• Support PF! Buy your school textbooks, materials and every day products Here!

Why a timelike vector and a null vector cannot be orthogonal?

  • Thread starter crit
  • Start date
  • #1
3
0
Why a timelike vector and a null vector cannot be orthogonal?
Isn't a null vector orthogonal to any vector, by definition? Anyway, each component of a vector is multiplied by zero, so in the end the sum is zero.
 

Answers and Replies

  • #2
dextercioby
Science Advisor
Homework Helper
Insights Author
12,988
543
Null 4-vector:
[tex] n^{\mu};n^{2}=:n^{\mu}n_{\mu}=0 [/tex] (1)

Timelike 4-vector:
[tex] l^{\mu};l^{2}=:l^{\mu}l_{\mu}<0 [/tex] (2)

Prove that
[tex] l^{\mu}n_{\mu} \neq 0 [/tex](3)

HINT:Use components and the property of the 'cosine' function.


Daniel.

P.S.Esti varza... :yuck:
 
  • #3
dextercioby
Science Advisor
Homework Helper
Insights Author
12,988
543
HINT:'cosine' appears in the expression of the scalar product between those vectors (space components).Pay attention with the metric...

Daniel.
 

Related Threads on Why a timelike vector and a null vector cannot be orthogonal?

  • Last Post
Replies
5
Views
9K
Replies
46
Views
12K
Replies
5
Views
2K
  • Last Post
Replies
7
Views
48K
Replies
7
Views
5K
  • Last Post
Replies
2
Views
23K
Replies
2
Views
1K
Replies
4
Views
184
Replies
17
Views
7K
Replies
2
Views
1K
Top