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The Lorentzfactor and the ether



The Lorentzfactor and the ether

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

The ether must be con­sis­tent with obser­va­tions. The assumed ether must describe the rel­a­tivis­tic phe­nom­ena in an abstract, math­e­mat­i­cal way. The dis­ad­van­tage of describ­ing physics only in math­e­mat­i­cal for­mu­las is that the math­e­mat­i­cal abstrac­tion dimin­ishes the per­cep­tion of phys­i­cal processes to the math­e­mat­i­cal out­come. The ether the­ory on the con­trary offers pos­si­bil­i­ties, apart from math­e­mat­i­cal for­mu­la­tion, to describe the phys­i­cal process through which new insights are achieved.

In high-​energy physics ele­men­tary par­ti­cles like elec­trons and pro­tons have exper­i­men­tally a speed limit c. The obser­va­tion that par­ti­cles can­not be accel­er­ated above the speed of light, is seen as an empir­i­cal proof of the SRT. This con­clu­sion is how­ever pre­ma­ture when there is ether. With ether the speed of light is the con­se­quence of the inert qual­i­ties of ether. If the speed of adjust­ment of elec­tro­mag­netic changes in the ether is lim­ited to c, it is not so hard to com­pre­hend that elec­tro­mag­netic par­ti­cles can­not be accel­er­ated beyond the elec­tro­mag­netic speed c, when the ether itself adjust with c.

Fig­ure 9. The charge divi­sion in ether between con­denser plates.

The dielec­tric move­ment and the elec­tric field in the ether are schemat­i­cally illus­trated in fig­ure 9. The over­lap­ping parts of the cir­cles rep­re­sent only fig­u­ra­tive the dielec­tric move­ment in the point-​volumes between the pos­i­tive and neg­a­tive plates of a con­denser. The charges of the plates are com­pen­sated by the charge dis­place­ment in the point-​volumes; the ether is in equilibrium.

A par­ti­cle with­out charge will, when placed in an elec­tric field, not be sub­dued to a force. When how­ever a charged par­ti­cle enters the field between the plates the elec­tric field of the par­ti­cle and that of the con­denser will inter­act. The result­ing elec­tric field will be a vec­tor sum­ma­tion of both fields, as sci­ence describes. We assume that a charged par­ti­cle +Q enters the field in the con­denser. The force in an elec­tric field on a charged par­ti­cle is real­ized by the ether itself. The charged plates draw and push on the par­ti­cle by means of the ether as the medium.

The polar­ized ether around a charged par­ti­cle, the induced elec­tric field in the ether by its own charge, is sym­met­ric around the par­ti­cle. The polar­ized ether around the sin­gle charge +Q is sym­met­ric and there­fore induces no result­ing force on the par­ti­cle. When how­ever this charged par­ti­cle is placed in an exter­nal elec­tric field this sym­me­try is lost. The force on the par­ti­cle +Q is no longer equal in all direc­tions. The result­ing force is pro­por­tional to the result­ing field; the vec­tor sum­ma­tion of both fields.

F=Q.E

The dielec­tric dis­place­ment around charge Q com­bined with the exter­nal elec­tric field in the ether between the con­denser plates will result in an asym­met­ric elec­tric field sur­round­ing Q. The result­ing force F will be pro­por­tional and in the direc­tion of the exter­nal field E.

Fig­ure 10. The force on a charged par­ti­cle +Q in an elec­tric field and ether.

The force F will result in an accel­er­a­tion of par­ti­cle Q in the direc­tion of E.

The speed v of Q, com­bined with the inert prop­er­ties of a vac­uum given by c, will be respon­si­ble for the fact that not all the ether around Q can adjust in time to the changed con­di­tions. The effect of this inert qual­ity of vac­uum is pre­sented in fig­ure 11. Par­ti­cle Q is pre­sented in fig­ure 11 by a black spot. Dur­ing the small time inter­val dt par­ti­cle Q moves a dis­tance vdt. The field around Q, pre­sented by a sphere with radius cdt, will adjust to the change of posi­tion of Q in dt sec­onds. The abil­ity of the ether to adjust in dt sec­onds is lim­ited to the space around Q with a radius of cdt. Because of the deter­min­is­tic law that reac­tion can only take place after action, the ether can adjust to the changed cir­cum­stances only after Q moved vdt meter. The inert prop­erty of the ether is thus respon­si­ble for the fact that the adjust­ment of the ether to the new sit­u­a­tion, where Q moved vdt meter, will take place after the change of posi­tion of Q.

Fig­ure 11. The decline of the elec­tro­sta­tic force in vac­uum caused by motion.

In the next dt sec­onds the ether can adjust. The adjust­ment of the ether will always lag the pri­mal change. After Q moved vdt meters the ether can adjust with speed c. The ether between the orig­i­nal posi­tion of Q and vdt can­not be adjusted in time because Q already passed. Only the ether around the orig­i­nal posi­tion of Q, between vdt and cdt, is adjusted in time to con­tribute to the force accel­er­at­ing Q in the next dt seconds.

The result­ing force on Q is there­fore real­ized by a frac­tion of the polar­ized ether. The radius of the cir­cle at vdt pass­ing the accel­er­a­tion force on to Q, with speed v, is a fac­tor of the orig­i­nal cir­cle (R=cdt). This is the Lorentz-​factor, which will be dis­cussed fur­ther in the chap­ter the “The Photon”.

The force on the par­ti­cle in the ether is how­ever not real­ized by a line, but by the sur­face of the ether still con­tribut­ing to the force. The sur­face of the ether still able to inter­act with the mov­ing par­ti­cle is a fac­tor the smaller than the sur­face that con­tributed the force when the speed of the par­ti­cle was zero; the pro­file of the sphere cdt at vdt.

The described sit­u­a­tion, where par­ti­cle Q is only accel­er­ated by the force , is com­pa­ra­ble with some­one push­ing a pram. In the begin­ning when the pram has no speed we can con­tribute all our energy to the accel­er­a­tion of the pram. When we run behind the pram as fast as we can we can­not accel­er­ate any­more, despite our effort. When the pram runs as fast as we can push all the energy we pro­duce is lost. We can­not accel­er­ate the pram faster than we can run. The same applies to the energy and force around Q. The elec­tric field around Q can­not push Q faster than it is able to trans­fer itself.

The sphere around Q in fig­ure 11 rep­re­sents the elec­tric field sur­round­ing Q with radius cdt. The light gray areas present the cone of the polar­ized ether sur­round­ing Q still able to adjust in time to the move­ment of Q and there­fore still able to induce a force on Q and accel­er­ate the par­ti­cle fur­ther. The dark gray area rep­re­sents the sur­face through which the field is still trans­port­ing the force from con­denser plates to +Q. The par­ti­cle is there­fore only accel­er­ated with a fac­tor of the orig­i­nal force. Now it becomes clear that in ether a charged par­ti­cle like elec­tron or pro­ton can­not be accel­er­ated above the speed of light. When v=c the elec­tric field is no longer able to induce a force to accel­er­ate Q. The Lorentz-​factor becomes zero and there­fore the force F also becomes zero as well. The inter­ac­tion between the elec­tric field of the par­ti­cle and the elec­tric field of the con­denser does not induce an accel­er­at­ing force anymore.

Sum­ma­riz­ing the pre­vi­ous; the force in an elec­tric field on a non-​moving par­ti­cle with charge Q is:

F=QE

When the par­ti­cle moves in the direc­tion of the force F with speed v the accel­er­at­ing force that remains is:

Par­ti­cle Q has not only a charge but also a cer­tain mass M. The accel­er­a­tion, the increase of speed per sec­ond, is pro­por­tional to the mass. The big­ger the mass the smaller the accel­er­a­tion will be by a given force. A small stone will have a much higher speed when accel­er­ated by a cat­a­pult than a big stone with the same cat­a­pult. In formula:

F=Ma

With M the mass and a the accel­er­a­tion in the direc­tion of the force. The result­ing force Fk of the elec­tric field E on par­ti­cle Q with mass Mqv gives the equa­tion for acceleration:

When the speed of par­ti­cle Q is v, and v approaches c one can see in the above for­mula that the force accel­er­at­ing Q becomes zero. In an elec­tric field in ether a charged par­ti­cle can never be accel­er­ated to the speed of light. The lag of the ether, for­mu­lated by the Lorentz­fac­tor, is respon­si­ble for the loss of force com­pared to a sit­u­a­tion where v=0. So the exper­i­men­tal limit c in the ether, vac­uum, is not deter­mined now by the rel­a­tiv­ity of time and space, but sim­ply by the lag of vac­uum to adjust to elec­tro­sta­tic changes. With ether the rea­son why a charged par­ti­cle can­not be accel­er­ated above c is that all elec­tro­sta­tic energy/​force is lost because of the inabil­ity of ether to trans­fer an elec­tro­sta­tic force/​energy to a par­ti­cle mov­ing with speed c.

The energy con­tributed by a force is the force F mul­ti­plied over the dis­tance S where the force is active: W=FS. When v is small (v«c) the ether will con­tribute to par­ti­cle Q all the energy W by accel­er­at­ing the par­ti­cle and increas­ing the speed. Is how­ever the speed v not very small com­pa­ra­ble to c than a part of the energy W=FS is “lost”. “Lost” does not mean that this energy has disappeared.

The orig­i­nal force F has to be split up in a force that still con­tributes to the accel­er­a­tion of the par­ti­cle and a part that is “lost”. “Lost” means here that the energy doesn’t con­tribute to the speed of the particle.

F=Fk+Fv

Fk is the force still accel­er­at­ing Q and Fv is the “lost” force. The energy ceded by the elec­tric field over a small dis­tance ds can also be split up in a “lost” part Fvds and a part Fkds that is trans­ferred to par­ti­cle Q and still con­tributes in the increase of speed:

Fds=Fkds+Fvds

The energy “lost” is:

As the speed v increases the “lost” energy of the elec­tric field increases. The adap­ta­tion of the elec­tric field to the new sit­u­a­tion is too slow. Charge Q already moved on. In fig­ure 12 the dark part of the sphere rep­re­sents the ether too late to con­tribute to the accel­er­a­tion. It pic­tures the energy that is “lost”, because it is not attribut­ing energy to Q. This “lost” energy presents itself as radi­a­tion. The lagged elec­tric field will excite the ether behind Q and the ether will release this lagged energy by means of elec­tro­mag­netic waves.

Fig­ure 12. The energy loss dur­ing accel­er­a­tion in an elec­tric field.

When Q moves in a straight line the “lost” energy can catch up with Q because elec­tro­mag­netic waves travel with the speed of light c and Q can never reach this speed. So the “lost” energy catches up with Q. Par­ti­cle Q can absorb the radi­a­tion and get in a state of elec­tro­mag­netic vibra­tion. This absorbed elec­tro­mag­netic energy ceded by the elec­tric field how­ever no longer accel­er­ates Q any­more; the “lost” elec­tro­sta­tic energy trans­formed from elec­tro­sta­tic energy to elec­tro­mag­netic energy. Par­ti­cle Q is able to absorb and also emit radi­a­tion. When the excite­ment stage of Q reaches a cer­tain level one can expect that Q will emit this energy in the form of an elec­tro­mag­netic wave. This char­ac­ter­is­tic is used to pro­duce syn­chotron radiation.

The “lost” energy of the field has an impulse of its own. When Q absorbs the elec­tro­mag­netic radi­a­tion the impulse of the radi­a­tion will be present in the oscil­la­tion of Q. If par­ti­cle Q’s path is bend the elec­tro­mag­netic vibra­tion energy of Q is pos­si­bly emit­ted. In physics the radi­a­tion emit­ted dur­ing accel­er­a­tion is known under the name “syn­chro­tron radi­a­tion” and is still not accounted for in theory.

The pre­sented per­cep­tion of the ether is still con­sis­tent with obser­va­tions. We have demon­strated that in ether the force of an elec­tric field on a charge dimin­ishes when the speed increases. To deter­mine the accel­er­a­tion of par­ti­cle Q with mass Mqv the equiv­a­lence of mass and energy of Ein­stein has to be accounted for. The mass Mq of a par­ti­cle at rest, increases to Mqv when the speed is v:

Later on we will demon­strate (chap­ter The Pho­ton), that with ether the mass will increase accord­ingly to the above for­mula. In the present per­cep­tion of sci­ence all the energy ceded by the elec­tric field con­tributes to the kinetic energy of the par­ti­cle. With ether this is not the case. Fv only estab­lishes accel­er­a­tion while Fk is lost.

Next chap­ter: The ether again

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

The ether must be consistent with observations. The assumed ether must describe the relativistic phenomena in an abstract, mathematical way. The disadvantage of describing physics only in mathematical formulas is that the mathematical abstraction diminishes the perception of physical processes to the mathematical outcome. The ether theory on the contrary offers possibilities, apart from mathematical formulation, to describe the physical process through which new insights are achieved.

In high-energy physics elementary particles like electrons and protons have experimentally a speed limit c. The observation that particles cannot be accelerated above the speed of light, is seen as an empirical proof of the SRT. This conclusion is however premature when there is ether. With ether the speed of light is the consequence of the inert qualities of ether. If the speed of adjustment of electromagnetic changes in the ether is limited to c, it is not so hard to comprehend that electromagnetic particles cannot be accelerated beyond the electromagnetic speed c, when the ether itself adjust with c.

Figure 9.  The charge division in ether between condenser plates.

The dielectric movement and the electric field in the ether are schematically illustrated in figure 9. The overlapping parts of the circles represent only figurative the dielectric movement in the point-volumes between the positive and negative plates of a condenser. The charges of the plates are compensated by the charge displacement in the point-volumes; the ether is in equilibrium.

A particle without charge will, when placed in an electric field, not be subdued to a force. When however a charged particle enters the field between the plates the electric field of the particle and that of the condenser will interact. The resulting electric field will be a vector summation of both fields, as science describes. We assume that a charged particle +Q enters the field in the condenser. The force in an electric field on a charged particle is realized by the ether itself. The charged plates draw and push on the particle by means of the ether as the medium.

The polarized ether around a charged particle, the induced electric field in the ether by its own charge, is symmetric around the particle. The polarized ether around the single charge +Q is symmetric and therefore induces no resulting force on the particle.  When however this charged particle is placed in an external electric field this symmetry is lost. The force on the particle +Q is no longer equal in all directions. The resulting force is proportional to the resulting field; the vector summation of both fields.

F=Q.E

The dielectric displacement around charge Q combined with the external electric field in the ether between the condenser plates will result in an asymmetric electric field surrounding Q.  The resulting force F will be proportional and in the direction of the external field E.

Figure 10.   The force on a charged particle +Q in an electric field and ether.

The force F will result in an acceleration of particle Q in the direction of E.

The speed v of Q, combined with the inert properties of a vacuum given by c, will be responsible for the fact that not all the ether around Q can adjust in time to the changed conditions. The effect of this inert quality of vacuum is presented in figure 11. Particle Q is presented in figure 11 by a black spot. During the small time interval dt particle Q moves a distance vdt. The field around Q, presented by a sphere with radius cdt, will adjust to the change of position of Q in dt seconds. The ability of the ether to adjust in dt seconds is limited to the space around Q with a radius of cdt. Because of the deterministic law that reaction can only take place after action, the ether can adjust to the changed circumstances only after Q moved vdt meter. The inert property of the ether is thus responsible for the fact that the adjustment of the ether to the new situation, where Q moved vdt meter, will take place after the change of position of Q.

Figure 11.   The decline of the electrostatic force in vacuum caused by motion.

In the next dt seconds the ether can adjust. The adjustment of the ether will always lag the primal change. After Q moved vdt meters the ether can adjust with speed c. The ether between the original position of Q and vdt cannot be adjusted in time because Q already passed. Only the ether around the original position of Q, between vdt and cdt, is adjusted in time to contribute to the force accelerating Q in the next dt seconds.

The resulting force on Q is therefore realized by a fraction of the polarized ether. The radius of the circle at vdt passing the acceleration force on to Q, with speed v, is a factor  of the original circle (R=cdt). This is the Lorentz-factor, which will be discussed further in the chapter the “The Photon”.

The force on the particle in the ether is however not realized by a line, but by the surface of the ether still contributing to the force. The surface of the ether still able to interact with the moving particle is a factor the smaller than the surface that contributed the force when the speed of the particle was zero; the profile of the sphere cdt at vdt.

The described situation, where particle Q is only accelerated by the force  , is comparable with someone pushing a pram. In the beginning when the pram has no speed we can contribute all our energy to the acceleration of the pram. When we run behind the pram as fast as we can we cannot accelerate anymore, despite our effort. When the pram runs as fast as we can push all the energy we produce is lost. We cannot accelerate the pram faster than we can run. The same applies to the energy and force around Q. The electric field around Q cannot push Q faster than it is able to transfer itself.

The sphere around Q in figure 11 represents the electric field surrounding Q with radius cdt. The light gray areas present the cone of the polarized ether surrounding Q still able to adjust in time to the movement of Q and therefore still able to induce a force on Q and accelerate the particle further. The dark gray area represents the surface through which the field is still transporting the force from condenser plates to +Q. The particle is therefore only accelerated with a factor  of the original force. Now it becomes clear that in ether a charged particle like electron or proton cannot be accelerated above the speed of light. When v=c the electric field is no longer able to induce a force to accelerate Q. The Lorentz-factor becomes zero and therefore the force F also becomes zero as well. The interaction between the electric field of the particle and the electric field of the condenser does not induce an accelerating force anymore.

Summarizing the previous; the force in an electric field on a non-moving particle with charge Q is:

F=QE

When the particle moves in the direction of the force F with speed v the accelerating force that remains is:

Particle Q has not only a charge but also a certain mass M. The acceleration, the increase of speed per second, is proportional to the mass. The bigger the mass the smaller the acceleration will be by a given force. A small stone will have a much higher speed when accelerated by a catapult than a big stone with the same catapult. In formula:

F=Ma

With M the mass and a the acceleration in the direction of the force. The resulting force Fk of the electric field E on particle Q with mass Mqv gives the equation for acceleration:

When the speed of particle Q is v, and v approaches c one can see in the above formula that the force accelerating Q becomes zero. In an electric field in ether a charged particle can never be accelerated to the speed of light. The lag of the ether, formulated by the Lorentzfactor, is responsible for the loss of force compared to a situation where v=0. So the experimental limit c in the ether, vacuum, is not determined now by the relativity of time and space, but simply by the lag of vacuum to adjust to electrostatic changes. With ether the reason why a charged particle cannot be accelerated above c is that all electrostatic energy/force is lost because of the inability of ether to transfer an electrostatic force/energy to a particle moving with speed c.

The energy contributed by a force is the force F multiplied over the distance S where the force is active: W=FS. When v is small (v<<c) the ether will contribute to particle Q all the energy W by accelerating the particle and increasing the speed. Is however the speed v not very small comparable to c than a part of the energy W=FS  is “lost”. “Lost” does not mean that this energy has disappeared.

The original force F has to be split up in a force that still contributes to the acceleration of the particle and a part that is “lost”. “Lost” means here that the energy doesn’t contribute to the speed of the particle.

F=Fk+Fv

Fk is the force still accelerating Q and Fv is the “lost” force. The energy ceded by the electric field over a small distance ds can also be split up in a “lost” part Fvds and a part Fkds that is transferred to particle Q and still contributes in the increase of speed:

Fds=Fkds+Fvds

The energy “lost” is:

As the speed v increases the “lost” energy of the electric field increases. The adaptation of the electric field to the new situation is too slow. Charge Q already moved on. In figure 12 the dark part of the sphere represents the ether too late to contribute to the acceleration. It pictures the energy that is “lost”, because it is not attributing energy to Q. This “lost” energy presents itself as radiation. The lagged electric field will excite the ether behind Q and the ether will release this lagged energy by means of electromagnetic waves.

Figure 12.  The energy loss during acceleration in an electric field.

When Q moves in a straight line the “lost” energy can catch up with Q because electromagnetic waves travel with the speed of light c and Q can never reach this speed. So the “lost” energy catches up with Q. Particle Q can absorb the radiation and get in a state of electromagnetic vibration. This absorbed electromagnetic energy ceded by the electric field however no longer accelerates Q anymore; the “lost” electrostatic energy transformed from electrostatic energy to electromagnetic energy. Particle Q is able to absorb and also emit radiation. When the excitement stage of Q reaches a certain level one can expect that Q will emit this energy in the form of an electromagnetic wave. This characteristic is used to produce synchotron radiation.

The “lost” energy of the field has an impulse of its own. When Q absorbs the electromagnetic radiation the impulse of the radiation will be present in the oscillation of Q. If particle Q’s path is bend the electromagnetic vibration energy of Q is possibly emitted. In physics the radiation emitted during acceleration is known under the name “synchrotron radiation” and is still not accounted for in theory.

The presented perception of the ether is still consistent with observations. We have demonstrated that in ether the force of an electric field on a charge diminishes when the speed increases. To determine the acceleration of particle Q with mass Mqv the equivalence of mass and energy of Einstein has to be accounted for. The mass Mq of a particle at rest, increases to Mqv when the speed is v:

Later on we will demonstrate (chapter The Photon), that with ether the mass will increase accordingly to the above formula. In the present perception of science all the energy ceded by the electric field contributes to the kinetic energy of the particle. With ether this is not the case. Fv only establishes acceleration while Fk is lost.

Next chapter: The ether again

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