The proper-force 3-vector

P Fraundorf (1)

1 University of Missouri [St. Louis]

The distinction between proper (i.e. cell-phone detectable) and geometric (i.e. connection-coefficient) forces allows one to use Newton's 3-vector laws in accelerated frames and curved spacetime. Here we show how this is assisted by use of quantities that are either (i) frame-invariant or (ii) synchrony-free i.e. do not rely on extended-networks of synchronized-clocks. The acceleration four-vector's invariant magnitude, and quantities that build on the metric-equation's book-keeper frame to define simultaneity, point the way to more robust student understanding at {\em both} low and high speeds. In the process, we gain a simple (3+1)D flat-space work-energy theorem using the proper-acceleration 3-vector α (net proper-force per unit mass), whose integrals of the motion simplify with a hyperbolic velocity angle (rapidity) written as 2/(γo + 1)ατ /c, where c is lightspeed and τ is traveler-time from " turnaround " when the Lorentz-factor is γo.

Mots clés: proper-velocity; proper-force; proper-acceleration

Domaines: Physique [physics]

P Fraundorf. The proper-force 3-vector. 2016. ⟨hal-01344268v2⟩