From a historical point of view, I appreciate Roger's
revisit of Archimedes "The Sand-Reckoner" - whose point
was that he could write down a number to express things
that were said to be "countless" or "infinite".
But as an astronomer, I can't help but remark that the
volume approach is flawed, as the volume of a sphere in
general relativity isn't just (4/3)pi r^3, but depends
on the curvature - and that depends upon the density of
the average volume - if you tried to fill the universe
with close-packed H atoms it would curl up and die.
We estimate the number of particles by observing that
the geometry is nearly flat (Euclidean) and that implies
a certain mean density -- but since we know that by far
most of this mass is "dark matter", presumably some type
of non-interacting particle, it's surely not hydrogen
atoms (or stars or black holes) - and since we don't
know the mass of the dark-matter particle(s) our attempts
to guess a number hits a wall.
So indeed this thread isn't J -- and it's not even
astronomy.
Patrick
On Sat, 25 Apr 2009, Raul Miller wrote:
> On Fri, Apr 24, 2009 at 10:04 PM, Mike Powell <[email protected]> wrote:
>> However, once the volume is established, I suggest that the Bohr atom
>> is not a good choice. If the Universe ever gets anything like full
>> there will not be atoms around. Gravitation will have squeezed
>> everything down to nuclei. There will be something like a sea of
>> particles, some will be recognizable as nuclei (of hydrogen,
>> helium, ... iron etc), but much may just be a mush of protons,
>> neutrons and electrons. As far as I can follow, the process could lead
>> further: for example, a sea of quarks, or string soup. From my
>> reading, those that study these things are contemplating matter in its
>> ground quantum state. Things don't get much denser than that.
>
> It would probably degrade into a black hole, with zero particles.
> This might be analogous to this thread degrading into a discussion
> of the character of _.
>
> However, I suspect Roger was not specifically hypothesizing
> to determine the character of some dense imaginary universe,
> but was attempting to find an upper bound on the capacity of
> our own. And, since our own universe does not currently seem
> to be in such a state, ...
>
>
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