'Volumes'

The Three (of four) Basic Types of Volumes

Consider a balloon (fig. A) and its cross-section (fig. B). It illustrates three of the four volume types; the fourth will be introduced later.

1. Mass volumes (fig. B): These contain mass, like the balloon’s envelope.
2. Empty volumes (fig. B): These occupy 3D space but are void, like the air inside the balloon.
3. Apparent volumes (fig. A): These are visible volumes, combining mass and empty volumes.

Open and Closed Volumes

Volumes are classified by their permeability to spacetime (see figure):

• Closed volumes (or 'volumes with mass', fig. B): Impervious to spacetime, which flows around them. Example: the balloon’s envelope.
• Open volumes (or 'Empty volumes', fig. B): Spacetime passes through them freely, as they are vacuums. Includes the air inside and around the balloon.
• Apparent volumes (fig. A): Visible combinations of closed and open volumes. Apparent volumes are what we observe under a microscope when examining an atom (see below).

Example: Atoms

In the figure below, there is an atom with the nucleus in Fig. A, and the orbitals around the nucleus in Fig. B.

Spacetime cannot penetrate closed volumes, as illustrated in Fig. A, whereas it flows freely through open volumes, as shown in Fig. B.

Imagine immersing these two volumes in water. Like spacetime, water cannot enter a closed volume (Fig. A), but it can pass through an open volume (Fig. B).

In summary, atoms consist of:

• Closed Volumes: These include electrons and the nucleus. Since they possess mass, they are impervious to spacetime.
• Open 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 closed volumes (nucleus and electrons) and open volumes (orbitals).

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

Hermetic Volumes

This is the fourth type of volume introduced earlier. Hermetic volumes consist of combinations of open and/or closed volumes. Figure C below illustrates an example of a hermetic volume.

Spacetime interacts differently with each type of volume. Three scenarios illustrate this:

• Volume A: A closed volume behaves like a billiard ball immersed in water—impervious to penetration. In the same way, closed volumes are impervious to spacetime.
• Volume B: The envelope, which is a closed volume, blocks spacetime. If a billiard ball were submerged in water, the water would not be able to pass through it.
• Volume C: A closed envelope containing other volumes (e.g., a balloon filled with marbles). Regardless of the contents, the envelope prevents spacetime from entering, making it behave like A or B.

In short, a hermetic volume may be full, empty, or mixed. In all cases, its behavior remains the same: spacetime is excluded by the enclosing envelope.

Can Mass be Replaced by Volume?

Newtonian Physics: In everyday life, and within Newtonian physics, mass and volume are treated as two distinct quantities. We can refer to "volumes" without specifying their nature — whether closed, open, apparent, or hermetic — because quantum mechanics is not involved. In this context, a volume is simply a volume.

Quantum Mechanics: To understand the behavior of mass, gravitation, general relativity, and quantum mechanics, we must distinguish between different types of volumes. Each type interacts with spacetime in a unique way. Since spacetime is central to both the structure of the universe and the realm of the infinitely small, understanding the nature of volumes becomes essential.

An Interesting Example: Protons, Quarks, and Gluons

Contrary to popular belief, the arrangement of quarks within the nucleus does not align with conventional quantum mechanical models. This topic is explored in greater depth in Part 3 of this site.

A proton consists of three quarks with individual masses of approximately 2 MeV/c² (u quarks), and 5 MeV/c² (d quarks). The combined mass of these quarks is around 9 MeV/c². However, the measured mass of a proton is 938 MeV/c² — far greater than the sum of its constituent quarks. What accounts for this discrepancy?

According to academic physics, three quarks are bound together by the strong nuclear force, which is mediated by gluons. However, the origin of this force — and of gluons themselves — remains unexplained.

We further show that the proton is enveloped by an electron in wave form, creating a hermetic volume. As illustrated in the figure above, the proton's volume significantly exceeds that of its three constituent quarks. Since mass is related to (closed) volume, this provides an explanation for why the proton's mass is much greater than the sum of the masses of its quarks.

In our book, we demonstrate in a PDF how closed volumes can be used to calculate mass in a straightforward manner, using a formula such as M = f(V).