Coulomb force

The motion of macroscopic bodies was described by Isaac Newton with the help of equations like:



[F = force; m = mass; a = acceleration]

The equation describes the alteration of the velocity of an object (m) by a force. It is not a relativistic equation thus the equation is not 100% in line with reality when the object gets a velocity that nears the speed of light. Moreover, Isaac Newton had no idea about the conservation of quanta transfer in space so his analytic concept of the involved phenomena was related to the sensory interpretation of reality.

That’s why the force (F) and the acceleration (a) are variables in Newton's equation because no alteration of the accelerated object (mass) was observable in Newton's age.

When mass (m) has a constant magnitude in the equation, we can replace mass with the help of a quantity of Planck's constant (see previous post about “Planck’s mass”):



[n = integer; h = Planck's constant]

So we can substitude:



The mass of the object has a boundary and the volume represents a certain amount of elements. All the elements transfer 1 quantum at the same time so the velocity of the object at a certain moment is the transfer of the local topological transformations of the involved elements (n h). In fact, we can assign a quantity of energy (Planck’s constant) to every involved element.

When there is a high quantity of topological transformations it will last a lot of time (n t) before all the transformations are transferred to adjacent elements of the structure of the quantum fields. So the observer will conclude that the object has a low velocity.

Suppose the object has the size of only 1 element and the transformation of this single element is 1020 h. Now it will last 1020 t (constant of time) to transfer all the energy of the element to the environment (adjacent elements). Anyway, how do we know the amount of transformations of the elements in the environment? Because all the elements around do not form a neat “flat space”.

Imagine we can manipulate the transformation of all those elements around: we increase the average transformations (deforming) of all the distinct elements with 1010 h. The result is clear: the velocity of our “object” will redouble. Just because the transfer of single quanta is conserved:



[t = constant of time; λ = constant of length; c = constant of velocity]

Our “experiment” changed the velocity of the object, because we increased the average deforming (= topological transformations) of the elements around the object. So we applied something we call “force” in physics and it shows to be impossible to distinguish the energy of a force from the energy of an object when our point of view is the structure of the quantumfields.

Now back to Isaac Newton's equation:



Applying a force to the mass of an object is nothing more than increasing the average deformation (n h) of the surroundings of the object. Thus we can write (to show the machanism):



Planck’s constant has mass so we increase also the mass of the phenomenon (with the object “inside”). In other words: the concept of an “underlying” structure of the quantum fields is according to the main insights of modern physics.

The last schematic equation shows the “physics” behind cold fusion. Because when we force an object to remain its velocity when we apply more deformations to the surrounding elements – so the acceleration a is forced to be a constant (underlined) – the mass of the object must change when we change the environment:

(n h) = (n h) a
 

Now let's examine the mechanism of palladium based cold fusion.

When we supply an electromagnetic wave to a single atom, the result is described by Newtonian mechanics.

F = m a

[F = force; m = mass; a = acceleration]

In other words: hydrogen atoms – locked inside a palladium lattice – must react very strange when we apply an electromagnetic wave to the lattice. They have to rocket away but they cannot.

The palladium atoms around differ from the hydrogen atoms because of their mass and the electrostatic attraction (metallic bonding). The result of a metallic bonding is like adding mass. When we want to accelerate 1 palladium atom, the electrostatic force is like a glue so all the other palladium atoms will accelerate too. Of course this is impossible.

So when we want to accelerate 1 palladium atom Newtons formula is:

F = (106 mh + me) a

[mh = mass hydrogen atom; me = energy electrostatic force expressed in mass].
The mass of a palladium atom is 106 x mass of a hydrogen atom and every palladium atom has adjacent palladium atoms (lattice configuration).

Conclusion: electromagnetic stimulation will alter the velocity of a hydrogen atom much more than the velocity of a palladium atom (maybe the typical relation is about 150 : 1).

In palladium based fusion there is electromagnetic stimulation with the help of free electrons (electromagnetic wave packets). So there is not a hit of 1 solitary atom, a bunch of atoms are involved (palladium and hydrogen atoms).

  • For a palladium atom the equation is:  F = mp a
  • For a hydrogen atom it is:  F = mh a

The force F (electromagnetic wave packet) is equal in both equations and mp = 150 x mh.

The hydrogen atoms cannot accelerate in a free way because they are “mechanically” bound by the palladium atoms. However, the mathematically relations between Force, mass and acceleration in Newtons equation cannot be changed.

When I substitute the acceleration of a solitary hydrogen atom with the acceleration of the palladium atoms, I have to write:

F = mh (a : 150)

Unfortunately, this is wrong because I have to decrease the force F too. But this is impossible because the force is equal for the involved hydrogen atoms and the involved palladium atoms.

So the only property that must be changed is the mass of the hydrogen atom.

F = (mh : 150) ap

[ap = acceleration palladium atoms]

Conclusion: the mass of the hydrogen atom has to decrease to met the acceleration of the palladium atoms.

Decreasing the mass of a nucleus is ruled by E = m c2 , so the energy of the nucleus drops down. However, c2 is a constant that represents the property of free quanta.

That’s why we have to conclude that the boundary of the nucleus is expanded because the mass is partly vanished. In other words: the Coulomb force of the hydrogen is temporarily vanished and the hydrogen atom starts to fuse with an adjacent hydrogen atom.




Next chapter:  "LENR in perspective"