Proper-kinematics and f ≤ mα from the metric
نویسنده
چکیده
(Dated: February 24, 2010) Proper acceleration and proper velocity are relativity-smart concepts that, along with propertime, can (i) inject conceptual-clarity into low-speed intro-physics applications and (ii) inoculate students against cognitive-dissonance when special and general relativistic applications are discussed. By calling the attention of introductory students to clock and free-float-frame perspectives from the start, the use of geometric (non-proper) forces in accelerated frames becomes intuitive. Moreover, taking derivatives of event-coordinates with respect to proper-time τ via Minkowski’s flat-space version of Pythagoras theorem yields 3-vectors for both propervelocity ~ w = d~x/τ and proper-acceleration ~ α that at any speed retain characteristics of their low-speed analogs. Dynamical quantities emerge on multiplying these derivatives by rest-mass m, which show that the scalar f ≡ dp/dt is less than or equal to mα with equality in the unidirectional case, long before students are tasked with application of Lorentz transforms and Reimann geometry.
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