On Jan 3, 6:29*pm, Koobee Wublee wrote:
On Jan 3, 3:02 am, Eric Gisse wrote:
On Jan 2, 10:42 pm, Koobee Wublee wrote:
On Jan 2, 12:03 am, Eric Gisse wrote:
ds^2 = dx^2 + dy^2 + dz^2
ds^2 = dr^2 + r^2(d\theta^2 + sin^2(\theta)d\phi^2)
ds^2 = dr^2 + r^2 d\theta^2 + dz^2
ds^2 = da^2 + db^2 + dz^2
They all describe the same thing, yet "look different". But I can find
a coordinate transformation relating all of them to eachother, so they
are the same thing.
Your notation is screwed up. *The r of the 2nd is not the same as r of
the 3rd. *The phi of the 2nd is the same as theta of the 3rd.
Otherwise, they can all represent the same geometry. *shrug
See? You are a **** hair's distance away from understanding.
What is that again?
THE LABELS DO NOT MATTER.
Wrong! *The labels do matter. *shrug
Prove it. Write something with two different labels, and PROVE that
you can measure something to be different.
I have an idea - let's see your proof that "other solutions" that
satisfy the conditions of Birkhoff's theorem produce something other
than 43 arcsec/centry for Mercury's perihelion precession. You did,
after all, assert that to be the case.
The COORDINATES do not matter. They all
represent the _same_ geometry.
Wrong again. *To describe a geometry, you need both the labels
(coordinate) and how the labels are connected (metric). *shrug
True - to write the metric down, you need coordinates. Except the
coordinates do not matter as I can easily transform from one system to
the next and write the metric down in the new coordinate system.
As has been done repeatedly. As has the explanation to you.
Consider that you are just too stupid to understand, like Androcles
and rbwinn before you.
This is not what I have been talking about. *It looks like very few
have understood what I am saying. *That is why I feel very lonely to
be the few who after Riemann and perhaps Christoffel that have
understood the curvature business very well. *shrug
So where did you properly learn this "curvature business"? All I'm
asking is for the book you learned it from. Is that asking so much?
Just my intelligence which you lack. *shrug
So you just expect me to believe you woke up with this knowledge one
morning?
I find it more likely that you arrived at this particular level of
understanding after trying to study modern general relativity
textbooks. Except you failed, and invented all these arguments to
protect your ego.
Why else would you get so defensive and insulting when I ask a simple
question like "where did you learn what you know?".
What I am talking about is that the following geometries are different
given the same dr, dLongitude, dLatitude.
** *ds1^2 = g1_11 dr^2 + g1_22 r^2 dO^2
** *ds2^2 = g2_11 dr^2 + g2_22 r^2 dO^2
Where
** *dO^2 = cos^2(Latitude) dLongitude^2 + dLatitude^2
Except the coordinate labels are not the same in both coordinate
systems.
What do you mean they are not the same? *I have chosen them to be the
same. *shrug
Then calculate the surface area of a sphere using the metric.
Calculate the surface area of a sphere - don't just write it
down, CALCULATE it.
I did. *Just look up on my older post.
Nope - you _asserted_ it was 4 pi r^2. You never _derived_ it.
In fact, you seem quite incapable of proving something as simple as
this. Why is the only person who has "truly understood" differential
geometry incapable of deriving the surface area of a sphere?
[...same idiocy as in 2006...]
http://groups.google.com/group/sci.p...c?dmode=source
JanPB explained this to you before with much greater patience than I
can muster. You used the same arguments then as you use now.
I cannot claim one solution is more unique than the other, which is
the whole point of my explanation. I just prefer Schwarzschild in
isotropic coordinates. I can easily convert from Schwarzschild and
every /OTHER/ "different" solution to yours - just chain the
transformations.
Hold your bullsh*t! *Both ds1 and ds2 are spherically symmetric in
isotropic coordinate system. *Again, for the n’th time, these
solutions are static, spherically symmetric, and asymptotically flat.
....and the same. How quickly you forget that this has all been
explained to you in detail before. With the same metrics no less.
http://groups.google.com/group/sci.p...7?dmode=source
I HAVE SHOWN YOU SOLUTIONS THAT ARE STATIC, SPHERICALLY SYMMETRIC,
ABUT NOT ASYMPTOTICALLY FLAT. *That proves Birkhoff’s theorem false by
example. *shrug
Except you didn't prove the solution wasn't asymptotically flat
because you never calculated something like CURVATURE which would
actually prove your point. Plus I showed you the coordinate
transformation to navigate between your "different solution" and
Schwarzschild.
Your ranting is because you refuse the God you worship [...]
Funny how you are always the one to bring up God in these little
conversations.