Vectors and the Speed of Light?

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Discussion Overview

The discussion revolves around the concept of whether the speed of light can be exceeded when considering vector addition of velocities. Participants explore the implications of the Lorentz Transformation and relativistic velocity addition in different directional contexts.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions if traveling at 3/4 the speed of light North and then 3/4 the speed of light East results in exceeding the speed of light at a 45-degree angle.
  • Another participant presents a scenario involving traveling at 1 m/s North and then 1 m/s East, asking whether the resultant speed is 1 m/s or 1.414 m/s.
  • A participant asserts that the speed of light cannot be broken using vectors, referencing the relativistic velocity addition formula that applies only to collinear velocities.
  • Another participant reiterates that the speed of light is invariant for all observers across different frames of reference.

Areas of Agreement / Disagreement

Participants express differing views on the implications of vector addition on the speed of light, with no consensus reached on the scenarios presented.

Contextual Notes

The discussion includes assumptions about the applicability of the Lorentz Transformation and the conditions under which the velocity addition formula is valid, which remain unresolved.

ryuunoseika
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Can the speed of light be broken using vectors? Why not? Where does the Lorentz Transformation come into play?

E.g. I accelerate to 3/4 the speed of light North and then to 3/4 the speed of light East. Am I traveling faster than the speed of light at 45 degrees North-East?
 
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If you travel 1 m/s for 1 hour to the north and the 1 m/s for 1 hour to the east, how fast did you travel? 1 m/s or 1.414 m/s?
 
ryuunoseika said:
Can the speed of light be broken using vectors?

No.

The usual relativistic "velocity addition" formula applies only when the velocities are along the same line.

For adding velocities that are at an angle with each other, see for example the section The velocity addition formula for non-parallel velocities on this page.
 
Can the speed of light be broken using vectors? Why not?

the speed of light is fixed for all obsevers. for all frames of reference.
 

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