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The Central Discoveries
of this Book
/a top-ten list/
/by Miles Mathis/
/nullius addictus iurare in verba magistri^1
/
It is no longer common for mathematicians or scientists to publish
entire books full of new information or theories. Due to specialization,
the normal procedure is to publish experimental findings augmented by
very limited theoretical suggestions. By and large, theory is left to a
select and limited number of specialists. Those in the center of the
field would claim that this is a sign of their maturity, humility, or
other positive quality, suggesting that those on the margin who are rash
enough to have their own ideas must be immature, immodest, or otherwise
deluded. In doing this they neglect to notice that the entire history of
science has proceeded along other lines, and that the contemporary
hierarchy would be seen as abnormal, inefficient, and ridiculously
regimented by anyone from the past, even by those from the recent past
like Einstein and Planck and Maxwell.
This is as much as to admit that I know that my book must seem an
anomaly as well as an anachronism. Both its form and its content must
seem strange to a modern reader. To counteract this I have found it
necessary to write this general overview. In it I will briefly describe
the highlights of my research, hopefully whetting the reader's appetite
for the longer papers. None of my papers contain difficult math or
esoteric ideas, but here I will simplify even further, offering the sort
of critical gloss a publisher or editor might make a hundred years from
now, assuming my ideas are correct. Most of these papers are now several
years old, and already I have a bit of hindsight regarding them. This
makes it possible for me to rank my findings in order of importance, and
to contextualize them for you as I list them. This may give you a place
to start in your readings, or it may supply you with a clearer
understanding of what I think I have achieved. Either way, given that
the book has now gone past 1,200 pages, I think it has become a PR
necessity, if nothing else.
I am probably most widely known online for my algebraic analysis of
special relativity. Many readers, if they were writing this, would
probably begin there. But I am going to start with other things here. I
do this for two reasons. One is that many readers coming to a new
website will be prejudiced against relativity naysayers. I am not a
normal relativity naysayer since I accept time dilation and the basic
claims of SR. All I do is fine-tune the transforms, so that they match
the latest experiments. But once people peg you as a naysayer of SR of
any kind or in any amount they have great difficulty taking anything
else you say seriously. This is a fact I have been forced to accept,
whether I agree with it or not. It is a sign of the times and cannot be
ignored. The second reason is that I believe a number of other findings
of mine will be considered to have more lasting importance than the
relativity corrections. These findings are both more fundamental and
more inventive. To add yet another level of tidiness, I will begin with
the oldest problem I have solved: meaning the problem that had persisted
for the most amount of time before I solved it.
That oldest mistake is one that Euclid made. It concerns the definition
of the point. Entire library shelves have been filled commenting on
Euclid's definitions, but neither he nor anyone since has appeared to
notice the gaping hole in that definition. Euclid declined to inform us
whether his point was a real point or a diagrammed point. Most will say
that it is a geometric point, and that a geometric point is either both
real and diagrammed or it is neither. But all the arguments in that line
have been philosophical misdirection. The problem that has to be solved
mathematically concerns the dimensions created by the definition. That
is, Euclid's hole is not a philosophical or metaphysical one, it is a
mechanical and mathematical one. Geometry is mathematics, and
mathematics concerns numbers. So the operational question is, can you
assign a number to a point, and if you do, what mathematical outcome
must there be to that assignment? I have exhaustively shown
that you cannot assign a counting
number to a real point. A real point is dimensionless; it therefore has
no extension in any direction. You can apply an ordinal number to it,
but you cannot assign a cardinal number to it. Since mathematics and
physics concern cardinal or counting numbers, the point cannot enter
their equations.
This is of fundamental contemporary importance, since it means
that the point cannot enter calculus equations. It also cannot exit
calculus equations. Meaning that you cannot find points as the solutions
to any differential or integral problems. There is simply no such thing
as a solution at an instant or a point, including a solution that claims
to be a velocity, a time, a distance, or an acceleration. Whenever
mathematics is applied to physics, the point is not a possible solution
or a possible question or axiom. It is not part of the math.
Now, it is true that diagrammed points may be used in mathematics
and physics. You can easily assign a number to a diagrammed point.
Descartes gave us a very useful graph to use when diagramming them. But
these diagrammed points are not physical points and cannot stand for
physical points. A physical point has no dimensions, by definition. A
diagrammed point must have at least one dimension. In a Cartesian graph,
a diagrammed point has two dimensions: it has an x-dimension and a
y-dimension. What people have not remembered is that if you enter a
series of equations with a certain number of dimensions, you must exit
that series of equations with the same number of dimensions. If you
assign a variable to a parameter, then that variable must have at least
one dimension. It must have at least one dimension because you intend to
assign a number to it. That is what a variable is?a potential number.
This means that all your variables and all your solutions must have at
least one dimension at all times. If they didn't, you couldn't assign
numbers to them.
This critical finding of mine has thousands of implications in physics,
but I will mention only a couple. It has huge implications in QED, since
the entire problem of renormalization is caused by this hole in Euclid's
definition. Because neither Descartes nor Newton nor Schrodinger nor
Feynman saw this hole for what it was, QED has inherited the entire
false foundation of the calculus. Many of the problems of QED, including
all the problems of renormalization, come about from infinities and
zeroes appearing in equations in strange ways. All these problems are
caused by mis-defining variables. The variables in QED start acting
strangely when they have one or more dimensions, but the scientists
mistakenly assign them zero dimensions. In short, the scientists and
mathematicians have insisted on inserting physical points into their
equations, and these equations are rebelling. Mathematical equations of
all kinds cannot absorb physical points. They can express intervals
only. The calculus is at root a differential calculus, and zero is not a
differential. The reason for all of this is not mystical or esoteric; it
is simply the one I have stated above?you cannot assign a number to a
point. It is logical and definitional.
This finding is not only useful in physics, it is useful to calculus
itself, since it has allowed me to show that modern derivatives are
often wrong. I have shown that the derivatives of ln(x)
and 1/x are wrong, for instance. I have
also shown that many problems are solved incorrected with calculus,
including very simple problems of acceleration.
This finding also intersects my first discoveries in special relativity,
which I will discuss in greater detail below. The first mistake I
uncovered in special relativity concerned Einstein's and Lorentz' early
refusals to define their variables. They did not and would not say
whether the time variable was an instant or a period. Was it t or ?t?
Solving this simple problem was the
key to unlocking the central algebraic errors in the math. Once it was
clear that the time variable must be an interval or period, at least two
of Einstein's first equations fell and could not be made to stand up again.
Next is my Unified Field Theory , just
added to this list. I haven't put it above the correction to the point,
since the correction to the point determined a part of my UFT. At the
heart of my UFT is the discovery that Newton's gravitational equation is
a compound equation, one that already includes the foundational E/M
field or charge field. I show that the current "messenger photon" cannot
be virtual and that the field must be both real and mechanical. This
means that Einstein's field equations are also compound equations.
Einstein already had a UFT and didn't know it. But my theory goes far
beyond this, since I don't just pull the lid off Newton and Einstein and
then stand back. I segregate and simplify their equations, showing many
many new things, including a correction to the perihelion of Mercury
, a mechanical solution to the Metonic
Cycle , and a new theory of tides
. I also show that the universal
gravitational constant G is a transform
between the two constituent fields of Newton's equation.
As the second part of this Unified Field Theory, I have also
deconstructed Coulomb's equation . I
show that Coulomb's constant k is tied to the Bohr diameter, and that
when applied to quanta we can drop this constant from the equation. Like
G, k is a scaling constant, and at the quantum level we have no need to
scale. Among other things, this changes the force between electron and
proton by a factor of 10^-19 . The charge part of this unified field has
also allowed me to easily solve Bode's Law
, resolving all the error, and to show
the physical cause of axial tilt .
Neither Bode's Law nor axial tilt are coincidences, as we have been told.
For the next important discovery we will stay in the 20th century and
look at the central problem of QED, which is superposition. The
Copenhagen interpretation has assured us that quantum experiments cannot
be explained in a logical mechanical way. That is, no possible
visualization can explain various interactions of quanta or various
mathematical and statistical outcomes. I have disproved this by
explaining it all mechanically and by drawing a picture
. Rather than focus on statistics or
math, as most or all have done up to now, I focus on the mechanics of
spin. Given an x-spin, I remind my reader of the gyroscope and show that
y-spin must be about an external axis. Meaning, if the radius of the
x-spin is 2, the radius of the y-spin must be 4. This not only creates
the mechanical and physical wave motion, it explains the statistical
outcomes of all mysterious experiments. Because the spins must be
orthogonal to eachother, only one can be an experimental constant. If
you maintain an experimental view that keeps the x-spin clockwise, for
instance, the y-spin will vary with time. The x-spin will be clockwise
100% of the time, but the y-spin will be clockwise only 50% of the time.
I show this with an easy visualization. I also draw the superimposing
/physical/ waves and show the simple mechanical reason for the variance.
I explain precisely how this solves the biggest statistical problems.
Using these same stacked spins, I am then able to create all the known
particles, including the electron, the proton,
the neutron, and all mesons and
bosons . I am able to develop a
simple quantum equation with which I can predict the masses of all known
particles. These spins then replace the quark model of QCD
, and I am able to show precisely why
the quark model must fail, including the loss of the weak force
, the strong force
, asyptotic freedom
, broken symmetries, and all the
rest. With this same quantum equation, I am able to unify the photon,
show how it creates its own wave
with spin , and show how Planck's
constant is hiding the mass of the
photon.
You would think this would also solve the double slit experiment
mystery, but that mystery is
actually solved by the foundational E/M field. This second field in
Newton's equation is emitted by the central wall in the double slit
experiment. The slits create an interference pattern in this field. So
the interference pattern actually exists, in a real field, before any
particle is sent through either slit.
A problem I recently solved is the perihelion precession of Mercury
. This problem has been thought for a
century to have been solved by Einstein, but I have shown major errors
in the initial derivations of the field equations. The central error is
applying the curvature of the field directly to the precession. Einstein
achieved a number (.45) which he admitted was the field curvature at the
distance of Mercury's orbit. To assign this curvature to precession
requires a good deal of math, including a time assignment, and Einstein
mistakenly assigned his number per Earth year. It should be assigned per
one orbit of Mercury, which is a Mercury year (88 days). Then the
curvature precession has to be compared in a vector analysis to the
Earth's curvature precession, and Einstein ignores that as well.
Finally, the precession due to perturbations has to be refigured using
the new field equations, and that has never been done. I show that a
correct analysis of the GR field requires a 4% correction to the
historical perturbation number, and this correction was ignored by
Einstein and is still ignored. This means that all the current numbers
are wrong. I have corrected them and achieved the right totals, without
using the tensor calculus (and explaining the mechanics at every step).
A much older problem I have solved goes all the way back to Archimedes.
It is closely tied to the one concerning the point. The pre-calculus was
invented by the Greeks and perfected by Archimedes. Archimedes solved
what we would call calculus equations by using infinite series and
exhaustion. We don't use exhaustion anymore, but, via Leibniz and Newton
and Cauchy, we have inherited the basic method of Archimedes. That is,
we use an infinite series. This method was so difficult to put a
foundation under because Newton and all the others kept trying to
introduce the point into their equations. Not only did they try to
introduce it into their axioms, they tried to force it to exit the
proofs as well, so that they could claim to find solutions at a point
and instant. The equations and proofs kept rebelling and continue to
rebel to this day. The proofs do not work, but we moderns have decided
to ignore that. After a century or more of worrying and arguing about
it, with little to show for it, we decided to let Cauchy put a lid on
it, and we have refused to open the pot since.
To solve this problem I re-invented what is now called the
calculus of finite differences. Although I did not know it at the time,
this form of the calculus has been around for centuries. It solves all
the same problems as the infinite calculus, but it is quite easy to
prove and to use. This form of the calculus falls like an apple out of
an elementary number table, and students can follow this table and see
for themselves how and why the calculus works, without any
mystification. I have strongly recommended the replacement of the
infinite calculus with the calculus of finite differences, not just for
educational reasons, but because it solves many of the problems of QED
and General Relativity. I have already shown how it impacts
renormalization, and it does the same sort of housecleaning on GR. Most
of the foundational inconsistencies in Einstein's expression of GR
immediately evaporate once we jettison the point and define all space
and time on intervals or non-zero differentials.
The next important problem I have solved is another one made famous by
Newton, although this time he invented it without much help from the
Greeks. By analyzing a diminishing differential applied to the arc of a
circle, Newton claimed to prove that as the arc length approached zero,
the arc, the chord, and the tangent all approached equality. I have
shown that Newton's analysis is
false. Newton monitored the wrong angle in the triangle created, which
skewed his analysis. He did not notice that another angle in the
triangle went to its limit before his angle, assuring that the tangent
remained longer than the arc and chord all the way to the limit. This
solves, all at once, many of the mysteries of trigonometry. Newton's
ultimate interval, which became the infinitesimal and then the limit, is
proved by me to be a real interval, where the variables do not go to
zero and they do not go to equality. This is the reason we find real
values for them. Even at the limit, the tangent is not zero and it is
not equal to the arc or chord. The tangent and the arc are expressed by
two different (perhaps infinite) series of differentials, and these
series do not approach zero in the same way. In fact, one reaches zero
after the other one, which makes it a lot easier to understand why the
equations work like they do.
Because Newton misunderstood circular motion in this way, he also
misunderstood the dynamics of circular motion itself, and the equation
that expressed it. His basic equation a = v^2 /r, which is still the
bedrock of circular motion, is wrong. If you express the orbital
velocity as v = 2?r/t, then the equation must be correct, of course. We
know that from millions of experiments. The problem concerns the fact
that that variable cannot be a velocity. A velocity cannot curve. The
circumference of a circle cannot be expressed by a simple velocity, even
though the apparent dimensions of the variable (m/s) would imply that it
could. Velocity is a vector, and there is no such thing, mathematically
or physically, as a curved vector. By definition, a velocity can have
only one spatial dimension. Any curve must have two spatial dimensions.
Of course a velocity has a time in the denominator, which gives it two
total dimensions. A circumference or orbit must have at least three
dimensions (x,y,t).
Flying in the face of this very simple fact, for some reason
Newton assigned 2?r/t to his velocity. To add to this error, he
conflated the tangential velocity with the orbital velocity. Going into
the series of equations that proved a = v^2 /r, he defined v as the
tangential velocity. That is, it was the velocity in a straight line, a
vector with its tail touching the circle at a 90^o angle to the radius.
But at the end, he assigned v to the orbital velocity, which curved. Any
elementary analysis must show that the orbital velocity is a compound
made up of the tangential velocity and the centripetal acceleration. In
fact, Newton said so himself. It is a fact we still accept to this day,
and it is taught in every high school physics class. If so, it cannot be
the tangential velocity and it should not be labeled v.
This is of paramount importance for any number of reasons, but I
will mention only a couple. Since contemporary physics has inherited
this confusion of Newton and utterly failed to correct it or notice it,
all our circular fields are compromised. I have shown that Bohr's
analysis of the electron orbit is affected by this
mis-labelling, and that the equations used to calculate the velocity of
quanta emitted by electrons must be falsified. Huge problems have also
been caused by the ubiquitous equation ma = mv^2 /r. The form of that
equation has led many to think that the numerator on the right side is a
sort of kinetic energy, but the mv^2 comes from Newton's equation, and
the velocity is not really a velocity. It is not a linear velocity, but
it is also not an orbital velocity. It is simply a mis-defined variable.
It is not a velocity of any kind. It should be labeled as an
acceleration. By correcting Newton's proof , I discovered that
v_t ^2 = a^2 + 2ar
a_o ^2 = 2a_c r
a_c = a_o ^2 /2r
Where a_o is the orbital acceleration, replacing the misnamed orbital
velocity, and a_c is the centripetal acceleration.
By cleaning up our variables and definitions, we can avoid many
problems. Just as a starter, the equation ma = mv^2 /r must become ma =
ma_o ^2 /r. That keeps us from thinking about kinetic energy when we
look at the right side, and solves many many errors, including several
of Bohr, Schrodinger and Feynman.
Another interesting find that intersects my book at this place
is the fact that ? is itself an acceleration. That is, I have shown that
C = 2?r is a distillation of v_o ^2 = 2ar, where ? stands for the
acceleration and C stands for the summed orbital velocity or orbital
acceleration. They are the same equation; the C equation is just the
orbital equation without its full time components. Plane geometry
ignores all time components, so that it allows for this simplification.
Divide both sides of the C equation by t^2 and you will begin to see
what I mean. It is fascinating.
In a related paper I finally show that ?, understood as the
number 3.14, is false. In kinematic or dynamic situations, where time is
a factor, ? is not 3.14 but 4. Since the circumference is an
acceleration, as in the orbit, it cannot be compared directly to the
diameter, which is a velocity. The line and curve cannot be compared one
to one, since the first has one implied time variable and the second has
at least two. Once we expand them physically, it turns out that 3.14 is
no longer applicable. In physics, it is not an esoteric number, it is
simply a mathematical error. In physics, you cannot straighten out a
curve like a string and measure it: straightening out a curve changes it
both mathematically and physically. Obviously this must impact a large
number of equations and a good deal of engineering.
Now we can look at my corrections to relativity. The first major
correction comes from my discoveries on the point. As I said above, the
time variable in SR must be a period. Einstein even admitted this in
later math, when he began writing it as ?t.* But once the time variable
is admitted to be a period, that variable must grow larger as the time
dilates. Einstein admits this also.** Dilation means "to grow larger"
and Einstein admits that as length contracts, the numerical value of t
grows larger. That is why he called it time dilation, in fact. But of
course this puts the two variables x and t in inverse proportion. This
is important since Lorentz and Einstein both use two light equations as
axioms.
x = ct
x' = ct'
The problem is, you see, that the variables in these two equations
are directly proportional, not inversely proportional. One of them must
be wrong. One must be wrong because the two equations are not analogous.
In the second equation, the variables are defined as measurements within
the system S'. But in the first equation, the variables are defined as
those same variables as seen from S. Let me put it another way: the
variables in the first equation are not defined as measurements _within_
S. This would be the analogous definition, one that was equivalent in
all ways to the first one. But that is not what we have. One equation
describes how a system looks to itself. The other equation describes how
one system sees another system. So they don't balance, definitionally.
And this makes the first equation false, given the second.
You can make the first equation true, if you define it as the way
S sees itself. But then you can't solve the problem of Relativity, since
you have no link between the systems. The long and short of it is that
Lorentz and Einstein have used a false equation.
This is not the only smashing error of SR. The other axiomatic equation
of SR, used by everyone from Einstein to Russell to Feynman and beyond, is
x' = x - vt
That equation is also false. We are told that it is the Galilean
or Newtonian expression of relativity, and that the Lorentz transform
resolves to that equation if you make the speed of light infinite. But
that is false. This may be the greatest error in the whole history of
science, since it is both spectacularly wrong and transparently obvious,
and yet it has survived in full view for more than a century. It is not
so stunning that Einstein made the mistake, since everyone knows he was
a poor mathematician. What is stunning is that it has not been
discovered by any of the towering geniuses of the 20th century. What the
Lorentz transform really resolves to if the speed of light is infinite is
x = x'
All you have to do is think about it for a moment. If x' is not
equal to x, then you have a difference in length. A difference in length
is defined as length contraction. But you can't have a length
contraction according to Galileo or Newton. It is impossible. That is
the whole reason that relativity was invented, to formalize length
contraction. And yet Einstein and everyone else has accepted that x' = x
- vt is not relativistic. It /is/ relativistic, by definition, since x
is not equal to x'. There is no way around it. And if it is
relativistic, then Einstein's proof must be circular. He is deriving a
relative transform from an equation that is already a relative transform.
If light's speed is infinite, that must mean that you see
everything that I do at the same time I do, no matter how far away we
are from eachother and no matter how fast we are traveling relative to
eachother. Galileo and Newton didn't need a transform of any kind
precisely because they thought that light had an infinite speed. The
whole universe was a single system. Everyone knows that, or should.
Therefore, you can't have two x's or two t's in a Galilean system.
Velocity just doesn't have anything to do with it. Prime variables are
disallowed in a Galilean equation, because here the prime variable
applies to a second system. A velocity in Galileo's time didn't create a
second system.
Fortunately, special relativity is easily solvable even without these
three equations. Once I corrected these errors, and several others, I
found new transforms that were close in form and output to the ones we
have, which explains why SR has been confirmed despite being wrong
mathematically. My corrections also allowed me to discover what I call
First-degree Relativity. Einstein skips an entire co-ordinate system,
jumping directly into Second-degree Relativity. That is, he finds
transforms for his man moving on the train, but neglects to find
transforms for the train itself. We know that all motion causes
contraction and dilation, and his train is moving; but with current
transforms we cannot go from numbers on the platform to numbers on the
train. Interestingly, the first-degree transform is equivalent to the
simple frequency transform in optics. But the second-degree transform is
not /gamma/ and does not include /gamma/.
I showed that relative motion toward an observer must cause time
contraction, rather than dilation. Relativity is the Doppler Effect
applied to clocks, and clocks moving toward us will be blue-shifted, not
red-shifted. This was already known experimentally from observing binary
pulsars, though no one has made the connection until now. This fact
explodes the Twin Paradox. My new solution to SR also solves the Pioneer
Anomaly and other anomalies.
Next I took my finding into a review of mass increase, where I
discovered that once again all the equations were wrong . The
basic theory was correct, the equations were nearly correct, but they
were compromised by many errors in many places. By making several fairly
subtle tweeks, I found that Newton's equation for kinetic energy was not
only an approximation, it was a precise equation. That is, if you
defined the mass correctly, and used the correct transform, Newton's
equation would resolve out of the mass transform equation in perfect form.
What is more, I discovered that /gamma/ didn't apply to mass
increase either?although here the form of the equation was a near match.
We don't have the square root of /gamma/, and we have an additional term
in the numerator. But you can see that we have that familiar
differential in the denominator.
E_T = m_r c^2 _[1 + (v/2c)]_
[1 - (v^2 /c^2 )]
This correction to the mass transform also allowed me to propose a cause
for the 108 limit to the mass increase of the proton in the accelerator,
a limit that has always remained a mystery.
Next I jump to General Relativity , where I use Einstein's
theory of equivalence to solve field equations without the tensor
calculus. Simply by reversing the central field vector (gravity), I am
able to create a rectilinear field that may be expressed with high
school algebra. I use this method to solve Einstein's bending of
starlight by the sun problem. In five lines of math I solve a problem
that took him 44 pages, and I get the same answer.
s = at^2 /2
t = time for light to travel from the tangent of the sun to the earth
= light distance from sun to earth + light distance of the radius of the sun
s = (9.8 m/s^2 )(501.32s)^2 ]/2 = 1,231,477m
tan? = opposite/adjacent = 1,231,477m/1.50696 x 1011m
? = 1.686 seconds of arc
I also show that his analysis of the spinning disk is false, as
well as his analysis of the bending of light. Perhaps most importantly,
I show that even Einstein's four-vector field is homogenous and
rectilinear at the limit. He gives us this equation,
?-g = 1, so that d?' = d?.
And he says, "The invariant ?-g(d?) is equal to the magnitude of
the four-dimensional element of volume in the 'local' system of
reference". This is extraordinary, because if the volume of every
infinitesimal is equal at the limit, then that means that everything is
equal at the limit. Time and distance must be equal at the limit, which
means that space is homogenous at the limit. No one has yet realized
what this means. It means that the "local" system does exist, even
according to Einstein. What is more, all local measurements are
equal?not just as metaphysics, but as math. The standard model likes to
treat relativity as if there is no way to assert or prove that all local
measurements are equal. But Einstein admits right here that it is one of
the assumptions of the entire theory. It is a mathematical axiom. An
axiom belongs to logic, not to metaphysics.
This brings us to my paper on Minkowski
. Since he relied on the basic
assumptions of Einstein?which I have shown are false?his math must fall
as well. Minkowski's numbers, like Einstein's, are not correct. Which
means that his math is useless no matter how elegant it is perceived to
be. It would be useless even if Einstein's equations had been true,
since his axioms are false. Minkowski allows the time variable to travel
at a right angle to the other variables, but this is false. It does not
do so, in fact, and cannot do so. Therefore his method must be false at
the axiomatic level. If your assumptions are incorrect, then your logic
is incorrect, even in the case that your deductions are true. A true
physical theory requires that both the assumptions and deductions are
unfalsifiable. Minkowski's assumption is not just an unknown, and
therefore a possible assumption. I show that it is known to be false.
Tying into this critique of Minkowski is my critique of 20th century
math in general. I have shown how non-Euclidean fields
are used to fudge equations, how
the complex number plane hides the mechanics of the electrical field,
why gauge math is intrusive and
misdirecting, and how tensor fields
are misdefined and misused.
Another important part of my work in relativity has been the analysis of
the Michelson/Morley interferometer, and with it the Light Clock
. Both ideas rely on the same basic diagram, and I show that
this diagram is false. Everyone from Poincare and Lorentz to Dirac and
Feynman have used an analysis of the right triangles created in these
diagrams to explain time dilation, relative motion, and the speed of
light. Like Newton, they have used a trigonometric diagram to prop up
their theory. But also like Newton, they have failed to draw or imagine
the correct diagram. In particular, the creators and viewers of the
interferometer diagram seem to believe that the scientist collecting
data from the machine is connected to the ether, instead of connected to
the interferometer. Mostly, they leave the observer out of the diagram
altogether, but when his presence is implied by the equations and the
motions, it always turns out that the observer is imagined to have no
velocity. In other words, the interferometer is in the ether stream, but
the observer is on the shore.
But this is not how the real interferometer worked, in operation.
In order to collect data from the interferometer, Michelson and Morley
had to sit very near it, and move as
it moved. They did not let the interferometer move with the earth while
they got off the earth and sat still relative to the imagined ether.
Because they had the same velocity as their machine, Michelson and
Morley should not have expected any fringe effect. Their expectation of
such data was simply a false expectation, based on a false diagram. The
interferometer could only provide a null set.
The same analysis destroys the Light Clock, since the position and
velocity of the clock's observer is never defined. Exactly the same
triangle is created in the diagram, and it is analyzed in precisely the
same faulty ways. The Light Clock does not explain time dilation, and it
leads the viewer into false equations like the ones Einstein used.
Of course, since time dilation is true, my attacks on the Light
Clock and interferometer are not fatal to Einstein or relativity. My
cleaner, more transparent analysis, combined with my better
illustrations, allow me to show that relativity is actually much simpler
and much more reasonable than we have been led to believe. It contains
no paradoxes, requires no leaps of faith, and may be expressed with
simple equations that anyone can comprehend.
My next major contribution to physics concerns the unseen hole in
orbital mechanics . This hole is a
direct outcome of Newton's mistake above. To explain the orbit, Newton
created a balance between the centripetal acceleration and the
tangential velocity. But because he later failed to differentiate
between the tangential velocity and the orbital velocity, both his and
Kepler's analyses of orbits have come down to us hiding magnificent
messes. Physicists now commonly sum the motions in the circuit to show
that the orbit is closed, but the problem is with the differentials. In
any problem with three or more bodies, Newton's balance between the two
motions cannot be maintained. An analysis of the differentials must show
a variation in the tangential velocity of all orbiters, in order to
correct for forces outside the main two. But orbiters cannot vary this
velocity. They are not self-propelled. Newton told us that this
tangential velocity was innate; an innate motion cannot vary. We have
not shown any mechanism or cause of this variance, therefore we cannot
let it vary. To put it another way, the variance is totally unexplained
and unsupported. It has been covered up, possibly on purpose.
What this means is that orbital mechanics is just magic. The
mechanics we have doesn't work and we haven't even tried to replace it
with one that does. General Relativity has nothing to say about this
problem, doesn't solve it, and doesn't address it. GR supplies us with
an orbital math that includes the finite speed of light, but it doesn't
even try to correct the mechanical foundation of the orbit. Courtesy of
the tensor calculus, the problem is just buried deeper, under a heavy
mathematical blanket.
Kepler's ellipse has the same
hidden problem, a problem caused by the general ignorance of the
difference between orbital and tangential velocity. Kepler's ellipse
doesn't work mechanically, since his second focus is uninhabited. The
orbiter is forced to vary its tangential velocity to suit the math of
the summed circuit, but no explanation of how it could do this is offered.
I solve this problem by using the E/M field as a third component.
Orbits are not caused only by gravity and innate motion. They require a
third motion, and this motion is caused by the combined E/M fields of
all bodies involved. With this third motion, it is possible to fully
explain all the motions we see.
For the same reason, Laplace's equations
for Jupiter and Saturn also fail.
Laplace "solved" the Great Inequality between the two planets
mathematically, but his mathematics has no mechanical underpinning. I
show that the foundational E/M field is required once again to explain
the resonance that Laplace's math contains.
Tides also enter this revolution in theory, since tides are not simply
gravitational either. In a long paper
I show that current tidal theory has huge fatal holes in it, holes that
can only be filled by the E/M field. Saltwater is a very good conductor,
and you will have to let that fact lead you into the longer paper, since
I will not address the full theory here. Suffice it to say that the idea
of the barycenter is a critical part of my analysis, and that I diagram
and analyze that idea even more fully than Feynman was able to do. This
proves that the field between the Earth and Moon is a unified field.
Finally, I think I must mention my critique of String Theory
, if only as a nod to current
physics. I do not think my critique of String Theory will actually have
any long lasting effect, since String Theory will have no long lasting
effect. However, my critique is as sharp and amusing as anything I have
written, and many readers have recommended it as one of their favorites.
If you need something a bit lighter to break up your more serious
reading, this might be one place to go.
/To recap:/
1) I show that you can?t assign a cardinal number
to a point, which begins the
revolution in both physics and mathematics. The point and the instant
are jettisoned from physics, and all math and science since Euclid must
be redefined.
2) In my Unified Field Theory , using
Newton's gravitational equation as a compound equation, I separate out
the foundational E/M field and then reunify, including Relativity
transforms. In a related paper , I show
that G acts as a transform between these two fields. Likewise, I pull
apart Coulomb's equation , showing
that it is another unified field equation in disquise. In another
related paper I show that this
foundational E/M field is emitted by the central wall in the double slit
experiment, creating the interference pattern before a single photon
moves through the apparatus.
3) Superposition is explained mechanically
and visually, in a rather simple
manner. Using the gyroscope, I physically create x and y spins and draw
the physical waves created. This explains the wave motion, it dispels
many statistical mysteries, and it falsifies the Copenhagen
interpretation. Using this same spin model, I am able to show the
make-up of all fundamental particles, including the electron and proton,
without quarks. I am able to unify the electron, proton, neutron
, and all mesons
, by developing a simple spin
equation. With four stacked spins I can produce all known particles and
effects.
4) I correct all the numbers involved in the perihelion precession of
Mercury , proving that Einstein's
analysis was very incomplete.
5) Calculus is redefined on the finite differential, which will
revolutionize the teaching of calculus as well as QED and Relativity. In
fact, the fields of all higher math must be redefined. This discovery
ultimately bypasses renormalization, making it unnecessary.
6) I show that many of Newton?s important lemmae are false, including
his basic trig lemmae. His proof of a = v^2 /r is compromised by this,
which forces us to re-analyze circular motion. The mechanics of his
orbit also falls, which requires us to hypothesize a third motion to
stabilize the orbit in real time. I have shown that this motion must be
caused by the E/M field. This also applies to Kepler?s ellipse. And it
explains the mechanics of tides.
7) I also redrew the line between tangential velocity and orbital
velocity , showing that the orbital
velocity must be an acceleration. This requires a rewriting of many
basic equations and cleans up many errors and mysteries, including a few
of those in renormalization.
8) I solved the problem of relativity ,
finding the simple and basic algebraic errors at their inception. I
offered corrected transforms for time, length, velocity, mass, and
momentum. I exploded the twin paradox, and did so by showing
incontrovertibly that relative motion toward causes time contraction,
not dilation. I solved the Pioneer Anomaly. I also proved that Newton's
kinetic energy equation is not an approximation; it is an exact
equation. I explain the cause of the mass limit for the proton in
accelerator.
9) I show the error in the interferometer
and light clock diagrams
, proving that no fringe effect should
have been expected. The light clock creates the same mathematical
triangle and falls to the same argument.
10) Minkowski's four-vector field is
shown to be false, not only because it uses Einstein's false postulates
and axioms, but because its own new axiom?that time may travel
orthogonally to x,y,z?is also false.
10a) I prove that General Relativity is
falsely grounded on the same misunderstandings as the calculus, which is
one reason it can?t be joined to QED. I prove that curved space is an
unnecessary abstraction and that the tensor calculus is a mathematical
diversion, a hiding in esoterica. I prove this by expressing the field
with simple algebra, taking five equations to do what Einstein did in 44
pages.
10b) As a bonus, I prove that String Theory
is an historical embarrassment.
^1 "I am not required to accept the word of any master." [Lat.] This is
the motto of the Royal Society of Science in England, meant to assert
the independence of science from various authorities; but ironically we
must now apply it to them, the various academic societies in the US, and
to the standard model worldwide, which has taken over the dictatorial
powers of the old Church and Monarch that Galileo and Newton had to
resist. Mainstream science has itself become the authoritative and
tyrannical /magister/ or master.
*See /The Meaning of Relativity/, eq. 22.
**See /Relativity/, XII, last paragraph.
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