K4 Force and Acceleration in the STR
How are accelerations and forces transformed from one inertial frame to another? For example, the derivation of the transformations of the electric and magnetic field depends heavily on one already knowing how the forces transform; the Lorentz force law F = q • (E + v x B) should turn into
F' = q • (E' + v' x B').
From the definitions a = dv / dt and a' = dv' / dt', and the transformations of velocity and time we could deduce how accelerations transform in the STR. Since the relation F = dp / dt continues to apply and since we already know how to transform masses and velocities, we could also infer how momentum is transformed. Taking the derivative with respect to time we would obtain the transformation formulas for force.
A more elegant solution is provided by four-vectors (see also K9). This tool provides a higher yield with a smaller algebraic effort! However, one must beforehand be comfortable using these vectors. We give references for both paths:
Transformation of forces and accelerations without four-vectors:
- by Horst Melcher: [27-45f]
- by Jürgen Freund: [26-95ff]
Transformation of forces and accelerations with four-vectors:
- by Roman Sexl and Herbert Schmidt: [25-115ff]
- by Jürgen Freund: [26, Chapters 28 bis 33]