Possible New Approach to Experimentally Creating Fusion Energy
Newton's Shell Theorems
Understanding Fusion, How the Sun Shines and Gravitation
We may not understand the fusion process correctly
For decades, we have believed that the Tokamak apparatus is the only
credible experimental method of creating Nuclear Fusion. Isaac Newton
may have provided us some knowledge three hundred years ago that may
open up new Fusion options today.
An important gravitation lesson was given to me in late 1963 as a First year
Physics student at the University of Chicago. Just two weeks earlier I
had never even seen an Integral Calculus symbol, and now I wound up having
to solve multiple Vector Integral Calculus problems as homework. The
Professor was teaching us about Newton and his Fluxions (which we call
Integral Calculus now). He had just taught us and derived for us Newton's
standard equation of gravitational force.
F = G * m1 * m2 / r2
I encourage all readers to examine Newton's beautiful math (Calculus)
derivation of his Shell Theorems. (Many internet pages present the
correct Integral Calculus involved. Actually, some of those mathematicians,
including Wikipedia, make a subtle error in their math, where they try
to use Cartesian (x,y,z) coordinates, where Newton had used the correct
Spherical coordinates (r,θ,φ).)
The far more interesting lesson was to be next. Clearly, the Professor had
decided to demonstrate how brilliant Isaac Newton was, even regarding the
Fluxions that he had just invented. The Professor then decided to do the
calculation (of Newton's) for a location halfway down inside the Earth. He
stated a requirement that the Earth must be uniformly symmetric, although
density increase with depth is allowed.
The Professor then decided to use a Spherical Polar coordinate system, as
Newton did, and then he set up a triple Integral Calculus problem (of
Newton's gravitational force equation mentioned above) in that coordinate
We students (me just barely 17 years old then) were given the actual math as
homework. U. of Chicago seemed to think that if you could not do the
math, you did not belong there. Unfortunately, my High School Physics
Teacher was not very good and we had never gotten to ANY of the more complex
Chapters in the Physics textbook, so I had a LOT to learn, really fast.
The Professor had given us some suggestions. Possibly the most important
of those was to first calculate the Integral Vector Calculus total for
the two angular coordinates for a very thin spherical shell centered on the
center of the Earth, but for such a shell which was at a radius which was
greater than the radius of the chosen location inside the Earth.
The start of the homework problem was initially just a double Vector Integral,
for all locations everywhere on that shell, which had delta-r (miniscule) shell
thickness. I encourage all readers of this to repeat that homework assignment.
Today, such Calculus problems are called Newton's Shell Theorems.
It turns out that, no matter what specific location is chosen inside the Earth,
an incremental location right "behind" you is close so the
inverse-square law applies, but there is such an enormous area "across" the
shell, that the net attractive force Vector from way over there EXACTLY EQUALS
the attractive force Vector from that tiny area "behind" you, which is
a Force Vector which is in the exact opposite direction. When you do the
complete Vector Integrals for that specific shell, Newton found that the
Calculus Vector Integral is EXACTLY ZERO.
The next part of that homework was to do a Third Integral, the third coordinate
in the radial direction, r, for the series of shells from your location within
the Earth up to the surface of the Earth. It was obvious to us students that
the Vector Integral of a bunch of zero-amplitude Vectors is zero.
What the Professor had taught us, of the Fluxions math which Newton had done
three hundred years ago is that the strength of the gravitational field at ANY
location inside the (symmetric) Earth was ONLY due to the Mass of the Earth
which happened to be in the Core part of the Earth which was the size of the
sphere of the Earth which was the size of the location you happened to be at.
For the homework problem the Professor gave us, of half the radius, that smaller
ball which actually was providing a gravitational field for you, was only 1/8
the volume of the entire Earth. The density of the Core of the Earth was much
higher than our Crustal rocks, but gravitation acts at an inverse-square law.
For the student, the net effective mass of the Earth acts as though it is at the
Center of the Earth, so the effective gravitational field would have a 4 times
factor compared to for us at the surface.
Therefore, there are four mathematical effects which must be calculated, (1) the
ignoring of all the mass of the Earth which was at greater radius than you are
at; (2) the average density of that portion of the Earth which is within that
radius (around 2.5 times as great); (3) the net mass of that portion of the
Earth, that is, density times volume or (2.5 * 1/8); and (4) the inverse-square
distance of you from the center of the Earth (which is 4 times greater).
For the specific homework problem, the Professor noted that the Core of the
Earth is considerably more dense than our Crust, and so the net measured effect
of all these factors would be a SLIGHT INCREASE in local gravitational field
(1/8 * 4 * 2.5), as you were halfway down inside the Earth as you did an entire
trip "Journey to the Center of the Earth" as Jules Verne wrote long ago.
If you continued that trip to the center of the Earth all the way to the
Core, there would be no remaining gravitational force Vector there at all!
A crisis regarding the logic for stars heating to accomplish fusion
I see an entirely different important application of Newton's mathematical analysis.
Consider the Sun or any other star. We usually describe it as though the whole
WEIGHT of the entire Sun is pressing down onto the very Core of the Sun, which
we then say creates spectacular pressures and therefore temperatures of many millions
of degrees Kelvin, which is then what we claim causes Hydrogen nuclei to FUSE
into each other to form Helium atoms and which releases the spectacular amounts
of energy from fusion that our Sun radiates away and which keeps us all alive.
However, consider Newton's reasoning and math above. Consider the very Core of the
Sun, maybe a space the size of the Earth. There is NOT the mass of 330,000
times the Earth pressing down on that Core (which has always been totally
accepted as logical for creating the enormous pressure and therefore
temperature). Per Newton's Integral Calculus, that simply cannot be true. That
portion of the Sun, its very Core, REALLY, only has roughly the weight of ONE
Earth gravitationally pressing down on it. How in the world could THAT create
enough pressure and therefore temperature of many millions of degrees Kelvin, to
initiate and maintain nuclear fusion?
Logic being what it is, this reasoning and math of Newton seems airtight. There
MUST BE some other explanation for how the Sun (and all other stars) creates
sufficient gravitational pressure and high temperature for Fusion. We
necessarily must be very wrong in our understanding of even this basic idea.
Newton WAS right, and a whole lot of Physics students did the homework problems
to confirm it.
We THINK that the Sun creates Nuclear Fusion due to the enormous heat of
the Core of the Sun being "crushed" by the gravitation of the
mass of 330,000 times the Earth. It seems likely to be somehow true,
that the heat of many millions of degrees Kelvin is necessary in order to
have the Hydrogen atoms crash into each other fast enough to fuse
together. But the logic which we try to use to describe how that
tremendous heat must exist in the Core of the Sun must certainly
be very wrong.
We SHOULD collectively be able to figure out the correct
explanation! Let's do it!
Experimental Fusion Physics
This might suggest that the experimental methods now used to try to
accomplish Fusion may not be the best approach. The assumption
described above suggests that the Sun requires tremendous gravitational
force, due to the entire mass of the Sun collapsing the Core of the Sun
so that temperatures of many millions of degrees Kelvin "must"
occur, which therefore encourages hydrogen nuclei to travel at such high
velocity that they Fuse when they crash together. In that, we assume that
Fusion occurs and produces all the enormous energy that the Sun (and all
other stars) radiate out into space.
But Newton seems to have been right in the logic and math described
above, which suggests that the Sun does NOT "crush" its Core
to cause the high temperatures there. This seems to suggest that we might
have some far better, and possibly simpler, method for creating Fusion.
Maybe the Tokamak equipment might not be the best approach. If so,
and we figure it out, we may yet have "unlimited energy for
Another crisis in the logic regarding Black Holes
Newton's reasoning and math must also apply to our understanding of black holes.
The same logical errors just discussed regarding stars being able to
gravitationally collapse to cause enormous pressure in their Cores, and
therefore cause the heating to many millions of degrees Kelvin, must apply even more
intensely regarding the current understanding of black holes. We claim that the
very center of a black hole is crushed to molecular size, entirely due to the
spectacular amount of mass which surrounded it and forced that collapse with all
the implications we credit to black holes. That logic MUST be totally wrong!
The same logical problem exists regarding the "alleged" neutron
stars, which are also assumed to have spectacularly collapsed into extremely
tiny and dense objects. They seem to have an even additional complication,
as it seems logically unlikely that any neutrons even exist within any
atomic nuclei. Consider the two following Research and mathematics
Nuclear Physics May be Fairly Simple
Nuclear Physics - Statistical Analysis of Isotope Masses
This presentation was first placed on the Internet in June 2017.
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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago