how-the-gravity-work-on-a-R-4-universe-does-any-R-3-people-will-be-atracted-by-some-ghost-object-

Question Number 4724 by 123456 last updated on 29/Feb/16

how the gravity work on a R^{4} universe ?

does any R^{3} people will be atracted by

some “ {ghost}^{″} object ?

Commented by Yozzii last updated on 29/Feb/16

R^{4} i s t h e d o m a i n g i v i n g t h e f i e l d F

o f p o s i t i o n s \boldsymbol u = (a_{1}, a_{2}, a_{3}, a_{4}) i n

4 - d i m e n s i o n a l s p a c e . G r a v i t y \boldsymbol g i s a

v e c t o r w h i c h h e n c e m u s t b e a b l e t o

a c t a l o n g a n y s t r a i g h t l i n e i n F . W e

c a n w r i t e \boldsymbol g = (g_{1} (a_{1}), g_{2} (a_{2}), g_{3} (a_{3}), g_{4} (a_{4}))

w h e r e g_{i} (1 ⩽ i ⩽ 4) a r e g r a v i t a t i o n a l

f o r c e f u n c t i o n s o f p o s i t i o n r e l a t i v e t o a

b o d y o f m a s s M . I n R^{3} g r a v i t y i s

d e p e n d e n t o n t h e m a s s e s m_{i} i n v o l v e d

a n d p o s i t i o n . {W e}^{'} d t h e n e x p e c t t h a t

g_{i} a r e d e p e n d e n t o n t h e p o s i t i o n s o f

b o d i e s a n d t h e i r m a s s e s . R e w r i t i n g \boldsymbol g

w e h a v e

\boldsymbol g = (\begin{matrix} g_{1} (m, M, a_{1}, b_{1}) \\ g_{2} (m, M, a_{2}, b_{2}) \\ g_{3} (m, M, a_{3}, b_{3}) \\ g_{4} (m, M, a_{4}, b_{4}) \end{matrix}) .

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