Preprint
A one-map two-clock approach to teaching relativity in introductory physics
This paper presents some ideas which might assist teachers incorporating relativity insights into intro physics, with help from proper time & velocity.
What is it about?
By choosing so-called "proper" variables for time, speed and acceleration that are local to one traveler, Newton's laws can be shown to be useful at any speed, in accelerated frames, and in curved spacetimes. Introphysics "laws" can then be introduced as approximations, one topic section at a time, to rules that work at any speed, and explain effects like differential aging from head to toe, and the invisibility of gravity to your cell-phone's accelerometer.
Why is it important?
Metric-first instead of Lorentz-first approaches to motion open the door to application of Newton-like 3-vector laws to motion at any speed, as well as in accelerated frames and curved spacetimes, via focus on use of synchrony-free and where possible frame-invariant variables defined in terms of the traveler point of view. For introductory physics, this lets one introduce time as a local variable, and Newton's laws as robust approximations that work at low speed and in unaccelerated frames. It also provides students with the ability to distinguish proper and geometric (connection-coefficient) "forces" in everyday life.
Perspectives
Starting with Minkowski's space-time version of Pythagoras' theorem, and the idea that time's passage is local to each clock, allows one to introduce Newton's laws as an approximation from the traveler's perspective that works to explain geometric forces (like gravity and centrifugal) which are connected to differential aging, and to model high speed motion without the need for multiple frames with synchronized clocks. It's about time that we provide clues to these connections at the outset of intro-physics courses, which of course reach a much larger audience than do later courses for physics majors mostly.
