Are 3-vectors Defined by Their Transformation Properties?

[Heirot]

Are the usual 3-vectors defined by their transformation properties wrt rotations or Galileian transformations? E.g. kinetic energy would be a scalar wrt rotations but not wrt Galileian transformations.

Thanks!

 

[dx]

Galilean tranformations are transformations of spacetime, not space. Vectors in space can be defined by their transformation properties wrt rotations and reflections. Free vectors which can start at any point can be defined wrt isometries of space, i.e. rotations + displacements.

 

[Heirot]

Oh, I see. Could it be possible to formulate nonrelativistic kinematics in terms of nonrelativistic 4-vectors? E.g. just put c->infinity in Lorentz transformations?

 

[dx]

Yes, the Lorentz transformations become Galilean transformations in the limit c → ∞.