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- W2588793755 abstract "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." @default.
- W2588793755 created "2017-02-24" @default.
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- W2588793755 date "2016-09-16" @default.
- W2588793755 modified "2023-09-27" @default.
- W2588793755 title "The proper-force 3-vector" @default.
- W2588793755 hasPublicationYear "2016" @default.
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