Why is gravity so weak?

One of the pressing questions in modern physics is why gravity seems so much weaker than the other forces. Compared to the electromagnetic force, the gravity we experience is 40 orders of magnitude weaker. Should we even expect these forces to be comparable?

It turns out that we should. The maximum force potential of gravity is the Planck force, which is the same as mechanical and electromagnetic forces. The Planck force appears in elementary formulas calculating the strength of gravity.

One such formula is the Einstein field equations which describe the relationship between mass-energy and the geometry of spacetime. This formula quantifies the maximum force of gravity with the Einstein gravitational constant. The historical form of the constant

\color{darkgray} \kappa = \displaystyle\frac{8 \pi G}{c^4}}

can be restated in elementary form by translating Planck’s constant and the Newtonian gravitational constant into elementary Planck units. The elementary form of the Einstein gravitational constant

Einstein gravitational constant shown in elementary Planck units

contains four Planck units creating the Planck force in the constant’s denominator.

The Einstein gravitational constant is the ratio of 8pi to the Planck force

The Planck force also appears in the simple formula for gravitational force. The equation

\color{darkgray}  g = -\displaystyle\frac{GMm}{r^2}}

can be restated in elementary Planck units. Combining formula inputs

Four inputs for calculating gravitational force; two masses in the numerator and the distance squared in the denominator
Formula inputs

with the gravitational constant

The gravitational constant in elementary Planck units
Gravitational constant

produces the elementary formula.

The elementary formula for gravitational force; four dimensionless proportionality operators reduce the Planck force
Gravitational force

A hidden quantity of Planck mass in the numerator and denominator produces the Planck force on the right-hand side of the formula and a set of proportionality operators on the left. These operators are generated from the masses of two bodies and the distance between them.

Since the maximum gravitational force potential is the same as the other forces, the question remains, why do we experience such a weak force of gravity?

The answer lies in the proportionality operators diluting the gravitational force in these equations. For example, the simple gravitational force equation shows that gravitational force grows stronger as mass density increases and weaker as mass is spread out over larger distances. A pair of black holes with adjacent event horizons will experience the maximal Planck force, while earth-like environments experience a force that is substantially more diffuse.

New Foundation Model of physics

The New Foundation Model of physics offers a framework for comparing the strengths of the different forces. By restating composite constants into elementary Planck units, the model explains each force in two parts:

  1. The maximum potential of the unit dimensions we are solving forβ€”in this case, force. The ratio of Planck momentum to Planck time generates the maximum force potential.
  2. Dimensionless proportionality operators in the ratios of a system’s attributes to the Planck scale. These dimensionless ratios characterize the dilution of Planck force potential.
The Planck force in elementary Planck units;
Planck force

Since the mechanical, gravitational, and electromagnetic forces all share the same Planck force potential, differences between the forces are explained entirely by the operators. The following table compares these operators.

The comparison draws from a single scenario in which all three forces are presentβ€”the ground state hydrogen atom. The table compares the electron’s mechanical force of motion with the gravitational potential between the particles due to their masses, and the electrostatic force between their electrical charges.

Like a balance sheet, the table begins with the maximum force potential and counts each reduction by the applicable operators. A detailed explanation of the table follows.

1.21 x 10441.21 x 10441.21 x 1044
Electron rest massπ‘š0 / π‘šπ‘ƒ4.19 x 10-234.19 x 10-23
Electron momentum adj.π‘š / π‘š07.30 x 10-3
Electron period𝑑𝑃 / 𝑇2.23 x 10-27
Proton rest massπ‘š0 / π‘šπ‘ƒ7.69 x 10-20
Electron distance𝑙𝑃 / π‘Ÿ3.05 x 10-253.05 x 10-25
Proton distance𝑙𝑃 / π‘Ÿ3.05 x 10-253.05 x 10-25
Electron chargeβˆšπ›Ό8.54 x 10-02
Proton chargeβˆšπ›Ό8.54 x 10-02
Total Reductions6.81 x 10-526.81 x 10-523.00 x 10-91
Force8.24 x 10-88.24 x 10-83.63 x 10-47

The first thing to note in the table is that the mechanical and electromagnetic forces are equal, explaining the electron’s ground state orbital. Meanwhile, the gravitational force is 4.4 x 10-40 kgm/s2 weaker.

Electron mechanical force

The table has a total of five operators reducing the electron’s mechanical force, grouped into three rows for comparison with the other forces.

The first two operators are the electron rest mass and electron momentum adjustment (typically identified as velocity). These operators quantify the electron’s spatial distribution characterized by its wavelength. The natural form of this operator is the ratio of Planck length to wavelength, but the traditional method for massive particles uses rest mass and velocity which give the mathematical equivalent.

The electron period tells us how dispersed the electron’s force is by its oscillation period. The simple ratio for quantifying this reduction is the ratio of Planck time to oscillation period.

Electrostatic force

The electrostatic force between the electron and proton is determined by four operators reducing the Planck force potential, all of which are different from the mechanical operators. Two operators quantify the distance between the particles. Each reduction is equal to the ratio of Planck length to distance π‘Ÿ which characterizes the diminishing field strength over larger distances.

The remaining two operators are fixed charge reductions taken for each unit of electric charge. This fixed reduction is the ratio of elementary charge to Planck charge, which is equal to the square root of the fine-structure constant. The total reduction between the particles is 𝛼.

The electrostatic force is unaffected by the particles’ masses or velocities. Furthermore, the two charge operators are fixed so that only the distance between the particles determines the dilution in electrostatic force.

Gravitational force

The gravitational force between the electron and proton is determined by the mass density of the region between them. Each particle contributes to the density based on the ratio of its mass to the Planck mass, and the ratio of Planck length to the distance π‘Ÿ.

These gravitational force operators appear in the natural formula for gravitational force

The natural formula for gravitational force potential in elementary Planck units
Natural formula for gravitational force

Comparing these operators with the operators determining the mechanical and electromagnetic forces shows why we experienced such a weak force of gravity.

Gravitational vs mechanical force

The mechanical and gravitational forces only have one operator in commonβ€”the rest mass of the electron. Since this operator is common to both forces it offers no distinction between them.

The remaining operators indicate that the mechanical force is further reduced by the electron’s momentum and oscillation period. While this is a sizable reduction of 27 orders of magnitude, the gravitational reductions are far greater. The gravitational force potential is reduced an additional 69 orders of magnitude by the proton rest mass and the distance squared between the particles.

Gravitational vs electrostatic force

The gravitational and electrostatic forces have two operators in common. Each force is reduced by the ratio of Planck length to distance, so the difference between these two forces is decided solely by the remaining operators.

For the gravitational force, the remaining operators are the ratios of particle rest masses to the Planck massβ€”a considerable reduction of 42 orders of magnitude. Meanwhile, the electrostatic force is only reduced by the fixed charge reduction of the fine-structure constant. This accounts for the difference between the forces.

New Foundation Model

The New Foundation Model of physics provides the answer to gravity’s secret by restating historical constants and formulas into natural units of length, mass, and time. These fundamental units reveal hidden information about the natural world that is otherwise obscured by the composite structure of historical constants.

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