The New Foundation Model distinguishes between rest mass and inertial mass in elementary particles. Inertial mass is a variable quantity of mass determined by a particle’s wavelength, while rest mass is a fixed quantity of mass for a given particle type. The mass formula works for both types of mass.

## Standard formula: Inertial mass

Inertial mass is inversely proportional to a particle’s wavelength, so the standard formula applies the wavelength operator to the Planck mass

Inertial mass is a measure of a particle’s spatial distribution in unit dimension **M**. It is one of the three correlated unit dimensions making up the first part of the 2-part energy mechanism.

Applying the wavelength operator in the mass unit dimension transforms the maximum Planck mass potential into an observable quantity of inertial mass.

### Potential

### Operator

### Observable

The standard form of the mass formula is created using any of three equivalent forms of the wavelength operator in each of the fundamental unit dimensions.

## Expanded formula: Inertial mass

The mass formula also uses the expanded form of the wavelength operator to find inertial mass. The expanded wavelength operator is the product of the rest mass and momentum operators

.

Substituting the expanded operators produces the same transformations in the mass unit dimension.

Replacing the wavelength operator with rest mass and momentum operators gives

### Potential

### Operators

### Observable

The expanded form of the mass formula applies the two operators to the Planck mass potential

The expanded form of the mass formula uses three equivalent forms of the rest mass and momentum operators multiplied by the Planck mass to produce a particle’s inertial mass.

Because the momentum and velocity operators are equal, additional forms of the mass formula can be created by substituting the velocity operator for the momentum operator

This form of the equation produces the right answer but gives the wrong physical description of the particle or system. Applying these two operators to the maximum Planck potential gives the inertial mass observable .

### Potential

### Operators

### Observable

This alternate form of the expanded mass formula uses three equivalent forms of the rest mass and velocity operators multiplied by the Planck mass to find the particle’s inertial mass.

## Rest mass formula

Rest mass is a fixed quantity of mass specific to a particle type. A particle’s rest mass does not change as its wavelength, inertial mass, and velocity change. However, rest mass can be quantified in terms of a particle moving at the speed of light. The energy equivalent of rest mass is defined by the Compton wavelength which is determined using the rest mass operator and the maximum value of the velocity operator, 𝑐/𝑐. Since the velocity operator is equal to one, the rest mass formula can be stated in the following three simple forms: