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Scalar Theory of Everything (STOE) unites the
big, the small, and the four forces (GUT) by
extending Newton’s model
John C. Hodge
Retired, 477 Mincey Rd., Franklin, NC, 28734
E-mail: jchodge@frontier.com
Abstract
Newton established a major physics advance that was confirmed by
predicting the late return of Halley’s comet. Newton identified three
characteristics of bodies that have been identified as three characteristics
of “mass”. Current standard physical models have become very complex
with divergent postulates for cosmology and quantum mechanics. Physics
theory restarting from Newton’s speculations and then describing the ex-
periments of the 19th and 20th centuries results in a model of the big,
the small, and the four forces (GUT) - the Scalar Theory of Everything
(STOE).
keywords: TOE, GUT, Newton, mass
1 INTRODUCTION
Human physical models must begin with some postulates, evolve to explain ob-
servations, and make useful predictions. Newton created a theory of gravity with
his three laws of motion [1]. This model related the motion of bodies on Earth
and of the Moon. The key measurable characteristics of bodies were assumed.
Later, Newton speculated on the common postulates for gravity and light - the
big and the small. The predicted late return of Halley’s comet confirmed New-
ton’s model for the solar system scale. Thus, astronomical happenings were
related to Earth-born experiments. A key characteristic of Newton’s model is
that it is simpler and describes a wider range of observations than the other
models it replaced.
Newton identified three characteristics of bodies that are different views of
mass characteristics. This is the postulates stage. Definitions become better de-
fined as they are related to observations. Weight (mw) was defined as a body’s
density times its volume and as the “quantity of matter” in a body. A body’s
density, volume, and innate force of matter are our everyday understood param-
eters. Inertial mass (mi) was defined as a body’s innate force of matter with
1
1 INTRODUCTION 2
the power of resisting a change in its state of motion. This force is exercised
only when another force impressed on the body changes the body’s motion.
Gravitational mass (mg) was presented in his third book of the Principia. It is
the body’s characteristic that instantaneously impresses an attractive force on
another body over a distance in absolute space. The electromagnetic forces were
unaccounted in Newton’s time. Fluid and other forces were outside Principia.
Newton recognized that a gravity only model created a problem in cosmology
requiring an infinite, eternal universe and requiring an infinite force as dis-
tances between centers of mass approached zero. The motion of the moon and
Sun suggested instantaneous reaction to the force of gravity. A more complete
description may be found in Assis [2, Section I and III].
Newton’s model works by defining (mapping) forces that are exerted on
matter then adding force vectors to arrive at a single force that predicts the
mass’s measurable motion by inverse mapping. This requires the mathematical
constants of proportionality to be such that the body’s motion is as observed.
Later, Newton expanded on how mgmay be impressed on another body and
the relation of gravity and light, stated in modern terms [3]:
Qu. 1 Masses bend passing light by an amount inverse to distance.
Qu. 3 Light passing close to edges are diffracted in fringes.
Qu. 4 Light path begins to bend BEFORE reaching a body or slit.
Qu. 5 Light heats mass.
Qu. 6 Black bodies absorb all light.
Qu. 8 Black body radiation.
Qu. 11 Sun and stars are black body radiators.
Qu. 17 Light is corpuscles that are pushed around (divergence of the aether’s
density) by waves of the aether that “overtake” the rays of light. The
waves in the aether travel faster than light - its not a big stretch to say
MUCH faster than light. That is, gravity is not force. Gravity is the effect
of the divergence of the aether, also.
Qu. 18 A Medium that refracts and reflects light also allows light to heat
bodies. Newton also suggested light travels faster in the void (denser
parts of the aether). This is the measured Shapiro delay.
Qu. 19 Refraction of light implies differing densities of the Medium (calls it
“...this aether Medium...”). Density of the aether is GREATER in “...free
and open spaces void of air and other grosser bodies...”. How the aether
became denser between bodies was unexplained.
Qu. 20 Increasing aether density (ie divergence) causes light refraction.
2 THE DEVIATION FROM NEWTON’S PATH 3
Qu. 21 Aether rarer within dense bodies and increase with distance and “...thereby
cause the gravity of those great bodies; every body endeavoring to go from
the denser parts of the medium towards the rarer?”. He also suggested
the aether is so rare as to not impede the planets revolution (no aether
wind).
Newton suggested a reductionism step by positing (1) an aether whose di-
vergence exerted a force that caused gravity and that caused the diffraction,
reflection, and refraction of light and (2) corpuscles as light and as components
of matter. That is, support for the aether and corpuscles was because the
model could explain several diverse observations then known but mysterious
rather than by direct observation.
This Paper suggests the Scalar Theory of Everything (STOE) is a continua-
tion of Newton’s model. Section 2 briefly describes the deviation from Newton’s
path and some observations after Newton’s time. Section 3 describes a STOE
model of the three types of mass as independent physical effects. The Discussion
and Conclusion are in section 4.
2 THE DEVIATION FROM NEWTON’S PATH
Young’s Experiment of interference was interpreted to indicate light was a wave
rather than corpuscles and rather than the wave interference was caused by the
aether (Newton used a rock-thrown-into-water analogy). This began the effort
to attempt to explain observations of the small scale by waves, fields, etc. This
effort has resulted in the very counterintuitive (no analogies with the classical
world) Quantum Mechanics and the loss of the connection to gravity. This has
resulted in the incompatibility of General Relativity and Quantum Mechanics.
Several experiments in electricity and magnetism were combined into Maxwell’s
Equations rather than discovering how Newton’s three masses and a single, con-
tinuous aether could explain the experiments. Because the experiments were
independently done, several simplifications resulted in incorrect descriptions
[4; 5; 6; 7]. The electromagnetic signals have a speed of light. If light is a wave,
then the speed of a wave is the speed of light. However, this has been falsified
for the speed of coulomb fields [8].
The invention of the Hamiltonian and the Lagrangian that calculated a
body’s motion in terms of energy resulted in the distinction of the three masses
being lost. The mwhad been considered as an miand these functions con-
sidered the distinction between kinetic energy and potential energy as caused
by one type of mass. However, Newton argued the miand mgwere distinct
but proportional which were included in the gravitational constant G. Models
currently exist that suggest the Gvaries across a galaxy such as MOND.
Mach’s Principle, which is vague, suggested that the stars in the universe
should influence measurements (inertia) on Earth. Mach’s Principle is viewed as
suggesting a total relativism and as a substitute for Newton’s “absolute space”.
However, because the influence is by bodies, the higher aether density required
by Newton (so the mgcan reduce the aether) is unaccounted.
3 THE STOE 4
The well–known Einstein thought experiment of a measuring system in a
(small) box (such as an elevator) being unable to determine if the box is in a
gravity well or under acceleration of a rocket resulted in the Strong Equivalence
Principle. But this is incorrect. Gravity acts as if from a point (center of mass).
Therefore, gravity shows the force vectors as converging. The rocket shows force
vectors as parallel. The “small” condition to achieve equality is more properly a
measurement uncertainty. The “small” condition was ignored and the equality
of acceleration and gravity was accepted.
The left side of the General Relativity Field equation (LHS) is a mathemat-
ical mapping of observed energy and momentum into sand tparameters called
“spacetime”. But like Newton’s aether it has a high value where no mass exists
such as between galaxies and depressed values around masses. From whence,
this “spacetime”? That is, the “spacetime” (LHS) cannot be real. Therefore, it
is a mapping that must be inverse–transformed to real energy and momentum
measurements.
General Relativity and other metric theories are NOT Machian models al-
though there have been several attempts.
Because the stars of galaxies are modeled as the source of the Machian influ-
ence, the background of all “spacetime” must decrease (like Newton’s model).
The Big Bang model suggests a high amount of the stuff of the universe between
galaxies that infalls into galaxies. However, observations falsify the infall model
for spiral galaxies. Rather, spiral galaxies eject matter. However, elliptical
galaxies do have infall characteristics [9].
The discovery of phenomena suggesting an atomic structure resulted in at-
tempting to describe the spectra as an orbital (angular momentum) characteris-
tic of electrons [10]. This became untenable because radiation should be emitted
and none was observed for stable structures. Later attempts became weirder
and more complex by using Quantum Mechanics combined with many ad hoc
exclusion rules.
Many observations suggest several parameters are “fine–tuned” such as the
temperature of the microwave background. Fine–tuning remains unexplained.
The increase number and accuracy of observations has resulted in physical
models becoming more complex and separated into at least 3 major incompatible
disciplines - Relativity, Quantum mechanics, and subatomic particles (group
theory) including the Grand Unified Theory (GUT).
3 THE STOE
The return to Newton’s path started with the Quasi Steady State Cosmology
(QSSC) [11; 12]. QSSC suggested a Source of the stuff of our universe at the
center of galaxies. The rotation curves of spiral galaxies were explained as a
medium density directing bodies to vary as 1/d (dbeing the distance from the
Source) according to the spherical principle. Note the positive value that causes
an outward force on bodies. Matter moving outward combines to form heavier
bodies that are gravitationally attracted inward in spiral galaxies. However,
3 THE STOE 5
some matter escapes as the 1/d pushes it beyond the galaxy’s gravitational
influence.
For the volume between galaxies to have low medium density, the universe
must expand. Because the Sources adds the stuff of the universe, the QSSC is
Machian. However, the QSSC fails when describing elliptical galaxy character-
istics.
The STOE posits the components of the universe are discrete hods and a
continuous plenum that is a medium that supports waves similar to Newton’s
aether. Because the plenum supports waves, it has the property of inertia
[13; 14], has plenum density ρ, it directs hods, and it has waves with a speed
much greater than light.
Hods are 2 dimensional, magnetic with a high ρon one side and ρ= 0
on the other, and particles are assemblies of hods [15; 16]. Hods travel at the
speed of light in the direction parallel to their surface and slower in a direction
perpendicular to their surface.
The STOE adds Sinks to the QSSC that are elliptical galaxies in galaxy
clusters that lowers the ρ[17; 18; 19]. The stuff of the universe flows into the
Sinks which explains the many differences between spiral and elliptical galaxies
[9]. The Sinks remove the need for an expansion of the universe and for infall
into spiral galaxies.
The universe begins as a single Source that eject other Sources [19; 20]. The
entire universe emerges (strong emergence) from the two components and their
interaction [21].
The STOE suggested a Universal Equation [22; 23; 24; 25]. The plenum
density at all points ρpin the universe is the sum of the effects of all galaxies
and all hods,
ρp=Kǫ
Nsource
X
i=1
ǫi
ri
−Kη
Nsink
X
j=1
ηj
rj
−Khods
Nhods
X
k=1
mg
rk
cos 2πrk
λT
−πexp−j(ωtk)
>0,(1)
where Kǫ,Kη, and Khods are constants that relate the relative influence of the
Sources, Sinks, and hods, respectively; ǫi,ηj, and mgare constants that relate
the value of a measurable parameter such as a galaxy’s B-band luminosity or
hod gravitational effect for Sources, Sinks, and hods, respectively; ri,rj, and rk
are distances from the center of each component to the point being evaluated;
λTand tkare wave characteristics generated in the plenum by moving hods.
The λTand tkdepend on the ρp[26].
The ρas the rincreases, like a fluid, becomes smoothed in the direction
perpendicular to r. This is the “spherical principle”. The number of hods
appear as if they were concentrated at the center of the structure (center of
mass) as rincreases beyond a minimum value. The Khods term looks like the
gravitational mass effect in Newtonian scale observations.
3 THE STOE 6
The Kǫand Kηterms become predominate on cosmological scale observa-
tions.
The inclusion of all Sources, Sinks, and matter means the STOE is a Machian
model.
Note the rvalues are for the determination of distance for the ρcalculation.
Therefore, the time required for a change in rto travel through the plenum
determines the position of the emitting object for the calculation of ρat a
point. The change-in–rwave can be very much faster than the speed of light
[27].
The divergence of ρpis proportional to a force ~
Fsthat acts on matter and
directs a hod,
~
Fs=KG
Nhodsl
X
l=1
mhod(~nl•~
∇ρpl)~nl,(2)
where mhod is the surface area of a hod that is the same for all hods and ~nlis
the unit vector perpendicular and centered on the hod’s surface. .
For matter, ~
Fs=Gsmw~
∇ρp,(3)
where the Gsis a proportionality constant analogous to the gravitational con-
stant Gwithout the mi/mgvalue. The mwis experienced as the effective surface
area of the particle, and the familiar negative sign is included in the ~
∇ρp.
Because electromagnetic signals speed is that of light, electromagnetic signals
are hods [5]. The amount of plenum captured by a hod is constant and is
the cause of miof bodies. Photons are a column of hods [26]. Because hods
are two dimensional, hods and photons experience no impressed force in their
direction of travel. That is, for smaller than electron structures such as photons
or neutrinos, there can be directions with varying force depending on direction
and mw= 0 in the direction of travel. Therefore, they travel at the maximum
allowed speed of other bodies.
The structure of baryonic matter has hod surfaces facing all three directions
such that the effective surface area is less than the number of hods times mhod
[15].
The inverse mapping produces the movement of a body:
~a =~
Fs
mi
,(4)
where mi6= 0 because it is the captured plenum around the hods in the body
and ~a is the acceleration of the body. Reference frames result when some terms
of Eq. 1 are ignored for calculation simplicity.
Newton’s three masses are (1) mwis the effective surface area on which the
~
Fsis exerted, (2) miis the captured plenum which is proportional to the number
of hods in a body, and (3) mgis the deformation of the plenum caused by the
hods and is proportional to the number hods in a body. Note the number of
effective hods vary by type of assembly (photon, neutrino, or baryon [15]).
3 THE STOE 7
The Universal Equation has quantitatively described many mysterious ob-
servations [23; 25; 28]:
Microwave background temperature is due to a fine-tuning due to a feed-
back loop between Sources and Sinks [29]. This suggests that if fine-tuning
is evident, then a physical feedback loop is present.
Redshift (z)was calculated by considering each galaxy’s effect on the photon
[30]. That is, the ρpis calculated for points along the photon’s path (line
of sight) using Eq. 1. The correlation coefficient of model distance versus
Cepheid distance for the best Doppler shift model is 0.80. The STOE
model correlation coefficient for the same galaxies is 0.88. The “Hubble
Law” was recovered without invoking a Doppler shift.
Periodic redshift was calculated by considering the Sink’s effect (the Kη
term) on redshift [30]. If a Sink is located between the target and the
Earth, the zis increased. If a Sink is located beyond the target from the
Earth, the zis decreased. A galaxy cluster is a shell of Source galaxies
around a core of Sink galaxies [9]. Therefore, galaxy clusters appear to be
elongated along the line-of-sight from Earth. This phenomenon is called
“the fingers-of-God” pointing toward Earth.
Rotation curves (RCs) were calculated by considering the Source strength.
The Source strength is the ǫterm minus the mgterm for the mass internal
to the radius in Eq. 1. The advantage is that all types of RCs are described
in addition to standard models that explain only flat RCs [31; 32; 33].
Asymmetric RCs , which are unexplained in standard models, were calcu-
lated by considering the galaxy’s’ strength and a neighbor galaxy’s strength
and position [31; 32; 33].
Correlation of central massive object mass and central velocity dispersion was
explained [34].
Pioneer Anomaly of all 10 characteristics (not just the general value of the
blueshift) were calculated by considering solar system matter (hods) and
the Milky Way Source [35]. The equation used derived from the equation
for galaxy redshift. That is, the ρpis calculated for points along the sig-
nal’s path (line of sight) using Eq. 1. For example, the annual periodicity
is explained by the Sun’s relative position to the signal’s path, which is
mathematically similar to the observed periodic redshift . Because the
same equation as the redshift equation was used, the similarity and sign
difference to the Hubble constant is explained.
Predictions made in 2006 about the Pioneer Anomaly were confirmed in 2013
[36].
Photon diffraction and interference intensity patterns of both Young’s Ex-
periment and experiments that reject wave models of light were duplicated
using a toy model computer simulation [26; 37; 38; 39; 40; 41; 42; 43].
3 THE STOE 8
Particle structure models and how the structures differ relative to photons
that determine speed were created [15].
Modifications to Maxwell’s Equations that better agree with experiment
were described. The Biot-Savart Law was restated based on experiment
[4; 5; 6; 44]. There are two different types of magnetic field, each with the
same symbol ( ~
B) [7].
The “Planet 9” observations and spiral galaxy rotation curves are due to
the Source effect at the center of the Milky Way [45]. The effect was
predicted in 2006 when examining the Pioneer Anomaly by noting the
orbit of Pluto and Neptune. This effect may also influence the perihelion
advance of Mercury [46].
The “ether wind” measurements are explained as the divergence of the plenum
rather than a “wind” [47]. The “wind” model failed because the indicated
direction did not match any possible Earth celestial movement direction.
The STOE model of the hod as a permanent magnet qualitatively suggested
how hods form particles, the nature of particles, and the four forces of the Grand
Unified Theory (GUT).
Magnetism in the STOE model is postulated to emerge from the hods and
is a gradient of the plenum. Magnetism is observed in small subatomic
particles and light. Therefore, the hods are magnets [5]. The application
of Eqs:1 and 2 suggests the ~
∇ρfollows the magnetic lines of force seen in
iron filings at the macro scale. The observation of two types of magnetic
fields [7] imply the hod is either rotating charges or is a permanent mag-
net. Because rotating charges would emit radiation energy, the rotating
charge model is rejected in the STOE. Therefore, the hod is a permanent
magnetic. The self-similar (fractal) postulate suggests disk permanent
magnets are a macro object that is analogous to hods.
Repulsion was measured between 2 columns of disk permanent magnets. The
measurements showed an asymmetry between South poles repelling and
North poles repelling [48]. Further, the repulsion force along the axis was
inverse–distance when the magnets were close, inverse distance–cubed a
bit further, and inverse distance–squared still further apart. The force
perpendicular and centered on the axis was attractive and inverse–cubed
of the distance from the dipoles.
Particles’ magnetic fields were studied [49] for structures suggested previously
identified (photons, neutrinos, electrons).
Electromagnets did not show the asymmetry that the permanent magnets
demonstrated [50].
Atomic structure in the standard model is orbiting electrons. The fundamen-
tal problem is that rotating charges should radiate and have a declining
4 DISCUSSION AND CONCLUSION 9
orbital radius. This is not observed. Also observed is that changing energy
radiation is photons. Photons in the STOE are columns of hods. So, the
STOE atomic structure is of rods of photons determining and magnetically
holding electrons in position around the nucleus [51].
Gravity emerges from magnetic effects in hod structures [52]. However, mag-
netic attractive and repulsive effects determine atomic structures. There-
fore the distance required before an only attractive force is at least the
atomic scale of Angstroms. That is, the “gravity” at more than atomic
scale is an approximation which becomes invalid at less than atomic scale
rather than being present and merely too small. The distance at which
this occurs may determine atomic size and may suggest instability in larger
atomic (dominated by inverse square distances) and nuclear (dominated
by inverse cube distances) size. The relative strength of the photon hod
binding and the gravity speaks to the “hierarchy problem”. The Newto-
nian problem of r→0 for gravity causing an infinite force is nonexistent.
Nuclear forces (weak and strong) are modeled as an assembly of hods into a
spherical ball which is the proton and neutron [53].
Grand Unified Theory is, therefore, that the magnetic force evolves with
distance into the four forces of the GUT.
4 DISCUSSION AND CONCLUSION
Like Newton, the STOE suggests a reductionism step by positing the charac-
teristics that can explain many problematic, mysterious observations.
The intent of ~
Fsis that it be all inclusive. The development of the STOE
to date has demonstrated the interference effects and gravity. The hod is a
magnet so the possibility is that electromagnetic effects may be modeled as
approximations as was gravity. However, the equation and effects for very small
values of the r’s in Eq. 1 are lacking. Therefore this is an area for continued
experimental research. Perhaps the STOE could be developed to model atomic
and nuclear decay and to improve the model of galaxy redshift by including
QSOs as H. Arp suggests [20].
Physics theory restarting from Newton’s speculations and then describing
the experiments of the 19th and 20th centuries results in a model of the big,
small, and the four forces (GUT) - the Scalar Theory of Everything (STOE).
ORCID iD
John C. Hodge: https://orcid.org/0000-0002-1520-2153
REFERENCES 10
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