Mass and inertia
Previous chapter ( Illumination ) | Table of contents | Next chapter ( Pressure of aether ) |
Corresponding Wikipedia articles: Mass, Inertia
Rest energy
The amers do not have their own physical mass, although they have a property of inertia, according to the 1st Newton's law. The amer mass depends on a magnitude of the magnetic flux density at the point. The mass is not a subject to the laws of conservation. The mass is invariant with respect to any reference frame as well as the magnetic field, which produces the mass.
The volumetric electromagnetic energy density is composed of two components (magnetic and electric), and it is equal to the doubled dynamic pressure of a beam: \[w=\rho v^2\tag{1}\] The mass density definition is based on (1):
Domain | SI | CGS | Simplified | \(\tag{2}\) |
---|---|---|---|---|
Vacuum (aether) | \[\rho=\varepsilon_0 B^2\] | \[\rho=\frac{1}{4\pi c^2}B^2\] | \[\rho=B^2\] | |
Matter | \[\rho=\varepsilon_0\varepsilon B^2\] | \[\rho=\frac{1}{4\pi c^2}\varepsilon B^2\] |
The electromagnetic energy of an aetheric vortex in a vacuum is equal to the well known rest energy of a material particle: \[E=\int{w\mathrm{d}V}=\varepsilon_0\int{B^2v^2\mathrm{d}V}=mc^2\tag{3 - SI}\] \[E=\int{w\mathrm{d}V}=\frac{1}{4\pi c^2}\int{B^2v^2\mathrm{d}V}=mc^2\tag{3 - CGS}\] \[E=\int{w\mathrm{d}V}=\int{B^2v^2\mathrm{d}V}=mc^2\tag{3 - Sim.}\] The approximate equation for the rest energy can be obtained by substituting the equation for the electrostatic field into (3): \[Bv=\frac{q}{4\pi\varepsilon_0 r^2}\tag{4 - SI}\] \[Bv=c\frac{q}{r^2}\tag{4 - CGS}\] \[Bv=\frac{q}{4\pi r^2}\tag{4 - Sim.}\] In this equation, all the vectors are considered orthogonal. The actual vector orientation is taken into account together with the vortex geometry anisotropy in the general dimensionless factor \(A\): \[E=A\frac{q^2}{4\pi\varepsilon_0}\int_R^{\infty}{\frac{1}{r^2}\mathrm{d}r}=\frac{A}{4\pi\varepsilon_0}\frac{q^2}{R}\tag{5 - SI}\] \[E=Aq^2\int_R^{\infty}{\frac{1}{r^2}\mathrm{d}r}=A\frac{q^2}{R}\tag{5 - CGS}\] \[E=A\frac{q^2}{4\pi}\int_R^{\infty}{\frac{1}{r^2}\mathrm{d}r}=\frac{A}{4\pi}\frac{q^2}{R}\tag{5 - Sim.}\] \(R\) is a characteristic radius of the central vortex region, in which the given field model is not applicable and which energy is included in the factor \(A\).
Kinetic energy
The additional energy intake in a form of the external beam produces a linear motion of the vortex by the law of conservation of momentum. When the energy is dissipating by the beam emission, the linear motion is decelerating.
The energy of a mobile vortex is associated with its kinematics. The full ámers velocity \(\mathbf{\overrightarrow{c}}\) is a sum of the circular motion velocity \(\mathbf{\overrightarrow{c_1}}\) around the vortex center and of the linear motion velocity \(\mathbf{\overrightarrow{v}}\) of a whole vortex: \[\mathbf{\overrightarrow{c}}=\mathbf{\overrightarrow{c_1}}+\mathbf{\overrightarrow{v}}\tag{6}\] The squaring of (6) is: \[|\mathbf{\overrightarrow{c}}|^2=|\mathbf{\overrightarrow{c_1}}|^2+2\mathbf{\overrightarrow{c_1}}\mathbf{\overrightarrow{v}}+|\mathbf{\overrightarrow{v}}|^2\tag{7}\] Assuming that the vortex beams distribution is uniform in all directions, the average velocity has the following property: \[\mathbf{\overrightarrow{c_1}}\mathbf{\overrightarrow{v}}=0\tag{8}\] Then the average velocity values are related by: \[c^2={c_1}^2+v^2\tag{9}\] Obviously, the average value of \(c\) is a constant speed of light, and \(c_1\) is a function of \(v\). The conversion from the velocities into the displacements per time unit, gives the well-known formula of relativistic length contraction: \[\frac{l_1}{l}=\frac{c_1}{c}=\sqrt{1-\frac{v^2}{c^2}}\tag{10}\] The relativistic length contraction relates only to the linear dimensions of the aetheric vortices. Since the vortex size is inversely proportional to its energy (5), there is a well-known formula of the relativistic energy: \[E=\frac{mc^2}{\sqrt{1-v^2/c^2}}\approx mc^2\sqrt{1+\frac{v^2}{c^2}}=mc^2\left(1+\frac{v^2}{2c^2}+\frac{3v^4}{8c^4}+\dotsc\right)=mc^2+\frac{mv^2}{2}+\frac{3mv^4}{8c^2}+\dotsc\tag{11}\] The relativistic time dilation relates only to a lifetime of the unstable material particles. An increase in their energy causes a proportional increase in their lifetime.
A part of the vortex energy, which depends on the linear velocity, is its kinetic energy, which causes its inertia of motion. The force of inertia is expressed by the mechanical power: \[P=\mathbf{\overrightarrow{F}}\mathbf{\overrightarrow{v}}=\frac{\mathrm{d}E}{\mathrm{d}t}=\frac{mc^2v\dot{v}}{(1-v^2/c^2)^{3/2}}\approx m\dot{v}\left(v+\frac{3v^3}{2c^2}+\dotsc\right)\tag{12}\] \[\mathbf{\overrightarrow{F}}\approx m\mathbf{\overrightarrow{a}}\left(1+\frac{3v^2}{2c^2}+\dotsc\right)\tag{13}\] In the reference frames, which move with respect to the zero point, the usual addition of the velocity vectors of the material points and the reference points takes place. In these frames the velocity can exceed the speed of light in a vacuum, but not exceeding the speed of light, which is determined for these frames and the propagation directions.
Example 1. The fixed point on the Earth's surface moves with respect to the absolute reference frame at a speed of several hundred kilometers per second (see "Electromagnetic waves and light"), causing the maximum deviation of the speed of light about ±0,1%.
Example 2. The particles in the accelerators almost reach the speed of light. The law of conservation of energy leads to the oscillation of particles velocity with respect to the accelerator, which is synchronous with the rotation inside it. The rotation makes the average particles velocity independent of the reference frame.
See also
Previous chapter ( Illumination ) | Table of contents | Next chapter ( Pressure of aether ) |