| Topic: |
Science > Physics |
| User: |
"Eefacm02" |
| Date: |
02 Nov 2003 01:58:08 PM |
| Object: |
The Right Angle Lever Paradox |
The Right Angle Lever Paradox
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://www.members.aol.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://www.members.aol.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://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.
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.
For a response send E-Mail to
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: "Uncle Al" |
|
| Title: Re: The Right Angle Lever Paradox |
02 Nov 2003 03:00:50 PM |
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Eefacm02 wrote:
The Right Angle Lever Paradox
[snip]
Psychotic ineducable boring spammer retic (Ernest Wittke),
http://b5.sdvc.uwyo.edu/bab5/snds/argcstpd.wav
http://w0rli.home.att.net/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.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.
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>
Experimental constraints on General Relativity.
http://arxiv.org/abs/gr-qc/0308010
Nature 425 374 (2003)
<http://rattler.cameron.edu/EMIS/journals/LRG/Articles/Volume6/2003-1ashby/index.html>
http://www.eftaylor.com/pub/projecta.pdf
Relativity in the GPS system
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>
http://users.powernet.co.uk/bearsoft/Paper6.pdf
http://users.powernet.co.uk/bearsoft/LPHrel.html
Longitudinal and transverse mass
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)
"Quis custodiet ipsos custodes?" The Net!
.
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| User: "The Ghost In The Machine" |
|
| Title: Re: The Right Angle Lever Paradox |
02 Nov 2003 04:36:51 PM |
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In sci.physics, Eefacm02
<eefacm02@aol.com>
wrote
on 02 Nov 2003 19:58:08 GMT
<20031102145808.13111.00000078@mb-m03.aol.com>:
The Right Angle Lever Paradox
[rest snipped]
..... is not a paradox. Let o be the origin and the
pivot point (we'll be considering torques in this
analysis). The horizontal length is L_h. The vertical
length is L_v. The torquing forces are F_h and F_v and
are set up such that L_h * F_h = -L_v * F_v, for a net
zero torque on the item and no movement apart from some
bending of the torque arms (which can be ignored for
the purposes of this discussion).
o-----------* - - - H
| v
|
*>
|
|
V
We now accelerate along the horizontal factor. Everything shrinks
horizontally (as observed by the stationary observer).
o----*
| v
|
*>
L_h is now smaller -- but it turns out so is F_v. Still
zero torque.
Or did I miss something when I snipped your post?
--
#191,
It's still legal to go .sigless.
.
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| User: "Harry" |
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| Title: Re: The Right Angle Lever Paradox |
17 Nov 2003 04:14:12 PM |
|
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The Ghost In The Machine <ewill@sirius.athghost7038suus.net> wrote in message news:<6obg71-iif.ln1@lexi2.athghost7038suus.net>...
In sci.physics, Eefacm02
<eefacm02@aol.com>
wrote
on 02 Nov 2003 19:58:08 GMT
<20031102145808.13111.00000078@mb-m03.aol.com>:
The Right Angle Lever Paradox
[rest snipped]
.... is not a paradox. Let o be the origin and the
pivot point (we'll be considering torques in this
analysis). The horizontal length is L_h. The vertical
length is L_v. The torquing forces are F_h and F_v and
are set up such that L_h * F_h = -L_v * F_v, for a net
zero torque on the item and no movement apart from some
bending of the torque arms (which can be ignored for
the purposes of this discussion).
o-----------* - - - H
| v
|
*>
|
|
V
We now accelerate along the horizontal factor. Everything shrinks
horizontally (as observed by the stationary observer).
o----*
| v
|
*>
L_h is now smaller -- but it turns out so is F_v. Still
zero torque.
Or did I miss something when I snipped your post?
Yes, you snipped his drawing away... and so you solved the wrong
problem! ;-)
http://www.members.aol.com/einsteinhoax/rf511.gif
Thus L_h * F_v = -L_v * F_h
Moving horizontally, both terms on the left side reduce, while both on
the right side remain constant, according to you.
And also according to Lorentz and Einstein, right?!
I had almost forgotten this one... but it's still there.
- Dirk, don't you know this one?! Silence from you about such a simple
puzzle is a bad sign...
Harald
.
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| User: "The Ghost In The Machine" |
|
| Title: Re: The Right Angle Lever Paradox |
18 Nov 2003 10:59:31 AM |
|
|
In sci.physics, Harry
<harald.vanlintel@epfl.ch>
wrote
on 17 Nov 2003 14:14:12 -0800
<3bff5641.0311171414.2a248190@posting.google.com>:
The Ghost In The Machine <ewill@sirius.athghost7038suus.net> wrote in message news:<6obg71-iif.ln1@lexi2.athghost7038suus.net>...
In sci.physics, Eefacm02
<eefacm02@aol.com>
wrote
on 02 Nov 2003 19:58:08 GMT
<20031102145808.13111.00000078@mb-m03.aol.com>:
The Right Angle Lever Paradox
[rest snipped]
.... is not a paradox. Let o be the origin and the
pivot point (we'll be considering torques in this
analysis). The horizontal length is L_h. The vertical
length is L_v. The torquing forces are F_h and F_v and
are set up such that L_h * F_h = -L_v * F_v, for a net
zero torque on the item and no movement apart from some
bending of the torque arms (which can be ignored for
the purposes of this discussion).
o-----------* - - - H
| v
|
*>
|
|
V
We now accelerate along the horizontal factor. Everything shrinks
horizontally (as observed by the stationary observer).
o----*
| v
|
*>
L_h is now smaller -- but it turns out so is F_v. Still
zero torque.
Or did I miss something when I snipped your post?
Yes, you snipped his drawing away... and so you solved the wrong
problem! ;-)
http://www.members.aol.com/einsteinhoax/rf511.gif
Thus L_h * F_v = -L_v * F_h
Moving horizontally, both terms on the left side reduce, while both on
the right side remain constant, according to you.
And also according to Lorentz and Einstein, right?!
I had almost forgotten this one... but it's still there.
- Dirk, don't you know this one?! Silence from you about such a simple
puzzle is a bad sign...
Harald
No, L_h and F_h are the two that reduce. L_v and F_v are constant.
My mistake. :-) My explanation of F_v and F_h wasn't the clearest.
Recall that f = ma, and if one accelerates in a direction,
f' = ma' shrinks.
--
#191,
It's still legal to go .sigless.
.
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