| Topic: |
Science > Physics |
| User: |
"Reckerq" |
| Date: |
03 Dec 2004 09:00:14 AM |
| Object: |
The Limitations of Mathematics in Physics |
The Limitations of Mathematics in Physics
The present philosophy in theoretical physics is to search for
mathematical relationships that predict experimental results that are then used
to verify the validity of the mathematics in defining our physical Universe,
from the microcosmic to the macrocosmic. The philosophy was expressed
succinctly by Dr. Hawking in Scientific American when he stated that he didn't
care about "reality" because he didn't know what "reality" was, all that he
cared about was whether the mathematics correctly predicted the results of
experiment. Unfortunately, requiring that the results of observation and of
mathematics be in agreement is NECESSARY BUT NOT SUFFICIENT in our study of the
Universe around us.
As a research tool, mathematics suffers from two basic limitations:
A:- It is a linear logic process rather than an area logic process. Any
error along the line of logic being used can easily propagate throughout the
remaining logic chain without giving warning of its presence. (A solution using
an area logic process, on the other hand, is similar to the solution of a
crossword or jigsaw puzzle. An error made anywhere in such a process is
revealed by an incongruity somewhere in the solution. As such, such a logic
process is self-correcting because it forces one to go back and rethink the
problem.)
B:- The logic associated with the mathematical treatment of a process can
lead to results in regions of the problem domain where another constraint is
imposed by Nature. To a mathematically trained physicist such a constraint may
well go unrecognized because it is not inherent in the mathematics. The
existence of such a constraint may render the mathematical conclusions involved
useless.
The limitation described in paragraph A is illustrated by the by the
derivation of the Lorentz Transformation for Transverse Force. Unlike the
derivation of the Lorentz Transformation for Parallel Force that provides the
correct result, the derivation of the Lorentz Transformation for Transverse
Force is incorrect. (The derivation of this transformation is straightforward
and is easily accomplished using the conventional Lorentz Transformations for
Mass, Length and Time. The infamous "Right Angle Lever Paradox", see diagram
http://members.aol.com/einsteinhoax/rf511.gif , provided a “common sense”
warning that an error had been made in that mathematical derivation. In this
diagram, if forces are applied at the ends of the right angle lever and the
lever is observed not to rotate in both the "moving" and "stationary" reference
frames, then the moments applied to each arm must be equal are equal in
magnitude and opposite in direction in each of the reference frames.
With the conventionally accepted values, the product of the Lorentz
Transformation for Parallel Length and the alleged Transformation for Parallel
Force is not equal to the product of the Lorentz Transformation for Transverse
Length and the alleged Transformation for Parallel Length. This inequality
implies that, if the torques applied to the arms are equal in one of the
reference frames ("moving" or "stationary") they cannot be equal in the other
reference frame ("stationary " or "moving") and the lever would then rotate in
one of the reference frames and not the other. Since the lever does not seem to
know of this requirement, it remains stationary, and it was necessary to
reconcile the dilemma that resulted.
One would think that rational men would accept that an error had been made
in the derivation of the force transformations and search for that error.
Instead, it was assumed that the derivation of the Lorentz Transformations for
the Forces had to be correct, after all they were derived mathematically. To
account for the difficulty, a convoluted explanation was devised which asserted
that the rate of increase of energy in the transverse lever produced by the
parallel force was balanced by the rate of increase of the angular momentum
supplied by the torque difference between the two directions. The explanation
conveniently ignored the fact that for moments to be applied to the lever by
the forces applied to its ends, equal and opposite forces would result at the
hinge pin. As a result, any energy that is added to the transverse lever arm by
the applied parallel force at its end will be removed at the hinge pin, and the
rate of change of energy in the lever is exactly zero.
What was also ignored was the fact that the angular momentum of the lever
is the product of its moment of inertia and its angular velocity. Since the
lever was observed not to rotate in either reference frames, the rate of change
of the lever's angular momentum is also zero. Properly done, the mathematical
explanation amounts to the statement that 0 = 0. This is certainly true but is
also meaningless. It is frightening that the advanced academic community could
overlook such an error and appear in a large number of postgraduate level
texts. It is even more frightening that individuals who would embrace such an
explanation are in a position to teach our best and brightest. For a derivation
of the correct Lorentz Transformations for Forces see
http://www.members.aol.com/einsteinhoax/relcor.htm ).
The type of error illustrated by paragraph B occurs in regard to the idea
of "action at a distance" being produced by the exchange of "virtual
particles". Mathematically, such particles are capable of providing both
attractive and repulsive forces. In reality, in the absence of an overlying
substrate for space (e.g.- the classical Aether or Dirac's "Sea of Negative
Energy") with which the "virtual photons" could interchange momentum, the
production by "virtual photons, of attractive forces acting at a distance would
seem to be impossible. But then, if such a substrate exists, why do we need the
concept of "virtual photons"?
Perhaps it would be constructive to illustrate this type of limitation on
the reliability of a purely mathematical treatment by considering the analysis
of a conventional FET transistor circuit, the cascode. This circuit consists of
two FET transistors with the drain of the first one driving the source of the
second one and with the gate of the second biased at a constant positive
voltage. For low frequency signals, the operation of such an amplifier is
completely defined mathematically by a property known as "transconductance".
The electron flow in the collector of the second FET is the product of the
signal voltage applied to the gate of the first FET times the transconductance
of the first FET. The mathematics tells us that a positive signal will produce
a positive flow of electrons at the output and a negative signal will produce a
negative flow of electrons at the output.
What the mathematics doesn't tell us is that the process will not work
unless there was a bias flow of electrons in the amplifier to which the output
signal was added. With the bias current, the amplifier can produce both
positive and negative electron flow signal outputs by adding to or subtracting
from the bias current. Without the bias current, the amplifier can only produce
positive electron flow outputs. The mathematics is NECESSARY BUT NOT SUFFICIENT
to define the process. Similarly, the writer asserts that the mathematics
associated with "virtual photons" is also NECESSARY BUT NOT SUFFICIENT. A
substrate (e.g.- the classical Aether or Dirac's "Sea of Negative Energy" or
one of the several "background energy of space" concepts) would seem to be
necessary for the idea of "virtual photons" as a force carrier to work, but, if
the substrate exists, why is the concept of "virtual photons" as force carriers
required?
Whether "virtual photons" exist can be evaluated by a rather simple
experiment as shown in the figure at
http://www.members.aol.com/einsteinhoax/cf43.gif . There is an even simpler
means of evaluating the concept. A recent news item revealed that a loose
oxygen cylinder was captured by the magnetic field of an MIR machine and flew
across the room to crush the skull of a child being examined. If such a strong
magnetic field existed in the room and that field involved "virtual photons",
those photons would be sufficiently numerous to produce an amount of
electromagnetic noise that would be easily measured. I doubt very seriously if
such noise would be found if s search were made.
Remember that Dr. Einstein warned "we have not proven that the Aether
doesn't exist, we have merely proven we do not need it (for calculations). Also
remember that it took 25 years of peer pressure to cause Dr. Einstein to
relinquish the idea of "absolute time" (equivalent to believing the Aether) and
accepting the unproven (and rather ludicrous) consensus viewpoint of space and
time as a single entity.
Theoretical physics has taken the easy position that only mathematics and
experiment are required to deal with reality. Unlike every other branch of
science, it is asserted that "mechanism" is irrelevant in physical theory.
Since we live in the "mechanism" represented by our Universe, the prime goal of
any responsible theoretician should be an understanding of the workings of that
"mechanism" with the mathematical and experimental results used to iteratively
improve our understanding of that "mechanization". What we have today, with the
idea of "mechanism" eliminated, is more akin to group quasi-religious
charlatanism (how many Angels can dance on the head of pin?) practiced by a
controlling cadre of self promoting "scientists" than it is to an organized
science.
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.
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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: "Uncle Al" |
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| Title: Re: The Limitations of Mathematics in Physics |
03 Dec 2004 12:12:51 PM |
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Reckerq wrote:
The Limitations of Mathematics in Physics
[snip 170 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.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-2003-1/>
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://relativity.livingreviews.org/Articles/lrr-2003-1/>
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://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 (so does the proposal)
<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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| User: "Sam Wormley" |
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| Title: Re: The Limitations of Mathematics in Physics |
03 Dec 2004 09:05:01 AM |
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Reckerq wrote:
The Limitations of Mathematics in Physics
Ref: http://math.ucr.edu/home/baez/RelWWW/wrong.html#aether
Albert Einstein, in his essay On the Aether (1924), made some
injudicious comments to the effect that relativity theory could be said
to ascribe physical properties to spacetime itself, and in that sense,
to involve a kind of "aether". He clearly did not mean the kind of
"aether" which had been envisioned by Maxwell and others in the
nineteenth century, but his remarks have been seized upon ever since,
by various cranks and other ill-informed persons, as evidence that
"gtr is an aether theory".
Luminiferous Ether
http://scienceworld.wolfram.com/physics/Ether.html
http://www.google.com/search?q=aether+site%3Awww.aip.org+update
Special Relativity
http://scienceworld.wolfram.com/physics/SpecialRelativity.html
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).
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
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: "robert j. kolker" |
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| Title: Re: The Limitations of Mathematics in Physics |
03 Dec 2004 10:56:39 AM |
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Reckerq wrote:
The Limitations of Mathematics in Physics
The present philosophy in theoretical physics is to search for
mathematical relationships that predict experimental results that are then used
to verify the validity of the mathematics in defining our physical Universe,
from the microcosmic to the macrocosmic.
That is physical science in a nutshell. Anything further is Wretched
(Retick) Excess.
Bob Kolker
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