Fundamental units

The Standard Model of particle physics attributes all of the matter and energy in the universe to a small collection of elementary particles. Particles are more appropriately characterized as vibrations or wave-like oscillations of an underlying field.

The physical environment for these oscillations is a four dimensional space-time, in which length and time constitute two unit dimensions, and mass gives a third unit dimension quantifying particle densities. These three unit dimensions quantify mechanical, gravitational, and electromagnetic phenomena on quantum and classical scales.

Each fundamental unit dimension has a natural quantity defined by a Planck unit.

Planck length

The minimum length interval or distance is called the Planck length. Spatial attributes of particles and fields are measured in relation to this natural unit.

Planck length

The Planck length has an SI value of 1.62 x 10-35 meters which is unimaginably small compared to everyday quantities of length. In orders of magnitude, however, the universe is about as small relative to the human scale as it is large. A Planck-sized object would look up to the scale of an average person as the average person looks up to the scale of the known universe.


Mass is a measure of strength in an elementary particle or field. A natural unit of mass is called the Planck mass, but rather than quantifying a minimum unit, the Planck mass quantifies the maximum mass potential of an individual elementary particle. In non relativistic terms, masses that exceed the Planck mass must be aggregations of multiple particles.

Planck mass

Mass comes in multiple forms. The most familiar form is rest mass, which quantifies the field resistance that some particle experiences, as well as the amount of energy those particles possess to meet that resistance. These two offsetting quantities of energy produce the latent form of rest mass.

A second form of mass arises from a particle’s spatial density quantified by its wavelength. This form of inertial mass is found in particles with and without rest mass, and is often referred to as effective mass in photons.


A natural unit of time is called the Planck time and represents the minimum interval of change in a particle’s distribution. The Planck time duration is defined by the Planck length where the maximum rate of change is one unit of length per unit of time.

Planck time

Observable physical dynamics like mass, momentum, energy, velocity, acceleration, and force are specific ratios of the three fundamental unit dimensions. These ratios describe the physical attributes of particles and field potentials.

Fundamental units