Kinetics

Kinetic Theory is the foundations of the Aether Mechanics. Aether Mechanics explains the cause of gravity and light based on the following two assumptions of kinetic theory:

  • Aether particles have mass.
  • Aether particles have both translational and spinning motions.

Aether particles are similar to gases except that aether particle are much smaller and are spinning much faster than gases. Based on the kinetic theory, Aether Mechanics provides a comprehensive aether theory to explain the cause of gravity and light.

 

Mass Density of Aether Particles

Aether Mechanics assumes all aether particles are spherical balls with a diameter D_a.
We do not know the exact size of an aether particle. However, we know the approximate size is very small compared to the size of a neutron.

Aether Mechanics assumes all aether particles have mass m_a. The mass of an aether particle is also very small compared to the mass of a neutron.

To simplify the derivation of the gravitational force and the electromagnetic force, we assume all aether particles have the same size and the same mass.

Even though aether particles have the same size and mass, the volumes they occupy in space are different. At some locations, aether particles are closer to each other. At other locations, aether particles are more distant from each other. It is important not to be confused with the size of particles and the volume it occupies.

Based on volume occupied, the mass density can be calculated by the total mass of aether particles divided by the total volume occupied. For example, the four aether particles shown on the left side of the figure above occupy a larger volume in space and have smaller mass density than the four aether particles shown on the right side of the figure that occupy a smaller volume in space.

It will be shown that lower mass density will result in lower aether pressure and higher mass density will result in higher aether pressure.

 

Microscopic Aether Colliding and Spin Motions

When we zoom in to see the microscopic motion of aether particles, we should see both colliding motion and spin motion:

• Aether particles’ colliding motion:
Aether particles’ microscopic colliding motion is translational movement that results in the colliding of particles. Aether particles’ colliding motion is very similar to the colliding motion of the gas particles. These translational colliding velocities can be represented by vectors: \vec{v}_{c1}, \vec{v}_{c2} and \vec{v}_{c3}. The directions of colliding velocity vectors are random in space. The magnitudes of colliding velocity vectors are random but follow Maxwell’s distribution.

• Aether particles’ spin motion:
Aether particles’ microscopic spin motion is self-spinning motion of aether particles. These rotational spin velocities can be represented by vectors: \dot{\vec{\theta}}_{c1}, \dot{\vec{\theta}}_{c2} and \dot{\vec{\theta}}_{c3}. The directions of spin velocity vectors are random in space. The magnitudes of spin velocity vectors are also random but follow Maxwell’s distribution.
Magnitudes of both colliding velocity and spin velocity follow Maxwell’s distribution. Maxwell’s distribution is the final steady state result of a bunch of particles colliding with each other starting with any arbitrary initial condition.

The spin motion of gas particles are usually neglected when deriving the ideal gas law because gas particles do not rotate very fast. However, spin motion of aether particles is as important as colliding motion when deriving electromagnetic force because the spin motion of aether particles is very fast.}

 

Fast Spin of Aether Particles

Aether mechanics assumes aether particles spin at a very fast speed. Electromagnetic wave is derived based on both fast colliding motion and fast spin motion. So, does it makes sense that tiny aether particles can spin at a very fast speed? The answer of course is yes. It can be explained by Newton’s laws of motion.

When two particles, as shown on the left, are moving toward each other at the same magnitude and opposite direction, it is assumed that the two particles are colliding with a friction force. Friction forces will act on the surfaces of the particles. The exact magnitude of friction force F is related to the roughness of the surface of aether particles and the colliding angle. It is reasonable to conclude that the magnitude of the force is proportional to the mass times the acceleration of the particle.

The friction force F on the surface of the particle will result in a torque T to this particle. This torque will result in a rotational angular acceleration of the particle following Newton’s 2nd law of motion where: torque is equal to the moment of inertia times the angular acceleration. The moment of inertia of a spherical ball is proportional to m D^2. Therefore, it can be concluded that the angular acceleration is proportional to the colliding acceleration but inversely proportional to the diameter of the particle. Because aether particles have a very small diameter, therefore, the spin acceleration is very large.

 

Aether Particles’ Translational Velocities

In order to explain the aether particle translational motion, an example is used to show the definition of three translational velocities.

In the example, three aether particles move randomly in a rectangular box. The box is attached to a boat with two springs. Because of these two springs, the box can oscillate forward and backward on the boat. Finally the boat floats on water.

When we want to study the kinetic action of the particles, we do not want to consider the motion of the box nor the boat. Therefore, particle colliding velocity is best defined from the box coordinate which is in oscillation on the boat.

When we want to study the vibration of the box, we do not want to consider the motion of the particles nor the boat. Therefore, box velocity is best defined from the boat coordinate.

When we want to study the flow velocity of the boat, we do not want to consider the motion of the particles nor the box. Therefore, boat velocity is best defined from the ground coordinate.

We can superpose (1) colliding velocity, (2) oscillation velocity and (3) flow velocity into a global (total) velocity of an aether particle. Note that this total velocity refers to an aether particle and is not a function of location.

 

Velocity Field as Macroscopic Aether Motions

In the previous example, microscopic colliding velocity of particles can be defined as (1) \vec{v}_c from the box coordinate or (2) \vec{v}_{tot} from the global coordinate. Both describe the same microscopic colliding velocities of an aether particle but from two different coordinate systems. Total velocities of colliding and spin motions observed from the global coordinate are shown in the figure. Note that both \vec{v}_{c.i} and \vec{v}_{tot.i} refer to an individual particle.

For the purpose of studying the aether particle oscillation and flow, the averaged motion is defined by taking the average velocity of all particles in the volume V at location (x,y,z) and at time (t). By taking the average, the result of the velocity becomes a field of function of (x,y,z) and (t) and no longer refers to an individual particle.

In the first equation, the translational total velocity of an aether particle is observed from the global coordinate and is defined by adding colliding, oscillation and flow velocities. The second equation reverses the definition and uses total velocity to define oscillation and flow velocities. These definitions are provided here in order to demonstrate the relationship between these three velocities.

Following the same manner, spin motion of an aether particle can also be observed from three different coordinates and is listed in the table for comparison to the colliding motion.
Note that the rotational flow velocity is zero. Otherwise, a steady magnetic field would exist.
Also note that the vortex motion comes from the curl of \dot{\vec{u}} and \vec{v}_f
but not the spin motion of aether particles.

 

Colliding Pressure Due to a Single Particle

Pressure is defined by force per unit area. Air pressure comes from impact forces due to the colliding velocity of gas particles with mass. When gas particles collide into a surrounding object, the momentum changes before and after the collision which will result in a force on the colliding particles. The particles are made of molecules such as O_2, N_2 , CO_2 or H_2O.

Following the same procedure for calculating air pressure, aether pressure from a single aether particle can be calculated as follows:

Assume a single particle with mass m_a is moving at the longest distance inside of a perfect spherical ball with a radius R_a. The pressure on the surface of the spherical ball can be calculated by the force divided by the surface area of the ball 4\pi R_a^2. The force due to collision is the momentum change 2m_a v_{ca} divided by the time it takes for the particle to travel from one wall to the other wall along the diameter \Delta t={2R_a\over v_{ca}}. Note that, the density is \rho = \frac{m_a}{V_a} and the volume is V_a={4\over 3}\pi R_a^3. We get pressure p = {1\over 3} {m_a\over V_a} v_{ca}^2 or
p={1\over 3}\rho v_{ca}^2.

Because calculating aether pressure is similar to calculating air pressure, the derived equation p={1\over 3}\rho v_{ca}^2, can be further transformed into the famous ideal gas law PV=nRT, by relating particle velocity v_{ca} to temperature T. However, temperature is not used in aether mechanics because aether energy is much higher than the energy related to the temperature due to gas collision. Therefore, the original form of pressure p={1\over 3}\rho v_{ca}^2 is used in aether mechanics.

 

Kinetic Energy Density of a Single Particle

In classical mechanics, kinetic energy includes both translational and rotational kinetic energy. Translational kinetic energy is half of the mass multiplied by the square of velocity. Rotational kinetic energy is half of the moment of inertia multiplied by the square of spin velocity.

As we mentioned before, aether particles have both translational colliding motion and spin motion. Both colliding motion and spin motion are important in deriving gravitational force and electromagnetic force. Therefore, the kinetic energy of an aether particle is written as K_a={1\over 2}I_a\dot{\theta}_{ca}^2+{1\over 2}m_av_{ca}^2.

Because spin velocity is induced by translational velocity, it is reasonable to assume a linear relationship between translational kinetic energy and spin kinetic energy by a coefficient of (\alpha\!-\!1), where (\alpha\!-\!1)>0. Based on this argument, kinetic energy can be written with a translational energy term using a constant coefficient \alpha.

Kinetic energy density is defined by total kinetic energy per unit of volume. Kinetic energy density
can be calculated by dividing total kinetic energy {\alpha\over 2}m_a v_{ca}^2 by the volume of the spherical ball V_a. We can rearrange terms to get kinetic energy density E_a = {\alpha\over 2}\rho v_{ca}^2.

Finally, a simple relationship between pressure and kinetic energy density can be concluded by comparing pressure p_a={1\over 3}\rho v_{ca}^2 and kinetic energy density E_a={\alpha\over 2} \rho v_{ca}^2.
The equation which relates pressure to energy density is E_a={3\alpha\over 2} p_a.

 

Colliding Pressure and Kinetic Energy Density of Multiple Particles

Aether pressure and kinetic energy density of a single aether particle are derived by assuming the particle is moving at a constant speed. In reality, the speed of perfect elastic particles will reach Maxwell’s distribution after colliding with surrounding particles. Therefore, the translational speed of both gas particles and aether particles should be Maxwell’s distribution. In Maxwell’s distribution, the Root-Mean-Square (RMS) speed is related to the most probable speed \hat{v}_c as v_{rms}=\sqrt{{3\over 2}}\hat{v}_c.

Note that aether pressure of multiple particles can be calculated by the mean pressure p={1\over 3}\rho v^2. Because pressure is directly related to the square of colliding speed, the RMS speed is
used to replace the speed of a single particle.

Similar to aether pressure, aether energy density of multiple particles can also be calculated by the mean kinetic energy density of aether particles. Aether kinetic energy density is very large because aether pressure is very high compared to air pressure. Aether mechanics assume the universe is made of only two types of particles: aether particles and neutron particles. The neutron particles have little energy. Most of the energy of the universe is stored in aether kinetic energy.

By comparing pressure and energy density, the previous simple relationship between pressure and energy density remains the same: E={3\alpha\over 2} p. Even though the most probable speed and the RMS speed can be used to express pressure and energy density, the RMS speed of aether particles is used in developing the theory.