`Version release date: 18 July 1996.`

## Cold ApplicationTest DeBrief

The revised draft of the
Andromeda Trip
provides a complete set of basic equations for solving relativistic
1D constant acceleration problems* from the vantage point of a
single inertial frame*. The only prerequisite for this initiative
is a familiarity with the "Galilean" constant acceleration equations
commonly introduced in the first few chapters of *all*
introductory physics texts.
The strategy is centered around the concept of a
proper velocity *w* = d*x*/d*τ*, defined as the
distance *x* traveled in our reference map frame per unit of
*traveler* time *τ* elapsed. It is convenient to
measure traveler-kinematic (proper) velocity in lightyears
per *traveler*-year. This unit for proper velocity has
been called a rodden-berry, as it is a "fundamental unit of hot rodding"
which allows folk to appreciate the capability of super-colliders
(e.g. a land speed record of 10^{5} [rb] results in
a head-on collision speed more like 10^{10} rb),
while reminding folks that relativity increases rather than
decreases the range of
human travel possible *as measured on the traveler's clock*. In contrast,
relativistic inertial coordinate velocity *v* is traditionally
measured in units of one lightyear per *coordinate*-year, or
*c*. There is **no** lightspeed limit on
proper velocity, even though it is a property of spacetime (not any
particular object's propagation) that coordinate velocity cannot
exceed *c*. The strategy also builds on Galileo's classical
equations for constant acceleration, which continue to work
for "Galilean variables" *V* and *T* when extended into
the relativistic regime by requiring that kinetic energy
remain *K* = 0.5 *mV*^2. The caveat is that at high
speeds supplementary
equations are needed to predict the behavior of
*physical clocks*, while Galilean time *T* becomes
simply a mathematical parameter for keeping track of events.

By measuring all distances in context of a single inertial reference frame,
the concepts of Lorentz transform, length contraction, and
frame-dependent simultaneity do not arise until after readers have a
quantitative familiarity with the concepts of differential aging
and relativistic acceleration. Another benefit of this strategy
is our ability to use
x-tv diagrams
for plotting the value of everyone's time and velocity variables
as a function of object position on a single graph, as illustrated
in the twin adventure plot here. *Note*: Assuming that
acceleration *a*_{o} is approximately 1 "gee" on
this plot, then distances are in [lightyears], times are in [years],
and velocities are in [lightyears per year].

## More Problems

Try the *Andromeda* Problem challenge for a trip of 4 lightyears
to the nearest star, *alpha*-*Centauri*, instead of 2 million
lightyears to the nearest galaxy. Since the exponential
"*e*-multiplying time *c*/*a*" is about a year,
for distance-traveled with 1 gee acceleration, the effects may not be
as large as they are for the longer journey.
## Solutions

**Hint:** If you could keep that 1 gee acceleration going for
*much less than a human lifetime* on the proposed trip, you
would find yourself 2 million lightyears away *and 2 million years
in the future*! If you want to see a full numerical solution
to the Andromeda problem, check
here.

Send comments, your answers to problems posed, and/or complaints,
to philf@newton.umsl.edu.
This page contains original material, so if you choose to echo
in your work, in print, or on the web, a citation would be cool.
` (Thanks. /philf :)`