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The electron



The electron

When you are inter­ested in physics you must read “Unbe­liev­able”!

The pic­tured process of oscil­la­tion and the assumed phys­i­cal enti­ties of ether are an “unsci­en­tific” account of what might hap­pen should ether exist. The sketched image was only nec­es­sary to explain physics when there is ether. The images are nec­es­sary to under­stand the mean­ing of derived math­e­mat­i­cal solu­tions. The math to come must be con­sis­tent with obser­va­tions. The story has the pur­pose to com­pre­hend the accom­pa­ny­ing math.

The best known and small­est ele­men­tary par­ti­cle, apart from the neu­trino, is the elec­tron. An elec­tron can have a pos­i­tive or a neg­a­tive charge Qe. The elec­tron with a pos­i­tive charge is called positron. When we men­tion the elec­tron we mean the neg­a­tive charged particle.

When we assume a com­pletely sep­a­rated point-​volume in a neg­a­tive and a pos­i­tive point-​volume this sep­a­ra­tion is tem­porar­ily. The charges will be anni­hi­lated by the sur­round­ing ether with the speed of light.

To be able to describe and explain a sta­ble pos­i­tive and neg­a­tive par­ti­cle like the elec­tron we have to ascribe to the sep­a­rated vol­ume energy in the form of rota­tion energy. Point-​volumes can vibrate, but it is also pos­si­ble that the point-​volume rotates around an axis. When a point-​volume spins, the rota­tion rep­re­sents pure mag­netic energy: move­ment of charge or volume.

In the ether the­ory it is more con­sis­tent to call neg­a­tive and pos­i­tive elec­tric charges neg­a­tive and pos­i­tive vol­umes. It is not nec­es­sary to intro­duce an elec­tric charge. It is only a name. We will how­ever con­form to the cus­tom and call the sep­a­rated vol­umes elec­tric charges.

Imag­ine now that the oscil­la­tion energy of a spin­ning point-​volume is large enough to sep­a­rate a neu­tral point-​volume com­pletely in a spin­ning neg­a­tive and pos­i­tive point-​volume. We con­sider the spin­ning neg­a­tive point-​volume, with charge –Qe, fur­ther.

The inter­ac­tion with the ether as described pre­vi­ously will be as fol­lows. The spin­ning neg­a­tive point-​volume misses pos­i­tive charge to be neu­tral. This pos­i­tive charge is trans­ferred to the point-​volume by the sur­round­ing point-​volumes respec­tively ether. When the pos­i­tive charge enters the spin­ning neg­a­tive point-​volume this absorbed charge will not only neu­tral­ize the neg­a­tive charge, but the absorbed charge will be drawn into a spin together with the spin­ning neg­a­tive charge of the point-​volume (mag­netic induction).

By absorb­ing the pos­i­tive charge from sur­round­ing point-​volumes the neg­a­tive point-​volume will become neu­tral again. The neg­a­tive charge is passed on to the sur­round­ing point-​volumes when their pos­i­tive charge is trans­mit­ted. These now partly neg­a­tive charged point-​volumes will attract the charge they trans­mit­ted from neu­tral point-​volumes sur­round­ing them, and so on. The neg­a­tive charge of the orig­i­nal neg­a­tive point-​volume is spread over space with the speed of light. The ether, trans­ferred to the spin­ning vol­ume, is dragged into the spin. The speed of rota­tion will be the high­est on the out­side, of the still neg­a­tively charged, spin­ning and expand­ing bulb.

Fig­ure 14 presents the pro­file of the expand­ing and rotat­ing neg­a­tive point-​volume. The black spot in the cen­ter rep­re­sents the orig­i­nal neg­a­tive point-​volume and the gray area the sur­face where the neg­a­tive charge is neu­tral­ized and dragged. While expand­ing, the trans­ferred charge is dragged into the spin.

Fig­ure 14. The spin­ning and expand­ing point-​volume.

When the rota­tion energy of the expand­ing and rotat­ing negative-​point-​volume is large enough to drag the rota­tion speed to the veloc­ity c at the end of the pro­file, the spin­ning charge at the end of the pro­file will lose con­tact with the sur­round­ing ether.

When the rota­tion speed reaches c the charge at the end of the pro­file rotates so fast that the inert qual­ity of the ether (c) pre­vents charge to be dragged any longer. There will still be charge sep­a­ra­tion at the out­side the pro­file, but the ether can­not pass charge any­more because the trans­ferred charge now has to be accel­er­ated to c.

The inert qual­ity of ether, the lag to trans­fer charge from one point-​volume to another with a speed larger then c makes this impos­si­ble. The expan­sion of the neg­a­tive charge in space has come to an end. An extremely sta­ble ele­men­tary par­ti­cle, the elec­tron, is born.

It is not pos­si­ble to explain by the Rel­a­tiv­ity The­ory that speed c is reached. The speed of light can only be approached. With ether there is how­ever no objec­tion at all to reach the speed of light for the ether itself, because the speed of light c is one of the char­ac­ter­is­tics of vacuum/​ether. The con­se­quence when the speed of light is reached is that the ether mov­ing with speed of light can­not drag the oppo­site charged ether any­more. The trans­fer of charge stops. The phe­nom­e­non, the Lorentz­fac­tor , shows its pres­ence again. The ether is too inert to inter­act in that way with the spin­ning charge.

The fol­low­ing sit­u­a­tion has occurred: sur­round­ing the, now neu­tral­ized, neg­a­tive point-​volume in the cen­ter of the pro­file, the dielec­tric replaced charges turn within the radius Re of the elec­tron. The dielec­tric dis­place­ment at Re has been dragged to the speed of light c.

The ether, from the orig­i­nal point-​volume until Re, is in bal­ance. The ether of the spin­ning elec­tron is com­pa­ra­ble with a spin­ning disc. There is now a sit­u­a­tion where the spin­ning charge on the bulb deter­mines its own space. Within the radius Re of the elec­tron the ether is at rest. The elec­tron is in con­trol of the space, ether, with radius Re. The neg­a­tive charge -Qe is anni­hi­lated inside the sphere with radius Re. The charge –Qe is now posi­tioned at the sur­face of the bulb with radius Re.

Fig­ure 16. The electron

The induced mag­netic spin energy in the ether, sur­round­ing the elec­tron, is directly linked to the elec­tron by means of the elec­tro­sta­tic field out­side the spin­ning radius of the electron.

The charge -Qe seeks a low as pos­si­ble energy level. Hence the elec­tro­sta­tic charge -Qe, sit­u­ated at the bulb with radius Re, tries to expand. The expand­ing elec­tro­sta­tic force of the -Qe charged bulb with radius Re is com­pen­sated by the con­tract­ing force of the mag­netic spin energy.

Fur­ther expan­sion of the elec­tron above Re is not pos­si­ble, because than the spin energy in the ether has to dimin­ish (equi­tation (e1) below). The expand­ing elec­tro­sta­tic force and the con­tract­ing mag­netic spin are in equi­lib­rium when the radius of the elec­tron is Re.

The positron emerges in a sim­i­lar way. The only dif­fer­ence is that the orig­i­nal point-​volume is pos­i­tively charged. The mag­netic energy of the spin­ning disc is given by the formula:

(e1)

(For deriva­tion of this for­mula see below “The Elec­tron Mathematically”)

Where Wm is the mag­netic energy of the spin­ning disc, Qe the charge of an elec­tron, c the speed of light and Re the radius of the elec­tron. If the neg­a­tive point-​volume has not enough energy to drag the ether to the speed of light then a sta­ble sit­u­a­tion can­not occur.

The radius Re of the elec­tron does not tell us any­thing about the size of the orig­i­nal point-​volume. Re presents the area of influ­ence of the elec­tron in the ether. Charge -Qe stopped expand­ing when the dielec­tric dis­place­ment at Re has a pace equal to the speed of light c. The trans­fer of charge stopped and the neg­a­tive charge -Qe is now sit­u­ated on a bulb with radius Re.

The pre­sen­ta­tion of the elec­tron math­e­mat­i­cally is not yet com­plete. The neg­a­tive point-​volume expanded to Re in all direc­tions with speed c. The elec­tron is cre­ated when the veloc­ity is c at Re. The charge -Qe is now sit­u­ated at a bulb with radius Re. The elec­tro­sta­tic energy Wp of charge -Qe sit­u­ated on the sur­face of a bulb with radius Re is in physics is given by the formula:

The for­mula of the elec­tro­sta­tic energy Wp is exactly the same as the for­mula for the mag­netic spin energy Wm (equa­tion (e1)), when 1/​εo is replaced by accord­ing to .

So the mag­netic and the elec­tro­sta­tic energy of the elec­tron are equal. This is not a coin­ci­dence because in “nature” energy is divided pro­por­tion­ally equally over the degrees of free­dom to store energy. The equipar­ti­tion prin­ci­ple divides the energy equally over the dif­fer­ent forms of energy. The elec­tron can store energy in two ways: elec­tro­sta­tic and magnetic.

The total energy of the elec­tron We is the sum of mag­netic and elec­tro­sta­tic energy:

We=Wm+Wp

Because the first part of this equa­tion is equal to the sec­ond part the intrin­sic energy of the elec­tron We is equal to:

and is there­fore in accor­dance with the prin­ci­ple of equiv­a­lence of energy and mass.

When the radius Re is cal­cu­lated from the for­mula for We we derive: meter, exact the clas­si­cal radius of the elec­tron: the Comp­ton Radius.

The sta­bil­ity of the elec­tron can be deducted from the for­mula for the total energy of the elec­tron We. When Re increases the energy of the elec­tron becomes less than the energy of the par­ti­cle and that is not pos­si­ble; energy can­not be lost.

The phys­i­cal inter­pre­ta­tion is that the induced mag­netic energy of the spin cap­tures the charge to the sur­face of a bulb with radius Re. Out­side the elec­tron radius the ether is spin­ning with the energy of the induced cur­rent Wm. The charged bulb with radius Re wants to expand but the mag­netic spin energy keeps the charge cap­tured at the bulb with radius Re. Other shape for the elec­tron than a bulb shape is not sta­ble because energy always seeks the min­i­mal energy level and that is a spin­ning charged bulb.

There is a phys­i­cal phe­nom­ena in the macro-​world of physics that is com­pa­ra­ble with the elec­tron; the bulb light­ning. The mag­netic spin energy of the bulb light­ning keeps the charge cap­tured. The ball light­ning, a macro-​world phe­nom­e­non, can how­ever trans­fer resp. lose mag­netic spin energy to other sys­tems and is there­fore not sta­ble in the long term.

The elec­tron mathematically

When we pre­sume the spin­ning neg­a­tive point-​volume with charge -Qe, then the ether will be polar­ized and dragged into the spin. The dielec­tric dis­place­ment in the ether sur­round­ing the expand­ing point-​volume is described by the formula:

The cur­rent in the ether caused by the dielec­tric dis­place­ment and the spin at R is:

When the rota­tion speed reaches c the pass­ing of charge between par­ti­cle –Qe and the sur­round­ing ether will end. The inert qual­ity of ether pre­vents the dielec­tric dis­place­ment to be dragged any fur­ther. Charge -Qe is now trans­ferred from the neg­a­tive point-​volume to the sur­face of a bulb with radius Re. In the rotat­ing pro­file R<Re the speed of rota­tion is: Vr=cR/Re

Inte­gra­tion of dIr over 2π radi­als and dr from 0 to Re gives:

The dielec­tric dis­place­ment takes place on both sides of the turn­ing “disc”, so the total sur­face cur­rent Ic of the spin is:

The energy of cur­rent dIr is:

Inte­gra­tion over 2π radi­als gives:

The sur­face cur­rent of the spin­ning disc induces on both sides a cur­rent in the ether:

The energy Wm presents the mag­netic spin energy of the elec­tron. The expan­sion of charge Qe over space comes to an end when the turnover speed becomes c at Re. The charge Qe is trans­ferred from the neg­a­tive point-​volume to the “sur­face” of a bulb with a radius Re; the poten­tial energy is given by:

The total energy of the elec­tron We is the sum of the dynamic mag­netic energy Wm and the elec­tro­sta­tic energy Wp; We=Wm+Wp

With the equiv­a­lence of mass and energy the radius Re of the elec­tron is cal­cu­lated at meter; exact the Comp­ton Radius.

Next chap­ter: The equiv­a­lence of mag­netic and kinetic energy

When you are interested in physics you must read “Unbelievable“!

The pictured process of oscillation and the assumed physical entities of ether are an “unscientific” account of what might happen should ether exist. The sketched image was only necessary to explain physics when there is ether. The images are necessary to understand the meaning of derived mathematical solutions. The math to come must be consistent with observations. The story has the purpose to comprehend the accompanying math.

The best known and smallest elementary particle, apart from the neutrino, is the electron. An electron can have a positive or a negative charge Qe. The electron with a positive charge is called positron. When we mention the electron we mean the negative charged particle.

When we assume a completely separated point-volume in a negative and a positive point-volume this separation is temporarily. The charges will be annihilated by the surrounding ether with the speed of light.

To be able to describe and explain a stable positive and negative particle like the electron we have to ascribe to the separated volume energy in the form of rotation energy. Point-volumes can vibrate, but it is also possible that the point-volume rotates around an axis. When a point-volume spins, the rotation represents pure magnetic energy: movement of charge or volume.

In the ether theory it is more consistent to call negative and positive electric charges negative and positive volumes. It is not necessary to introduce an electric charge. It is only a name. We will however conform to the custom and call the separated volumes electric charges.

Imagine now that the oscillation energy of a spinning point-volume is large enough to separate a neutral point-volume completely in a spinning negative and positive point-volume. We consider the spinning negative point-volume, with charge –Qe, further.

The interaction with the ether as described previously will be as follows. The spinning negative point-volume misses positive charge to be neutral. This positive charge is transferred to the point-volume by the surrounding point-volumes respectively ether. When the positive charge enters the spinning negative point-volume this absorbed charge will not only neutralize the negative charge, but the absorbed charge will be drawn into a spin together with the spinning negative charge of the point-volume (magnetic induction).

By absorbing the positive charge from surrounding point-volumes the negative point-volume will become neutral again. The negative charge is passed on to the surrounding point-volumes when their positive charge is transmitted. These now partly negative charged point-volumes will attract the charge they transmitted from neutral point-volumes surrounding them, and so on. The negative charge of the original negative point-volume is spread over space with the speed of light. The ether, transferred to the spinning volume, is dragged into the spin. The speed of rotation will be the highest on the outside, of the still negatively charged, spinning and expanding bulb.

Figure 14 presents the profile of the expanding and rotating negative point-volume. The black spot in the center represents the original negative point-volume and the gray area the surface where the negative charge is neutralized and dragged. While expanding, the transferred charge is dragged into the spin.

Figure 14.  The spinning and expanding point-volume.

When the rotation energy of the expanding and rotating negative-point-volume is large enough to drag the rotation speed to the velocity c at the end of the profile, the spinning charge at the end of the profile will lose contact with the surrounding ether.

When the rotation speed reaches c the charge at the end of the profile rotates so fast that the inert quality of the ether (c) prevents charge to be dragged any longer. There will still be charge separation at the outside the profile, but the ether cannot pass charge anymore because the transferred charge now has to be accelerated to c.

The inert quality of ether, the lag to transfer charge from one point-volume to another with a speed larger then c makes this impossible. The expansion of the negative charge in space has come to an end. An extremely stable elementary particle, the electron, is born.

It is not possible to explain by the Relativity Theory that speed c is reached. The speed of light can only be approached. With ether there is however no objection at all to reach the speed of light for the ether itself, because the speed of light c is one of the characteristics of vacuum/ether. The consequence when the speed of light is reached is that the ether moving with speed of light cannot drag the opposite charged ether anymore. The transfer of charge stops. The phenomenon, the Lorentzfactor , shows its presence again. The ether is too inert to interact in that way with the spinning charge.

The following situation has occurred: surrounding the, now neutralized, negative point-volume in the center of the profile, the dielectric replaced charges turn within the radius Re of the electron. The dielectric displacement at Re has been dragged to the speed of light c.

The ether, from the original point-volume until Re, is in balance. The ether of the spinning electron is comparable with a spinning disc. There is now a situation where the spinning charge on the bulb determines its own space. Within the radius Re of the electron the ether is at rest. The electron is in control of the space, ether, with radius Re. The negative charge –Qe is annihilated inside the sphere with radius Re. The charge -Qe is now positioned at the surface of the bulb with radius Re.

Figure 16.  The electron

The induced magnetic spin energy in the ether, surrounding the electron, is directly linked to the electron by means of the electrostatic field outside the spinning radius of the electron.

The charge –Qe seeks a low as possible energy level. Hence the electrostatic charge –Qe, situated at the bulb with radius Re, tries to expand. The expanding electrostatic force of the –Qe charged bulb with radius Re is compensated by the contracting force of the magnetic spin energy.

Further expansion of the electron above Re is not possible, because than the spin energy in the ether has to diminish (equitation (e1) below). The expanding electrostatic force and the contracting magnetic spin are in equilibrium when the radius of the electron is Re.

The positron emerges in a similar way. The only difference is that the original point-volume is positively charged. The magnetic energy of the spinning disc is given by the formula:

 (e1)

(For derivation of this formula see below “The Electron Mathematically”)

Where Wm is the magnetic energy of the spinning disc, Qe the charge of an electron, c the speed of light and Re the radius of the electron. If the negative point-volume has not enough energy to drag the ether to the speed of light then a stable situation cannot occur.

The radius Re of the electron does not tell us anything about the size of the original point-volume. Re presents the area of influence of the electron in the ether. Charge –Qe stopped expanding when the dielectric displacement at Re has a pace equal to the speed of light c. The transfer of charge stopped and the negative charge –Qe is now situated on a bulb with radius Re.

The presentation of the electron mathematically is not yet complete. The negative point-volume expanded to Re in all directions with speed c. The electron is created when the velocity is c at Re. The charge –Qe is now situated at a bulb with radius Re. The electrostatic energy Wp of charge –Qe situated on the surface of a bulb with radius Re is in physics is given by the formula:

The formula of the electrostatic energy Wp is exactly the same as the formula for the magnetic spin energy Wm (equation (e1)), when 1/εo is replaced by  according to .

So the magnetic and the electrostatic energy of the electron are equal. This is not a coincidence because in “nature” energy is divided proportionally equally over the degrees of freedom to store energy. The equipartition principle divides the energy equally over the different forms of energy. The electron can store energy in two ways: electrostatic and magnetic.

The total energy of the electron We is the sum of magnetic and electrostatic energy:

We=Wm+Wp

Because the first part of this equation is equal to the second part the intrinsic energy of the electron We is equal to:

and is therefore in accordance with the principle of equivalence of energy and mass.

When the radius Re is calculated from the formula for We we derive:  meter, exact the classical radius of the electron: the Compton Radius.

The stability of the electron can be deducted from the formula for the total energy of the electron We. When Re increases the energy of the electron becomes less than the energy of the particle and that is not possible; energy cannot be lost.

The physical interpretation is that the induced magnetic energy of the spin captures the charge to the surface of a bulb with radius Re. Outside the electron radius the ether is spinning with the energy of the induced current Wm. The charged bulb with radius Re wants to expand but the magnetic spin energy keeps the charge captured at the bulb with radius Re. Other shape for the electron than a bulb shape is not stable because energy always seeks the minimal energy level and that is a spinning charged bulb.

There is a physical phenomena in the macro-world of physics that is comparable with the electron; the bulb lightning. The magnetic spin energy of the bulb lightning keeps the charge captured. The ball lightning, a macro-world phenomenon, can however transfer resp. lose magnetic spin energy to other systems and is therefore not stable in the long term.

The electron mathematically

When we presume the spinning negative point-volume with charge –Qe, then the ether will be polarized and dragged into the spin. The dielectric displacement in the ether surrounding the expanding point-volume is described by the formula:

The current in the ether caused by the dielectric displacement and the spin at R is:

  

When the rotation speed reaches c the passing of charge between particle –Qe and the surrounding ether will end. The inert quality of ether prevents the dielectric displacement to be dragged any further. Charge –Qe is now transferred from the negative point-volume to the surface of a bulb with radius Re. In the rotating profile R<Re the speed of rotation is: Vr=cR/Re

Integration of dIr over 2π radials and dr from 0 to Re gives:

The dielectric displacement takes place on both sides of the turning “disc”, so the total surface current Ic of the spin is:

The energy of current dIr is:

  

Integration over 2π radials gives:

The surface current of the spinning disc induces on both sides a current in the ether:

The energy Wm presents the magnetic spin energy of the electron. The expansion of charge Qe over space comes to an end when the turnover speed becomes c at Re. The charge Qe is transferred from the negative point-volume to the “surface” of a bulb with a radius Re; the potential energy is given by:

The total energy of the electron We is the sum of the dynamic magnetic energy Wm and the electrostatic energy Wp; We=Wm+Wp

  

With the equivalence of mass and energy  the radius Re of the electron is calculated at  meter; exact the Compton Radius.

Next chapter: The equivalence of magnetic and kinetic energy

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