Magnitude of Vectors in Special Relativity

In summary, the conversation discusses the formula for finding the magnitude of a vector, specifically in the context of special relativity where velocities cannot exceed the speed of light. The formula for magnitude in SR is not different, but it is important to note that velocities in natural units cannot exceed 1. Additionally, the conversation mentions that all vectors in special relativity should be considered as 4-dimensional. The provided reference explains how to calculate the magnitude of a 4D vector.
  • #1
MrBillyShears
Gold Member
14
0
So for finding the magnitude of a vector, velocity for example, we use v=√(vx2+vy2+vz2), but in special relativity, velocities can not exceed c. Is their a different formula for magnitude in SR, or could a velocity like(in natural units) v=(.9,.9,.9) not exist, since the magnitude comes out to be about 1.5588c, which obviously exceeds c?
 
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  • #3
That vector could not be a velocity. Velocity is limited by v_x^2+v_y^2+v_z^2<1.
 
  • #4
Ok, thanks I get it now.
 
  • #5
In special relativity, all vectors should really be regarded as 4 dimensional. UltrafastPED's reference give the method for how to get the magnitude of a 4D vector.

Chet
 
  • #6
How much about 4-vectors do you already know?
 

FAQ: Magnitude of Vectors in Special Relativity

What is the magnitude of a vector in special relativity?

The magnitude of a vector in special relativity is a measure of its length or size in the context of spacetime. It takes into account both the spatial and temporal components of the vector, and is calculated using the Minkowski metric.

How is the magnitude of a vector affected by special relativity?

In special relativity, the magnitude of a vector can be affected by the relative motion of an observer. This is because special relativity states that the laws of physics should appear the same to all observers, regardless of their relative motion. As a result, the magnitude of a vector may appear differently to different observers depending on their relative velocity.

Can the magnitude of a vector in special relativity ever be negative?

No, the magnitude of a vector in special relativity is always a positive quantity. This is because the Minkowski metric, which is used to calculate the magnitude, only takes into account the squared values of the vector components, which will always be positive.

How is the magnitude of a vector related to the concept of spacetime interval?

The magnitude of a vector in special relativity is closely related to the concept of spacetime interval. The spacetime interval is a measure of the distance between two events in spacetime, and the magnitude of a vector can be used to calculate this distance. This is because the magnitude of a vector represents the shortest path between two points in spacetime, also known as a geodesic.

Can the magnitude of a vector in special relativity be greater than the speed of light?

No, the magnitude of a vector in special relativity cannot be greater than the speed of light. This is because the speed of light is considered to be the maximum speed at which anything can travel in the universe. The magnitude of a vector cannot exceed this speed, as it would violate the fundamental principles of special relativity.

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