Mike Raiford wrote:
> Yeah, quicken. Though intuit pisses me off.

Me too. But what do you expect from a company with a monopoly on such useful 
software?

-- 
Darren New, San Diego CA, USA (PST)
  "How did he die?"   "He got shot in the hand."
     "That was fatal?"
          "He was holding a live grenade at the time."

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Orchid XP v8 <voi### [at] devnull> wrote:
> Oh. You mean something *outside* the mass itself causes it to become a 
> black hole?

> But then, wouldn't that just mean that as soon as you remove the force, 
> it wouldn't be a black hole any more?

  Remember that little detail that nothing can come out of the black hole?
That means that the black hole cannot stop being a black hole because the
material it's made of cannot come out. (Hawking radiation notwithstanding.)

-- 
                                                          - Warp

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Mike Raiford <"m[raiford]!at"@gmail.com> wrote:
> > Oh. You mean something *outside* the mass itself causes it to become a
> > black hole?
> >
> > But then, wouldn't that just mean that as soon as you remove the force,
> > it wouldn't be a black hole any more?
> >

> Which is why a small black hole would be short lived.

  A black hole cannot stop being a black hole (according to GR) because
nothing can come out. Once it has become a black hole, it will be like
that forever. (Quantum mechanics might cause something else to happen,
but from a purely GR point of view.)

> But, then, it does 
> have an event horizon, and nothing can escape a black hole. So, wouldn't 
> it remain a black hole after being compacted?

  There's no other possibility (in GR). A black hole can only grow (if
more matter is fed to it), not shrink.

-- 
                                                          - Warp

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clipka <ano### [at] anonymousorg> wrote:
> Am 07.03.2011 14:26, schrieb Invisible:

> >> Take any mass and collapse it down small enough and it'll become a black
> >> hole. Once it reaches a critical ration of mass/volume, then you'll have
> >> a black hole. It may not last too long, or it may; and if it does, it
> >> would be rather irresponsible to create one so close to our own planet.
> >
> > But if you have a small mass, why would it be crushed to a small size?

> Non-gravitational external force. Smash two particles into each other 
> hard enough, and you /might/ get them close enough together that they 
> can't escape each other's gravitational well anymore.

  I'm not sure how that would work. All the mass in those particles would
need to be compressed into a volume smaller than the Schwarzschild radius
of those masses, which is really, really small. Could we be hitting the
limits of planck volumes?

  And this assumes that the "volume" of the particles (if that term even
makes sense at quantum levels) gets smaller when particles hit each other.
It's not like particles are little balls that get compressed when they hit
each other.

  Perhaps if you get enough particles close enough to each other by
colliding them all at the same time, you could get a mass that is so
dense that it's smaller than its own Schwarzschild radius.

  Btw, AFAIK in theory eg. a black hole with the mass and charge of an
electron (assuming such a thing is physically possible) would basically
be indistinguishable from a normal electron. (Ok, maybe it would behave
differently in collisions with other particles. I don't know enough of
physics to say for sure.)

-- 
                                                          - Warp

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clipka <ano### [at] anonymousorg> wrote:
> (I personally favor the idea that leptons, quarks and the like might be 
> black holes themselves; kind of like the smallest black holes you can 
> possibly get.)

  Hawking would probably disagree with that.

-- 
                                                          - Warp

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Roman Reiner <lim### [at] gmxde> wrote:
> That depends on what numbers you are using. The number of points in the unit
> square of rational numbers is countable, the number of points in the unit square
> of irrational numbers is not.

  Is the set of irrational numbers in a unit square larger or equal to
the set of irrational numbers in a unit line?

-- 
                                                          - Warp

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Warp wrote:
>> But, then, it does 
>> have an event horizon, and nothing can escape a black hole. So, wouldn't 
>> it remain a black hole after being compacted?
> 
>   There's no other possibility (in GR). A black hole can only grow (if
> more matter is fed to it), not shrink.

Warp is right. But what happens in QM is, essentally, particles of negative 
and positive mass spontaneously spring into existence close to the edge of 
the black hole, and the particle of negative mass falls into the hole while 
the particle of positive mass escapes. Hence, it looks like it's leaking mass.

According to the math, the likelihood of this asymptotically approaches zero 
at the size of the hole approaches how big it has to be to turn into a black 
hole anyway. In other words, if a sun of 4.9 solar masses doesn't turn into 
a black hole, and a sun of 5.1 solar masses does, the likelihood of a 
positive/negative pair splitting and having half escape approaches zero as 
the size of the black hole approaches 5 solar masses.

-- 
Darren New, San Diego CA, USA (PST)
  "How did he die?"   "He got shot in the hand."
     "That was fatal?"
          "He was holding a live grenade at the time."

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Warp wrote:
>   I'm not sure how that would work. All the mass in those particles would
> need to be compressed into a volume smaller than the Schwarzschild radius
> of those masses, which is really, really small. Could we be hitting the
> limits of planck volumes?

Wikipedia implies a mass the hole of the moon would be about 1/10th a 
milimeter in diameter. (Altho, technically, you'd have to measure the 
circumference, as the diameter would actually be infinite.)


>   Perhaps if you get enough particles close enough to each other by
> colliding them all at the same time, you could get a mass that is so
> dense that it's smaller than its own Schwarzschild radius.

That's basically what you have to do.

http://en.wikipedia.org/wiki/Black_hole#Evaporation

Given that, I'm pretty sure this is exactly the kind of situation where QM 
and GR conflict, so I'm not sure any of this is other than speculation.

-- 
Darren New, San Diego CA, USA (PST)
  "How did he die?"   "He got shot in the hand."
     "That was fatal?"
          "He was holding a live grenade at the time."

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Warp wrote:
> Roman Reiner <lim### [at] gmxde> wrote:
>> That depends on what numbers you are using. The number of points in the unit
>> square of rational numbers is countable, the number of points in the unit square
>> of irrational numbers is not.
> 
>   Is the set of irrational numbers in a unit square larger or equal to
> the set of irrational numbers in a unit line?

It's the same. Aleph2 = N ^ Aleph1.  The only way to get a bigger infinity 
is to put it in an exponent.

-- 
Darren New, San Diego CA, USA (PST)
  "How did he die?"   "He got shot in the hand."
     "That was fatal?"
          "He was holding a live grenade at the time."

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Invisible <voi### [at] devnull> wrote:
> The unit square contains an infinite number of points. But is it 
> countably or uncountably infinite?

  I don't really understand why you are asking that. If there are uncountably
many reals in the range [0,1], why wouldn't there likewise be uncountably
many coordinates inside a unit square?

  The more interesting question is if those two sets are of equal size.
If I understand correctly, the set of reals in the range [0,1] has the
same cardinality as the set of points inside a unit square, hence there
exists a one-to-one mapping between them, hence they have the same size.
(Defining the "size" of an infinite set is a bit complicated of a subject,
but an interesting one, if you are in any way into math.)

  In fact, likewise they are equal to the set of points inside a unit cube,
the set of points inside a 4-dimensional unit hypercube, and so on. Even if
you had a multi-dimensional unit cube of countably infinite dimensions, the
set of points would still be the same size as the reals in the range [0,1].

  Now, if the unit cube had uncountably infinite dimensions, the question
becomes more complicated. The cardinality of this set is larger than the
set of reals, but is there a one-to-one mapping between the set of reals
and the set of points inside this uncountably-infinite-dimensional cube?

  I don't fully understand the generalized continuum hypothesis to such
extent as to be certain, but I think that whether such a mapping exists
or not cannot be either proven nor disproven using "regular" set theory
math (for a definition of "regular" that goes well beyond my area of math
knowledge).

-- 
                                                          - Warp

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