What is the true meaning of

Volumes in Quantum Physics

The Fundamental Meaning of Volumes

Volume plays a central role in spacetime, mass, gravitation, and quantum mechanics.

Contrary to everyday intuition, quantum physics does not rely on a single notion of volume. Instead, four distinct types of volumes exist, each interacting with spacetime in a different way. Understanding these four categories is essential for explaining the nature of mass, the origin of gravitation, and several quantum phenomena.

The Three Quantum Volume Types

Consider a balloon (Fig. A) and its cross section (Fig. B). These simple objects illustrate three of the four types of volumes; the fourth will be introduced later.

Mass volumes (fig. B): These volumes contain mass, such as the balloon’s envelope. They are impervious to spacetime, which flows around them without penetrating.
Empty volumes (fig. B): These occupy three dimensional space but contain no mass, like the air inside the balloon. Spacetime passes through them freely, as they behave like a vacuum.
Apparent volumes (fig. A): These constitute the visible volumes formed by combining mass volumes and empty volumes.

The three main volumes are: Mass volume, Empty volume, and Apparent volume.

Apparent volumes =
Mass volumes + Empty volumes

A useful analogy of volumes in atoms is water:

Water cannot enter a mass volume (Fig. A, below).
Water flows freely through an empty volume (Fig. B).

In this example, spacetime and atoms behave in exactly the same way.

Mass and gravitation — Empty and mass volumes in atoms

Atomic Volume Structure

Atoms provide a clear example of these three types of volume:

The nucleus and electrons are mass volumes.
The orbitals are empty volumes. They are geometric volumes, not physical nothingness.
Together, they form the apparent volume observed with an electron microscope. These are visible volumes.

Mass and gravitation — Structure of atoms

In summary, as any volume in quantum mechanics, atoms consist of:

Mass Volumes: These include electrons and the nucleus. Since they possess mass, they are impervious to spacetime.
Empty Volumes: Orbitals represent the paths of electrons around the nucleus. Although empty, they exist in three dimensions and play a role in phenomena such as quark formation.
Apparent Volumes: When observing an atom with an electron microscope, the orbitals become visible. These are the apparent volumes we perceive. Atoms are composed of both mass volumes (nucleus and electrons) and empty volumes (orbitals).

Note: These statements align with Einstein's assertion that any mass — that is, any mass volume — curves spacetime. Here, we have simply replaced the term "mass" with "mass volume." As we will see later, substituting "mass" with "mass volume" (or "volume with mass") allows us to resolve many enigmas in quantum mechanics.

Hermetic Quantum Volumes

This is the fourth type of volume introduced earlier. A hermetic volume is a set of empty and/or mass volumes enclosed within a mass envelope. This envelope blocks spacetime entirely, so the hermetic volume behaves like a mass volume, regardless of what lies inside.

Important: Hermetic volumes are defined by their envelope, not by their content.

Example: a balloon filled with marbles. The envelope is a mass volume, so spacetime cannot enter. The internal structure does not matter: the whole behaves as a single mass volume.

Mass and gravitation — This page explains Hermetic volumes

A hermetic volume may contain mass, be empty, or include both. In all cases, its behavior remains the same: spacetime is excluded by the enclosing envelope.

Hermetic volumes act as Mass Volumes
because spacetime cannot penetrate them

Mass vs. Volume

Newtonian Physics: In everyday life and classical mechanics, “mass” and “volume” are treated as separate concepts. We can refer to a volume without specifying its nature, because spacetime does not play a role at this scale.

Quantum Mechanics and General Relativity: At the quantum scale, this distinction becomes crucial. Each type of volume interacts differently with spacetime, and these interactions determine:

the structure of the universe,
the nature of mass,
the origin of gravitation,
several quantum phenomena.

Replacing “mass” with mass volume (or “volume containing mass”) provides a more coherent interpretation of many quantum effects, as later chapters will show.

Protons, Quarks, Gluons

A proton contains three quarks whose combined mass is about 9 MeV/c², yet the measured mass of the proton is 938 MeV/c². This enormous discrepancy is traditionally attributed to the strong nuclear force mediated by gluons — as of today, no rational explanation is given to this speculation.

In the Spacetime Model, the proton is surrounded by an electron in wave form (see Parts 2 and 3 for the explanation), creating a hermetic volume. The proton’s effective volume is therefore much larger than the volume occupied by its three quarks.

Mass and gravitation — Example of hermetic volumes : protons, quarks, and gluons

Since mass is linked to mass volume, this naturally explains why the proton’s mass greatly exceeds the sum of the masses of its quarks.

This example illustrates why distinguishing volume types is essential.

In the book, a simple relation of the form M = f(V) shows how mass volumes can be used to compute mass.

Summary of the Four Types of Volumes

In quantum theory, volume is defined not by physical size but by how spacetime interacts with it. Two volumes of identical dimensions may behave completely differently depending on their permeability to spacetime.

Mass volumes (or volume with mass). Contain mass. Spacetime cannot enter.
Empty volumes. Allow spacetime to pass freely.
Apparent volumes. Visible combinations of mass and empty volumes (mainly atoms and molecules).
Hermetic volumes. Groups of volumes enclosed within a mass shell. Spacetime cannot penetrate the shell, so the entire structure behaves like a mass volume.

This classification provides a simple and intuitive explanation of the fundamental principles of mass and gravitation. The following chapters explore how these interactions illuminate general relativity and quantum mechanics.

Important

General relativity and Quantum mechanics can be
understood if, and only if, we know the behaviour of
each type of volume in regard with spacetime.