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Random, and rather curious, fact about the history of astronomy:
In the 1920's it was still not clear to astronomers whether the
Universe had approximately the size of the Milky Way galaxy, or
whether it was much larger than that.
This is rather baffling, given that even such a modern and innovative
theory (still considered valid today) as general relativity was published
in 1915.
They knew about other galaxies, of course, but they weren't sure if
they were just small objects in our galaxy, of whether they were large
galaxies of their own, very far away.
Today we take for granted that the Universe is incomprehensibly larger
than our galaxy, but this has been so for much less than a century.
Source: http://en.wikipedia.org/wiki/The_Great_Debate
--
- Warp
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Warp <war### [at] tag povrayorg> wrote:
> They knew about other galaxies, of course, but they weren't sure if
> they were just small objects in our galaxy, of whether they were large
> galaxies of their own, very far away.
so, they thought our Milky Way was in the center of the Universe much like the
Earth was before, huh? it's always about us, the spoiled children of God...
perhaps our own Universe is nothing but a side-effect of something bigger...
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nemesis nous apporta ses lumieres en ce 2007/12/28 03:48:
> Warp <war### [at] tagpovrayorg> wrote:
>> They knew about other galaxies, of course, but they weren't sure if
>> they were just small objects in our galaxy, of whether they were large
>> galaxies of their own, very far away.
>
> so, they thought our Milky Way was in the center of the Universe much like the
> Earth was before, huh? it's always about us, the spoiled children of God...
>
> perhaps our own Universe is nothing but a side-effect of something bigger...
>
>
The universe is so large that when you see it from just about anywhere, it looks
like you are at it's center. Just looking at the night sky, you can hardly say
if you are at the center of the galaxy or not.
The Universe is like a large sphere whose center is everywhere and the
circumference nowhere. (sory, I don't remember the source)
--
Alain
-------------------------------------------------
Grandchildren are God's reward for not killing your own.
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Alain <ele### [at] netscapenet> wrote:
> Just looking at the night sky, you can hardly say
> if you are at the center of the galaxy or not.
If you were at the center of the galaxy you wouldn't be looking at the
sky. I think you would be infinitely small.
> The Universe is like a large sphere whose center is everywhere and the
> circumference nowhere. (sory, I don't remember the source)
If the universe is finite, it must have a border, no?
--
- Warp
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Warp escribió:
> Alain <ele### [at] netscapenet> wrote:
>> The Universe is like a large sphere whose center is everywhere and the
>> circumference nowhere. (sory, I don't remember the source)
>
> If the universe is finite, it must have a border, no?
>
But is it finite?
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>> If the universe is finite, it must have a border, no?
>>
>
> But is it finite?
Now there's a question...
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Warp nous apporta ses lumieres en ce 2007/12/28 15:14:
> Alain <ele### [at] netscapenet> wrote:
>> Just looking at the night sky, you can hardly say
>> if you are at the center of the galaxy or not.
>
> If you were at the center of the galaxy you wouldn't be looking at the
> sky. I think you would be infinitely small.
>
>> The Universe is like a large sphere whose center is everywhere and the
>> circumference nowhere. (sory, I don't remember the source)
>
> If the universe is finite, it must have a border, no?
>
Finite? Maybe.
Must have a border? Maybe not. Or it may just be that there is no way to
perceive it, even if you are almost "touching" it...
You can have an unbounded thing that is finite. A 4 dimention sphere can be
finite, but it don't have any edge in 3D. And the universe probably contains
more than 7 dimentions...
--
Alain
-------------------------------------------------
My wife is such a bad cook, in my house we pray after the meal.
Rodney Dangerfield
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Orchid XP v7 nous apporta ses lumieres en ce 2007/12/28 15:32:
>>> If the universe is finite, it must have a border, no?
>>>
>>
>> But is it finite?
>
> Now there's a question...
>
It could be infinite but with a definite, mesurable, edge, or finite with no
edge, or something else...
--
Alain
-------------------------------------------------
You know you've been raytracing too long when you've convinced your boss that
raytracing is really an integral part of your job title (and you really don't
work in a position that requires it).
Quietly Watching
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Nicolas Alvarez <nic### [at] gmailisthebestcom> wrote:
> > If the universe is finite, it must have a border, no?
> But is it finite?
According to the current consensus in science, it probably is. There's
no reason to believe otherwise.
--
- Warp
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Alain <ele### [at] netscapenet> wrote:
> Finite? Maybe.
> Must have a border? Maybe not. Or it may just be that there is no way to
> perceive it, even if you are almost "touching" it...
If there is a border, it's probably impossible for us to ever reach it.
There's this thing called "cosmological horizon" which, if true, means
that there's just no way, even theoretical, for as to "see" it in any way.
But that doesn't mean there is no border.
--
- Warp
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>> Finite? Maybe.
>> Must have a border? Maybe not. Or it may just be that there is no way to
>> perceive it, even if you are almost "touching" it...
>
> If there is a border, it's probably impossible for us to ever reach it.
> There's this thing called "cosmological horizon" which, if true, means
> that there's just no way, even theoretical, for as to "see" it in any way.
>
> But that doesn't mean there is no border.
Einstein postulated a finite universe as part of his formulation of
relativity. He said that, since space-time can curve, eventually if
you travel in a straight line far enough you will come back to your
starting point. This would mean that there is no well defined edge.
Modern astronomers can find no evidence of such a large scale
warping of space-time. This is part of why the theories of parallel
universes are in vogue, if the universe is infinite, then if you
travel in a straight line far enough you might reach a region
that is very similar to earth, but isn't quite. It would be "parallel".
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Warp <war### [at] tagpovrayorg> wrote:
> Alain <ele### [at] netscapenet> wrote:
> > Just looking at the night sky, you can hardly say
> > if you are at the center of the galaxy or not.
>
> If you were at the center of the galaxy you wouldn't be looking at the
> sky. I think you would be infinitely small.
I think he'd be dead, actually... :P
But if you're not exactly in the center of that supposed massive black-hole,
you'd likely be astounded by the huge number of very bright stars at the sky.
You'd definitely feel as being in the center of something...
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Tim Attwood <tim### [at] comcastnet> wrote:
> Einstein postulated a finite universe as part of his formulation of
> relativity. He said that, since space-time can curve, eventually if
> you travel in a straight line far enough you will come back to your
> starting point. This would mean that there is no well defined edge.
I understand how GR describes the curvature of space-time in relation
to masses, and given the enormous amount of experimental evidence which
corroborates this, I see no reason to doubt it.
However, I don't understand why GR would predict a curved universe
where each geodesic line is closed. What would cause it? Certainly not
the mass in the universe. I don't think it would be even nearly enough.
(Because if it was caused by mass, it would mean that the entire universe
is actually inside its own Schwarzschild radius, which is clearly not the
case.)
> Modern astronomers can find no evidence of such a large scale
> warping of space-time. This is part of why the theories of parallel
> universes are in vogue, if the universe is infinite, then if you
> travel in a straight line far enough you might reach a region
> that is very similar to earth, but isn't quite. It would be "parallel".
I don't find any kind of logic in that. Why would there be a "similar",
"parallel" version of anything if you travel far enough? It doesn't make
any logical sense.
--
- Warp
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nemesis <nam### [at] gmailcom> wrote:
> > If you were at the center of the galaxy you wouldn't be looking at the
> > sky. I think you would be infinitely small.
> I think he'd be dead, actually... :P
Being infinitely small kind of implies being dead.
> But if you're not exactly in the center of that supposed massive black-hole,
> you'd likely be astounded by the huge number of very bright stars at the sky.
> You'd definitely feel as being in the center of something...
Assuming that the staggering amounts of radiation and tidal forces don't
rip you into separate atoms.
--
- Warp
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nemesis wrote:
>
> perhaps our own Universe is nothing but a side-effect of something bigger...
Some of the new theories point an explanation regarding this. According
to the theories, only certain particles can pass between dimensions, or
branes. Two of these particles are tachyons and gravitons (not sure if
the latter have been identified yet though).
It would be interesting if alternate realities were someday discovered.
Might explain some things.
Sam
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stbenge wrote:
>
> It would be interesting if alternate realities were someday discovered.
> Might explain some things.
>
My dad the math teacher used to say cool things sometimes. I remember
one time he said to me, "What if what we think of as the solar system is
really a carbon atom...it's clinging onto the exhaust manifold of a
car...and, ten seconds from now, the driver is going to rev the engine
really, really hard..."
That sort of thing will really jack around with your mind when you're,
like, five years old...
Yeah, I probably ought to be in therapy.....
--Sherry Shaw
--
#macro T(E,N)sphere{x,.4rotate z*E*60translate y*N pigment{wrinkles scale
.3}finish{ambient 1}}#end#local I=0;#while(I<5)T(I,1)T(1-I,-1)#local I=I+
1;#end camera{location-5*z}plane{z,37 pigment{granite color_map{[.7rgb 0]
[1rgb 1]}}finish{ambient 2}}// TenMoons
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Sherry Shaw wrote:
> stbenge wrote:
>>
>> It would be interesting if alternate realities were someday
>> discovered. Might explain some things.
>>
>
> My dad the math teacher used to say cool things sometimes. I remember
> one time he said to me, "What if what we think of as the solar system is
> really a carbon atom...it's clinging onto the exhaust manifold of a
> car...and, ten seconds from now, the driver is going to rev the engine
> really, really hard..."
My dad once told me about a science fiction story he read once. It was
about a man who discovered a way to shrink himself. The man kept
shrinking, past the molecular, atomic and even subatomic level. He then
noticed that his surroundings looked like galaxies, star systems and
then matter as we see it now. He kept shrinking, and the pattern
repeated itself...
> That sort of thing will really jack around with your mind when you're,
> like, five years old...
I suppose. Or it could just give you a difference perspective on things.
> Yeah, I probably ought to be in therapy.....
Over that? Nah!
Sam
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stbenge wrote:
> Sherry Shaw wrote:
>> stbenge wrote:
>>>
>>> It would be interesting if alternate realities were someday
>>> discovered. Might explain some things.
>>>
>>
>> My dad the math teacher used to say cool things sometimes. I remember
>> one time he said to me, "What if what we think of as the solar system
>> is really a carbon atom...it's clinging onto the exhaust manifold of a
>> car...and, ten seconds from now, the driver is going to rev the engine
>> really, really hard..."
Maybe 10 seconds at the larger scale equals 10 billion years at ours...
>
> My dad once told me about a science fiction story he read once. It was
> about a man who discovered a way to shrink himself. The man kept
> shrinking, past the molecular, atomic and even subatomic level. He then
> noticed that his surroundings looked like galaxies, star systems and
> then matter as we see it now. He kept shrinking, and the pattern
> repeated itself...
"He Who Shrank" by Henry Hasse. I read it about 30 years ago in a
collection
of classic SF stories edited by Isaac Asimov.
Not to be confused with the book and film "The Man Who Fell To Earth".
>
>> That sort of thing will really jack around with your mind when you're,
>> like, five years old...
Had a similar effect on me to what you describe.
>
> I suppose. Or it could just give you a difference perspective on things.
>
>> Yeah, I probably ought to be in therapy.....
>
> Over that? Nah!
>
> Sam
Then there is the same concept expressed thus:
"Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on,
While these again have greater still, and greater still, and so on."
by the mathematician De Morgan.
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stbenge <stb### [at] hotmailcom> wrote:
> Some of the new theories point an explanation regarding this. According
> to the theories, only certain particles can pass between dimensions, or
> branes.
Theories are usually devised to try to explain otherwise unexplained
observed phenomena, or in some cases, some consequence of an existing
theory if it is true (eg. the black hole theory is a consequence of GR).
Exactly which phenomena are these theories trying to explain?
A theory which doesn't even try to explain some observed phenomenon
is pure speculation and useless.
--
- Warp
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On Sun, 30 Dec 2007 18:16:07 +1100, Paul Fuller <pgf### [at] optusnetcomau>
wrote:
>
>"He Who Shrank" by Henry Hasse. I read it about 30 years ago in a
>collection
>of classic SF stories edited by Isaac Asimov.
I remember that. I also remember a story line in Garth from the 60's that was
the same.
Garth?
http://en.wikipedia.org/wiki/Garth_(comic_strip)
Regards
Stephen
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Warp wrote:
> stbenge <stb### [at] hotmailcom> wrote:
>> Some of the new theories point an explanation regarding this. According
>> to the theories, only certain particles can pass between dimensions, or
>> branes.
>
> Theories are usually devised to try to explain otherwise unexplained
> observed phenomena, or in some cases, some consequence of an existing
> theory if it is true (eg. the black hole theory is a consequence of GR).
>
> Exactly which phenomena are these theories trying to explain?
>
Most of these attempts are aimed at unification of quantum and
relativity. Another thing that annoys physicists a great deal and that
does seem to justify any means is: WTH has the fine structure constant
that silly value of nearly 1/137? This might also have played a role, I
don't know for sure.
> A theory which doesn't even try to explain some observed phenomenon
> is pure speculation and useless.
>
No, it is pure mathematics. And an interesting branch at that. Who knows
someday it will move from pure to applied mathematics. It leaves open
the question why so many physicist nowadays do pure mathematics.
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andrel <a_l### [at] hotmailcom> wrote:
> WTH has the fine structure constant that silly value of nearly 1/137?
One would expect chaos and unexplained numbers in physics. It has for
long fascinated me that there is a lot of chaos and unexplained numbers
in pure mathematics too.
Prime numbers are a prime (no pun intended) example. They are the
quintessential form of chaos and unpredictability in mathematics.
If you think about prime numbers as a result of the sieve of Eratosthenes,
they are rather simple, really: Any multiple of a prime is not a prime.
If you think how you would construct a list of primes using this sieving
technique, it's quite simple and straightforward. One could hastily think
that primes are very regular and predictable this way. One would be very
wrong.
Many of the unsolved problems in mathematics are relatively simple
problems related to primes. Problems which have been puzzling mathematicians
even for centuries. That's how unpredictable they are.
The thing which fascinates me is: Why? Why is there such an unpredictable
chaos as a result of such a simple thing?
Individual results sometimes fascinate me too. For example, the smaller
counter-example to the Polya conjecture is 906150257. Why precisely that
value? What's so special about that value that it breaks the conjecture?
Why there and not somewhere else?
--
- Warp
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Warp wrote:
> andrel <a_l### [at] hotmailcom> wrote:
>> WTH has the fine structure constant that silly value of nearly 1/137?
>
> One would expect chaos and unexplained numbers in physics.
I think most physicists would disagree.
> It has for
> long fascinated me that there is a lot of chaos and unexplained numbers
> in pure mathematics too.
>
> Prime numbers are a prime (no pun intended) example.
In this case physicists have a gut feeling (no pun intended) that the
fine structure constant should follow from some theory. The main reason
is that it is a dimensionless quantity.
> They are the
> quintessential form of chaos and unpredictability in mathematics.
>
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Warp <war### [at] tagpovrayorg> wrote:
> andrel <a_l### [at] hotmailcom> wrote:
> Individual results sometimes fascinate me too. For example, the smaller
> counter-example to the Polya conjecture is 906150257. Why precisely that
> value? What's so special about that value that it breaks the conjecture?
> Why there and not somewhere else?
maybe it's the telephone number of someone really special. :)
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>> Einstein postulated a finite universe as part of his formulation of
>> relativity. He said that, since space-time can curve, eventually if
>> you travel in a straight line far enough you will come back to your
>> starting point. This would mean that there is no well defined edge.
>
> I understand how GR describes the curvature of space-time in relation
> to masses, and given the enormous amount of experimental evidence which
> corroborates this, I see no reason to doubt it.
>
> However, I don't understand why GR would predict a curved universe
> where each geodesic line is closed. What would cause it? Certainly not
> the mass in the universe. I don't think it would be even nearly enough.
> (Because if it was caused by mass, it would mean that the entire universe
> is actually inside its own Schwarzschild radius, which is clearly not the
> case.)
If the universe is finite it must have a barycenter therefore
masses would tend to orbit. According to Wikipedia, "an object of
any density can be large enough to fall within its own Schwarzschild
radius", this leads to the question of expanding universe vrs collapsing
universe... if the universe has a finite mass, then the density of the
universe is very low, and the Schwarzchild radius is very
very large. Since by definition if a mass traveling outward is included
into the barycenter mass, the density of the universe could be
decreasing, and the Schwarzschild radius would be increasing...
>> Modern astronomers can find no evidence of such a large scale
>> warping of space-time. This is part of why the theories of parallel
>> universes are in vogue, if the universe is infinite, then if you
>> travel in a straight line far enough you might reach a region
>> that is very similar to earth, but isn't quite. It would be "parallel".
>
> I don't find any kind of logic in that. Why would there be a "similar",
> "parallel" version of anything if you travel far enough? It doesn't make
> any logical sense.
If the universe is infinite, with infinite mass, then at some distance
the same patterns of atoms would be there. There are only a fixed
number of atom types, all the same laws of physics apply, and even
if the number of atom arrangements on a planet is very huge, it's not
infinite, so it must be repeated at some point in an infinite universe.
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Tim Attwood <tim### [at] comcastnet> wrote:
> if the universe has a finite mass, then the density of the
> universe is very low, and the Schwarzchild radius is very
> very large. Since by definition if a mass traveling outward is included
> into the barycenter mass, the density of the universe could be
> decreasing, and the Schwarzschild radius would be increasing...
Schwarzchild radius is not dependent on density, only on the amount of
mass.
> > I don't find any kind of logic in that. Why would there be a "similar",
> > "parallel" version of anything if you travel far enough? It doesn't make
> > any logical sense.
> If the universe is infinite, with infinite mass, then at some distance
> the same patterns of atoms would be there. There are only a fixed
> number of atom types, all the same laws of physics apply, and even
> if the number of atom arrangements on a planet is very huge, it's not
> infinite, so it must be repeated at some point in an infinite universe.
I call this the shakespeare-monkey fallacy.
Just because there's an infinite amount of data doesn't mean that every
possible finite pattern appears, nor that a given finite pattern appears
an infinite number of times.
Even if the universe had an infinite amount of mass (the current
consensus is that this is not so), only a finite amount of it may be
forming atoms. The rest can be eg. singularities, dark energy, dark
matter, etc. (And even if there's an infinite amount of atoms, it doesn't
necessarily mean that that certain patterns must repeat.)
--
- Warp
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> Schwarzchild radius is not dependent on density, only on the amount of
> mass.
That's only true for black holes. For normal matter it varies by density,
or is posed as the answer to the question, "If I have some mass and turn
it into a black-hole, how big will it be". That's not to say that the
universe
is all in a black hole, but if the mass of the universe is infinite it falls
inside
it's Schwarzschild radius, since rs = 2Gm/c^2 ... and infinity divided by
a large number is still infinity.
>> If the universe is infinite, with infinite mass, then at some distance
>> the same patterns of atoms would be there. There are only a fixed
>> number of atom types, all the same laws of physics apply, and even
>> if the number of atom arrangements on a planet is very huge, it's not
>> infinite, so it must be repeated at some point in an infinite universe.
>
> I call this the shakespeare-monkey fallacy.
>
> Just because there's an infinite amount of data doesn't mean that every
> possible finite pattern appears, nor that a given finite pattern appears
> an infinite number of times.
>
> Even if the universe had an infinite amount of mass (the current
> consensus is that this is not so), only a finite amount of it may be
> forming atoms. The rest can be eg. singularities, dark energy, dark
> matter, etc. (And even if there's an infinite amount of atoms, it doesn't
> necessarily mean that that certain patterns must repeat.)
It's not a fallacy, it's a paradox, there's a difference. It's not possible
to predict random events, but it's still possible to know that they will
occur. For example if you use a simple coin toss, and toss the coin
forever, the distribution will be 50/50, so you can say with 100%
confidence that sometime in the future there will be another "heads",
yet at the same time you don't know at all if the next toss will be
a "heads".
If the universe is finite then such super low probability odds as
a parallel earth would never occur, but if the universe is infinite,
then not only will there be parallels, but there will be an infinite number
of them. I'm not convinced that the universe is infinite, but
astronomers haven't seen any uniform expanding or contracting that
is predicted by general relativity, they do see bubble like areas where
it looks like some repulsive force is at play. And there's the dark matter.
General relativity didn't predict most of these observations, in some
ways it's great, like Newton's theory, in others ways it falls short.
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Tim Attwood <tim### [at] comcastnet> wrote:
> > Schwarzchild radius is not dependent on density, only on the amount of
> > mass.
> That's only true for black holes. For normal matter it varies by density,
"The Schwarzschild radius (sometimes historically referred to as the
gravitational radius) is a characteristic radius associated with every
mass. It is the radius for a given mass where, if that mass could be
compressed to fit within that radius, no known force or degeneracy
pressure could stop it from continuing to collapse into a
gravitational singularity."
"The Schwarzschild radius is proportional to the mass, with a
proportionality constant involving the gravitational constant and the
speed of light."
http://en.wikipedia.org/wiki/Schwarzschild_radius
No mention of density anywhere, only of mass. The Schwarzschild radius
of a mass can be calculated directly as the mass multiplied by a
*constant* (which is 2*G/c^2). Volume doesn't appear anywhere in the formula.
> if the mass of the universe is infinite it falls inside
> it's Schwarzschild radius, since rs = 2Gm/c^2 ... and infinity divided by
> a large number is still infinity.
Which is a rather definite proof that there's a finite amount of mass
in the universe.
> > I call this the shakespeare-monkey fallacy.
> It's not a fallacy, it's a paradox, there's a difference. It's not possible
> to predict random events, but it's still possible to know that they will
> occur. For example if you use a simple coin toss, and toss the coin
> forever, the distribution will be 50/50, so you can say with 100%
> confidence that sometime in the future there will be another "heads",
> yet at the same time you don't know at all if the next toss will be
> a "heads".
It's a fallacy. An infinite amount of data, even if all values have the
same "chance" of appearing in the data, does not automatically mean that
every possible pattern appears.
The proof is rather simple: For example, the ordered set of natural
numbers is an infinite set where each value has an equal "chance" of
appearing, yet eg. the pattern "2 1" never appears.
Note that nowhere did I imply randomness. And even if randomness is
implied, the question is still non-trivial. If what you want is an
evenly-spaced random natural number generator, you'll have to define
what "random" means. That's not a trivial definition.
Even if you pop random natural numbers (by whichever definition of
"random" you may want to use), it's still possible that a certain pattern
never appears. Given that there's an infinite amount of finite patterns,
it may take an infinite amount of time to pop a certain one. The probability
of that pattern appearing may asymptotically approach 1, but it's still
possible that it never appears.
> General relativity didn't predict most of these observations
That depends on your definition of "predict".
If by "predict" you mean "Einstein never mentioned it in his papers"
then it's true.
However, if "predict" means "the result can be derived from the theory"
(which is usually the meaning of that word in science), then most cosmological
phenomena (except quantum level phenomena) can be derived from GR.
For example the expansion of the universe can be derived from GR in
this way.
--
- Warp
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nemesis wrote:
> Warp <war### [at] tagpovrayorg> wrote:
>> They knew about other galaxies, of course, but they weren't sure if
>> they were just small objects in our galaxy, of whether they were large
>> galaxies of their own, very far away.
>
> so, they thought our Milky Way was in the center of the Universe much like the
> Earth was before, huh?
More like that all of (a small amount of) space was filled with a
relatively flat distribution of stars, rather than a large amount of
space having clusters of stars.
I saw an interesting analysis recently that pointed out that every time
"astronomy" discovers some major new fact, a major new theory is
required to explain it. I.e., that the number of "free variables" being
used to explain things remains one greater than the number of major
observations needed to explain cosmology. Flat background radiation?
Inflation after the big bang! Lumpy galaxies in spite of inflation? Dark
matter! Expansion not slowed from all that dark matter? Dark energy!
Sadly, I really don't know enough about cosmology to know whether to
take it seriously, since it wasn't a peer-reviewed paper or anything.
--
Darren New / San Diego, CA, USA (PST)
It's not feature creep if you put it
at the end and adjust the release date.
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Warp wrote:
> If you were at the center of the galaxy you wouldn't be looking at the
> sky. I think you would be infinitely small.
I'm not sure anyone is sure what happens in the middle of a black hole.
If "you" were in a position to see, you could certainly see the sky. The
sky couldn't see you, mind.
>> The Universe is like a large sphere whose center is everywhere and the
>> circumference nowhere. (sory, I don't remember the source)
>
> If the universe is finite, it must have a border, no?
Surely you're not asking seriously? A sphere is a 2D finite surface with
no border.
--
Darren New / San Diego, CA, USA (PST)
It's not feature creep if you put it
at the end and adjust the release date.
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Warp wrote:
> However, I don't understand why GR would predict a curved universe
> where each geodesic line is closed. What would cause it? Certainly not
> the mass in the universe. I don't think it would be even nearly enough.
Last I saw, estimates were that we're within experimental uncertainty
about whether we're within our own Schwartzchild radius. I.e., depending
on what 'dark energy' does, and just how much 'dark matter' is out
there, the universe may be flat, positively curved, or negatively curved.
> (Because if it was caused by mass, it would mean that the entire universe
> is actually inside its own Schwarzschild radius, which is clearly not the
> case.)
Not sure why you would think that. If there's enough mass to eventually
collapse the universe back to the "big crunch", then by definition we're
in a "black hole" out of which no light can escape. It's just a really
big one, hundreds of billions of light years in diameter. :-)
I'm not sure the singularity math works from the inside, either.
> I don't find any kind of logic in that. Why would there be a "similar",
> "parallel" version of anything if you travel far enough? It doesn't make
> any logical sense.
Probably in the "inifinite monkeys type shakespear" kind of way.
--
Darren New / San Diego, CA, USA (PST)
It's not feature creep if you put it
at the end and adjust the release date.
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stbenge wrote:
> nemesis wrote:
>>
>> perhaps our own Universe is nothing but a side-effect of something
>> bigger...
>
> Some of the new theories point an explanation regarding this. According
> to the theories, only certain particles can pass between dimensions, or
> branes. Two of these particles are tachyons and gravitons (not sure if
> the latter have been identified yet though).
And Dust!
--
Darren New / San Diego, CA, USA (PST)
It's not feature creep if you put it
at the end and adjust the release date.
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In article <4778f2c3@news.povray.org>, war### [at] tagpovrayorg says...
> Tim Attwood <tim### [at] comcastnet> wrote:
> > > Schwarzchild radius is not dependent on density, only on the amount
of
> > > mass.
>
> > That's only true for black holes. For normal matter it varies by densit
y,
>
> "The Schwarzschild radius (sometimes historically referred to as the
> gravitational radius) is a characteristic radius associated with every
> mass. It is the radius for a given mass where, if that mass could be
> compressed to fit within that radius, no known force or degeneracy
> pressure could stop it from continuing to collapse into a
> gravitational singularity."
>
> "The Schwarzschild radius is proportional to the mass, with a
> proportionality constant involving the gravitational constant and the
> speed of light."
>
> http://en.wikipedia.org/wiki/Schwarzschild_radius
>
> No mention of density anywhere, only of mass. The Schwarzschild radius
> of a mass can be calculated directly as the mass multiplied by a
> *constant* (which is 2*G/c^2). Volume doesn't appear anywhere in the form
ula.
>
> > if the mass of the universe is infinite it falls inside
> > it's Schwarzschild radius, since rs = 2Gm/c^2 ... and infinity divide
d by
> > a large number is still infinity.
>
> Which is a rather definite proof that there's a finite amount of mass
> in the universe.
>
> > > I call this the shakespeare-monkey fallacy.
>
> > It's not a fallacy, it's a paradox, there's a difference. It's not poss
ible
> > to predict random events, but it's still possible to know that they wil
l
> > occur. For example if you use a simple coin toss, and toss the coin
> > forever, the distribution will be 50/50, so you can say with 100%
> > confidence that sometime in the future there will be another "heads",
> > yet at the same time you don't know at all if the next toss will be
> > a "heads".
>
> It's a fallacy. An infinite amount of data, even if all values have the
> same "chance" of appearing in the data, does not automatically mean that
> every possible pattern appears.
>
Snort. But you are proving his point. In any infinite universe in which
"every" combination possible doesn't exist, then some combinations
**must** be identical. Worse, if you have infinite mass, but finite
numbers of ways it can combine, then there **must** be instances where
some large number of duplications exist. The only question is, how
limited is the set of possible configurations, and how infinite is the
range of places they can take place in. Obviously, the odds of getting
an identical sequence from a set that *only* contains 50 combinations,
given an infinite number of tries, is much more likely than one that
requires 500 trillion identical combinations, even with an infinite
number "tests" (or in this case, places where such might happen). While
its true that any *single* such sequence/set of combinations are no more
likely than any other, it is simply not possible to have an infinite
number of such combinations, and not have duplicates. The only
"fallacy" is if you pointed at this planet, and said that some place
there **must be** one just like it. We could be the one single set of
very large number of combinations of matter that *wasn't* duplicated an
infinite number of times, just as there could be some subset of cases
that have "never" happened. But its just not mathematically sound to
imply that there would *never* be such duplicated. That just isn't
possible, unless you also have an infinite number of ways that it "can
be" combined. Simple economies of scale imply that the smaller the
object you are describing, the less "possible" it is for it not to exist
some place else, in such a universe.
> The proof is rather simple: For example, the ordered set of natural
> numbers is an infinite set where each value has an equal "chance" of
> appearing, yet eg. the pattern "2 1" never appears.
>
Again, only if you are looking at it in terms of *each* number being its
own unique thing. However, if you presume that the "set" of possible
forms was 0-9, and that there is simply an infinite number of
combinations, then obviously you *do* get "2 1", in 21, 210, 211, 212,
etc. Your example assumes an infinite number of unique "combinations",
in an infinite set of possible combinations. That is true. If you found
an identical Earth, you might not find one that is both identical *and*
in a solar system with the same number of other planets, comets,
asteroids, constellations, etc. Something **would** be different. But
that doesn't mean that the "object" of your examination "isn't" nearly
identical, save for those things that are not directly "part" of it,
which make it different, any more than you can claim that the sequence
21 doesn't happen in 213, just because there happens to be a 3 in it.
Or, to put it in terms that one cartoon did, just because an infinite
number of monkeys, typing randomly or otherwise, on an infinite number
of type writers, might never reproduce Shakespeare, that doesn't mean
they wouldn't reproduce Terry Pratchett instead. Your setting an
artificial standard from the beginning, implying that one improbable
solution doesn't have to happen. Its way different than saying that
**no** improbable solution will ever happen.
--
void main () {
If Schrödingers_cat is alive or version > 98 {
if version = "Vista" {
call slow_by_half();
call DRM_everything();
}
call functional_code();
}
else
call crash_windows();
}
<A HREF='http://www.daz3d.com/index.php?refid=16130551'>Get 3D Models,
3D Content, and 3D Software at DAZ3D!</A>
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stbenge wrote:
>
> Over that? Nah!
>
It's just the "revving the engine" part.....
--Sherry Shaw
--
#macro T(E,N)sphere{x,.4rotate z*E*60translate y*N pigment{wrinkles scale
.3}finish{ambient 1}}#end#local I=0;#while(I<5)T(I,1)T(1-I,-1)#local I=I+
1;#end camera{location-5*z}plane{z,37 pigment{granite color_map{[.7rgb 0]
[1rgb 1]}}finish{ambient 2}}// TenMoons
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Patrick Elliott <sel### [at] rraznet> wrote:
> Snort. But you are proving his point. In any infinite universe in which
> "every" combination possible doesn't exist, then some combinations
> **must** be identical.
Well, if we have an infinite amount of singularities, I wouldn't call
them "parallel universes", even though they are all identical to each
other (except for mass, rotation and electric charge).
Also, if we have, for example, an infinite amount of evenly-distributed
hydrogen (or dark matter, or dark energy, or anything) I also wouldn't call
that "parallel universes".
> Worse, if you have infinite mass, but finite
> numbers of ways it can combine, then there **must** be instances where
> some large number of duplications exist.
Duplication can be trivial. It's enough to have an infinite amount of
evenly-distributed mass (or just energy).
But anyways, as pointed out, if there was an infinite amount of mass
in the Universe, the Schwarzschild radius of the Universe would also
be infinite, which would mean that the entire Universe is a black hole,
which is clearly not the case. (Black holes have all kinds of funny
features which clearly don't happen in this universe. For example, all
geodesics would point to the singularity and there's no way to avoid
everything going there. Even timelines go to the singularity, so just
advancing in time makes everything go to the singularity.)
> Or, to put it in terms that one cartoon did, just because an infinite
> number of monkeys, typing randomly or otherwise, on an infinite number
> of type writers, might never reproduce Shakespeare, that doesn't mean
> they wouldn't reproduce Terry Pratchett instead. Your setting an
> artificial standard from the beginning, implying that one improbable
> solution doesn't have to happen. Its way different than saying that
> **no** improbable solution will ever happen.
I have never said that it cannot happen. I just oppose the claim that
something will inevitably happen.
--
- Warp
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Darren New <dne### [at] sanrrcom> wrote:
> Last I saw, estimates were that we're within experimental uncertainty
> about whether we're within our own Schwartzchild radius.
If GR is right, then the universe would look a lot different if we were
inside that radius. The GR equations have funny properties inside this
radius. For instance, all geodesics, including timelines, go to the
singularity, and there's no escaping it. Even if you try to keep away
from the singularity you just can't, because advancing in time is equal
to advancing towards the singularity.
As far as I know, the universe is *expanding*, not going towards a single
point.
> > (Because if it was caused by mass, it would mean that the entire universe
> > is actually inside its own Schwarzschild radius, which is clearly not the
> > case.)
> Not sure why you would think that. If there's enough mass to eventually
> collapse the universe back to the "big crunch", then by definition we're
> in a "black hole" out of which no light can escape. It's just a really
> big one, hundreds of billions of light years in diameter. :-)
A star is not a black hole even during its own collapse. Not until it
gets inside its own Schwarzschild radius. Collapse does not mean that
the thing which collapses is a black hole.
> > I don't find any kind of logic in that. Why would there be a "similar",
> > "parallel" version of anything if you travel far enough? It doesn't make
> > any logical sense.
> Probably in the "inifinite monkeys type shakespear" kind of way.
Which is a fallacy.
--
- Warp
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Darren New <dne### [at] sanrrcom> wrote:
> Warp wrote:
> > If you were at the center of the galaxy you wouldn't be looking at the
> > sky. I think you would be infinitely small.
> I'm not sure anyone is sure what happens in the middle of a black hole.
> If "you" were in a position to see, you could certainly see the sky. The
> sky couldn't see you, mind.
It's true that nobody dares to even guess what is happening inside the
event horizon of a black hole. However, if GR is right, everything inside
the event horizon inevitably goes to the singularity and there just isn't
escaping it. You just can't keep away from it no matter what you try.
> Surely you're not asking seriously? A sphere is a 2D finite surface with
> no border.
The sphere is its own border.
--
- Warp
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Warp wrote:
> which is clearly not the case. (Black holes have all kinds of funny
> features which clearly don't happen in this universe. For example, all
> geodesics would point to the singularity and there's no way to avoid
> everything going there. Even timelines go to the singularity, so just
> advancing in time makes everything go to the singularity.)
I think the problem with trying to say what happens in a singularity is
that we have only mathematical models of what happens. The reason
they're even *called* a "singularity" is that the mathematical models
break down there, like dividing by zero.
Saying we're not inside a black hole implies we know what happens inside
a black hole. Plus, a sufficiently large black hole can have a
surprising amount of livable space inside.
How do you know everything doesn't go to a singularity in the future?
That would be the "big crunch" theory, which I understand scientists
believe is true if the universe contains enough mass to be finite in size.
--
Darren New / San Diego, CA, USA (PST)
It's not feature creep if you put it
at the end and adjust the release date.
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Warp wrote:
> As far as I know, the universe is *expanding*, not going towards a single
> point.
If there's enough mass, then eventually gravity will pull everything
into a "single point", just like everything came from a single point
during the big bang. (At least, that's my lay understanding.)
>> Not sure why you would think that. If there's enough mass to eventually
>> collapse the universe back to the "big crunch", then by definition we're
>> in a "black hole" out of which no light can escape. It's just a really
>> big one, hundreds of billions of light years in diameter. :-)
>
> A star is not a black hole even during its own collapse. Not until it
> gets inside its own Schwarzschild radius. Collapse does not mean that
> the thing which collapses is a black hole.
I'm not sure "Schwarzschild radius" makes sense in the context of "all
of space-time". I.e., what does "radius of the universe" mean?
>>> I don't find any kind of logic in that. Why would there be a "similar",
>>> "parallel" version of anything if you travel far enough? It doesn't make
>>> any logical sense.
>
>> Probably in the "inifinite monkeys type shakespear" kind of way.
>
> Which is a fallacy.
I didn't say it was right. :-) But yah, I guess if you strictly mean
"in any logical sense", it isn't logical.
--
Darren New / San Diego, CA, USA (PST)
It's not feature creep if you put it
at the end and adjust the release date.
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Warp wrote:
> Darren New <dne### [at] sanrrcom> wrote:
>> Warp wrote:
>>> If you were at the center of the galaxy you wouldn't be looking at the
>>> sky. I think you would be infinitely small.
>
>> I'm not sure anyone is sure what happens in the middle of a black hole.
>> If "you" were in a position to see, you could certainly see the sky. The
>> sky couldn't see you, mind.
>
> It's true that nobody dares to even guess what is happening inside the
> event horizon of a black hole.
Not true. They just won't guess what happens at the singularity. It's
called a singularity because the math breaks down there.
Calculate the gravitational curvature at the Schwartzchild radius for a
galaxy-sized black hole. It's not that great. You likely wouldn't even
notice you'd crossed any sort of boundary. (At least, that's what I've
read. I am not sure how to do the math myself.)
> However, if GR is right, everything inside
> the event horizon inevitably goes to the singularity and there just isn't
> escaping it. You just can't keep away from it no matter what you try.
Sure. Let me know when you figure out how to escape the universe. :-)
>> Surely you're not asking seriously? A sphere is a 2D finite surface with
>> no border.
>
> The sphere is its own border.
No, the sphere is a border for a ball, not a sphere.
(Sorry if that "surely" comment sounded insulting. It just surprised me
that anyone with a background in technology and graphics wouldn't be
familiar with this.)
Take, as an alternate example, a video game like "asteroids", where the
stuff that goes off the top of the screen comes on the bottom, and the
sides are connected. This is geometrically equivalent to a torus. There
are no boundaries for the spaceship to run into, but the space is still
finite. It is postulated that the universe could be like that.
You can even have a space where the sides are boundaries but the top and
bottom are connected (forming a cylinder), meaning finite space but only
bounded in some places and not others.
--
Darren New / San Diego, CA, USA (PST)
It's not feature creep if you put it
at the end and adjust the release date.
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Darren New <dne### [at] sanrrcom> wrote:
> Saying we're not inside a black hole implies we know what happens inside
> a black hole.
If we were inside a black hole, GR would be wrong, because GR predicts
certain things about the inside of a black hole (such as all space-time
geodesics going to the singularity), and this is clearly not the case
in our observable universe.
Given that it's GR which predicts the existence of black holes, and
saying that we may be inside a black hole, which means that GR doesn't
apply after all, it would be a statement that defeats itself: If GR doesn't
apply, then how can be was we are inside a black hole, which is a consequence
of GR?
> Plus, a sufficiently large black hole can have a
> surprising amount of livable space inside.
But according to the GR equations everything inside the event horizon
of the black hole would inevitably crunch into the singularity. There's
no avoiding it. Inside the event horizon moving in time is equivalent to
moving in space, and all the timelines go to the singularity. Even if a
force was applied to an object to try to keep it away from the singularity
it wouldn't help, because the object travels in time.
Source:
http://en.wikipedia.org/wiki/Schwarzschild_metric#Singularities_and_black_holes
Basically what you are saying is that GR applies inside the event
horizon as if there was no event horizon and no singularity, which is,
of course, contradictory.
Of course this is how I understand it. I wouldn't be surprised if I'm
wrong. There are many features of GR which I have had and still have
difficulties in understanding (the most recent case being the concept of
the cosmological horizon, which to me seemed impossible at first).
> How do you know everything doesn't go to a singularity in the future?
> That would be the "big crunch" theory, which I understand scientists
> believe is true if the universe contains enough mass to be finite in size.
If all geodesics and timelines point towards the singularity, how can
anything go away from the singularity?
Anyways, the current consensus, based on measurements, seems to be that
the universe is not only expanding, but is doing so at an accelerated rate.
It seems that there will not be a big crunch. The big rip seems more likely.
--
- Warp
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Darren New <dne### [at] sanrrcom> wrote:
> Warp wrote:
> > As far as I know, the universe is *expanding*, not going towards a single
> > point.
> If there's enough mass, then eventually gravity will pull everything
> into a "single point", just like everything came from a single point
> during the big bang. (At least, that's my lay understanding.)
Even if that was so, it still doesn't mean we are inside a black hole.
Anyways, it seems that this is not so after all.
> > A star is not a black hole even during its own collapse. Not until it
> > gets inside its own Schwarzschild radius. Collapse does not mean that
> > the thing which collapses is a black hole.
> I'm not sure "Schwarzschild radius" makes sense in the context of "all
> of space-time".
Why not? The Schwarzschild radius of a given mass is simply a distance
which is the product of the mass and a constant. The Schwarzschild radius
of the universe is the mass of the universe times a that constant.
If all the mass of the universe was compressed inside a volume smaller
than a sphere with that radius, it would form a black hole.
> I.e., what does "radius of the universe" mean?
It's not the "radius of the universe". It's the Schwarzschild radius.
Different thing.
--
- Warp
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Darren New <dne### [at] sanrrcom> wrote:
> > It's true that nobody dares to even guess what is happening inside the
> > event horizon of a black hole.
> Not true. They just won't guess what happens at the singularity. It's
> called a singularity because the math breaks down there.
No, I think it's inside the event horizon. While GR equations tell us
what happens if GR holds inside the event horizon in the same way as
outside it, it's still speculation.
> Calculate the gravitational curvature at the Schwartzchild radius for a
> galaxy-sized black hole. It's not that great. You likely wouldn't even
> notice you'd crossed any sort of boundary. (At least, that's what I've
> read. I am not sure how to do the math myself.)
I think you could clearly see the event horizon regardless of its size
because of the way it bends light.
Once inside, you are doomed. There's no escaping the singularity.
You'll go there no matter what you do.
> > However, if GR is right, everything inside
> > the event horizon inevitably goes to the singularity and there just isn't
> > escaping it. You just can't keep away from it no matter what you try.
> Sure. Let me know when you figure out how to escape the universe. :-)
Nothing is going towards a global singularity in the universe. On the
contrary, everything is going away from everything else.
> >> Surely you're not asking seriously? A sphere is a 2D finite surface with
> >> no border.
> >
> > The sphere is its own border.
> No, the sphere is a border for a ball, not a sphere.
A ball is a sphere.
Perhaps you are confusing it with a spherical surface?
--
- Warp
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Warp wrote:
> Of course this is how I understand it.
You probably understand it somewhat better than I do. :-)
> If all geodesics and timelines point towards the singularity, how can
> anything go away from the singularity?
But if it's a closed system that's (say) the 4D equivalent to the
surface of a sphere, all geodesics *do* point towards the singularity,
given enough time. I think.
> Anyways, the current consensus, based on measurements, seems to be that
> the universe is not only expanding, but is doing so at an accelerated rate.
Yep. I wouldn't be surprised if this changes again, tho. :-)
--
Darren New / San Diego, CA, USA (PST)
It's not feature creep if you put it
at the end and adjust the release date.
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Warp wrote:
> Why not? The Schwarzschild radius of a given mass is simply a distance
> which is the product of the mass and a constant.
What's the distance from the universe? Doesn't a distance have to be
between two events?
> If all the mass of the universe was compressed inside a volume smaller
> than a sphere with that radius, it would form a black hole.
>
>> I.e., what does "radius of the universe" mean?
>
> It's not the "radius of the universe". It's the Schwarzschild radius.
> Different thing.
How do you measure the "center" from which you take the radius of the
sphere? I.e., "distance" implies two space-time events between which
you're measuring a distance.
Certainly with enough mass, a finite universe *could* be within its
Schwartzchild radius. But I don't think I know enough about this to
really make any factual statements beyond that. :-)
--
Darren New / San Diego, CA, USA (PST)
It's not feature creep if you put it
at the end and adjust the release date.
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Warp wrote:
>> Not true. They just won't guess what happens at the singularity. It's
>> called a singularity because the math breaks down there.
>
> No, I think it's inside the event horizon. While GR equations tell us
> what happens if GR holds inside the event horizon in the same way as
> outside it, it's still speculation.
Fair enough. Altho people have spoken of time travel via rotating black
holes and such, but I suppose that's speculation until someone finds one
for sure. :-)
> I think you could clearly see the event horizon regardless of its size
> because of the way it bends light.
Yes, but all mass bends light. Even "dark matter". :-) It's kind of the
GR definition of "mass".
> Once inside, you are doomed. There's no escaping the singularity.
> You'll go there no matter what you do.
Yep. Big Crunch. :-) I think the math for charged rotating black holes,
or those taking into consideration quantum effects, are less obvious.
>> > However, if GR is right, everything inside
>>> the event horizon inevitably goes to the singularity and there just isn't
>>> escaping it. You just can't keep away from it no matter what you try.
>
>> Sure. Let me know when you figure out how to escape the universe. :-)
>
> Nothing is going towards a global singularity in the universe. On the
> contrary, everything is going away from everything else.
At the moment, yes.
>>>> Surely you're not asking seriously? A sphere is a 2D finite surface with
>>>> no border.
>>> The sphere is its own border.
>
>> No, the sphere is a border for a ball, not a sphere.
>
> A ball is a sphere.
Mathematically speaking, when mathematicians distinguish "sphere" from
"ball", the latter includes the points at distance < radius, while the
former includes only points at distance = radius.
http://mathworld.wolfram.com/Ball.html
(Occasionally I surprise myself with the useless information that sticks
in my head. Last week it was the reproductive cycle of jellyfish.)
The reason I made the distinction was to imply that the surface of a
sphere would be unbounded (as in, without any boundaries) to an entity
restricted to the surface. Sure, you couldn't change your radius, but
that's by definition of it being restricted to a sphere. An entity in a
ball, on the other hand, can move outwards from the center and hit a
boundary at the radius.
I believe Aristotle had an interesting insight (right or wrong). If
there is a boundary to the universe, and you throw a rock at the
boundary, what stops the rock? There can't be anything outside the
boundary to stop the rock.
> Perhaps you are confusing it with a spherical surface?
--
Darren New / San Diego, CA, USA (PST)
It's not feature creep if you put it
at the end and adjust the release date.
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In article <477a9e54$1@news.povray.org>, dne### [at] sanrrcom says...
> Warp wrote:
> > As far as I know, the universe is *expanding*, not going towards a si
ngle
> > point.
>
> If there's enough mass, then eventually gravity will pull everything
> into a "single point", just like everything came from a single point
> during the big bang. (At least, that's my lay understanding.)
>
Actually, one aspect of at least one multi-universe system implies that
the big bang may have been a "white hole". Which is to say, something
that spews out matter, rather than condensing it. The math implies that
nearly any such structure though is unstable. I.e., it will only spew
matter for a short duration, from a singularity, before it stops doing
so. The question then becomes, "Did the white hole generate enough
matter, and with it, other forces, to prevent the whole thing falling
into a singularity again?" However, you are talking about GR. Quantum
mechanics, which GR doesn't apply to so well, implies that at the level
of a singularity its impossible to everything to fall into one, without
something getting back out again at all (i.e. Hawking's Radiation). Even
nastier is the implication that the structure of what comes out is
derivative of the material that goes in, such that information is never
lost in the system. Prior assumptions implied that the structure of a
thing, once in a black hole, would be randomized, such that it would
never come out in a mathematically predictable form.
--
void main () {
If Schrödingers_cat is alive or version > 98 {
if version = "Vista" {
call slow_by_half();
call DRM_everything();
}
call functional_code();
}
else
call crash_windows();
}
<A HREF='http://www.daz3d.com/index.php?refid=16130551'>Get 3D Models,
3D Content, and 3D Software at DAZ3D!</A>
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Darren New <dne### [at] sanrrcom> wrote:
> > If all geodesics and timelines point towards the singularity, how can
> > anything go away from the singularity?
> But if it's a closed system that's (say) the 4D equivalent to the
> surface of a sphere, all geodesics *do* point towards the singularity,
> given enough time. I think.
I must admit that I have no idea what the GR equations say about this,
but I got the impression that inside the event horizon all geodesics point
straight at the singularity, when going forward in time. I would expect
that no geodesic points away from the singularity at any point.
--
- Warp
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Darren New <dne### [at] sanrrcom> wrote:
> Warp wrote:
> >> Not true. They just won't guess what happens at the singularity. It's
> >> called a singularity because the math breaks down there.
> >
> > No, I think it's inside the event horizon. While GR equations tell us
> > what happens if GR holds inside the event horizon in the same way as
> > outside it, it's still speculation.
> Fair enough. Altho people have spoken of time travel via rotating black
> holes and such, but I suppose that's speculation until someone finds one
> for sure. :-)
I think the time travel is related to wormholes. Travelling inside a
wormhole does not imply going inside the event horizon of a black hole.
> > I think you could clearly see the event horizon regardless of its size
> > because of the way it bends light.
> Yes, but all mass bends light. Even "dark matter". :-) It's kind of the
> GR definition of "mass".
I said "they way it bends light", not "because it bends light".
No mass is dense enough to bend light like a black hole does because,
obviously, if the mass was dense enough, it would collapse into a black
hole...
> > Once inside, you are doomed. There's no escaping the singularity.
> > You'll go there no matter what you do.
> Yep. Big Crunch. :-)
I think the analogy is not correct.
The Big Crunch means that the universe, ie. space itself, contracts
until everything collapses into a singularity. Contraction of space doesn't
involve objects moving. (This is one of the hardest things to understand
about the expansion (and theoretical contraction) of the universe. One
counterintuitive result of the expansion of the universe is that the
distance between two objects can grow faster than c, which at first sounds
like it would break GR, but this is not so.)
A black hole doesn't contract. Instead, objects physically move towards
the singularity.
> > Nothing is going towards a global singularity in the universe. On the
> > contrary, everything is going away from everything else.
> At the moment, yes.
I can't say for sure, but I have the understanding that anything going
away from the singularity inside the event horizon of a black hole would
be against GR equations.
> (Occasionally I surprise myself with the useless information that sticks
> in my head. Last week it was the reproductive cycle of jellyfish.)
Whatever floats your boat. ;)
--
- Warp
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Warp wrote:
> I must admit that I have no idea what the GR equations say about this,
> but I got the impression that inside the event horizon all geodesics point
> straight at the singularity, when going forward in time.
I wouldn't think they point *straight* at the singularity, unless a
photon spiraling to its death is considered to be going in a "straight"
line. The fact that two particles can take different paths starting from
the same place would seem to imply that "straight at the singularity" is
either mistaken or so counter-intuitive that I don't understand what it
means. :-)
Take a photon that's halfway to the S-radius (for some meaning of
"halfway"). Fire it perpendicular to the radius (for some meaning of
"perpendicular"). I would think the photon would follow a spiraling
descent, rather than fall straight towards the singularity. Fire one in
the opposite direction. It'll take a different path. If photons always
follow geodesics, either you can have multiple geodesics pointing
"straight at" the singularity, or your impression is wrong. I don't know
which it would be, tho.
> I would expect
> that no geodesic points away from the singularity at any point.
Yeah. I'm just not sure the math works the same when you consider the
whole universe to be the black hole. If it were true, how could you
measure the "center" of the black hole? *I* sure don't understand the
subject well enough to be sure. I'm just saying what I've heard other
reputable GR scientists say.
Fun to babble about it, tho. ;-)
--
Darren New / San Diego, CA, USA (PST)
It's not feature creep if you put it
at the end and adjust the release date.
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