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Welcome to our mobile-ready google-site about descriptions of motion from a traveler perspective, 

as complement to our Fun in One Dimension webpage here.

Traveler point dynamics uses parameters for time, velocity, and acceleration that are defined most simply [1] in dynamical terms using only one map or bookkeeper-frame, the traveler's clock, and an on-board accelerometer. It allows one to seamlessly extend Newton's 3-vector dynamics (with physical units) to application in gravitationally curved spacetimes (like that here on earth) and in accelerated frames at any speed. 

By way of background, special relativity (SR) traditionally describes motion in terms of two or more "inertial" frames, which (e.g. in order to keep their clocks synchronized internally) cannot be allowed to accelerate. SR's coordinate velocities have a hard upper limit, and don't add as 3-vectors. The 3-vector coordinate acceleration is even less useful at relativistic speeds.

General relativity (GR), on the other hand, can do most anything (including gravity and acceleration). However it requires use of 4-vectors and 4-tensors, and naturally measures time and distance (perhaps even mass) using a single common unit (like meters).  

With help from "minimally frame-variant" traveler-point variables [2], in this context metric-first "anyspeed-engineering" works simply (with ordinary units) in curved spacetimes and in accelerated frames. Following the metric equation, it uses only a single "bookkeeper" or map frame to define simultaneity. It also finds many uses for "synchrony-free" proper-velocities, which have no upper limit framed as momenta per unit mass i.e. p/m = γv = w ≡ dx/dτ, and can be locally added as three-vectors (with extra bookkeeping to account for frame-shift rotation when needed).

The metric-first approach further uncovers many uses for frame-invariant proper-time, as well as for proper-acceleration and proper-force three-vectors with frame-invariant magnitudes [3,4], some of which have already worked their way into introductory undergraduate texts. One caveat is that in curved-spacetimes like that on earth, coordinate-time (and simultaneity) might have to be rigorously defined by readings on non-local (e.g. "far-time") clocks because special relativity's "inertial" frames (with their flat-space yardsticks and synchronized clocks) may be hard to find.