The Role of the Planck Mass in a Novel Framework for Gravity

J. Rogers, SE Ohio, 26 Jan 2025, 0148

Abstract:

This paper explores the role of the Planck mass (m_p) within a novel framework for understanding gravity, mass, and frequency. It demonstrates that m_p acts not merely as a scale but as a fundamental parameter that sets the correct magnitude for gravitational interactions. The Planck mass, when combined with other fundamental constants, is used to scale a ratio between mass and length to a wavenumber with the correct correct value, which then converts to frequency, then to a mass, and then finally that mass is converted to an energy. We show that when the ratio between interacting masses and the square of their separation (m1m2/r²) is equal to 1 (in appropriate units), the gravitational force emerges naturally when our reference point for mass and frequency is used, highlighting its importance for a proper scaling.

Introduction:

The Planck mass (m_p), defined as the square root of (hc/G), is traditionally considered the mass scale where quantum gravity effects become significant. However, this paper argues that the Planck mass also plays a broader role in defining the magnitude of gravitational interactions at all scales. This framework introduces a "wavenumber," a value proportional to the gravitational force, which incorporates m_P, and how this value is scaled to a frequency and then to a mass and finally to an energy, with specific reference to when the masses and radius squared are equal to 1.

The Role of m_P as a Scaling Parameter:

In this framework the definitions of the framework are

m_p = sqrt ( hc / G )
Q_m kg s = h / c^2 = G * m^2 /c^3
h = Q_m * c^2
G = Q_m * c^3 / m_p^2 

The Planck mass arises in the calculation of a "wavenumber" which is proportional to the ratio of the product of two masses to the distance squared separating them: m1m2 / r². This value is scaled by 1/m_P² to transform it into a quantity with the correct units. This highlights that m_P is what scales the ratio between mass and distance to force. This scaled value, which we term a "wavenumber" , is then used to derive a "gravitational frequency," by multiplying it by the speed of light, c.

Step by step calculation of force happening inside G. The last column F(N) is the traditional result just using G. wn is wavenumber. What G is doing when the ratio is one is telling, it has to scale this 1 into the correct value by using 1/m_p to convert to a wavenumber, then convert that to a frequency by multiplying by c, then  scale by the equivalent of h to convert frequency to mass and then accelerate that mass to c^2.

The program link is here: dddd01.py

This frequency is the next crucial step, and is the frequency at which mass is generated. When we then scale it by Q_m ( which relates frequency to mass), we arrive at a mass that has this relationship with spacetime. This mass then is finally accelerated by the speed of light squared, c², to get the force equivalent equivalent of that system.

It is the Planck mass that establishes the magnitude of those forces so they match our units of measure for force.

The Specific Case: 

The Planck mass and the scaling of the equations becomes particularly clear when the mass-distance ratio equals one. When m1m2 / r² = 1, then this relationship represents an equilibrium of sorts, where the system is in a default state of balance. It is also at this state, that the force is equal to G itself. Without the m_p² scaling the resulting forces and their equivalent energies would be off by a scaling of 1/m_p². The scaling that Planck mass introduces is what allows the magnitude of the force to be correct, demonstrating the fundamental nature of m_p in our framework.

Implications and Conclusions

The Planck mass is not just a scale for quantum gravity, it is an essential scaling factor that allows our framework to accurately connect mass, length, frequency, and force in our system and to match the values that we measure in the real world. The use of m_p² scales a ratio between mass and length to a wavenumber, so that the rest of the steps in the constant can do their part. This analysis reinforces that m_p scales the ratio of 1 between mass and length to the correct magnitude for force.

When the specific condition where the mass-density relation (m1m2/r²) equals 1 is met, G emerges directly from the equations in our system. This is only possible, when the relationships are scaled using the Planck mass, suggesting that m_p² is the ratio of 1 to the proper force for that ratio. These new insights suggest that the Planck mass is a fundamental part of how we measure the universe, and not a property of nature itself. These insights have the potential to revolutionize our understanding of gravity and its relationship to the quantum world.

Further Research:

Further research will explore these implications and test them by relating to other known phenomena, and by attempting to make testable predictions using this new framework.