Sum of Spacelike Vectors: Always Spacelike?

In summary, the conversation discusses the concept of spacelike vectors and whether the sum of any two spacelike vectors is also spacelike. The speaker initially believes this to be true, but upon further consideration, realizes that it is not always the case. They also mention a problem from a book on general relativity that addresses this topic. The speaker concludes that this is a trivial problem for a book on general relativity.
  • #1
ehrenfest
2,020
1

Homework Statement


Is it true that the sum of any two spacelike vectors is spacelike? I spent forever on this problem (5.4 from the link) and I think not...
http://books.google.com/books?id=xm...ts=aowTGAbHj6&sig=EIQ6_W2eCQmMnHVP0l6FH2dEehg

Actually, I think it is clearly not true if you think about the light-cone. But go to the link and tell me if there is something I am missing.

Homework Equations


The Attempt at a Solution

 
Last edited:
Physics news on Phys.org
  • #2
It is very true that the sum of two spacelike vectors is not necessarily spacelike. Like, (t,x)+(t,-x)=(2t,0) where (t,x) is spacelike. It's not clear to me what the author is thinking about.
 
  • #3
He must mean in the same direction. In any event it is a silly problem for a GR book.
 

What is the definition of "sum of two spacelike vectors"?

The sum of two spacelike vectors is a mathematical operation that combines two vectors in a specific way. It is used in the study of relativity and describes the combination of two vectors that are both oriented in space and have no time component.

How is the sum of two spacelike vectors calculated?

The sum of two spacelike vectors is calculated by adding the x, y, and z components of each vector separately. This results in a new vector with a magnitude that is the combined length of the two original vectors and a direction determined by the angles between them.

What is the significance of the sum of two spacelike vectors?

The sum of two spacelike vectors is significant in the study of relativity because it allows us to describe the combined motion of two objects in space. It also helps us understand the concept of relative velocity and how it changes when two objects are moving in different directions.

Can the sum of two spacelike vectors be greater than the speed of light?

No, the sum of two spacelike vectors cannot be greater than the speed of light. The speed of light is the maximum speed at which any object can travel in the universe, and it is a fundamental constant in physics that cannot be exceeded.

How is the sum of two spacelike vectors related to special relativity?

The sum of two spacelike vectors is related to special relativity as it is used to calculate the relative velocity between two objects in motion. This is a key concept in special relativity, which states that the laws of physics are the same for all observers in uniform motion.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
5
Views
2K
  • Other Physics Topics
Replies
21
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Calculus
Replies
3
Views
1K
  • Linear and Abstract Algebra
Replies
3
Views
2K
  • Calculus and Beyond Homework Help
Replies
4
Views
2K
  • Calculus and Beyond Homework Help
Replies
6
Views
2K
Replies
22
Views
5K
  • Advanced Physics Homework Help
Replies
4
Views
2K
  • Special and General Relativity
6
Replies
192
Views
15K
Back
Top