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Warp wrote:
> stbenge <stb### [at] hotmail com> 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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