Introduction

The New Foundation Model is a new formulation of physics that presumes elementary quantities of length, mass, and time are fundamental building blocks of the natural world, and that traditional constants, including Planck’s constant and the gravitational constant, are composites.

The New Foundation Model is mathematically consistent with traditional physics because historical constants are equivalent to the fundamental units they embody. The model restates constants and equations in their most elementary form, and reveals a physical structure that is otherwise hidden by the composite values of historical constants.

Modern physics treats Planck’s constant and the gravitational constant as fundamental, and defines natural quantities of length, mass, and time as complex ratios of 𝐺, ℏ, and 𝑐. The New Foundation Model shows the simplicity and elegance of the physical universe when we treat the Planck units as fundamental and the traditional constants as composite.

The simple forms of Planck’s constant and the gravitational constant are:

The composite structure of the constants is easy to see in formulas with Planck’s constant and the gravitational constant.

Fundamental units

The physical universe is constructed from three fundamental unit dimensions of length, mass, and time. The mechanical, gravitational, and electromagnetic dynamics of particles and fields have spatial and temporal attributes in these dimensions. Length and mass quantify the spatial distribution of elementary particles while time quantifies rates of change.

Each of the three unit dimensions has a natural quantity called a Planck unit, named after Max Planck who related these quantities to his famous constant of proportionality. The three Planck units coincide at the Planck scale, where Planck length and time represent the minimum intervals of length and time, and Planck mass quantifies the maximum mass limit of an elementary particle.

Observable physical phenomena such as momentum, force, and energy are specific ratios of these three unit dimensions. These phenomena describe the spatial and temporal distributions of elementary particles and systems.

Potentials

Standard model particles can be characterized as having maximum potentials in the amount of the Planck units. Length and time potential are inverse to their unit values, and mass potential is proportional to its unit value.

Elementary particles are re-distributions of conserved potentials over space and time. Mass is distributed over a particle’s wavelength giving it a proportional quantity of strength. This spatial distribution is one of two components determining a particle’s kinetic energy.

Time potential quantifies the rate of a particle’s displacement, giving it a temporal quantity of strength proportional to its velocity. Temporal displacement is the second component of a particle’s kinetic energy.

The three fundamental units give a general formula for calculating the physical properties of elementary particles and systems. This formula establishes a basis in the maximum potentials of certain physical properties quantified by the Planck units. The function transforms inputs of measured values into one or more proportionality operators based on their ratios to the Planck units. The magic of the function is that a simple reduction from the maximum potential determines the output. In non-relativistic terms, the maximum mass, momentum, and energy of an elementary particle cannot exceed these Planck scale potentials.

Operators

The spatial and temporal distribution of a particle’s conserved potential is described by dimensionless proportionality operators. An operator is the ratio of a particle’s length, mass, or time to the Planck scale potential. For example, the wavelength operator determines a particle’s momentum.

Multiplying the wavelength operator by the Planck momentum gives the correct momentum of a particle whether it has rest mass or not.

Operators reflect the physical properties of particles. The wavelength operator gives the correct momentum because the particle is distributed over its wavelength. Momentum grows proportionally stronger or weaker as the wavelength changes in relation to the Planck length.

Symmetries

The spatial and temporal distributions of conserved potentials are correlated in the three unit dimensions. These correlations gives rise to natural symmetries which conserve mass, momentum, and energy. The correlation of unit dimensions for particles that do not have rest mass, such as photons, is characterized by the following illustration.

A photon’s spatial distribution is quantified by its wavelength. Any given wavelength has a corresponding quantity of mass and time in the same proportions. This proportional quantity of mass is often called a photon’s effective mass and is consistent with traditional formulas using Planck’s constant.

A photon’s velocity is fixed at the maximum rate of displacement. The illustration shows maximum velocity as a single vertical line crossing the dx and dt potentials, signifying the maximum rate. Selecting the particle’s wavelength as the change in position produces the particle’s oscillation period in the dt dimension.

The introduction of rest mass produces the following correlations in the same unit dimensions:

Rest mass effectively reduces a particle’s length, mass, and time potentials from the Planck scale down to the scale of the Compton wavelength–shown by the dashed line in the illustration. The Compton scale represents the particle’s shortest possible wavelength and oscillation period, as well as its maximum mass potential in non relativistic terms. The particle reaches its maximum velocity at the Compton scale.

The Compton scale effectively replaces the Planck scale as the particle’s maximum potential and establishes a new reference point for reduced quantities of mass, momentum, and energy. A reduction in potential from the Compton scale is partitioned evenly between the particle’s wavelength and its velocity–changing the ratio of the particle’s Compton wavelength to its actual wavelength in the same proportion as its velocity to the speed of light. The equivalence of these two ratios suggests that momentum only represents a particle’s wavelength and not its velocity. This new definition of momentum is consistent for particles with and without rest mass.

2-part energy mechanism

The kinetic energy of an elementary particle–whether it has rest mass or not–is determined simply by the product of its spatial and temporal distributions. The two parts of the mechanism are:

1. A particle’s strength due to the concentration of its wavelength, where shorter wavelengths produce greater energy in proportion to the Planck length.
2. A particle’s strength due to the rate of its displacement, in which greater velocity produces greater energy in proportion to the speed of light.

For particles without rest mass, the velocity component is fixed at the maximum potential and the particle’s energy is determined entirely by its wavelength.

For particles with rest mass, the equipartition of energy between wavelength and velocity creates a squared quantity of kinetic energy in relation to changes in either the wavelength or velocity.

Formulas

The 2-part energy mechanism yields a simple template for determining the kinetic energy of particles with and without rest mass. The following illustration expresses the formula in terms of the traditional unit dimensions of energy.

The 2-part energy mechanism accounts for the kinetic energy of all particles except for a one-half reduction in the energy of particles with rest mass. The New Foundation Model attributes this reduction to a particle’s spin, where the energy of half-spin particles is diluted over an extended cycle.

The transformation of conserved potentials into an observable quantity of kinetic energy is shown in the following illustration. The maximum potential is transformed by three proportionality operators–one for the particle’s spin, one for its wavelength (applied in all three unit dimensions), and one for its velocity.

Observable quantities include the particle’s wavelength in the length unit dimension, a quantity of mass in the mass unit dimension that is historically treated as momentum, and the particle’s oscillation period.

The natural energy formula is equal to the historical equation 𝐸_𝑘 = ½𝑚𝑣²

Applying the same template to particles without rest mass gives the natural formula

which is equal to the historical formula 𝐸 = ℎ𝑐 /𝜆. The two equations reveal a consistent structure in particles that have rest mass and those that do not.

These natural formulas show the distribution of a conserved Planck energy potential over space and time. Both distributions can be summarized by a single temporal operator in the ratio of the particle’s oscillation period to the Planck time. Both formulas agree with traditional energy formulas.

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