Note 1

Part 1

## Volumes with/without mass

This webpage is part of www.higgs-boson.org

#### Elasticity of spacetime:

This property of elasticity of spacetime has been demonstrated by Einstein in his "Einstein Field Equations" (EFE).

#### M and V variables:

In closed volumes, we can switch from the mass variable to the volume variable and conversely applying a simple conversion parameter, the density of nuclear matter: 5.92E-17 kg/m3 for the proton, from CODATA 2010. However, a more precise formulation is given in the Mathematics Webpage. This allows us to replace the mass variable "m" of closed volumes with its 4D expression m = f(x,y,z,t). Strictly speaking, it is a 3D expression, but it is better to remain in 4D because SR, GR and many constants such as c or G use 4D.

#### Examples of closed volumes:

Sure: Leptons. Probably: some fermions, black holes and other similar objects. Some objects such as atoms are "apparent volumes", i.e. combinations of closed and open volumes. See the explanation of Apparent Volumes in the "Mass" webpage.

#### Spacetime curvature and mass:

Contrary to what we think, it is not the mass that produces the curvature of spacetime but the reverse. The mathematical demonstration is given in our section "Energy-Momentum Tensor" in the Mathematics Webpage.

#### About the principle:

The principle discussed here is nothing but an application of the Bulk Modulus Theory of the 1850's Fluids Mechanics, which connects curvature to pressure: ΔP = -KB ΔV/V. See our demonstrations "Newton Law" and "Einstein Field Equations" in the Mathematics Webpage.