x 10^-10 (from C squared).

But still, it seems counterintuitive that the radius would be so large, since in the case of the earth it's much smaller than the actual radius of the visible earth. Does the universe really have a lot more mass / volume (density) than the earth?

(bolding mine)

c=3*10^8 m/s , so your (divided by c^2) term should be of the order of 10^-16. That matches things up fairly well.
edit to add: Sorry Jens I only saw your post above after I posted this

With the formula you gave for the schwartzchild radius, doubling the mass doubles the radius, right?
But if you double the radius of a sphere, you multiply it's volume by eight.(volume goes with the cube of radius).
So doubling mass multiplies the volume it can occupy while still being a black hole by eight.
Density is equal to mass/volume.
This means that doubling the mass divides the density of the black hole by fourhttp://instagiber.net/smiliesdotcom/contrib/ruinkai/winknudge.gif

[Jens]

Thanks Sock Puppet for that wonderful insight. Not only does that help my understanding, but it also helps me to understand the origin of the idea of a "holographic universe." Apparently the idea that the universe is a hologram comes at least partly from that insight, that the Schwarzchild radius expands as though it were a two-dimensional rather than three-dimensional rule.

As a liberal arts major and editor I can offer one suggestion in return, though it is much less deep:

You wrote "multiply it's volume by eight."

That should be "multiply its volume by eight."

"It's" with an apostrophe is a contraction of "it is." :-)

[worzel]

So doubling mass multiplies the volume it can occupy while still being a black hole by eight.
Density is equal to mass/volume.
This means that doubling the mass divides the density of the black hole by fourhttp://instagiber.net/smiliesdotcom/contrib/ruinkai/winknudge.gifSo, any amount of matter can be a black hole if dense enough. And any density of matter can be a black hole if it goes on far enough. And if it goes on further than the Schwarzschild radius, everything within that radius would still be a black hole, right?

So if we assume that the density of the universe is roughly uniform on the large scale, and assume it goes on beyond the Schwarzschild radius for its density, then we must live inside a black hole.

There must be something wrong with that! :eh:

EDIT: A quick back of the envelope calculation tells me that the Schwarzschild radius is proportional to the inverse of the root of the density -

r(s)=sqrt{(3*c^2) / (8G*pi*d)}

which seems to be in the right direction. Can anyone confirm or correct this for me?

[Jens]

There must be something wrong with that! :eh:


Well, it doesn't have to be wrong. As Antoniseb wrote, it might be telling us something, but we don't know what.

[Dave Mitsky]

http://www.astro.ucla.edu/~wright/cosmology_faq.html#HOLE

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html

Dave Mitsky

[worzel]

http://www.astro.ucla.edu/~wright/cosmology_faq.html#HOLE (http://www.astro.ucla.edu/%7Ewright/cosmology_faq.html#HOLE)

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html

Dave MitskyAh, so even if the universe were so big that the radius for the assumed density covers only a tiny part of it, it still wouldn't apply because of expansion.

[Matthew]

EDIT: A quick back of the envelope calculation tells me that the Schwarzschild radius is proportional to the inverse of the root of the density -

r(s)=sqrt{(3*c^2) / (8G*pi*d)}

which seems to be in the right direction. Can anyone confirm or correct this for me?

While this isn't a "proof", I've subbed in some data. Using the density of the universe as 3x10^-30 g/cm3 or in SI units 3x10^-27 kg/m^3. This density value is taken from here (http://curious.astro.cornell.edu/question.php?number=342) and confirmed by this Space.com article (http://www.space.com/scienceastronomy/astronomy/universe_density_010307.html).

Using this data the equation set out by Worzel can be solved.

r(s)=sqrt{(3*c^2) / (8G*pi*d)}
r(s)=sqrt{(3*c^2)/(8G*pi*3*10^-27)}
r(s)=2.32 x 10^26 m.

This value seems to match up with accepted values for the observable universe. And the formula is dimensionally correct.

[Mosheh Thezion]

so how big is the universe???

and how much matter does it contain then?

-MT