Magnitude of Vectors in Special Relativity

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Discussion Overview

The discussion centers on the magnitude of vectors, specifically velocities, in the context of special relativity. Participants explore whether the standard formula for vector magnitude applies in special relativity and how the constraints of the speed of light affect these calculations.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions whether the standard formula for vector magnitude, v=√(vx²+vy²+vz²), is applicable in special relativity, given that velocities cannot exceed the speed of light (c).
  • Another participant asserts that a velocity vector with components v=(.9,.9,.9) cannot exist, as its magnitude would exceed c.
  • A third participant introduces the concept of 4-dimensional vectors in special relativity, suggesting that all vectors should be treated in this higher-dimensional context to properly account for relativistic effects.
  • A later reply asks about the participants' prior knowledge of 4-vectors, indicating a potential shift towards discussing the properties and calculations related to these vectors.

Areas of Agreement / Disagreement

There is no consensus on the application of the standard magnitude formula in special relativity, as participants express differing views on the existence of certain velocity vectors and the necessity of 4-dimensional treatment.

Contextual Notes

Participants have not fully explored the implications of 4-vectors or provided detailed definitions, leaving some assumptions and mathematical steps unresolved.

MrBillyShears
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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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That vector could not be a velocity. Velocity is limited by v_x^2+v_y^2+v_z^2<1.
 
Ok, thanks I get it now.
 
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
 
How much about 4-vectors do you already know?
 

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