"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://einstenhoax.com/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://einsteinhoax.com/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://einsteinhoax.com/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
http://einsteinhoax.com/hoax.htm ("The Einstein Hoax" {1997});
http://einsteinhoax.com/gravity.htm; ("Gravity" {1987}); and
http://einsteinhoax.com/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.

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http://einsteinhoax.com/postinglog.htm.

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exception for which a correction was provided.

Ecuas 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. 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:

[etc.] This is an example of the cranky disdain for mathematics we've
been discussing on another thread.

What it's really saying is "I found out I was unable - for whatever
reason - to learn the mathematics necessary for doing physics and since
I simply *must* pretend to be a physicist - for whatever reason - I'm
going to declare all that mathematics an unecessary burden. In fact,
why don't I simply claim that mathematics distorts and poisons physics,
so the less mathematics the better."

Now, if he only wrote THAT instead of all those pretentious treatises
then we could have an interesting philosophical discussion about
mathematics and its role in physics.

--
Jan Bielawski

"JanPB" wrote in message
oups.com...
Ecuas 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. 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:

[etc.] This is an example of the cranky disdain for mathematics we've
been discussing on another thread.

What it's really saying is "I found out I was unable - for whatever
reason - to learn the mathematics necessary for doing physics and since
I simply *must* pretend to be a physicist - for whatever reason - I'm
going to declare all that mathematics an unecessary burden. In fact,
why don't I simply claim that mathematics distorts and poisons physics,
so the less mathematics the better."

Now, if he only wrote THAT instead of all those pretentious treatises
then we could have an interesting philosophical discussion about
mathematics and its role in physics.

--
Jan Bielawski

We know what you find interesting, you've already told us.
http://www.androcles01.pwp.blueyonde....htm#Bielawski
Androcles