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Balancing Apples & Oranges
"We go through life on earth experiencing
a downward geometric-acceleration on each ounce of our being,
whose effects may be cancelled by an upward proper-acceleration
on the soles of our feet, if we wish to stand and not fall."
/Onana Namuh (1998)
Staying in Our Own Seat
"We go around curves experiencing
an outward geometric-acceleration on each ounce of our being,
whose effects may be cancelled by an inward proper-acceleration
from someone/thing nearby, if we wish to sit and not slide."
/Orcim Namuh (2001)
What's Young: A non-trivial set of web puzzlers to solve with these equations , a light-meme on the relation between circular and hyperbolic angles, and some map-based rules of motion, patterned after those of Newton but good at any speed. For more on this cf. physics/9704018. As to curved space-time on earth, here's how Newton-like gravity arises from one non-flat metric and it's derivatives. An any-speed primer is excerpted here.
What's Mature: We have MathCAD worksheets (snapshot of one here) on constant acceleration in two-clock and three-clock relativity, readable with MathSoft's free browser. These allow one to ``play with'' the equations discussed here in both uni-directional and 3D applications.
What's Ancient: An upgrade of physics/9611011 for teachers starting relativity with the metric equation, rather than with Lorentz transforms. It uses a ``synchrony-free'' speed with no limit, a way to add velocities fast, and a frame-invariant ``oriented-scalar'' form for Newton's 2nd law. The revision adds clearer language, discussion of classroom applications, and 3 tables.
Check out the browser-readable (and most up-to-date) version here . Share your thoughts here. A copy optimized for printing with Adobe's free Acrobat PDF reader is here. April APS/AAPT conference abstract.
Hot Lists: Our Accel-1D Solver won a National Academies Press ``coolest science site'' award in November 1996.
Soon: The high (over 30%) fixed "annual percentage rate" on fuel mass during 1 "gee" accelerations. These commentable tutorials below might provide some clues in this context...
Check out a Synopsis of the Science These pages contain resources to empower students familiar with only classical kinematics, in the solution of relativistic acceleration problems with variables defined in context of a single inertial frame. They include web-interactive solvers, a variety of examples and derivations, the self-contained Andromeda problem, and a list of yet unanswered questions. The key to these is a more careful operational definition of time (to bypass Newtonian misconceptions from square one), and use of the metric equation as a spacetime extension of Pythagoras' theorem with traveler-time the invariant. These naturally lead to use of multiple kinematics (time/velocity pairs) defined in terms of distances measured with respect to a single inertial reference frame. Such "non-coordinate" variables allow us to see things more simply, and in the process to find surprising uses for Newton's and Galileo's equations.
Something you might discover herein, for example, is that you can describe accelerated uni-directional motion at any speed by replacing "coordinate", by "proper", acceleration and velocity, and then using c2γ in place of ½v2 in the work-energy equation. In other words:
To list some current outside web-links that point in to the map-based relativity stuff at this site...
Other references from this site to the strategies described in this "one of many side-projects" include: