"Examining Mathematical Approaches"

I have received communications from a mathematician who
asserted that my statements about the validity of non-Euclidean Geometry
were
erroneous. He apparently objected to the assertion that the definition of a
straight line was faulty for all geometries and that any non-Euclidean
Geometry
of N dimensions could be contained in a Euclidean geometry of N+1
dimensions.
(The latter objection might be considered important because it implies that
GR
has a responsibility to describe the Euclidean geometry of 4 spatial
dimensions
implied by its assertion that our space of three dimensions is curved. The
failure to include a description of such a space does General Relativists
little
credit.)

One of the arguments presented is that the geometry
represented by a circle, a mobius strip or a klein bottle cannot be embedded
in
a three dimensional Euclidean geometry but can only described isometrically.
If
I were to take his arguments literally I, as someone who IS embedded in a
three
dimensional Euclidean space, could not draw a circle on a piece of paper,
and
could not construct a klein bottle or a mobius strip! Obviously I, and
anyone
else, can do so. It is apparent then that the correspondent's mathematical
approach is faulty. What he should be doing is making sure that his
mathematics
is sufficient to do the job before asserting that someone else's
understanding
is deficient.

To illustrate the second conclusion, that the true definition
of a straight line for any geometry is the shortest distance between two
points
WHICH REMAINS WITHIN THE GEOMETRY, consider the distance between New York
and
Los Angeles. In the two dimensional geometry which represents the surface of
the
Earth, the shortest distance is along a great circle. It will be noted that
this
meets the revised definition of the straight line for that geometry. In
terms of
the three dimensional geometry represented by the Earth as a whole, the
definition also is valid. The shortest distance which remains within the
three
dimensional geometry is though a tunnel which passes about 200 miles below
the
Mississippi River. The revised definition works for all geometries.

It is asserted that the force which we sense as gravity
results from the geometry of space. If one would take the trouble to examine
this conclusion he would recognize that there is no way that this would
occur.
Imagine a perfectly smooth spherical planet sufficiently isolated so that
external gravitational effects could be ignored. On this planet are scribed
two
great circles at right angle to each other. At the intersection of the two
lines
rests a perfectly smooth steel ball and along the first line, perhaps 30
degrees
away, rests an identical ball. To simplify the argument let us consider that
the
balls can roll over the planet's surface with zero friction. If the balls
are
started rolling in a direction at right angles to the first line, they will
follow great circle paths and will approach each other. A GR geometer would
assert that, due to the curved space represented by the two dimensional
geometry, the balls experienced a force which would cause them to approach
each
other since they followed a curved path. There is a difficulty with this
idea
however. The balls could be stopped anywhere along the path and they would
remain where they were showing that an attractive force between them did not
exist! The force that caused them to approach each other is a vector
component
of the force of gravity which is at all times normal to the surface and
therefore cannot be sensed in the two dimensional geometry of the surface.
To
make the statement more forcefully, THERE IS NO WAY IN @#$% THAT GEOMETRY
CAN
PRODUCE THE FORCE OF GRAVITY!

The source material for this posting may be found in
http://einsteinhoax/hoax.htm ("The Einstein Hoax" {1997});
http://einsteinhoax/gravity.htm; ("Gravity" {1987}); and
http://einsteinhoax/relcor.htm ("Corrections to Special Relativity" {1997}).
EVERYTHING WHICH WE ACCEPT AS TRUE MUST BE CONSISTENT WITH EVERYTHING ELSE
WE HAVE ACCEPTED AS TRUE, IT MUST BE CONSISTENT WITH ALL OBSERVATIONS, AND
IT MUST BE MATHEMATICALLY VIABLE. PRESENT TEACHINGS DO NOT ALWAYS MEET THIS
REQUIREMENT. THE WORLD IS ENTITLED TO A HIGHER STANDARD OF WORKMANSHIP FROM
THOSE IT HAS GRANTED WORLD CLASS STATUS.

All of the Newsposts made by this site may be viewed at
http://einsteinhoax.com/postinglog.htm .

Please make any response via E-mail as Newsgroups are not
monitored on a regular basis. Objective responses will be treated with the
same
courtesy as they are presented. To prevent the wastage of time on both of
our
parts, please do not raise objections that are not related to material that
you
have read at the Website. This posting is merely a summary.

E-mail:-

The material at the Website has been posted continuously for
over 5 years. In that time THERE HAVE BEEN NO OBJECTIVE REBUTTALS OF ANY OF
THE
MATERIAL PRESENTED. There have only been hand waving arguments by
individuals
who have mindlessly accepted the prevailing wisdom without questioning it.
If
anyone provides a significant rebuttal that cannot be objectively answered,
the
material at the Website will be withdrawn. Challenges to date have revealed
only
the responder's inadequacy with one exception for which a correction was
provided.

Sknil wrote:
"Examining Mathematical Approaches"


Thanks for registering "The Einstein Hoax" at crank dot net.
http://www.google.com/search?q=einst...Awww.crank.net

Sknil wrote:

"Examining Mathematical Approaches"
[snip ignorant crap]

http://www.freefarts.com/farts.html
Move cursor over blinkers to hear Retic's lecture.

Psychotic ineducable boring spammer retic (Ernest Wittke),

You see yourself this way,
http://www.mazepath.com/uncleal/effete6.jpg
The entire remainder of the planet sees you this way,
http://www.mazepath.com/uncleal/effete3.png

http://www.edu-observatory.org/cranks.html
http://www.pagetutor.com/idiot/idiot.html

http://www.mazepath.com/uncleal/sunshine.jpg
http://www.albinoblacksheep.com/flash/youare.swf
http://www.****inggoogleit.com/
http://www.meninhats.com/d/20040430.html
http://www.you-moron.com/
http://groups.google.com/groups?q=gr...uthor%3Awittke

http://www.apa.org/journals/psp/psp7761121.html
http://insti.physics.sunysb.edu/~siegel/quack.html
http://www.firehead.org/~jessh/film/kubrick/Kubrick-Psycho.html
http://www.naturalchild.com/elliott_barker/prisons.html

The source material for this posting may be found in "Gravity" (1987),
"The Einstein Hoax" (1997), and "Corrections to Residual Errors in Special
Relativity (1999)
[snip]

Hey, stooopid spammer Ernest Wittke - Do you want EVIDENCE? Each of
the 24 GPS satellites carries either four cesium atomic clocks or
three rubidum atomic clocks in orbit, with full relativistic
corrections being applied. NAVSTAR Block II GPS satellites (currently
being launched as replacements) have two rubidium and two cesium
atomic clocks.

Internal inconsistencies in SR (meaning inconsistencies of a purely
mathematical logical nature) automatically lead to contradictions in
number theory, itself, and arithmetic, since the mathematics of
Minkowski geometry is equiconsistent with the theory of real numbers
and with arithmetic.

http://optoelectronics.perkinelmer.com/content/Datasheets/rfs2f.pdf

http://math.ucr.edu/home/baez/RelWWW/tests.html
Mathematics of gravitation
http://wugrav.wustl.edu/people/CMW/update98.pdf
http://www.astro.northwestern.edu/AspenW04/Papers/lorimer1.pdf
http://www.vallis.org/publications/tesidott.pdf
Equivalence Principle testing
http://arXiv.org/abs/hep-th/0111236
Geometric structure of reality
http://arxiv.org/abs/gr-qc/0103044
http://arXiv.org/abs/hep-th/0307140
GR structure, especially Part 4/p. 7
http://relativity.livingreviews.org/Articles/lrr-2001-4/index.html
http://arXiv.org/abs/gr-qc/0311039
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/experiments.html
Experimental constraints on General Relativity
http://tycho.usno.navy.mil/ptti/ptti2002/paper20.pdf
Nature 425 374 (2003)
http://www.eftaylor.com/pub/projecta.pdf
http://www.public.asu.edu/~rjjacob/Lecture16.pdf
http://relativity.livingreviews.org/Articles/lrr-2003-1/index.html
Relativity in the GPS system
http://arXiv.org/abs/gr-qc/9909014
Amer. J. Phys. 71 770 (2003)
Phys. Rev. Lett. 92 121101 (2004)
falling light
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html
http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
http://www.hawaii.edu/suremath/SRtwinParadox.html
http://physics.syr.edu/courses/modules/LIGHTCONE/twins.html
Twin Paradox
Science 303(5661) 1143;1153 (2004)
http://arXiv.org/abs/astro-ph/0401086
http://arxiv.org/abs/astro-ph/0312071
http://relativity.livingreviews.org/Articles/lrr-2003-5/index.html
http://skyandtelescope.com/news/article_1473_1.asp
Deeply relativistic neutron star binaries
http://arxiv.org/abs/hep-th/0405160
Black hole evaporation
Physics Today 57(7) 40 (2004)
http://physicstoday.org/vol-57/iss-7/p40.shtml
No aether
http://fsweb.berry.edu/academic/mans/clane/
http://physicsweb.org/articles/world/17/3/7
No Lorentz violation
http://arXiv.org/abs/gr-qc/0409089
Spin-2 gravitons have problems
http://groups-beta.google.com/group/sci.physics.strings/msg/ba31a00f5f26277a
(so does the proposal)
http://arxiv.org/abs/gr-qc/0507083
http://arXiv.org/abs/gr-qc/0411113
http://www.npl.washington.edu/eotwash/pdf/prl83-3585.pdf
http://arXiv.org/abs/gr-qc/0301024
Phys. Rev. Lett. 93 261101 (2004)
Nordtvedt Effect
http://map.gsfc.nasa.gov/
http://arxiv.org/abs/astro-ph/0403292
http://arXiv.org/abs/astro-ph/0310723
WMAP + Sloane Digital Sky Survey
http://arxiv.org/abs/hep-ph/0404175
Dark matter candidates
http://nedwww.ipac.caltech.edu/level5/March01/Carroll/frames.html
Carroll on what it all means.

Special Relativity is physics on a topologically trivial Lorentzian
manifold with a metric whose curvature tensor is zero. This is a
perfectly diffeomorphism-invariant condition and does not require
any particular coordinate choice. It is invariant under
the full group of diffeomorphisms. The Poincare group is
the group of *isometries* of the metric in special relativity.

The Special Relativity metric is *non-dynamical* (unlike GR). It
defines the coupling *constants* of your theory. If you change the
metric in any nontrivial way you are changing your theory. An
operation can only be called a "symmetry" of a special-relativistic
(non-gravitational) theory if it preserves the metric, and therefore
the symmetry of special-relativistic theories is the Poincare group
only. General Relativity (gravitation) has a dynamic metric.

NIM A 355 537 (1995)
Physics Letters B 328 103 (1994)
Physical Review Letters 64 1697 (1990)
Physical Review Letters 39 1051 (1977)
Physical Review 135 B1071 (1964)
Physics Letters 12 260 (1964)
Europhysics Letters 56(2) 170-174 (2001)
General Relativity and Gravitation 34(9) 1371 (2002)

http://fourmilab.to/etexts/einstein/specrel/specrel.pdf
http://www.geocities.com/physics_world/sr/ae_1905_error.htm
http://www.physics.gatech.edu/people/faculty/finkelstein/relativity.pdf
Longitudinal and transverse mass
Physics Today 58(3) 34 (2005)
Time passage, equator vs. poles

http://arxiv.org/abs/gr-qc/0306076
http://www.metaresearch.org/solar%20system/gps/absolute-gps-1meter-3.ASP
http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf
http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm
http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm
http://www.trimble.com/gps/index.html
http://sirius.chinalake.navy.mil/satpred/
http://www.phys.lsu.edu/mog/mog9/node9.html
http://egtphysics.net/GPS/RelGPS.htm
http://www.schriever.af.mil/gps/Current/current.oa1
http://edu-observatory.org/gps/gps_books.html
http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

If anyone
provides a significant rebuttal that cannot be objectively answered, the
material at the Website will be withdrawn.

Right, like your head has ever been withdrawn from your ass - even
when you ****.


--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf