| Topic: |
Science > Physics |
| User: |
"Lenaczq" |
| Date: |
11 Aug 2004 08:59:33 AM |
| Object: |
"Examining Mathematical Approaches" |
"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 "Gravity" (1987),
"The
Einstein Hoax" (1997), and "Corrections to Residual Errors in Special
Relativity
(1999) located at http://www.members.aol.com/einsteinhoax/site.htm. 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 Newsposts by this Website are available at
http://www.members.aol.com/postinglog/newspostings.com
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.
.
|
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| User: "Sam Wormley" |
|
| Title: Re: "Examining Mathematical Approaches" |
11 Aug 2004 09:30:08 AM |
|
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Lenaczq wrote:
"Examining Mathematical Approaches"
Observational and Experimental Evidence Bearing on General Relativity
http://math.ucr.edu/home/baez/RelWWW/tests.html
General Relativity Tutorial
John Baez
http://math.ucr.edu/home/baez/gr/gr.html
Relativity on the World Wide Web
http://math.ucr.edu/home/baez/relativity.html
General Relativity and Cosmology FAQs
http://math.ucr.edu/home/baez/physics/
Developments in General Relativity: Black Hole Singularity and Beyond
http://arxiv.org/abs/gr-qc/0304052
Improved Test of General Relativity with Radio Doppler Data from the Cassini Spacecraft
http://arxiv.org/abs/gr-qc/0308010
What is the experimental basis of Special Relativity?
http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html
Physics is an experimental science, and as such the experimental basis for
any physical theory is extremely important. The relationship between
theory and experiments in modern science is a multi-edged sword:
1.It is required that the theory not be refuted by any experiment within
the theory's domain of applicability.
2.It is expected that the theory be confirmed by a number of
experiments which cover a significant fraction of the theory's
domain of applicability.
3.It is expected that the theory be confirmed by a number of
experiments which examine a significant fraction of the theory's
predictions.
Special Relativity (SR) meets all of these requirements and expectations.
There are literally hundreds of experiments which have tested SR, with
an enormous range and diversity, and the agreement between theory and
experiment is excellent. There is a lot of redundancy in these experimental
tests. There are also a lot of indirect tests of SR which are not included
here. This list of experiments is by no means complete!
Other than their sheer numbers, the most striking thing about these
experimental tests of SR is their remarkable breadth and diversity. An
important aspect of SR is its universality - it applies to all known physical
phenomena and not just to the electromagnetic phenomena it was
originally invented to explain. In these experiments you will find tests
using electromagnetic and nuclear measurements (including both strong
and weak interactions); gravitational tests are the province of General
Relativity, and are not considered here, see Experimental Tests of GR.
There are several useful surveys of the experimental basis of SR:
Y.Z.Zhang, Special Relativity and its Experimental Foundations,
World Scientific (1997).
G.Holton, "Resource Letter SRT-1 on Special Relativity Theory",
Am. J. Phys., 30 (1962), p462.
D.I.Blotkhintsev, "Basis for Special Relativity Theory Provided by
Experiments in High Energy Physics", Sov. Phys. Uspekhi, 9 (1966),
p405.
Newman et al. Phys. Rev. Lett. 40 no. 21 (1978), p1355.
Zhang's book is especially comprehensive.
Textbooks which have good summaries of the experimental basis of
relativity are:
M.Born, Einstein's theory of Relativity.
Bergmann, Introduction to the Theory of Relativity.
Moller, The Theory of Relativity.
M. von Laue, Die relativitätstheorie (in German).
Crank Information
http://groups.google.com/groups?q=group%3Asci.physics+author%3AGRAVITYMECHANIC
http://groups.google.com/groups?q=group%3Asci.physics+author%3AGRAVITYMECHANIC2
http://www.google.com/search?q=einstein+hoax+site%3Awww.crank.net
http://groups.google.com/groups?q=group%3Asci.physics+author%3Aretic
http://groups.google.com/groups?q=group%3Asci.physics+author%3Aretiche
http://groups.google.com/groups?q=group%3Asci.physics+author%3Areticher
http://groups.google.com/groups?q=group%3Asci.physics+author%3Areticher1
http://groups.google.com/groups?q=group%3Asci.physics+author%3Awittke
.
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| User: "Uncle Al" |
|
| Title: Re: "Examining Mathematical Approaches" |
11 Aug 2004 11:29:03 AM |
|
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Lenaczq wrote:
"Examining Mathematical Approaches"
I have received communications from a mathematician who asserted that my
statements about the validity of non-Euclidean Geometry were erroneous.
[snip 100 lines of ignorant crap]
A high school kid could tell you that - and be entirely corect.
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://b5.sdvc.uwyo.edu/bab5/snds/argcstpd.wav
<http://www.albinoblacksheep.com/flash/youare.swf>
http://www.mazepath.com/uncleal/sunshine.jpg
http://www.you-moron.com/
http://groups.google.com/groups?q=group%3Asci.physics+author%3Awittke
http://www.mazepath.com/uncleal/effete0.jpg
http://www.mazepath.com/uncleal/effete1.png
http://www.mazepath.com/uncleal/effete2.png
http://www.mazepath.com/uncleal/effete3.png
http://www.mazepath.com/uncleal/effete4.png
http://www.mazepath.com/uncleal/effete5.jpg
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.
<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>
Equivalence Principle testing
http://arXiv.org/abs/hep-th/0111236
Geometric structure of reality
http://arXiv.org/abs/hep-th/0307140
GR structure, especially Part 4/p. 7
<http://rattler.cameron.edu/EMIS/journals/LRG/Articles/Volume4/2001-4will/index.html>
http://arXiv.org/abs/gr-qc/0311039
<http://www.weburbia.demon.co.uk/physics/experiments.html>
Experimental constraints on General Relativity
<http://tycho.usno.navy.mil/ptti/ptti2002/paper20.pdf>
Nature 425 374 (2003)
<http://rattler.cameron.edu/EMIS/journals/LRG/Articles/Volume6/2003-1ashby/index.html>
http://www.eftaylor.com/pub/projecta.pdf
<http://www.public.asu.edu/~rjjacob/Lecture16.pdf>
Relativity in the GPS system
http://arXiv.org/abs/gr-qc/9909014
Phys. Rev. Lett. 92 (2004) 121101
falling light
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
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
Deeply relativistic neutron star binaries
http://arxiv.org/abs/hep-th/0405160
Black hole evaporation
Physics Today 57(7) 40 (2004)
No aether
<http://www.npl.washington.edu/eotwash/pdf/prl83-3585.pdf>
http://arXiv.org/abs/gr-qc/0301024
Nordtvedt Effect
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
http://arxiv.org/abs/gr-qc/0306076.pdf
<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 ***** -
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
.
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