| Topic: |
Science > Physics |
| User: |
"Enon" |
| Date: |
27 Apr 2005 08:40:48 AM |
| Object: |
The Right Angle Lever Paradox |
The Right Angle Lever Paradox
"Great spirits have always encountered violent oppositions from mediocre
minds." - A. Einstein
The "Right Angle Lever Paradox" is a classic construct which is taught
in most courses in Special Relativity. As with all paradoxes, it reveals
that and error has been made in our thinking. It may be interesting then to
examine this paradox and the means that is conventionally used for its
resolution.
The Right Angle Lever paradox reveals itself when we consider a right
angle lever with forces applied to the ends in two different velocity
reference frames. The arrangement is diagrammed in the Figure shown in
http://members.isp.com//einsteinhoax/rf511.gif . In this
diagram the lever is shown as observed in its own reference frame in Figure
B and as observed in a reference frame which is moving at velocity V with
respect to the lever in figure A. The lever is aligned with one of its arms
parallel to the velocity vector between the reference frames and in both
reference frames the lever is observed not to rotate in response to the
forces applied to its ends.
In order for the lever not to rotate in response to the forces applied
to the ends of the lever, it is necessary that the torques generated on each
of the arms be equal and opposite, as observed in both reference frames (A
and B). Because of the relativistic contraction observed for the parallel
arm, as observed in reference frame B, the moment applied to the parallel
arm is observed to be reduced by the factor (1-V^2/C^2)^0.5 multiplied by
the Lorentz Transformation for Parallel Force as compared to the moment
observed in reference frame A. In the transverse axis there is no
relativistic shortening of the lever arm and the moment applied to the
transverse arm, as observed in reference frame B is equal to the transverse
force multiplied by the Lorentz Transformation for Transverse Force and it
would seem that, for the lever not to rotate in either reference frame, the
Lorentz Transformation for Transverse Force would have to be (1-V^2/C^2)^0.5
times the Lorentz Transformation for Parallel Force. These transformations
were derived (Minkowski) and, most embarrassingly, the required relationship
was not obtained. The Lorentz Transformation for Transverse force was found
to be the inverse of what was required to prevent the rotation of the lever,
or (1-V^2/C^2)^0.5!
It was obvious early on that the paradox required a further
explanation. Either the derivation of the Parallel and/or Transverse
Transformations for force were faulty or the moments applied to the arms of
the lever did not have to balance in order to prevent rotation. Instead of
accepting that there was a flaw in the derivation(s) of the Parallel and/or
Transverse Transformations, a different and highly creative approach was
taken. It was asserted that, in reference frame B, the force applied to the
end of the parallel lever added energy to it at the rate of Fp*V and added
angular momentum to the lever at the rate of Fp*L. It was then argued that
the rate at which energy was added to the lever and the rate at which
angular momentum was added to the lever produced equal and opposite effects
and the lever did not rotate in either reference frame! IT SHOULD BE NOTED
THAT THE DISCUSSION UP TO THIS POINT IS IN COMPLETE AGREEMENT WITH STANDARD
TEXTS ON THE SUBJECT. From this point on , however, the discussion diverges
from the texts.
If one examines the expression for the angular momentum of an object
one will note that its angular momentum about an axis is the product of the
moment of inertia about that axis and the angular velocity about that axis.
Since the lever is observed not to rotate about its pivot pin axis in either
reference frame, one must conclude that, since its moment of inertia is not
infinite, ITS RATE OF CHANGE OF ANGULAR MOMENTUM MUST BE ZERO as observed in
both reference frames! Next, if one examines any text on basic mechanics one
observes that, in order for a torque to exist, a couple must ales exist. (A
couple is defined by the presence of equal and opposite forces separated by
a distance. The torque is equal to the product of the separation between
these forces and their magnitudes.) In the case of the lever, the couple
results from the presence of the force at the end of the lever and the
resulting reaction force component at the hinge pin which is equal in
magnitude and opposite in direction to the force at the end of the lever.
(This is a requirement of classical mechanics. Advanced physics and cannot
be by-passed by the use of more advanced physics.) When these effects are
considered, the supposedly elegant solution to the Right Angle Lever Paradox
breaks down to the statement that zero=zero. This is most certainly true,
BUT IT IS HARDLY MEANINGFUL.
The Lorentz Transformations for Parallel and Transverse Force are
readily derived without the use of advanced mathematics or Electromagnetic
Theory (apparently used by Minkowski and which has the potential for
introducing error). All that is needed are the well known Lorentz
Transformations of the Special Theory of Relativity, the recognition that
E=M*C^2, and simple algebra. It is readily shown that the Lorentz
Transformation for Parallel Force as currently provided is correct but the
correct value for the Lorentz Transformation for Transverse Force is the
reciprocal of the accepted value. The correct transformation is 1/
(1-V^2/C^2)^)0.5. With this transformation, the right angle lever paradox is
no longer a paradox. What it signified is that the accepted derivation of
the Transformation for Transverse Force was erroneous. Apparently this error
was not recognized because it was inconceivable that a mathematical approach
could produce a faulty conclusion. Lesson:- anyone or anything can screw up.
The material which derives the writer's conclusions is provided at
http://members.isp.com//einsteinhoax/relcor.htm for your
reference. The writer has received an E-mail from an individual which
asserted that he had derived the Lorentz Transformation for Transverse Force
using Maxwell's Equations and found its accepted value to be correct. He
probably used the method used by Minkowski. That method, since it involves
using the velocity of light, would probably produce the observed error since
the velocity of light is must be considered in both reference frames and
velocity is measured using both length and time. The writer doesn't know the
exact nature of his error and frankly, he doesn't care.
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://members.isp.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://members.isp.com//einsteinhoax/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.
.
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| User: "Uncle Al" |
|
| Title: Re: The Right Angle Lever Paradox |
27 Apr 2005 12:38:31 PM |
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Enon wrote:
The Right Angle Lever Paradox
[snip 130 lines of 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.fuckinggoogleit.com/
http://www.meninhats.com/d/20040430.html
http://www.you-moron.com/
http://groups.google.com/groups?q=group%3Asci.physics+author%3Awittke
http://b5.sdvc.uwyo.edu/bab5/snds/argcstpd.wav
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>
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.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://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/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.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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| User: "Sam Wormley" |
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| Title: Re: The Right Angle Lever Paradox |
27 Apr 2005 09:44:44 AM |
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Enon wrote:
The Right Angle Lever Paradox
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
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: "tj Frazir" |
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| Title: Re: The Right Angle Lever math error |
27 Apr 2005 01:30:26 PM |
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Math error ..idiot.
No paradox ,,just some idiot with a math error.
YER math sucks .
The tex can be writen by an ***** doing the same mistake.
Tex books compair water in pipes with electric wires !!!!! Thier math
sucks too.
Want me to use 8th grade math and fix it for you idiot ??
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| User: "tj Frazir" |
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| Title: Re: The Right Angle Lever Paradox |
27 Apr 2005 01:39:57 PM |
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The world is entitled to good math .
The fucking loonnns on that hoax page you posted is mathmatic/retarted.
allways doint the wrong math because the dumbfuck dont know ny physics
,,he's plugging forms in because he's retarted.
Like 20 mistakes as I glance down the page.
Paradox my *****.
corect yur math.
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