...What is Mass?

...What is Gravity?

Physicists who prefer a mathematical demonstration of the proposed theory can download the original document, a 54 pages PDF file. The download URL is located at the end of this web page. This PDF document is more accurate than the present HTML web page and contains experimentations and validation using mathematics. In particular, the Schwarzschild Metric and Newton Law are not calculated from EFE (Einstein-Hilbert Field Equations) but from scratch, using a new method based on the Hooke Law. This mathematical demonstration validates the proposed theory.

The Spacetime Curvature

If we drop a billiard ball in a container filled with water, it is the volume of the ball, and not its mass, which produces the water displacement.

The same phenomenon also exists in spacetime. Contrary to preconceived ideas, it is the volume of elementary particles, and not their mass, which deforms spacetime. So:

Any volume inserted in spacetime necessarily produces a curvature of it

This deduction leads to a question: "what is a volume?"

Notes: 1) This example does not correspond exactly to spacetime since water is not elastic. It would be more exact to compare spacetime to a kind of deformable crystal or a flexible polystyrene foam. Since spacetime is elastic, if the volume of the central object is removed, the curvature disappears. 2) The figure was simplified to two dimensions for teaching purposes. 3) The constitution of the central object is important. However, this subject is covered in Part 2 of the Spacetime Model. 4) The time component of spacetime is also curved.

Open and Closed Volumes

Let's now replace the billiard ball used in the preceding example by a balloon having the same volume. This does not change anything.

The same phenomenon also exists in quantum mechanics. We have two classes of volumes:

• Closed volumes (fig. A): These volumes make a displacement of spacetime. As we will see further, the spacetime curvature produces a "mass effect". So, closed volumes have a real mass-volume equivalence, which may be written: m=k.v, with k=conversion constant, 5.9239x10¹⁷ kg/m³ for the proton (CODATA 2006). Nuclear matter like quarks, electrons, protons, neutrons, muons, mesons, lambdas... are examples of closed volumes.

• Open Volumes (fig. B): These volumes exist but do not produce any displacement of spacetime. If there is no curvature, there is no "mass effect" either. Orbitals of atoms are examples of open volumes.

All objects of the universe are combinations of closed volumes (with mass) and open volumes (massless). This is why we have the illusion, on Earth, that mass and volume are two different dimensions.

Gravity

Since spacetime is elastic (Einstein), its curvature produces pressures on two volumes. This tends to bring them closer to each other.

The "principle of split", which comes from the fluid theory of the nineteenth century, also confirms this explanation.

Let's imagine a sphere (fig. A). If we split this sphere down the middle (fig. B), each half is subjected to only one force. We have a movement of each half toward the other. Transposed to spacetime, this phenomenon is simply “gravity”, which is a pressure force on volumes.

It is important to note that, in these two examples, it is the volume (not the mass) which makes the curvature of spacetime.

Therefore, contrary to preconceived ideas,

Gravity is not a mysterious attractive force between masses, but a simple pressure force (Hooke Force) exerted by spacetime on (closed) volumes.

Finally, the explanation of mass and gravity is quite simple and, as we see, doesn't need extra dimensions as in the Higgs Model or the String Theory.

Current Theory vs Proposed Theory

Note: Any massive object is made of two quantities: a closed volume, which curves spacetime, and a "mass effect" produced by the curvature of spacetime. Therefore, a "mass effect" is associated to each closed volume. Only volume physically exists. Mass doesn't exist in concrete terms. Mass is an "effect" due to the pressure of spacetime on closed volumes. Mass is a kind of virtual quantity.

Examples

Attractive Force vs Pressure Force

In this first example, imagine that you hold a very light polystyrene ball in your hand. A flexible polystyrene foam, which is curved by the ball, replaces spacetime. The curvature of the foam (= spacetime) produces a pressure on the top of the ball, toward Earth (not represented on the figure). If you close yours eyes, you will sense that the ball is heavier. It is not the mass of the ball, which increases, as we could think, but the pressure on the top of it. However, the result is identical. It we replace the foam by spacetime, we can say:

Attractive force (gravity) = Pressure force produced by spacetime

What is Volume?

In this theory, we must reconsider what we call "Volume". For example, what is the real volume of earth + moon? We have two different points of view.

• A: The individual volume of the earth is added to that of the moon.
• B: The empty space between the earth and the moon has been added too.

Translated into quantum mechanics, the earth is the nucleus, the moon is an electron, and empty space is the vacuum between the nucleus and electrons, i.e. 99,999 % of the atom volume. Since the empty space doesn't curve spacetime, there is no reason to take into account this empty space for mass and gravity calculations.

Therefore, experimentations measuring the volume of atoms or molecules with the (B) scheme may be interesting for various reasons, but in General Relativity, we must take into account only closed volumes, as in (A).

In other words, for mass and gravity calculations, all open volumes must be excluded.

The Atom Volume

In atoms, electrons are on empty orbitals already crossed on both sides by spacetime. Orbitals are "open volumes" since they do not curve spacetime. Orbitals are massless. Finally, an atom is a combination of closed volumes (with mass) and open volumes (massless).

• Closed volumes, with mass : protons, neutrons and electrons
• Open volumes, massless : orbitals

If we need to know the volume of an atom, we can take either the "matter volume" (nucleus + electrons), or the entire "visible volume" (nucleus + electrons + empty space, or orbitals). However, as indicated in the preceding paragraph, we must always have in mind that the only kind of volumes which must be taken into account in mass and gravity calculations is the real volume of the nuclear matter (nucleus and electrons), excluding orbitals since empty space doesn't curve spacetime.

Hydrogen vs Oxygen

Oxygen has 16 times more nucleons than hydrogen. So, the curvature of spacetime will be x16. The pressure of spacetime on closed volumes (the nucleus and electrons) will be x16. Finally, the "mass-effect" of the pressure of spacetime on the closed volumes of an oxygen atom will be x16 too.

Since m = k.v, we can say: "(closed) volumes curve spacetime" instead of "masses curve spacetime".

Mass-Volume Equivalence

This last example, very simple to understand, demonstrates that spacetime is curved by volumes, which seems logical, not by masses.

On our left, we have an eraser and, on our right, a pen that weighs two times more.

If we remove the 99.999% of vacuum existing inside the atoms of the two objects, we obtain two "heaps" of nucleons. We will have two times more nucleons for the pen than for the eraser because all the mass is practically concentrated in nucleons (for teaching purposes, electrons, binding energy, gluons etc... have been ignored).

Since all nucleons have the same volume (proton ≠ neutrons), the pen nucleons will have a total volume twice superior to those of the eraser.

Therefore, the pen will produce 2X more curvature of spacetime since its "closed" volume is twice that of the eraser. In other words, the spacetime will produce a pressure x2 times stronger over the pen than over the eraser in the pen/eraser-Earth context.

So, the pen will be two times heavier than the eraser.

This simple experiment demonstrates that, contrary to a preconceived idea:

Gravity isn't an attractive force between masses but a pressure force (Hooke Force) exerted by spacetime on closed volumes

Conclusions

In conclusion, the following points must be noted:

• Contrary to other theories (Higgs...), the Spacetime Model is very simple. The latter matches with the simplicity of Nature.
• The Spacetime Model exactly matches Einstein's ideas: "The universe would have only 4 dimensions, no one more". It's not a proof per see, but an important indication.
• The dimensions of a theory must match those of corresponding experimentations, i.e. 4D/4D, 5D/5D... nD/nD. Until today, all mass and gravity experimentations has been conducted in 4D (x, y, z and t). So, the mass and gravity theory associated to these experimentations are necessarily in 4D. Indeed, it seems strange to have a 5D (Higgs), 6D ... nD theories which lead to 4D experimentations... Why should we have more dimensions in theories than in experimentations?
• The mass and gravity phenomena already exists on Earth, like demonstrated in our example of a billiard ball into water. Another experimentation is described in the PDF document. Since we know that Nature always tends to repeat itself, the "Spacetime Model" is much more credible than theories which have no counterpart on Earth.
• Contrary to other theories, this explanation is in perfect accordance with the Stress Tensor used in fluid mechanics, which is at the origin of Einstein Field Equations. The PDF document covers thoroughly this subject.
• This explanation is also in accordance with the constitution of atoms: nucleus is a closed volume with mass, and orbitals are massless open volumes.
• At last, the PDF document contains validation using mathematics. In particular, the Schwarzschild Metric and Newton Law are not calculated from EFE (Einstein-Hilbert Field Equations) but from scratch, using the Hooke Law.

These considerations mean that the proposed theory in 4D is much more credible than any other theory using more dimensions.

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This explanation of Mass and Gravity is Part 1 of the Spacetime Model. To download the four other parts, please hit the corresponding URL link:

Author and site designer: Jacky JEROME

Author's email: diaverre@orange.fr

Last update: 29/06/09

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