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Three
Problems Solved Mechanically: PARTIAL
REFLECTION BY GLASS THE RIGHTHAND RULE AND FEYNMAN'S
SHRINKANDTURN
METHOD
by
Miles Mathis milesmathis.com
A
smith is put to shame,
And
learns from the lad he taught;
All
the master's lore is useless now.
—Wagner, Siegfried
Abstract: In this paper I will show
why Richard Feynman’s “shrinkandturn” method
works. In doing so, I will be able to show a mechanical cause of
partial reflection by glass, one that is different from that of
Feynman, Newton, Huygens, or anyone else in history. Finally, I
will show how the righthand rule of E/M is caused by the simple
motions of photons.
The subject for this paper occurred
to me while I was rereading my
recent paper on QCD. There, I mention in a footnote that I
followed the emitted photon out through the four spins of the
baryon by using a toy dog. I would sit in a chair, holding my
plush friend up in front of me, and like Einstein riding his
lightray, would imagine the two of us actually making the trip
out through the spins. At each intersection of spins, I would
turn the dog 90^{o}
to the left or right, and also spin him 90^{o}.
In this way I could compare his final position to his initial
position, and find in that way both the correct vector and the
correct spin orientation at emission from the zspin. In
rereading this drole footnote, I realized that my method had
somewhat in common with Feynman’s “shrinkandturn”
method with arrows and clocks, which he used to find amplitudes
or probabilities. Feynman always considered this method just a
trick, and in his book QED
he calls it “absolutely ridiculous.”^{1}
But in my second
paper on Feynman, I critique this book, and there I mention
that Feynman’s method seemed to me to be very suggestive, a
pointer to some real mechanics. I even stated that it was so
suggestive that I suspected a cover up. I suspected (and still
suspect) that Feynman knew his method implied a particular
mechanics, and I suspected that contemporary physicists were
resisting Feynman’s method precisely because it had a
mechanical flavor to it. Back in the 70’s and 80’s,
this shrinkand turnmethod was often taught to graduate
students, especially on the West Coast, but you don’t hear
much about it anymore. In fact, a web search leaves you pretty
much empty handed. I take this to mean that the current masters
of QED prefer to keep the theory under the heavy mathematical
blankets, rather than allow the theory to be taught in visual or
fauxmechanical terms. The last thing these physicists want is a
rigorous mechanical analysis of QED, since that would bring all
their gigantic holes into view.
At any rate, I soon saw that I now
had a physical explanation for what I only suspected a few years
ago. I now had a way to show exactly why Feynman’s method
worked, from a fundamental, kinematic perspective. The “turn”
part of the “shrinkandturn” method was coming right
out of my stacked spins.
Before I clarify that connection,
though, I want to take a look at the righthand rule. Both
Feynman’s method with the arrows and clocks and my method
with the toy dog are connected to the righthand rule. Once I
point it out, this connection is not hard to see, and others may
have made the connection before me between Feynman’s
turning and the righthand rule. But until now, no one has been
able to say exactly what that connection is.
The righthand rule is just a rule
of thumb for finding the direction of the magnetic field given
the electric field (or vice versa). Using your right hand, you
curl your four fingers and point your thumb straight up. If you
match the direction of your thumb to the direction of the
electric current, then your fingers will tell you the direction
of the magnetic field. This has been known for a long time, but
it has never been explained mechanically using quantum
relationships. In other words, until now the righthand rule has
been heuristic or experimental knowledge, not physical knowledge
of the field. Up till now, no one could tell you why we don’t
have a lefthand rule instead. It is a loss of parity in the
field that has been pretty much left in the dark.
The reason we have a righthand
rule is that the charge field is righthanded itself. This is new
information, coming out of my field analysis: it is unknown to
the standard model and was unknown to classical E/M theory. For
prequantum electrical theory, the charge field was simply a
field of potentials. Neither wave mechanics nor spin had any
place in the theory. Faraday’s field was a field of lines,
and so was Maxwell’s. The charge field of QM and QED was
also not given spin, chirality, or any other nonsymmetry. All
the spins of QM are given to the electron. To give the charge
field spin would have required giving the virtual photon spin or
some other heterogeneity, but the standard model has never
reached that level of cleverness, even to this day. Quantum
Mechanics gave up on mechanics 80 years ago, and any new
necessary “degrees of freedom” were given to the
math, not to the particles.
But in my field, the charge itself
has charge. The first charge is the emission of the photons.
Charge energy is transferred by the linear motion of these
photons. The second charge is the spin of these photons, since it
can either be CW or CCW. The charge field can either be plus or
minus, since it creates potentials; but the spin of the field can
also be plus or minus, in a way, since we can always assign a
plus to CW and a minus to CCW. So the electron actually needs two
signs on it, not just one. It needs the first minus sign to
signify that it is at a lower potential regarding charge, being
on the receiving end of the charge field in all relations with
the proton or nucleus. And it needs a second sign to
differentiate it from the positron. This sign tells us the spin
direction of the emitted photons.
Now, the standard model knows this,
in a way. It knows that the positron and electron are opposites
in some way, and it often uses a charge sign to designate this
difference. But it cannot say what the charge sign applies to,
mechanically or physically. It has certainly never assigned this
difference to the spin of the photons emitted. It could hardly do
so, since the charge photons of the standard model are virtual.
Beyond that, they are point particles with no size and no mass.
They could hardly spin without size and radius.
The reason the charge field is
righthanded is strictly a local phenomenon, decided by a
confluence of natural factors beyond the reach of this paper. The
charge field can be either righthanded or lefthanded or
neutral, but on the Earth it happens to be righthanded. Why?
Because on the Earth, in almost all cases, the charge field is
emitted by matter rather than by antimatter.
The entire and defining difference
between matter and antimatter is that matter emits a
righthanded charge field and antimatter emits a lefthanded
charge field. To say it even more clearly, matter emits photons
upsideup, and antimatter emits photons upsidedown. Emitted
photons are always spinning, so antimatter emits photons that
are spinning “the wrong way.”
Now, the Earth contains both matter
and antimatter, but it contains a preponderance of matter.
Contrary to popular opinion, matter and antimatter do not
annihilate one another when they meet. No, their charge fields
cancel each other, and the particles therefore have no cushion or
protection. They collide, and in collision their outer spins
cancel. In this way they loose a large portion of their energy
and therefore of their mass. But they do not dissipate into
nothing. They dissipate into small nonspinning particles, which,
due to this lack of spin, become invisible to detectors. But,
given time, they can, through more collisions, develop new spins
and new higher energies.
What explains the preponderance of
matter over antimatter in our region is that antimatter that
has been stripped of spin in this way will reform as matter. Say
you start with an antiproton. It collides with a proton and
loses all four spins. At this point it is like a nonspinning
electron. What is a nonspinning electron? I
have shown that a nonspinning electron is nine times smaller
than an electron at rest with axial spin, which is what we call
an electron. A nonspinning electron is also invisible to normal
detection, since ionization detectors and other detectors cannot
detect nonspinning quanta. They have no velocity relative to the
field and make no tracks.
But very soon these quanta are
bumped by other quanta, and they gain both velocity and spin in
this way. In most cases, they are bumped by photons, since
photons make up the charge field. Photons outnumber everything
else by a very large margin, so the odds are very good that this
nonspinning electron will gain its new energy from photons. But
most of these photons are righthanded photons, so the particle
will rebuild as a proton. It gets its spin from the field, and if
the field is righthanded, the particle’s new spin will
also be righthanded. This means that a normal charge field, as
we know it, will turn antimatter into matter, through this
simple process. Over time, all local antimatter will be turned
into matter, and the entire local field and everything in it will
become righthanded. Only the fact that the macrofield is not
homogeneous, rectilinear, and unidirectional keeps the field from
being completely righthanded. Because the field of the Earth is
spherical, and receives emission from all directions, it
maintains a fraction of antimatter. It also receives antimatter
via the Solar Wind.
You would think this would be the
default case in most situations, but it isn’t. Even in our
Solar System, it isn’t the default case. One would think
that a balance would be hard to maintain, and once the balance
was lost the field would quickly become either left or right
handed. But the planets nearest to us, Mars and Venus, appear as
proof against this assumption. Both planets are nearly
nonmagnetic, and I
have interpreted this to mean that their overall charge
fields are neutral. They lack a magnetic field because their
charge field is neither righthanded nor lefthanded, and this is
due to equal charge emission by matter and antimatter. The
planetary system as a whole on Mars and Venus has not lost its
charge symmetry, and therefore the antimatter has not been
turned into matter. I don’t yet have a firm theory for why
this is, though it might be that life is a catalyst for loss of
charge symmetry. Life on Earth causes an increase in all
interactions and events, and this increase may increase overall
ionization and collision, which increases the likelihood of
imbalance in the charge field. A charge field that mediates fewer
events, as on Venus or Mars, may find it easier to maintain
symmetry. A symmetric field, in this case, is a nonmagnetic
field.
By this analysis, it is likely the
universe, the galaxy, and perhaps even the Solar System, has many
planets where the lefthand rule is correct. There is nothing
intrinsically strange about antimatter, and we could not easily
tell the difference between a world made of matter and one made
of antimatter. The only difference would be in rules like the
righthand rule.
As
I have shown with my stacked spins, you can build either a
proton or an antiproton from an electron. You do not need to
make antimatter from antimatter or matter from matter. They are
not fundamentally different. Just as you can turn a neutron into
a proton, simply by reversing the zspin, you can turn a proton
into an antiproton simply by reversing the yspin. You can’t
do this just by applying a field to a proton, since you can’t
reverse inner spins without affecting outer spins; but you can do
it by building the antiproton from an electron or meson. You
simply have to hit it with the right fields in the right order.
But my point is, you do not have to build an antiproton from a
positron. So there is no fundamental difference between matter
and antimatter. Antimatter is not freakish or foreign, it is
just emitting photons upsidedown compared to “normal”
photons, and it is emitting them this way only because of the way
its spins stack up.
From this we can see that the
nonmechanical nature of both QED and QCD have kept them from
answering questions like this. I have argued in many places that
the mathematical complexity of QED and QCD and their lack of a
physical foundation have made them impervious to understanding,
correction, and almost all critique, but the most critical
failing of both is their lack of explanatory power. A successful
mechanics, once understood, can be exported into other fields and
other problems. A clearly stated solution leads to a line of
solutions, since one can easily see how to move from problem to
problem. But with dense modern theories, connections like this
are difficult to make. Nothing is ever a clear pointer to any
other problem or solution, so that physics gets bogged down in
minutiae and esoterica. Instead of striding boldly from one
success to the next, the field becomes stale and academic, and
has to be defended from all rigorous analysis and outside
influence.
My explanation of the righthand
rule is neither esoteric nor especially creative: it is simply
putting together a series of logical steps. In fact, it is much
less “inventive” than most things that pass for
theoretical these days. But this explanation was made possible by
my initial
explanation of superposition, in which I first discovered
stacked spins. And that explanation was made possible by my
insistence that quantum interactions could be and must be
explained sensibly and mechanically, with all classical rigor.
Now
let us return to Feynman. Feynman begins his shrinkandturn
analysis in the book QED
by analyzing partial reflection by glass. He tells us that it has
long been a great mystery: that Newton couldn’t solve it,
that Huygens couldn’t solve it, and that wave theory
couldn’t solve it. Newton couldn’t solve it, he says,
because, despite the fact that Newton correctly chose the
corpuscle or particle theory of light, Newton couldn’t
explain how the light knew how many reflective surfaces an object
had. Wave theory couldn’t solve it because classical waves
would be expected to diminish with dimmer light. But the
detectors do not detect a diminution with dimmer light. Dim
reflected light “clicks” less often, but just as
“loud,” and Feynman takes this as proof that light is
not a wave.
Feynman admits that QED also has no
mechanical explanation for partial reflection by glass,
but it is superior, he tells us, because it can supply a very
precise math. Of course, Newton also supplied a successful math,
but because Newton tried and failed to explain it mechanically,
and because QED gives up on attempting an explanation, QED is
supposed to be superior. We must suppose that Feynman believes it
is better to have never loved at all, rather than to have loved
and lost. It is better to refuse to explain a phenomenon, rather
than try to explain it and fail.
At any rate, with partial
reflection, experiment shows that it is the thickness of the
glass that is important. Given a type of glass with an overall
reflective index of .04, the real reflection will vary from 0 to
.16. Yes, very thick pieces of glass, of just the right
thickness, will allow all the light to pass without reflection.
And thinner pieces, of just the right thickness, will square the
reflection. Other thicknesses give values between these maxima
and minima.
The crucial part of Feynman’s
method is that he assigns a vector or arrow to each photon. The
length of the vector is predetermined by the reflective index,
but the direction of the vector is determined by the how far the
photon travels before being detected. Feynman uses a dial clock
to measure this distance, letting the second hand move as the
photon moves. He lets the photon reflect from both the front
surface and the back surface of the glass, and then does a vector
addition of the two draws. The angle difference between the two
vectors becomes his final amplitude or probability.
Feynman spends a lot of time in
this book telling us light is a particle and not a wave, but the
turning dial on his clock is acting just like a wave function
here, as is clear to anyone awake. And not just like a wave
function, but like a physical wave. A turning clock IS a wave,
since the numbers come in waves. The number 12 comes with a
definite period, of wavelength twelve and frequency 1/12.
Feynman’s method works only because his clock is a wave.
But why does this method work? We
will suppose that Feynman didn’t know, although, as I have
said, it is very possible the masters of QED have known all along
that a fairly simple mechanics underlies these interactions. They
may have suppressed the mechanics for two reasons: one, the
arcane sells better than the simple, and is easier to control;
two, the simple explanation could not be made to work with the
old electrical field, which QED has kept hidden underneath its
mathematical blankets. If we admit that the photon has spin, we
have to admit that it has radius, which means it has mass, which
means it is not virtual, which means the charge field has mass,
which means energy is not conserved in emission, which means that
QED has to be rebuilt from the ground up. No one wanted to do
that, so it was better to pretend that QED was a big mystery,
unlocked only by magicians with blackboards full of math.
Feynman wants you to believe that
this problem of partial reflection is very great, as I have
already shown—to the point, in fact, that it is physically
insoluble. He wants to add it to the list of things you don’t
need to try to solve, since Newton couldn’t solve it and
neither can he. He stops just short of adding it to the
Copenhagen list of things you are forbidden to look at, since
they are impossible to solve.
Despite this, I think we can say
that Feynman makes some astonishing assumptions. Feynman shows
that Newton dismissed the idea that reflection took place at the
first surface, because, “how could light reflected from the
first surface be captured again when the thickness is such that
there was supposed to be no reflection at all?”^{2}
This is obviously a good point, but Feynman runs past it without
analysis, dismissing Newton’s analysis in toto because
Newton then proposes “fits of easy reflection or easy
transmission.” Yes, Newton’s idea of these
unexplained “fits” is not a good one, but the idea of
“fits” is separate from the idea of nontransmission
from the first surface.
I bring this up because, as I have
shown, Feynman lets his photons reflect only from surfaces. But
he does not give any reason for doing so. Why should reflection
take place only at surfaces? How can Newton be wrong in his
deduction that reflection cannot take place from the first
surface? In fact, Newton cannot be wrong about this.
Feynman’s method of using front and back surfaces can work
only by averaging, as I will now show.
Since molecules exist throughout
the glass, and since the light must be interacting either with
these molecules or with their E/M field, we must assume that
reflection occurs throughout the material, not just at the
surfaces. Something special may be occurring at the surfaces, but
the main effect must be taking place within the material.
Rather than treat photons as point
particles, we will treat them as particles with spin. This spin
will immediately provide us with a wavelength, and we will see if
that wavelength can explain partial reflection. Feynman tells us
that wave theory cannot explain the way our detector works, but
that is only in the case that light is a field wave, like sound.
If light is a particle with spin, then the wave belongs to
the particle itself, and will not diminish with dimming light. In
this case, each photon has a wave, and this solves the first big
mystery all by itself. The wavelength does not belong to the
wavefront or to a large group of photons; it belongs to each
photon individually. In this way, the wave can be carried full
strength to the detector, even with only one photon.
From this point on, my solution is
just a restatement or variation of the wave solution Feynman
dismissed. Up to the 19^{th}
century, there existed a wave solution to this problem, as
Feynman admits. Since I have already shown that his critique of
the wave solution no longer applies, I have already proved my
point, and we can resuscitate the wave solution. Feynman says the
wave solution can’t be right because wave theory predicts
wave diminution. But his critique doesn’t apply to my waves
as spins, since the wave is now carried by each particle. My spin
theory fills in the holes left by classical wave theory, and the
mechanics is fully explained. In this way, Newton, Huygens, and
Feynman are all partially correct, and so is Bohr. Light is both
a particle and a wave. It has a duality, if you like, although
that duality is no longer squishy or undefined. Light is a
spinning particle, and the spin creates the wave in a simple
mechanical fashion. The wavelength is simply the spin radius.
This spin radius is then stretched by the linear velocity of the
photon, as I have
shown elsewhere in detail.
What does this have to do with
Feynman’s clocks? Feynman’s clocks follow the motion
of this wave as the photon travels through the glass, telling us
where the photon proper is in its spin wave at each dt. Like
the electron, the photon must have at least two spins to show
a wave and to explain these physical effects. It must have an
axial spin and an xspin, with the xspin twice the radius of the
axial spin. Feynman’s clock measures one spin against the
other, and tells us where the body of the photon is in the
greater xspin. The body of the photon cannot inhabit all the
space in the xspin, obviously, since the photon has a radius of
1, say, and the xspin has a radius of 2. Since reflection is a
collision, we need to know where the body of the photon is in the
wave. We then combine that information with the molecular
structure of the glass, to determine how much space is in the
glass, how likely a collision is, and what the deflection or
reflection angle must be. Feynman’s clock tells us the
first of these variables: where the photon is in its own wave.
The length of his vector or arrow is taken from the known index
of the glass, and that is second variable here: the molecular
structure of the glass. This molecular structure, being
structure, then
acts as another wave. A sort of standing wave.
It is a standing wave not in any
esoteric sense, but only in the sense that any patterned
structure is a wave. A cattle guard is a standing wave, in this
sense, because its structure is a definite and fixed pattern, one
that we can mathematically treat like a wave. Since we have one
wave meeting a second wave, we can use pretty basic wave
mechanics to predict collisions.
After that, Feynman’s use of
front and back surfaces actually has nothing to do with surfaces.
It has only to do with limiting the math. Feynman’s method
does not happen at these surfaces, it happens between
these surfaces. His waves interact between these surfaces, so
that he is actually averaging from front to back. Or, to say it
another way, he is summing over that width, from front to back.
His integral is taken from front to back. If your integral goes
from 0 to 1, that does not mean that things are happening only at
0 and at 1, it means that things are happening between 0 and 1.
^{1}QED,, p. 24.
^{2}QED, p. 23 footnote.
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