243 research outputs found
A one-map two-clock approach to teaching relativity in introductory physics
This paper presents some ideas which might assist teachers incorporating
special relativity into an introductory physics curriculum. One can define the
proper-time/velocity pair, as well as the coordinate-time/velocity pair, of a
traveler using only distances measured with respect to a single ``map'' frame.
When this is done, the relativistic equations for momentum, energy, constant
acceleration, and force take on forms strikingly similar to their Newtonian
counterparts. Thus high-school and college students not ready for Lorentz
transforms may solve relativistic versions of any single-frame Newtonian
problems they have mastered. We further show that multi-frame calculations
(like the velocity-addition rule) acquire simplicity and/or utility not found
using coordinate-velocity alone.Comment: 10 pages (1 fig, 3 tables) RevTeX; classroom-focus improved; also
http://www.umsl.edu/~fraundor/a1toc.htm
Three Self-Consistent Kinematics in (1+1)D Special Relativity
When introducing special relativity, an elegant connection to familiar rules
governing Galilean constant acceleration can be made, by describing first the
discovery at high speeds that the clocks (as well as odometers) of different
travelers may proceed at different rates. One may then show how to parameterize
any given interval of constant acceleration with {\em either}: Newtonian
(low-velocity approximation) time, inertial relativistic (unaccelerated
observer) time, or traveler proper (accelerated observer) time, by defining
separate velocities for each of these three kinematics as well. Kinematic
invariance remains intact for proper acceleration since . This
approach allows students to solve relativistic constant acceleration problems
{\em with the Newtonian equations}! It also points up the self-contained and
special nature of the accelerated-observer kinematic, with its frame-invariant
time, 4-vector velocities which in traveler terms exceed Newtonian values and
the speed of light, and of course relativistic momentum conservation.Comment: RevTeX, 3 tables and 1 figure available from the author and in prep
for a replacement preprint; also http://newton.umsl.edu/~run
Friendly units for coldness
Measures of temperature that center around human experience get lots of use.
Of course thermal physics insights of the last century have shown that
reciprocal temperature (1/kT) has applications that temperature addresses less
well. In addition to taking on negative absolute values under population
inversion (e.g. of magnetic spins), bits and bytes turn 1/kT into an informatic
measure of the thermal ambient for developing correlations within any complex
system. We show here that, in the human-friendly units of bytes and food
Calories, water freezes when 1/kT ~200 ZB/Cal or kT ~5 Cal/YB. Casting familiar
benchmarks into these terms shows that habitable human space requires coldness
values (part of the time, at least) between 0 and 40 ZB/Cal with respect body
temperature ~100 degrees F, a range in kT of ~1 Cal/YB. Insight into these
physical quantities underlying thermal equilibration may prove useful for
budding scientists, as well as the general public, in years ahead.Comment: 3 pages, 2 figures, 21 refs, RevTeX4 cf.
http://www.umsl.edu/~fraundor/ifzx/zbpercal.htm
Heterogeneity, and the secret of the sea
This paper explores tools for modeling and measuring the compositional
heterogeneity of a rock, or other solid specimen. Intuitive ``variation per
decade'' plots, simple expressions for containment probability, generalization
for familiar error-in-the-mean expressions, and a useful dimensionless sample
bias coefficient all emerge from the analysis. These calculations have also
inspired subsequent work on log-log roughness spectroscopy (with applications
to scanning probe microscope data), and on angular correlation mapping of
lattice fringe images (with applications in high resolution transmission
electron microscopy). It was originally published as Appendix E of a
dissertation on ``Microcharacterization of interplanetary dust collected in the
earth's stratosphere''.Comment: 9 pages (3 figs, 14 refs) RevTeX, comments
http://www.umsl.edu/~fraundor/covariances.htm
Modernizing Newton, to work at any speed
Modification of three ideas underlying Newton's original world view, with
only minor changes in context, might offer two advantages to introductory
physics students. First, the students will experience less cognitive dissonance
when they encounter relativistic effects. Secondly, the map-based Newtonian
tools that they spend so much time learning about can be extended to high
speeds, non-inertial frames, and even (locally, of course) to curved-spacetime.Comment: 7 pages (0 figs, 27 refs) RevTeX4; for more see
http://www.umsl.edu/~fraundor/a1toc.htm
Localizing periodicity in near-field images
We show that Bayesian inference, like that used in statistical mechanics, can
guide the systematic construction of Fourier dark-field methods for localizing
periodicity in near-field (e.g. scanning-tunneling and electron-phase-contrast)
images. For crystals in an aperiodic field, the Fourier coefficient Ze^{i phi}
combines with a prior estimate for background amplitude B to predict background
phase (beta) values distributed with a probability p(beta - phi | Z,phi,B)
inversely proportional to the amplitude P of the signal of interest, when this
latter is treated as an unknown translation scaled to B.Comment: 5 pages (4 figs, 13 refs) RevTeX; apps
http://newton.umsl.edu/stei_la
Some minimally-variant map-based rules of motion at any speed
We take J. S. Bell's commendation of ``frame-dependent'' perspectives to the
limit here, and consider motion on a ``map'' of landmarks and clocks fixed with
respect to a single arbitrary inertial-reference frame. The metric equation
connects a traveler-time with map-times, yielding simple integrals of constant
proper-acceleration over space (energy), traveler-time (felt impulse), map-time
(momentum), and time on the clocks of a chase-plane determined to see Galileo's
original equations apply at high speed. Rules follow for applying frame-variant
and proper forces in context of one frame. Their usefulness in curved
spacetimes via the equivalence principle is maximized by using synchrony-free
and/or frame-invariant forms for length, time, velocity, and acceleration. In
context of any single system of locally inertial frames, the metric equation
thus lets us express electric and magnetic effects with a single
frame-invariant but velocity-dependent force, and to contrast such forces with
gravity as well.Comment: 9 pages (1 table, 1 fig, 17 refs/context updated) RevTeX, cf.
http://www.umsl.edu/~fraundor/a1toc.htm
Non-coordinate time/velocity pairs in special relativity
Motions with respect to one inertial (or ``map'') frame are often described
in terms of the coordinate time/velocity pair (or ``kinematic'') of the map
frame itself. Since not all observers experience time in the same way, other
time/velocity pairs describe map-frame trajectories as well. Such coexisting
kinematics provide alternate variables to describe acceleration. We outline a
general strategy to examine these. For example, Galileo's acceleration
equations describe unidirectional relativistic motion {\it exactly} if one uses
, where is map-frame position and is clock time in a
chase plane moving such that . Velocity in the traveler's kinematic, on the other hand, has dynamical
and transformational properties which were lost by coordinate-velocity in the
transition to Minkowski space-time. Its repeated appearance with coordinate
time, when expressing relationships in simplest form, suggests complementarity
between traveler and coordinate kinematic views.Comment: RevTeX, full (3+1)D treatment w/5 tables, 1bw and 1greyscale figure.
Mat'l on 1D origins at http://www.umsl.edu/~fraundor/a1toc.htm
Teaching Newton with anticipation(...)
Care making only clock-specific assertions about elapsed-time, and other
``space-time smart'' strategies from the perspective of a selected inertial
map-frame, open doors to an understanding of anyspeed motion via application of
the metric equation.Comment: 2 pages (6 figs, 6 refs) RevTeX for broadened readership;
http://www.umsl.edu/~fraundor/a1toc.htm
The thermal roots of correlation-based complexity
Bayesian maxent lets one integrate thermal physics and information theory
points of view in the quantitative study of complex systems. Since net
surprisal (a free energy analog for measuring "departures from expected")
allows one to place second law constraints on mutual information (a
multi-moment measure of correlations), it makes a quantitative case for the
role of reversible thermalization in the natural history of invention, and
suggests multiscale strategies to monitor standing crop as well. It prompts one
to track evolved complexity starting from live astrophysically-observed
processes, rather than only from evidence of past events. Various gradients and
boundaries that play a role in availability flow, ranging from the edge of a
wave-packet to the boundary between idea-pools, allow one to frame wide-ranging
correlations (including that between a phenomenon and its explanation) as
delocalized {\em physical} structures.Comment: 8 pages, 3 figures, 43 reference
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