/sci/ - Science & Math

>>3639375
okay sucker
>string theory
>math

ask me anything.

>>3038990
In general relativity it is a set of points

http://en.wikipedia.org/wiki/Set_theory

which are there, even without an observer, and which admit a metric and therefore a topological structure

topology: "which point is close to another?"
http://en.wikipedia.org/wiki/Topology

metric: "how far away are two points"
http://en.wikipedia.org/wiki/Riemannian_geometry

the concept of topology makes sense even without a metric, but we have one, yay.
in general relativity, in empty space (additional fields), if you consider a single point, then there is no structure (since the metric is always locally flat)
if you consider some neightborhood, then in empty space there is the metric structure, which you might consider a (tensor-)field.

so the only thing in space are points and some field, which basically tells you how far away things are and how curved the space is.

http://en.wikipedia.org/wiki/Metric_tensor_%28general_relativity%29

you can compute the metric using the einstein equations

http://en.wikipedia.org/wiki/Metric_tensor_%28general_relativity%29

which depend (on the global topology and) if there is some matter around (matter influences the metric in empty space even from a distance (but not instantaneously (gravitational waves)))

1/3

\[ScriptN] /: \[ScriptN][1] := 1
\[ScriptN] /: \[ScriptN][x_] \[ScriptN][y_] := \[ScriptN][x y]

\[ScriptP][x_] := \[ScriptN][x] /; Element[x, Complexes]
\[ScriptP][x_ y_] := \[ScriptN][x] \[ScriptP][y] /;
Element[x, Complexes]
\[ScriptP][\[ScriptN][x_]] := \[ScriptN][x]
\[ScriptP] /: \[ScriptP][\[ScriptP][x_]] := \[ScriptP][x]
\[ScriptP] /: \[ScriptP][x_] \[ScriptP][y_] := \[ScriptP][x y]
\[ScriptP] /: \[ScriptP][x_ \[ScriptP][y_]] := \[ScriptP][x y]
\[ScriptP] /: \[ScriptP][x_ + \[ScriptP][y_]] := \[ScriptP][x + y]
\[ScriptP][\[ScriptN][x_] y_] := \[ScriptN][x] \[ScriptP][y]
\[ScriptP][\[ScriptN][x_] + y_] := \[ScriptP][x + y]

>>3012274
at least you don't use expressions like
%%%%
like I do.

However, I have a present for your init.m file:

sexy[output_]:=Text[Style[output//Simplify,15,Hue[.64, 1, .7]]//TraditionalForm]

it's to emphasize*

>that's not a quotient group is it?
yes it is
http://en.wikipedia.org/wiki/Cyclic_group
Z/nZ is
the integers with "+" where a+ni=a for example
Z/5Z is "the circle
0123401234012340123401234
hence 2+4='6'=1
you always factor out 5Z.

Z/Z2 (the finite simple group of order two *sing*)
is the group
0101010101010 with puls
i.e.
0+0=0
0+1=1
1+0=1
1+1=0
this group is abelian (because 0+1=1+0) and therfore you might use "+" as the operaton. however, in our context it's better to use a representation with "·" i.e.
you identify

+0 with ·1 (the neutral elements, respectively)
and
+1 with ·(-1)

i.e.

1·1=1
1·(-1)=(-1)
(-1)·1=(-1)
(-1)·(-1)=1

notice that this is the same structure as above just with · and not +. They are isomorphic, see also
http://en.wikipedia.org/wiki/Representation_theory

now my group was {A|A=exp(a), a element reals}, i.e. all the numbers R>0
and your group was R\{0}
but
(R\{0})=+/- exp(a)=+/- (R>0)
so
your group = my group cross Z/2Z
;)

>>2854840
I gave some examples to indicate that
>Chemistry
is a bit too much. I mean more specific fields (not that String Theory would be a very specific term)

>>2731657