| Author | Message |
|---|
LTF
Salvaged from Archive | Posted: · [Salvaged from Archive]
Just kidding. LOL |
MontysDouble
Salvaged from Archive | Posted: · [Salvaged from Archive]
Who was that banned Filecabier?
Happy yo mama's so *.* day. |
freestyler_3
Salvaged from Archive | Posted: · [Salvaged from Archive]
I knew you were joking.
You have 2 dads. |
MontysDouble
Salvaged from Archive | Posted: · [Salvaged from Archive]
Nah, he has a mum and a dad.
http://i165.photobucket.com/albums/u61/JPryde_2007/150px-…
Same person though. |
Josh85
Salvaged from Archive | Posted: · [Salvaged from Archive]
it annoys me that this thread is the only place where anything is happening in filecabi.
I need mental stimulation before these sleepy pills kick in. The world is lonely at midnight. |
freestyler_3
Salvaged from Archive | Posted: · [Salvaged from Archive]
Quote:
Originally Posted by Josh85
View Post
it annoys me that this thread is the only place where anything is happening in filecabi.
I need mental stimulation before these sleepy pills kick in. The world is lonely at midnight.
Only A miracle can save us now riight???? |
MontysDouble
Salvaged from Archive | Posted: · [Salvaged from Archive]
That we can do.
The mathematics
The single most important equation in (first quantisized bosonic) string theory is the N-point scattering amplitude. This treats the incoming and outgoing strings as points, which in string theory are tachyons, with momentum ki which connect to a string world surface at the surface points zi. It is given by the following functional integral which integrates (sums) over all possible embeddings of this 2D surface in 27 dimensions.
A_N = \int{D\mu \int{D[X] exp \left( -\frac{1}{4\pi\alpha} \int{ \partial_z X_{\mu}(z,\overline{z}) \partial_{\overline{z}} X^{\mu}(z,\overline{z})}dz^2 + i \sum_{i=1}^{N}{k_{i \mu} X^{\mu}(z_i,\overline{z}_i) } \right) }}
The functional integral can be done because it is a Gaussian to become:
A_N = \int{D\mu \prod_{0<i<j<N+1}{ |z_i-z_j|^{2\alpha k_i.k_j} } }
This is integrated over the various points zi. Special care must be taken because two parts of this complex region may represent the same point on the 2D surface and you don't want to integrate over them twice. Also you need to make sure you are not integrating multiple times over different parameterizations of the surface. When this is taken into account it can be used to calculate the 4-point scattering amplitude (the 3-point amplitude is simply a delta function):
A_4 = \frac{ \Gamma (-1+\frac12(k_1+k_2)^2) \Gamma (-1+\frac12(k_2+k_3)^2) } { \Gamma (-2+\frac12((k_1+k_2)^2+(k_2+k_3)^2)) }
Which is a beta function. It was this beta function which was apparently found before full string theory was developed. With superstrings the equations contain not only the 10D space-time coordinates X but also the Grassman coordinates θ. Since there are various ways this can be done this leads to different string theories.
When integrating over surfaces such as the torus, we end up with equations in terms of theta functions and elliptic functions such as the Dedekind eta function. This is smooth everywhere, which it has to be to make physical sense, only when raised to the 24th power. This is the origin of needing 26 dimensions of space-time for bosonic string theory. The extra two dimensions arise as degrees of freedom of the string surface.
[edit] D-Branes
D-Branes are membrane-like objects in 10D string theory. They can be thought of as occurring as a result of a Kaluza-Klein compactification of 11D M-Theory which contains membranes. Because compactification of a geometric theory produces extra vector fields the D-branes can be included in the action by adding an extra U(1) vector field to the string action.
\partial_z \rightarrow \partial_z +iA_z(z,\overline{z})
In type I open string theory, the ends of open strings are always attached to D-brane surfaces. A string theory with more gauge fields such as SU(2) gauge fields would then correspond to the compactification of some higher dimensional theory above 11 dimensions which is not thought to be possible to date.
Head asploded yet? |
loadrunner
Salvaged from Archive | Posted: · [Salvaged from Archive]
Quote:
Originally Posted by MontysDouble
View Post
That we can do.
The mathematics
The single most important equation in (first quantisized bosonic) string theory is the N-point scattering amplitude. This treats the incoming and outgoing strings as points, which in string theory are tachyons, with momentum ki which connect to a string world surface at the surface points zi. It is given by the following functional integral which integrates (sums) over all possible embeddings of this 2D surface in 27 dimensions.
A_N = \int{D\mu \int{D[X] exp \left( -\frac{1}{4\pi\alpha} \int{ \partial_z X_{\mu}(z,\overline{z}) \partial_{\overline{z}} X^{\mu}(z,\overline{z})}dz^2 + i \sum_{i=1}^{N}{k_{i \mu} X^{\mu}(z_i,\overline{z}_i) } \right) }}
The functional integral can be done because it is a Gaussian to become:
A_N = \int{D\mu \prod_{0<i<j<N+1}{ |z_i-z_j|^{2\alpha k_i.k_j} } }
This is integrated over the various points zi. Special care must be taken because two parts of this complex region may represent the same point on the 2D surface and you don't want to integrate over them twice. Also you need to make sure you are not integrating multiple times over different parameterizations of the surface. When this is taken into account it can be used to calculate the 4-point scattering amplitude (the 3-point amplitude is simply a delta function):
A_4 = \frac{ \Gamma (-1+\frac12(k_1+k_2)^2) \Gamma (-1+\frac12(k_2+k_3)^2) } { \Gamma (-2+\frac12((k_1+k_2)^2+(k_2+k_3)^2)) }
Which is a beta function. It was this beta function which was apparently found before full string theory was developed. With superstrings the equations contain not only the 10D space-time coordinates X but also the Grassman coordinates θ. Since there are various ways this can be done this leads to different string theories.
When integrating over surfaces such as the torus, we end up with equations in terms of theta functions and elliptic functions such as the Dedekind eta function. This is smooth everywhere, which it has to be to make physical sense, only when raised to the 24th power. This is the origin of needing 26 dimensions of space-time for bosonic string theory. The extra two dimensions arise as degrees of freedom of the string surface.
[edit] D-Branes
D-Branes are membrane-like objects in 10D string theory. They can be thought of as occurring as a result of a Kaluza-Klein compactification of 11D M-Theory which contains membranes. Because compactification of a geometric theory produces extra vector fields the D-branes can be included in the action by adding an extra U(1) vector field to the string action.
\partial_z \rightarrow \partial_z +iA_z(z,\overline{z})
In type I open string theory, the ends of open strings are always attached to D-brane surfaces. A string theory with more gauge fields such as SU(2) gauge fields would then correspond to the compactification of some higher dimensional theory above 11 dimensions which is not thought to be possible to date.
Head asploded yet?
Time travel is not just stepping in a phoneboot, and push a button.
What happens meanwhile if you travel trough time:
Location of the whole planet is changed, every 24 ours it moves, around and trough space, there is a big posibility if you travel \trough time, you would end up in a concrete wall, or even worse somewhwew in the centre insode a boiling lava bubble.
btw the 11 dimension can be seen as 1 point in total empty space, so it be 1 demensional again. |
MontysDouble
Salvaged from Archive | Posted: · [Salvaged from Archive]
Quote:
Originally Posted by loadrunner
View Post
Time travel is not just stepping in a phoneboot, and push a button.
What happens meanwhile if you travel trough time:
Location of the whole planet is changed, every 24 ours it moves, around and trough space, there is a big posibility if you travel \trough time, you would end up in a concrete wall, or even worse somewhwew in the centre insode a boiling lava bubble.
Now that's an interesting thought. Earth travels around Sol of course, covering about 942 million km per year.
Time travel for a day, and Earth would be 2.58 million km away. Travel for a mere hour and Earth moves on a mere 108 000 km, putting our unfortunate time traveller within the Moon's orbit, but still well beyond the distance no-one except exactly thirty men have been.
Of course, the Sun's motion about the centre of the Milky Way and the Milky Way's motion with respect to other galaxies make Earth's orbital speed of 108 000 km/h seem like standing still, so if one was to time travel for an hour the spatial jump would be orders of magnitude greater than 108 000 km.
Quote:
btw the 11 dimension can be seen as 1 point in total empty space, so it be 1 demensional again.
This I don't know about, although some superstring theories have higher dimensions "collapsed" into subatomic scales... pretty mindfucking stuff, even if -like me- one can't possibly imagine the maths. |
freestyler_3
Salvaged from Archive | Posted: · [Salvaged from Archive]
http://www.meranch.com/curly/curly13.jpg
COULDNT FUCKING FIND THE ORIGINAL HORSE FROM THAT MOVIE GRR! |
AlternativeEgo
Salvaged from Archive | Posted: · [Salvaged from Archive]
http://forums.joerogan.net/attachment.php?attachmentid=25… |
tgd_02
Salvaged from Archive | Posted: · [Salvaged from Archive]
fuck |
uso
Salvaged from Archive | Posted: · [Salvaged from Archive]
wtf is wrong with you Monty? |
MontysDouble
Salvaged from Archive | Posted: · [Salvaged from Archive]
Quote:
Originally Posted by uso
View Post
wtf is wrong with you Monty?
Nothing, apart from a minor excess earwax problem and almost uncontrollable rage at the shortsighted excess and general fuckheadedness of the society I live in.
Thanks for asking anyway USO. |
uso
Salvaged from Archive | Posted: · [Salvaged from Archive]
Quote:
Originally Posted by MontysDouble
View Post
Nothing, apart from a minor excess earwax problem and almost uncontrollable rage at the shortsighted excess and general fuckheadedness of the society I live in.
Thanks for asking anyway USO.
You can use warm baby oil to loosen the excess ear wax. I'm sorry, but I have no solution for the latter. |
MontysDouble
Salvaged from Archive | Posted: · [Salvaged from Archive]
Quote:
Originally Posted by uso
View Post
You can use warm baby oil to loosen the excess ear wax.
I know, but squeezing the babies is hard work.
Quote:
I'm sorry, but I have no solution for the latter.
I'd let you in on my plan, but if I spilled the beans it'd probably make the Feds go mediaeval on our asses. |
boo_cocky
Salvaged from Archive | Posted: · [Salvaged from Archive]
What happened to LTF?
Did his stalker 'love posts' towards LB get a little too creepy?
Did the degenerate gambler owe one of the Admins money on a bet and he couldn't make good on it?
Let's all hope and pray he uses this time to get in touch with his 'inner Guido'. |
Supplemental Persona
Salvaged from Archive | Posted: · [Salvaged from Archive]
Quote:
Originally Posted by boo_cocky
View Post
What happened to LTF?
Did his stalker 'love posts' towards LB get a little too creepy?
Did the degenerate gambler owe one of the Admins money on a bet and he couldn't make good on it?
Let's all hope and pray he uses this time to get in touch with his 'inner Guido'.
He worked hard to and succeeded in fulfilling a self-fullfilling prophecy. |
