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The photon and the constant of Planck (h)



The photon and the constant of Planck (h)

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

After the elec­tron we dis­cussed the pho­ton. This was nec­es­sary to explain the observed time dilata­tion of cos­mic par­ti­cles. The stim­u­lated elec­tron and the pos­si­bil­ity to emit the oscil­la­tion energy has been dis­cussed. We how­ever did not dis­cuss the pos­si­ble phys­i­cal pre­sen­ta­tion of the pho­ton. We have now more deducted infor­ma­tion to be able to describe the pho­ton. High ener­getic pho­tons can split up and pro­duce a positron and elec­tron. The assump­tion that in a pho­ton a sep­a­ra­tion of charge is estab­lished is not too far-​fetched. How else can a pos­i­tive and neg­a­tive par­ti­cle emerge from a pho­ton? Pho­tons with less energy prob­a­bly also have a sep­a­ra­tion of charge dur­ing the oscil­la­tion, but the energy is insuf­fi­cient to obtain two elec­trons. The charge of a positron is +Qe and of the elec­tron -Qe. We assume that the charge sep­a­ra­tion in any arbi­trary pho­ton is +Qe/​n and -Qe/​n. The attract­ing force between the two sep­a­rated charge +Qe/​n and -Qe/​n is:

with R the dis­tance between both charge Qe/​n.

The prob­lem when energy is cal­cu­lated from force x dis­tance, is that one does not know until what dis­tance the force is active. When R approaches zero the force between both charges becomes infi­nitely high and a sin­gu­lar­ity arises. When we dis­cussed the pro­ton and neu­tron we cal­cu­lated the radius of both at Rp and Rn. We assumed that the fusion of positrons and elec­trons would stop when the radius of the com­piled par­ti­cle reached the radius of the point-​volume. So we con­sider Rp and Rn to be an approx­i­ma­tion of the radius of the point-​volume. When both charges +Qe/​n and -Qe/​n approach and merge to one point-​volume (R<=Rn), there is no exter­nal force in the ether to accu­mu­late and con­cen­trate energy any­more. The sin­gu­lar­ity is avoided.

We have the radius Rn as an indi­ca­tion to what dis­tance the force is active. We how­ever have no idea to what dis­tance both charges sep­a­rate in the oscil­la­tion. The wave­length of a pho­ton λ decreases pro­por­tion­ally with the energy of the pho­ton. To be able to inte­grate the force F between both par­ti­cles we assume the arbi­trary max­i­mum dis­tance of ¼ of the wavelength.

The still unknown fac­tor is the value of n. We know the force and energy increases with , there­fore the wave­length λ of the pho­ton must be pro­por­tional with . To solve the prob­lem and to be able to cal­cu­late the energy of the oscil­la­tion we need the exact rela­tion between λ and n. We know that , but we do not know the value of a. We how­ever know that if n=1 the charge sep­a­ra­tion is +Qe and -Qe and that the radius of an elec­tron is Re. The most direct and there­fore most likely assump­tion for the rela­tion between is a=Re. All fac­tors to cal­cu­late the energy of the oscil­la­tion are known. We cal­cu­late for the energy of the oscillation :

With Re the radius of the elec­tron, Rn the radius of the neu­tron, as an approx­i­ma­tion for the radius of the point-​volume, Qe the ele­men­tary charge of the elec­tron and λ the wave­length of the pho­ton. The cal­cu­lated energy accounts only for the oscil­la­tion. The pho­ton not only oscil­lates, but it trav­els also with the speed of light c. Assum­ing the energy of the pho­ton is, like the energy in the elec­tron, equally divided over both degrees of free­dom, the total energy of the pho­ton will be Wf=2 (oscil­la­tion + kinetic energy).

The cal­cu­lated energy of the oscil­la­tion, between two charges +Qe/​n and -Qe/​n, and the kinetic energy of the pho­ton (c), is equal within 6% of the energy of a pho­ton accord­ing to Wf=hv. The con­stant of Planck h is there­fore the­o­ret­i­cally accounted for within an error of approx. 6%. Again pure coincidence?

It is very unlikely that the con­stant of Planck is derived the­o­ret­i­cally by a sim­ple and straight­for­ward approach, if the cal­cu­lated radius Rn is not related to h. The above deriva­tion impli­cates that a pho­ton can be described as an oscil­la­tion of two charges mov­ing with speed c. Fig­ure 21 illus­trates the elec­tro­mag­netic oscil­la­tion of both charges schematically.

Fig­ure 21. The schemat­i­cal illus­tra­tion of the posi­tion of charges in the photon.

The arbi­trary max­i­mum dis­tance between both charges was put on ¼λ. When the dis­tance between both charges is ¼λ they reach max­i­mum dis­tance and do not sep­a­rate any fur­ther. The oscil­la­tion energy is now fully elec­tro­sta­tic and equal to ; half the energy of the pho­ton. When both charges approach each other within the point-​volume the oscil­la­tion energy is trans­formed from poten­tial to dynamic or in other words from elec­tro­sta­tic to magnetic/​kinetic. The con­se­quence of the pre­sen­ta­tion is that a pho­ton can sim­ply be described as an oscil­la­tion of two oppo­site charges. Each charge rep­re­sents a mass of ½Mf; with Mf the mass equiv­a­lence of a pho­ton. The oscil­la­tion is right-​angled at the direc­tion of the pho­ton. The impulse of a pho­ton, pre­sented as two oscil­lat­ing charges/​masses, mov­ing with speed c in the direc­tion of move­ment, is If=Mfc. The impulse of the pho­ton is there­fore equal to the impulse I of any mov­ing mass M with speed v (I=Mv). The impulse of the pho­ton is equal to the impulse of any ordi­nary mov­ing mass accord­ing to clas­si­cal mechan­ics. This is so because half the energy/​mass of the pho­ton does not con­tribute to the impulse in the direc­tion of move­ment. The oscil­la­tion does not show an impulse out­side the oscillation.

Fig­ure 22. The instant charge posi­tion and dielec­tric dis­place­ment of a photon.

When the charges approach each other the poten­tial energy decreases and the mag­netic energy increase. When both charges merge the oscil­la­tion energy is kinetic . The schemat­i­cally com­plete cycle of the oscil­la­tion of a pho­ton is pre­sented in fig­ure 23. The pho­ton shows all its secrets in a sim­ple straight­for­ward clas­sic mechan­i­cal descrip­tion. This way there is noth­ing mys­te­ri­ous or rel­a­tivis­tic about the pho­ton. The ether makes the pre­sen­ta­tion sim­ple and under­stand­able and should not be rejected for that.

When the reader dri­ves in a car with speed v, and the mass of the car is Ma, than the kinetic energy is . Imag­ine your car has two com­part­ments, where both can move sep­a­rately of each other. You are in one com­part­ment and your pas­sen­ger in the other.

Fig­ure 23. The pho­ton mov­ing through the ether.

The car moves with speed v, and both com­part­ments move with v oppo­site and right-​angled with the speed of the car. You and your pas­sen­ger pass each other with v in oppo­site direc­tion right-​angled at the direc­tion of the car. Both com­part­ments are held together with a spring, so the speed of the com­part­ments dimin­ishes when they sep­a­rate. When you and your pas­sen­ger stop sep­a­rat­ing the energy of the oscil­la­tion is poten­tial. The spring pulls you together and you pass each other again with speed 2v. Now the energy of the oscil­la­tion is dynamic. The energy of the oscil­la­tion is also , so the total energy (speed + oscil­la­tion) of the mov­ing and oscil­lat­ing car is and the impulse in the direc­tion of move­ment is MaV: com­pa­ra­ble with the pho­ton. In the com­par­i­son only mass and speed differ.

Next chap­ter: The pho­ton and the con­stant of Planck mathematically

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

After the electron we discussed the photon. This was necessary to explain the observed time dilatation of cosmic particles. The stimulated electron and the possibility to emit the oscillation energy has been discussed. We however did not discuss the possible physical presentation of the photon. We have now more deducted information to be able to describe the photon. High energetic photons can split up and produce a positron and electron. The assumption that in a photon a separation of charge is established is not too far-fetched. How else can a positive and negative particle emerge from a photon? Photons with less energy probably also have a separation of charge during the oscillation, but the energy is insufficient to obtain two electrons. The charge of a positron is +Qe and of the electron –Qe. We assume that the charge separation in any arbitrary photon is +Qe/n and –Qe/n. The attracting force between the two separated charge +Qe/n and –Qe/n is:

with R the distance between both charge Qe/n.

The problem when energy is calculated from force x distance, is that one does not know until what distance the force is active. When R approaches zero the force between both charges becomes infinitely high and a singularity arises. When we discussed the proton and neutron we calculated the radius of both at Rp and Rn. We assumed that the fusion of positrons and electrons would stop when the radius of the compiled particle reached the radius of the point-volume. So we consider Rp and Rn to be an approximation of the radius of the point-volume. When both charges +Qe/n and –Qe/n approach and merge to one point-volume (R<=Rn), there is no external force in the ether to accumulate and concentrate energy anymore. The singularity is avoided.

We have the radius Rn as an indication to what distance the force is active. We however have no idea to what distance both charges separate in the oscillation. The wavelength of a photon λ decreases proportionally with the energy of the photon. To be able to integrate the force F between both particles we assume the arbitrary maximum distance of ¼ of the wavelength.

The still unknown factor is the value of n. We know the force and energy increases with , therefore the wavelength λ of the photon must be proportional with . To solve the problem and to be able to calculate the energy of the oscillation we need the exact relation between λ and n. We know that , but we do not know the value of a. We however know that if n=1 the charge separation is +Qe and –Qe and that the radius of an electron is Re. The most direct and therefore most likely assumption for the relation between is a=Re. All factors to calculate the energy of the oscillation are known. We calculate for the energy of the oscillation :

With Re the radius of the electron, Rn the radius of the neutron, as an approximation for the radius of the point-volume, Qe the elementary charge of the electron and λ the wavelength of the photon. The calculated energy accounts only for the oscillation. The photon not only oscillates, but it travels also with the speed of light c. Assuming the energy of the photon is, like the energy in the electron, equally divided over both degrees of freedom, the total energy of the photon will be Wf=2Wψ (oscillation + kinetic energy).

The calculated energy of the oscillation, between two charges +Qe/n and –Qe/n, and the kinetic energy of the photon (c), is equal within 6% of the energy of a photon according to Wf=hv. The constant of Planck h is therefore theoretically accounted for within an error of approx. 6%. Again pure coincidence?

It is very unlikely that the constant of Planck is derived theoretically by a simple and straightforward approach, if the calculated radius Rn is not related to h. The above derivation implicates that a photon can be described as an oscillation of two charges moving with speed c. Figure 21 illustrates the electromagnetic oscillation of both charges schematically.

Figure 21. The schematical illustration of the position of charges in the photon.

The arbitrary maximum distance between both charges was put on ¼λ. When the distance between both charges is ¼λ they reach maximum distance and do not separate any further. The oscillation energy is now fully electrostatic and equal to ; half the energy of the photon. When both charges approach each other within the point-volume the oscillation energy is transformed from potential to dynamic or in other words from electrostatic to magnetic/kinetic. The consequence of the presentation is that a photon can simply be described as an oscillation of two opposite charges. Each charge represents a mass of ½Mf; with Mf the mass equivalence of a photon. The oscillation is right-angled at the direction of the photon. The impulse of a photon, presented as two oscillating charges/masses, moving with speed c in the direction of movement, is If=Mfc. The impulse of the photon is therefore equal to the impulse I of any moving mass M with speed v (I=Mv). The impulse of the photon is equal to the impulse of any ordinary moving mass according to classical mechanics. This is so because half the energy/mass of the photon does not contribute to the impulse in the direction of movement. The oscillation does not show an impulse outside the oscillation.

Figure 22. The instant charge position and dielectric displacement of a photon.

When the charges approach each other the potential energy decreases and the magnetic energy increase. When both charges merge the oscillation energy is kinetic . The schematically complete cycle of the oscillation of a photon is presented in figure 23. The photon shows all its secrets in a simple straightforward classic mechanical description. This way there is nothing mysterious or relativistic about the photon. The ether makes the presentation simple and understandable and should not be rejected for that.

When the reader drives in a car with speed v, and the mass of the car is Ma, than the kinetic energy is . Imagine your car has two compartments, where both can move separately of each other. You are in one compartment and your passenger in the other.

Figure 23. The photon moving through the ether.

The car moves with speed v, and both compartments move with v opposite and right-angled with the speed of the car. You and your passenger pass each other with v in opposite direction right-angled at the direction of the car. Both compartments are held together with a spring, so the speed of the compartments diminishes when they separate. When you and your passenger stop separating the energy of the oscillation is potential. The spring pulls you together and you pass each other again with speed 2v. Now the energy of the oscillation is dynamic. The energy of the oscillation is also , so the total energy (speed + oscillation) of the moving and oscillating car is and the impulse in the direction of movement is MaV: comparable with the photon. In the comparison only mass and speed differ.

Next chapter: The photon and the constant of Planck mathematically

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