Planck's Constant from Gravity


Planck's Constant is derived from gravity using the momentum in each proton and neutron. That linear momentum is V / tau, where V is a proton volume and tau is a new constant of 5.1ns. Tau is confirmed for the gravity of five planets, the Sun, the Moon, and the gravity of the asteroid Vesta, all giving tau within 1% of the average tau. Mass is redefined.

Executive Summary

Planck's Constant (h) is an angular momentum. A new gravity theory gives the proton's internal linear momentum. Using the Bohr Radius, the angular momentum is produced from the linear momentum. That angular momentum is part of the derivation of h. The rest of the derivation is about justifying two dimensionless constants, (k/G) and (m/q) to multiply the angular momentum from the four dimensional Gravity Continuum to get to the 4D Electricity Continuum, where h is used. The momentum of graviticspansion enables the non-momentous electrical physics. Eight dimensions are used. See the Periodic Table of the Units of Measure. Gravity is caused by baryons shrinking space and growing time in the following ratio: V/tau, where V is a proton volume and tau is 5.1ns. That ratio has units of momentum. Mass does not cause gravity, it is affected by it. Mass is area, so units are advanced beyond The Standard Model. The derivation is in the Conclusion, after you are exposed to Continuum Science, the revolutionary foundation of physics.


The new gravity theories use primitive dimensions instead of compound units like energy. Only meters and seconds are needed to show all of the factors of any unit in physics. Mass is a compound unit having the two factors of meters times meters. (See Appendix A). Force is area times acceleration. Charge is area of Electricity Continuum fluid. The proton's internal linear momentum is from gravity and the expansion of the universe, and that is coupled to electrical and nuclear physics. Planck's Constant is derived by using primitive momentum from a proton that is calculated from gravity. Momentum is V / tau where V is a proton volume and tau is 5.1ns. The linear momentum is very small from gravity. That is modeled as a long time, tau, of 5.1 nanoseconds. That is how long a proton gives for its own volume to be absorbed out of the surrounding space. To model electrical charge repulsion , tau gets multiplied by G/k. The resulting taue is only 3.74 * 10-29 seconds. That is how long a proton volume takes to grow out of a proton into electrical space. The cross continuum coupling is modeled by dimensionless ratios of m/q and k/G. That unifies gravity and electricity while deriving the h to adequate precision. The two dimensionless ratios are called the charge to mass ratio and the traxxion ratio. They couple the mass and momentum into a realm where there is no real momentum: The Electricity Continuum. The real momentum of mass is reflected in the unreal-seeming and amazing performance of electronic and nuclear changes. Planck's Constant's angular momentum is calculated using the linear momentum and multiplying by a length, the a0 Bohr Radius, .53 Angstrom and by two ratios. The full formula is inspired by the Bohr Magneton Formula and magnitude searches.

h = 4 pi (V/tau)(k/G)(m/q)*a0

The formula for h has 9 constants multiplied together. 8 of them are from Old Science. Only the tau is from the new theory of the cause of gravity. See Table 1 for five planets' gravities being used to get an average tau calculated from the volume of protons over the shell volume per second. All values of tau were within 1.1% of the average, including the Sun and the asteroid Vesta. Matter causes gravity, not mass. Mass is area, matter has volume, and a volume change is required to cause gravity. The derivation of h is in the Conclusion, using the tools from the Details section. The formula for h can be manipulated to get other relations. By substituting the Bohr radius formula into the the h formula, the Bohr radius can be eliminated and new insights found. a0 = (h2 / ((2 pi)2) / (me * q2 * k) Therefore, G = h mP V / (q3 me tau) and q = cuberoot( 2 pi h mp2 / me) also h = q3 me / (2 pi mp2) acf Feb. 15, 2016


Planck's Constant has units of angular momentum called a "magnetic moment" for atoms and protons. When protons are mentioned for gravity, neutrons are assumed to be equally involved, but not always mentioned, for brevity in this paper. Planck's Constant is h:

h = 6.63 * 10-34 Joule Seconds

Another angular momentum is bigger. The Bohr Magneton is defined for an electron to be mu mu = 9.274 * 10-21 erg per Gauss per particle mu = 9.274 * 10-24 Joule seconds per particle mu = q h / (4 pi me) The linear momentum of the interior of a proton is known from new gravity research. L = V / tau = 7.12055 * 10-37 meter3 per second me is the electron mass
V = proton volume
tau = 5.1 ns tau is the Universal Constant for the Conservation of Graviticspansive Continuum The internal linear momentum times a length gives a Candidate angular momentum: Candidate = La0

The kilogram definition is enhanced

See Appendix A and Appendix B.
mass units are meter2 Therefore force has units of meter3 per second2 Therefore charge is area, square meters. Based on those formulas, conversions, and ideas, it will be shown in the Conclusion that Planck's Constant is:

h = 4 pi a0 (V/tau) (k/G) (m/q)

(V/tau) = linear momentum in proton due to graviticspansion
a0 = 5.3 * 10-11 meters for the Bohr Radius
V = 3.59 * 10-45 , proton volume
tau = 5.043655 * 10-9 seconds Universal Constant of Conservation of Continuum
k = 8.99 * 109 meter per square second, Coulomb's little k
G = 6.67 * 10-11 meter per square second, Newton's big G
m = 1.67 * 10-27 kilogram per proton or neutron (sq meters)
See Appendix C for notes on the electron's elimination from this derivation.
q = 6.02 * 10-19 square meters, proton charge
M is the mass is a planet or star

tau = 5.1 nanoseconds

calculated for 5 planets' gravity

Mars, Mercury, Jupiter, the Sun, the asteroid Vesta, Venus, the Moon, and Earth all get 5.1 nanoseconds for the ratio of V2 / V1. All of those eight values for tau were within 1.1% of the average tau.
V2 = volume of all protons and neutrons on each planet
V1 = planet shell volume = Height Fallen in a second times planet area.
V1 has momentum units, meter3 per second
tau = V2 / V1
tau = 5.1 nanoseconds for any planet or star. The ratio V2 / V1 is designed by theory to show the cause of gravity. Gravity is caused by baryons shrinking space and growing time. A proton volume enters a proton internal process and 5ns are produced by the proton as a result of the space shrinking into the proton. That space loss is proportional to the acceleration of gravity. V1 uses a height fallen in one second to calculate the average velocity during the one second acceleration. That height per second may be the integral of the acceleration, as expected for a differentiating aether. Any velocity is relative, so falling from a rest speed is a good representation of any acceleration, from any initial velocity.
At the planet shell for falling objects, the same volume falls as was shrunk at the baryons. The result is that 200 million times per second, each proton consumes its own space and grows 5ns of time. So in a second at the planet surface, that volume lost into baryons is replenished by conserved fluid continuum. Laminar flow and fluid continuity keep gravity easy to understand.
The average velocity (height / 1 second) is only the space part of gravitational acceleration, and time is the other part of the cause of acceleration. Space at the planet surface is falling, but time is rising, so that makes acceleration. See Folmsbee's Fourth Law of Diffusion of 4D Continuum. Acceleration is velocity change per second so the change from zero to the average velocity is divided by time to get acceleration. Time divides because it is departing the planet. Space multiplies for motion because it drains into a planet. See Law 3 and 4 for diffusion of continuum.

Table of Five Planets' Gravities to Find tau=5.1ns

This is a new Universal Constant, tau. 5.131534 nanoseconds is the Universal Constant for the Conservation of Graviticspansive Continuum (tau). It is averaged from five planets in the next table.
tau = V2 / V1
tau = MV / (2 pi m g R2 * second)
That can be rearranged to get g for any planet from any distance:
g = (1/ (2 pi R2)) * (M/m) * (V/tau) per second
g = (M/R2) * (V / (2 pi m tau)) per second
G = (V / (2 pi m tau))second-1
But Newton did not know about protons. They were introduced by Rutherford in 1920, so Einstein never knew about protons while making his general theory. They have an excuse for not understanding the cause of gravity. You do not. So get with the program. Now organizing a team to design The Generator. email me in Switzerland: folmsbee @ protonmail dot ch

Table 1

Five Planets Confirm the Cause of Gravity
Mercury Venus Earth Moon Mars
g = meter / second2 3.700000 8.900000 9.800000 1.600000 3.700000
M = kg x 1024 kg 0.330000 4.870000 5.970000 0.073000 0.642000
R = 106 meter 2.440000 6.052000 6.378000 1.737000 3.396000
A = Planet Area*1012 meter2 74.81600 460.2640 508.0000 37.96100 144.9240
z 1.850000 4.450000 4.900000 0.800000 1.850000
V1 = z A 138.4080 2048.175 2489.200 30.33280 268.1094
N=M/m=baryons*1051 0.197600 2.912000 3.569200 0.043640 0.383828
V2 = N Vproton 0.709650 10.45410 12.73910 0.156730 1.378500
V2/V1 = tau ns






Variance from average 0.08% 0.5% 0.26% 0.69% 0.19%
December 8, 2015, by Alan Folmsbee Average tau 5.131534ns The Sun's gravity was calculated to give tau = 5.126330 nanoseconds.
The asteroid Vesta gives tau = 5.173767 nanoseconds! This proves my theory of the cause of gravity!
Jupiter gives tau = 5.116222 nanoseconds from each proton due to space shrinking by a proton volume into the proton.
m is proton mass
M is planet mass
R is the radius from the center of the planet to where g is valid.
g is the acceleration due to gravity from Old Science for five planets
z = (1/2) * g * (1 second)2 per second
z = 9.8 meters / (2 seconds) , Earth example for g
z = height fallen per one second experiment dropping an apple (velocity)
z is used as height and the second for z is sometimes placed elsewhere in the formulas that involve tau's derivation, so be sensitive this time
V2 is volume
V1 is a volume per second
V1 is momentum = zA/second = average velocity times area of planet
tau = V2 / V1

7 Digit Precision Calculation of Planck's Constant from Gravity

h = 4 pi a0 (V/tau) (k/G) (m/q)

m = 1.6726219 x 10-27 kg
k = 8.987551 x 109 meter / second2
a0 = 5.291772 x 10-11 meters
V = 3.591364 x 10-45 meter3
q = 1.602175 x 10-19 Coulombs
tau = 5.131534 x 10-9 seconds
G = 6.674083 x 10-11 meter / second2
First multiply mantissas, then add exponents.
m = 1.6726219
k = 8.987551
a0 = 5.291772
V = 3.591364
Numerator = 3590.1249 mantissa
q = 1.602175
t = 5.131534
G = 6.674083
Denominator = 54.871744
The result of that calculation gives h:
h = 65.42753 mantissa
Add exponents :
exponent = -27+9-11-45+19+9+11 = -35
h = 6.542753 x 10-34 Joule seconds (1.36% too low)
If tau is set to its older value of 5.043655 ns, h is:
h = 6.6567518 x 10-34 Joule Seconds

Old Science does not have a foundation, they have Planck's Constant, grams, degrees, and The Big G. Now, the foundation of physics has been laid on matter, space and time. Protons, neutrons; meters and seconds. Primitive dimensions interact with eternal matter by the converse momentum. That is where matter shrinks space and grows time, literally.
Dimensional Analysis of G and k
Since kilogram = meter * meter , G and k have units of acceleration. G = meter per second squared.
G is Newton's lump model of the weakness of gravitational attraction between protons. (And neutrons).
k is Coulomb's lump model of the strength of proton repulsion
The cause of gravity is now known so Newton's Big G is now re-evaluated as follows for Continuum Science. These two formulas were fabricated using the Axiom Powers Theorem and the new baryon theories about the directions of 8 primitive dimensions:
G = (3.1 cuberoot(V(t)) / sqrt(5.13*10-9 second * second) * second)
k = (87.98 meter5 sqrt(3.74*10-29 second*second) / sqrt(V(t))second3)*meter2
The ratio 87.98 / 3.1 is called "the local blue shift" which may be due to stretching of space in this galaxy, relative to intergalactic space density.
V(t) is the space going into protons during a time. During fusion, time changes its density. So that increases the space rate of consumption, causing a chain reaction for fusion. The inverse relation for gravity and electric charge repulsion is shown in the formulae, as V(t) is in the denominator for electricity, but in the numerator for gravity. Therefore, when time gets denser, gravity is stronger and charge repulsion is weaker, as during fusion. The denser time also increases acceleration, perhaps to the next derivative order.


Here is another version from October 25, 2016

Home Test for Planck's Constant Calculation
Here is the proposed formula for h, based on a home gravity test:

h = (zakm) * ((4 pi R)^2) / (NqG * 1 second)

z = height fallen in 1 second gravity test at radius R from planet center
a = Bohr Radius = .5 Angstrom
k = Coulomb Constant
m = proton mass
R = radius from planet center to test object that falls under gravity
N = number of baryons in planet
q = proton charge
G = Newton's Constant

Conclusion: Planck's Constant can be calculated from dropping a rock for 1 second on any star or planet. The test drops a rock a distance of z in a 1 second test. Calculate h for any planet, same result. z is 4.9033 meters on Earth with R = 6378000 meters, N = 3.569*10^51 baryons. The derivation is available. Do the test on your next planet or moon.

h = (zakm) * ((4 pi R)^2) / (NqG * 1 second)

verified magnitude within 2% on Earth.

The derivation is inspired by The Bohr Magneton (mu), which can
be calculated using Error Bars for Sergio:

mu = q*h / (4 pi m) = Bohr Magneton for proton


h = 4 pi * mu * (m/q)

That formula for Planck's Constant is used as a model for my new formula. But instead of a "magneton" I use the baryon's momentum of free space (p) times the Bohr Radius (a).

N*p = z*A/(1 second)
h = 4 pi (zA/(N*1 second)) * a * (m/q)*(k/G)
A = 4 pi R^2 for area of star or planet in rock drop test of h
h = 4 pi (z*4*pi*R^2/(N*1 second)) * a * (m/q)*(k/G)
where m/q is dimensionless at abstraction level 2, and k/G is a dimensionless ratio using the mass-area theorem. The first 4 pi is for a proton spherical area, the second 4 pi is for the star's spherical area.
h = z*(4*pi*R)^2/(N*1 second)) * a * (m/q)*(k/G)

ERROR BARS INCLUDED using 10 digits
z is measured when you drop a rock for 1.000000000 seconds using an atomic clock
t = 1.000000000 second
z = 1/2 g t^2
g = 9.806650000 meter per second^2
z = 4.903320000 meter
R = 6,378,140.000 meters
N = M/m baryons in the star or planet
m = (1.674928600 + 1.6726231 )*10^-27 kg / 2 average of neutron and proton
m = 1.67377585 * 10^-27 kg
M = 5.972300000 * 10^24 kg
N = M/m = 3.56820000 * 10^51 baryons
a = 5.291772109 * 10^-11 meter
q = 1.602176621 * 10^-19 Coulombs
k = 8.987551787 * 10^9 (meter/second^2 when charge=area in E-continuum)
G = 6.674080000 *10^-11 9 (meter/second^2 when mass=area in G-continuum)

Error bar summary: The least precise variable is N, with 5 digits of precision.
A loss of a digit would cause an error bar of 1/3568 = 0.028 %.
Also,  G has only 6 digits of precision, so increase the error bar total to 0.04%.
Multiply the latest numbers' mantissas:
h = z*(4*pi*R)^2/(N*1 second)) * a * (m/q)*(k/G)
h = (774.301232 R^2/N) * 7.444542916
R^2 / N = 1.1400893 mantissa
h = 6.571838130 * 10^-34 Js
difference from standard h :
6.626070040 - 6.571838130  = 0.05423191
0.05423191 / 6.626070040  = 0.82% error

Conclusion, This suggests the mass of the Earth is 0.8% more than the current estimate.


Planck's Constant is derived here. Gravity is caused by matter shrinking space and growing time in the following ratio, with units of momentum p = V / tau = 7.02*10-37 meter3 / second
pis linear momentum inside proton
V(t) is proton volume (or neutron volume)
V(t) = 3.6*10-45 cubic meters
tau is a constant to conserve continuum
tau = 5.1315 ns, confirmed within 1.1% on five planets, an asteroid, and the Sun
V(t) is a variable space into a proton as time (t) changes during fusion. Thick time density occurs during fusion, causing a chain reaction. When no fusion is occurring, V(t)=V, the proton volume.

The momentum L is a linear momentum but h is angular momentum. To derive Planck's Constant h from the V/tau proton momentum, a length must multiply p. The Bohr Radius a0 was a first guess at candidate atom-related lengths.
V*a0 /tau = angular momentum candidate = 3.71*10-47 meter4 / second
The next step in the derivation is to observe the formula for a Bohr Magneton
mu = q*h/4 pi me = 9.274*10-24 meter4 / second
and to use the known magnitude of mu and the involvement of h to advantage.
If this Bohr Magneton is to be a template for a new formula for h, the proton mass can replace the electron mass and the gravitic angular momentum pa0 can replace the mu. Then check for the magnitude that results from those substitutions compared to the magnitude of h. I tried this:
V*a0 /tau = X * q*h/4 pi mp
where X is the unknown ratio between h and the candidate formula.
Notice that the charge to mass ratio q/m is in the formula from the Bohr Magneton. That links inertia to charge, two disparate concepts. Since this derivation is intended to unify gravity and electricity, that charge to mass ratio is retained for the formula candidate for h. If charge is area and mass is area, that charge to mass ratio is dimensionless. That is how it will be used.
Next, evaluate how far off the answer is so far. Solve for X:
X = 3.71*10-47 / (q*h/(4 pi mp))
X= 7.33*10-21
I recognized that X is close to the inverse of k/G, Coulomb's Constant divided by Newton’s Constant. Since those are related to my research, k/G was applied to the candidate formula for Planck's Constant. See Volume I of the Trilogy on Theoretical Physics, page 83. In that book, The Strength of Gravity vs. Charge that G/k ratio multiplied tau to get the time constant for The Electricity Continuum: 3.74*10-29 seconds. Therefore its already known to me that this ratio was a way to go from the Gravity Continuum to the continuum where Planck's Constant is applied in physics, The Electricity Continuum of 4 more dimensions.
k/G = 1.348*1020
The final result was now expected to be accurate as the value of h:
h = (k/G)(mp/q)(V/tau)(4 pi a0)
The accuracy was confirmed and reported in the Details section, above.
That was how the derivation occurred, but next are given more justifications for using the dimensionless ratios k/G and m/q. Gravity was not understood before and the units for mass and charge baffled scientists for centuries. Now that area is used for mass and charge, it became apparent that this new formula can be developed using dimensionless ratios to adjust any angular momentum to be a candidate formula.
Max Planck measured black bodies to get h, Planck's Constant. He did not derive it from fundamental constants of nature like atomic radius, proton mass, proton charge, proton volume, The Big G of gravity, or the little k of Coulomb's force. Now that derivation is provided: h is proportional to several known constants, with no mystery values. Gravity is unified with electricity. The little h is no longer a fundamental invariant. The h is a derived invariant. That is progress.

Appendix A

Mass is area.
Mass is square meters of Gravity Continuum fluid. Inertia is caused by mass. Mass does not cause gravity. Matter's volume causes gravity. Mass is affected by gravity's gradient of continuum.
There are three derivations available for setting mass to have primitive units of meter2. The 4D fluid method, the inductive reasoning method, and the 3D fluid method. Like in my book, Volume I pages 22 to 26, Chapter 2 of "The Strength of Gravity vs. Charge" published March, 2015.
I will summarize that soon...
In addition to the three method in Volume I, there is a fourth method to show that mass is area.

Proton Mass Derived from Geometry of Cross-Section

Two formulas were given in the Details section for The Big G. One formula was from deriving Planck's Constant using tau. That had q in the derivation but it was eliminated when deriving G because h is a known number. With h available, q disappears from the derivation of Proton Mass m. The two formulas above for G have one factor that differs especially: m. The first equation has m in the formula for G and the second equation has no m for the formula of G. That fact allows an algebraic change to prove that mass is area. That is because both formulas have V. The volume of the proton is a known geometry that causes gravity, without mass. So when one side of the m formula is isolated from powers of V on the right hand side of the formula, than mass gets defined by powers of meters and seconds, if any.
h = 4 pi a0 (V/tau) (k/G) (m/q)
tau = V2 / V1 = volume/momentum = volume/(velocity*area)
tau = MV / (2 pi m g R2 * second)
That can be rearranged to get g for any planet from any distance:
g = (1/ (2 pi R2)) * (M/m) * (V/tau) per second
g = (M/R2) * (V / 2 pi m tau)
therefore, because g has a well known version like that,
G = 6.67 * 10-11 Newton meter2 per kilogram2 from Newton and Einstein
G = (V / (2 pi m tau))second-1 from the tau = V2/V1 work, above
G = (3.1 cuberoot(V) / sqrt(5.13*10-9 second * second) * second)
from Axiom Powers Theorem, Vol. I of Trilogy of Theoretical Physics (March 2015)
Set both equations equal to each other because G has 2 versions!
(V / (2 pi m tau))sec-1 = (3.1 cuberoot(V(t)) / sqrt(5.13*10-9 sec * sec) * sec)
Solve for m, the proton mass:
m = (V2/3 * 7.163473) / (3.09*2* pi * 5.131534 x 10^-4)
m = 1.686207 * 10-27 meter2
m is area, like was expected. But this time, tau was involved to derive "the mass equals area theory". And tau has credibility.
To convert kilograms to square meters, multiply by 1.0 for now.

Appendix B

How can 1.0000 kilogram be exactly 1.0000 square meters? Answer...
It is true for some mathematical applications :
1.00000000000 kg = 1.00000000000 square meters
The precision is true for the following applications:
A : for ratios of mass over charge
B : for ratios of mass times a 1/R^2 Law
C : Geometrical situations where areas cancel in the models
The precision is not true for :
D : unitary application: pay $6 for a kilogram of salt. Do not pay for a square meter of salt! That is not a ratio, so mass is a kilogram compared to a paragon mass of Iridium in a bunker.
E : Irrational Dimensions, as in polytropic models, see Relativistic Hydrodynamics by Rezzolla and Zanotti, page 118.
Summary of Appendix B
The mass = area precision is perfect, within constraints on the perspective of the geometrical realities of physics calculations. The area is proportional to the mass, so some factors cancel. The remaining dimensions are a primitive aspect of a compound unit of measure, mass. Unitary mass is expected to have an absolute magnitude that is close to 1.0 kg per 1.0 sq meter because Avogadro was a practical man. Preliminary calculations indicate that lead (Pb) is similar in size to its mass area, for chunks of lead that can fit in Avagadro's hand. A 1kg volume of Pb has an area like its baryon area! More research is planned.

Appendix C

Why was the electron removed from the derivation? The electron has no volume, so it cannot cause gravity.
The electron mass was deleted from the Bohr Magneton formula for mu and the proton mass was used to derive h, Planck's Constant.
The electron is not matter, it is a fraction of matter. Proton charge repulsion is primary. Electrons are paired with protons, strictly and with brittle deviations from loyalty fluid dynamics. Magnets pair an electron with a proton that is many meters away. When a magnetic field is known to cover 1 million miles and exert a force, then know that a pairing across a million miles exists from a proton sending 2D space to an electron and getting time back. In that 2D electron space is 1D of electrical time. The remaining 1D of space is from the proton to a neutron. Hydrogen is a alone in avoiding that neutron dimensional interaction.
The electron was not used, it causes no gravity.

Helium 3

The End
Planck's Constant was derived from a more primitive universal constant.
The proton mass to area conversion factor was derived from geometry 1:1 within 1%.
Newton's Universal Gravitational Constant was derived from a more fundamental constant for time growing out of matter.
The Universal Constant for the Conservation of Graviticspansive Continuum.
December 25, 2015
Scale formula for atoms
Atoms have a diameter from one Angstrom to three Angstroms. Here is a simple formula I found that relates to that scale of matter. :
m / (alpha*r) = e / (4*pi* a)
2 Angstroms = 2 Angstroms
m is proton mass
alpha = 1/137 = fine structure constant
r is proton radius = 0.92fm (adjustable to get right answer)
e = electron charge
pi = 3.2
a = Bohr Radius = .53 * 10^-10 meters
m / (alpha*r) = 2 Angstrom
e / (4*pi* a) = 2 Angstrom
Mass m and charge e are both treated as areas of the eight dimensional continuum fluid. The balance of nature has combined m and e in each atom. The derivation is done by combining two formulas that have Planck's Constant :
h = RV/5.1ns
V is proton volume
R is 947 meters, the arm of an angular momentum
V/5.1ns is a linear momentum for gravity volume theory
Also it was known that h is
h = 4 pi a (V/5.1ns)(k/G)(m/e)
k is Coulomb's constant
G is Newton's Universal Gravitational Constant.
The scale of the atom is related to the proton mass and electron charge.
April 8, 2016

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