"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 figure below) provided a "common sense" warning that an error
had been made in that mathematical derivation. In this thought experiment
shown by the 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
treference frames, then the moments applied to each arm must be equal in
magnitude and opposite in direction in each of the reference frames.
http://einsteinhoax.com/rf511.gif.

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 equirement, 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 diagram below. 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.
http://einsteinhoax.com/cf43.gif.

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 (1997); http://einsteinhoax.com/gravity.htm
(1987); and http://einsteinhoax.com/relcor.htm (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.

All of the Newsposts made by this site may be viewed at the
http://einsteinhoax.com/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:- . If you wish a reply, be sure that your
mail reception is not blocked.

The material at the Website has been posted continuously for over 8
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.

On Aug 18, 11:03 am, "Emit" wrote:
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.

In A Flower for Einstein I prove that the Lorentz Transformations
are restricted to systems moving on the same line as each other. here
is a bit of the proof:
The LTE do hold good for deformed systems whose velocity is on or
parallel to the same line. We will now see what happens in one of the
infinity of possible cases where their relative motion, which
Relativity asserts is the only kind of motion that exists, is on the
same line but their absolute velocities are not.
As before, the absolute velocity of a system is denoted by abv. The
relative velocity between two systems as measured by Euclidean system
S will be denoted as vp and the relative velocity between two moving
relativistic systems, as measured by each other, will be denoted as
vr. We will use the LTE physics in which there are q-contractions in
the direction of abv and rates of all moving clocks are q-slow.
In the following example we will let ... cs k move at .6c in a W
direction which coincides with Z; and let cs k' move in a W' direction
at .8c, at an angle such that vr of k and k' is upon their coinciding
XX' axes and Y and Y' of k and k' are perpendicular to the plane of
W'.
The enclosing boundary joining the totality of points delineated by
the outer ends of unit rods pointing out in all directions from the
origin of a deformed system is an ellipsoid. The short axis is in the
abv direction. The shape of the ellipsoidal envelope per system is a
function of the amount of deformation, thus of abv. Each ellipsoid
remains permanently centered on its referent object. Each system's
unit rods are of variable lengths, depending on the angle in which
they are placed within its ellipsoid.
Letting each ellipsoid have its own internal Euclidean co-ordinate
system, the axes of k can be denoted as X1,Y1,Z1 (with Z1 on Z) and
those of k' as X2,Y2,W2 (with W2 parallel to W'). Thus Z1 and W2 are
the contracted semi minor axes of each ellipsoid respectively.
An easy way to visualize the relations is to imagine the ellipsoidal
envelope of each system to be centered on a common origin at t=t'=0.
The axes of cs k' are parallel to those of k, thus are tilted upon the
axes of its own ellipse. Similarly, the axis of relative motion, XX'
is tilted from the semi major X2 axis.
The angle between any k rod and Z and the angle between any k' rod
and W2 governs the co-ordinates of where a unit rod per system, in any
direction from its origin, touches the ellipsoidal boundary. This lets
the physical lengths of the respective rods be calculated via the
equation for the co-ordinates of that point, coupled with the
Pythagorean Theorem. The resulting value of their ratios of lengths
per parallel rods can then be found by comparing the results.
The lengths of variously aligned rods are a function of the absolute
velocities and the angle of tilt from W or W'. Since that angle is a
function of the direction of their absolute velocities, the values of
f(vr) and ©ª(vr) are not only a function of the physical deformations
per abv, but also of the actual direction in which each system moves!


Several pages later the following appears:
Since both those possibilities are ruled out by the case we are
treating, the LTE failed the test. Nevertheless, even though - other
than for a bit of tweaking - the rest of this chapter was written 16
years ago, we will peruse the small and tedious steps all the way to
the end.

A bit later:
As will be seen below, the length of a moving unit rod as measured
by the viewing system is not necessarily the same as the calculated
size of a viewed system's units; and neither necessarily is the
determined size. There are at least three ways cs k could "determine"
the length of a Z' unit of k'. The first (as treated above by plotting
ends A' and B' of unit rod k' on Z), finds that ©ª(vZ') =/=
©ª(vY'). ... If, however, we consider the co-ordinates plotted for ends
A' and B' of rod k' "at the same time" in terms of the clocks of cs k,
some new choices need to be explored.
In the Y' direction rod k' remains physically non-deformed and k
clocks have no offsets. Therefore, ©ª = ©ª(v) = ©ª(+/- v) = 1. In the Z
direction there are -vz/c2 offsets in k clocks.
At t = 0, end A' is at P(0,0,0,0). At that instant end B'Z' is at P(0,
0, .8838, -.6 * .8838); in which t = -vz/c2 = -.6 * .8838. It takes
t/.8 = tau = .6629+ seconds
before all clocks on this z level register t = 0. Cs k' will have
moved vptau = .529 * .6629+ = .3507+ units to the right by the time k
plots B'Z' at x=.3507+; z=.8838+; t = 0. Cs k observers thus find
unit rod k' tilted to the right of Z, its length thus being equal to
that of the hypotenuse of a right triangle whose base is .3507 units
long and whose height is .883... units long. They decide to calculate
the length of the moving rod via Euclidean geometry.
By Pythagoras, rod k' is sqrt(.35072 + .88382) = .9509... units
long. This sets ©ª(vZ) equal to 1.05, which is neither the value found
above nor that of ©ª(vY) = 1. Hence, the LTE still do not apply ... .
Suppose, however, the k observers decide to measure "the length of the
(moving) rod in the 'stationary' system" by laying their own unit rod
upon the hypotenuse joining the separate points A' and B' they plotted
at "t = 0". When it is realigned in this new direction, their rod
tilts within its own ellipsoidal envelope; so its physical length
therefore changes.
To discover how many times the tilted unit rod of k fits into the
actual plotted distance A'B', we must first calculate the Euclidean
length of A'B' and then the physical length of tilted rod k, which is
used to determine the length of A'B' in cs k units.
¦£¦¡a¦¡¦¡B'
¦¢ /
b c
¦¢ /
¦¢/
A'
The base (line b) of the above triangle, whose point A' is at the
origin of the ellipsoid attached to cs k, is sqrt.5 Euclidean units
long. The height (line a) was found to be .3507804 units long by cs
k, or any attached Euclidean system. Hence, the hypotenuse of the
triangle is c = sqrt(.3507+2 + .5) = .789+ Euclidean units long. [The
triangle is drawn in the given position in order to set its "height"
parallel to the X axis of zero deformation and its "base" parallel to
the Z axis of q contraction.]
The slope of the hypotenuse is then a/b = .3507/sqrt.5 = .49607837151.
(Line a represents the "rise", x1, and line b the "run", z1, for this
upside down and 90 degrees rotated triangle.) The angle between Z and
this slanted rod of k is therefore 26.38...degrees.

A little later:
Pythagorean value of line c as calculated by
k:

wrote in message
...
On Aug 18, 11:03 am, "Emit" wrote:
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.

In A Flower for Einstein I prove that

==================================

You couldn't prove a cow's udder has four teats, you dork.
You don't even know what shape (x,y,z,t) is.

On Aug 19, 12:48 pm, "Androcles" wrote:
wrote
In A Flower for Einstein I prove that
You couldn't prove a cow's udder has four teats, you dork.
You don't even know what shape (x,y,z,t) is.
Given that x, y, z and t are co-ordinate
points on an infinitely extending co-ordinate
system X, Y, Z with the time t, then the shape
of point (x,y,z,t) is an infinitely small
space-time point.
The android doubtlessly thinks it is an
infinitely large sphere, or, since he has
cow-teats on his little mind, an ovoid.

wrote in message
...
On Aug 19, 12:48 pm, "Androcles" wrote:
wrote
In A Flower for Einstein I prove that
You couldn't prove a cow's udder has four teats, you dork.
You don't even know what shape (x,y,z,t) is.

Given that x, y, z and t are co-ordinate
points on an infinitely extending co-ordinate
system X, Y, Z with the time t, then the shape
of point (x,y,z,t) is an infinitely small
space-time point.

f: (x,y,z,t) |- (x',y',z',t')

then the shape of point (x',y',z',t') is an infinitely small
space-time point,

g: (x',y',z',t') |- (\xi, \eta, \zeta, \tau)

then the shape of point (\xi, \eta, \zeta, \tau) is an infinitely small
space-time point, that you complain is drawn ovoid because I
circled a set.

Oh wait, according to you we have
(x, x', y, z, t) is an infinitely small space-time 5D point, an obvious
clueless stupidity on your part.

g o f: (x,y,z,t) |- (\xi, \eta, \zeta, \tau)

The question is, cretin, if the infinitely small space-time point
(x',y',z',t')
moves with velocity v with respect to the infinitely small space-time point
(x,y,z,t),
how fast does the infinitely small space-time point (\xi, \eta, \zeta, \tau)
move with respect to the infinitely small space-time point (x',y',z',t') ?

Eh, ****head?

Androcles wrote in message

wrote in message
...
On Aug 19, 12:48 pm, "Androcles" wrote:
wrote
In A Flower for Einstein I prove that
You couldn't prove a cow's udder has four teats, you dork.
You don't even know what shape (x,y,z,t) is.

Given that x, y, z and t are co-ordinate
points on an infinitely extending co-ordinate
system X, Y, Z with the time t, then the shape
of point (x,y,z,t) is an infinitely small
space-time point.

f: (x,y,z,t) |- (x',y',z',t')

then the shape of point (x',y',z',t') is an infinitely small
space-time point,

g: (x',y',z',t') |- (\xi, \eta, \zeta, \tau)

then the shape of point (\xi, \eta, \zeta, \tau) is an infinitely small
space-time point, that you complain is drawn ovoid because I
circled a set.

Oh wait, according to you we have
(x, x', y, z, t) is an infinitely small space-time 5D point, an obvious
clueless stupidity on your part.

g o f: (x,y,z,t) |- (\xi, \eta, \zeta, \tau)

The question is, cretin, if the infinitely small space-time point
(x',y',z',t')
moves with velocity v with respect to the infinitely small space-time point
(x,y,z,t),
how fast does the infinitely small space-time point (\xi, \eta, \zeta, \tau)
move with respect to the infinitely small space-time point (x',y',z',t') ?

Eh, ****head?

He doesn't know that twin-paradoxically, you are even more
stupid than he is, and he is *even even* more stupid than you
are.
He can't help it, and you wouldn't even want to help it.

Dirk Vdm

On Aug 20, 3:59 am, "Androcles" wrote:
wrote
Given that x, y, z and t are co-ordinate
points on an infinitely extending co-ordinate
system X, Y, Z with the time t, then the shape
of point (x,y,z,t) is an infinitely small
space-time point.

f: (x,y,z,t) |- (x',y',z',t')
then the shape of point (x',y',z',t') is an infinitely small
space-time point,
g: (x',y',z',t') |- (\xi, \eta, \zeta, \tau)
then the shape of point (\xi, \eta, \zeta, \tau) is an infinitely small
space-time point, that you complain is drawn ovoid because I
circled a set.

Oh wait, according to you we have
(x, x', y, z, t) is an infinitely small space-time 5D point, an obvious
clueless stupidity made by Androcle's.

The question is, if the infinitely small space-time point
(x',y',z',t') moves with velocity v with respect to the infinitely
small space-time point (x,y,z,t),
how fast does the infinitely small space-time point (\xi, \eta, \zeta, \tau)
move with respect to the infinitely small space-time point (x',y',z',t') ?

In Einstein's 1905 paper, which the android obviously doesn't
understand,
system K' with co-ordinates x', y', z', t', was AT REST relative to
system K (x, y, z' t'). it is totally obvious, therefore, that the
answer
to his question is v = 0.

Wait another day or so, Android, and I will help you understand
Einstein's
STR algebra as you never did before. Meanwhile, shut your ****ing
mouth!

glird

wrote in message
...
On Aug 20, 3:59 am, "Androcles" wrote:
wrote
Given that x, y, z and t are co-ordinate
points on an infinitely extending co-ordinate
system X, Y, Z with the time t, then the shape
of point (x,y,z,t) is an infinitely small
space-time point.

f: (x,y,z,t) |- (x',y',z',t')
then the shape of point (x',y',z',t') is an infinitely small
space-time point,
g: (x',y',z',t') |- (\xi, \eta, \zeta, \tau)
then the shape of point (\xi, \eta, \zeta, \tau) is an infinitely small
space-time point, that you complain is drawn ovoid because I
circled a set.

Oh wait, according to you we have
(x, x', y, z, t) is an infinitely small space-time 5D point, an obvious
clueless stupidity made by Lobotomised Lebau who

wrote in message
...
" If x, x', and t are coordinates of K,"

whereas Einstein said
"it is clear that a point at rest in the system k must have a system of
values x', y, z, independent of time"

It is clear you really are completely stupid, glird the tord.




The question is, if the infinitely small space-time point
(x',y',z',t') moves with velocity v with respect to the infinitely
small space-time point (x,y,z,t),
how fast does the infinitely small space-time point (\xi, \eta, \zeta,
\tau)
move with respect to the infinitely small space-time point (x',y',z',t')
?

In Einstein's 1905 paper, which the android obviously doesn't
understand,
system K' with co-ordinates x', y', z', t', was AT REST relative to
system K (x, y, z' t'). it is totally obvious, therefore, that the
answer
to his question is v = 0.


\xi = (x-vt) /(sqrt (1-0^2/c^2)
= (x-vt) /sqrt(1-0)
= (x-vt) /1
= x-vt
= x-0t
= x-0
= x

Thank you, now we agree.


Wait another day or so, Android, and I will help you understand
Einstein's
STR algebra as you never did before. Meanwhile, shut your ****ing
mouth!

**** off, you useless, stupid, ignorant ****, you couldn't help a fish
get a hook out of its mouth.

On Aug 20, 5:05 pm, "Androcles" wrote
to himself:

**** off, you useless, stupid, ignorant ****, you couldn't help a fish
get a hook out of its mouth.