Gravitation as the result of the reintegration of migrated electrons and positrons to their atomic nuclei. Osvaldo Domann

Transcription

1 Gravitation as the result of the reintegration of migrate electrons an positrons to their atomic nuclei. Osvalo Domann (This paper is an extract of [6] liste in section Bibliography.) Abstract This paper presents the mechanism of gravitation base on an approach where the energies of electrons an positrons are store in funamental particles (FPs) that move raially an continuously through a focal point in space, point where classically the energies of subatomic particles are thought to be concentrate. FPs store the energy in longituinal an transversal rotations which efine corresponing angular momenta. Forces between subatomic particles are the prouct of the interactions of their FPs. The laws of interactions between funamental particles are postulate in that way, that the linear momenta for all the basic laws of physics can subsequently be erive from them, linear momenta that are generate out of oppose pairs of angular momenta of funamental particles. 1 Introuction. Our Stanar Moel escribes a particle as a point-like entity with the energy concentrate on one point in space. The mechanism how forces between charge particles are generate is not explaine. This limitation of our Stanar Moel results in the introuction of a series of artificial particles an constructions like Gluons, Bosons, Gravitons, Quarks, Higgs, particle s wave, etc., to explain the mechanism of interaction between particles. The present approach postulates that a particle is forme by rays of Funamental Particles (FPs) that move through a focal point in space. The relativistic energy of the particle is store by the FPs as longituinal an transversal rotations. Interactions between two particles are now the result of the interactions between FPs of the two particles. The steps followe to escribe mathematically the new moel are: 1. Definition of a istribution function κ that assigns to each volume V in space a ifferential energy E of the total relativistic energy of the particle. 1

2 . Definition of a fiel magnitue H associate with the angular momenta of FPs. 3. Definition of interaction laws between H fiels of FPs in that way, that all forces between particles can be mathematically erive. In what follows electrons an positrons are calle Basic Subatomic Particles (BSPs). The total relativistic energy of a BSP is E e = Eo + Ep = E s + E n with E s = E o E o + E p E n = E o E p + E p (1) The ifferential energies for each ifferential volume are: with κ the istribution function, ν the angular frequency an J the angular momenta. E e = E e κ = ν J e E s = E s κ = ν J s E n = E n κ = ν J n () κ = 1 r o rr r sin ϕ ϕ γ π V = r r ϕ r sin ϕ γ (3) κ is inverse proportional to the square istance to the focal point an gives the fraction of the relativistic energy for the volume V of the FP. FPs leaving the focal point (emitte FPs) have only longituinal angular momenta J e an associate to it a longituinal emitte fiel H e efine as H e = H e κ s e = ν J e κ s e with He = E e (4) FPs moving to the focal point (regenerating FPs) have longituinal J s an transversal J n angular momenta an associate to them respectively a longituinal emitte fiel H s efine as H s = H s κ s = ν J s κ s with H s = E s (5) an a transversal emitte fiel H n efine as H n = H n κ n = ν J n κ n with Hn = E n (6) For the total fiel magnitue H e it is He = Hs + Hn. Fig. 1 shows at the origin of the Cartesian coorinates the focus of a BSP moving with spee v. The vector s e is an unit vector in the moving irection of the emitte funamental particle (FP). The vector s is an unit vector in the moving irection of the

3 s e FP s n BSP r o v n - Figure 1: Unit vector s e for an emitte FP an unit vectors s an n for a regenerating FP of a BSP moving with v c regenerating FP. The vector n is an unit vector transversal to the moving irection of the regenerating FP an oriente accoring the right screw rule relative to the velocity v of the BSP. The ifferential linear momentum p of a moving BSP is generate out of pairs of oppose transversal fiels H n at the regenerating FPs of the BSP. Oppose pairs of transversal fiels H n are generate because of the axial symmetry relative to the velocity v of the BSP as shown in Fig. 1. Conclusion: Basic subatomic particles (BSPs) are structure particles with longituinal an transversal angular momenta. The sign of the angular momenta of emitte FPs efine the sign of the BSP (electron or positron). The transversal fiel H n gives the mechanical linear moment an the magnetic moment. Interaction laws between FPs of two BSPs are efine as proucts between their H fiels. Coulomb law: The close path integration of the cross prouct between longituinal H s fiels gives the Coulomb equation. Ampere law: The close path integration of the cross prouct between transversal H n fiels gives the Lorentz, Ampere an Bragg equations. Inuction law: The close path integration of the prouct between the transversal fiel H n an the absolute value of the longituinal H s fiel of a static BSP gives the Maxwell equations an the gravitation equations. The funamental equation to calculate the ifferential force between two BSPs is 3

4 F = p t = 1 c t E p = 1 c t H 1 H (7) Mechanism of Gravitation. To explain the mechanism of gravitation, the concept of reintegration of BSPs that have migrate out of their nuclei is require. Because of H s = H s s an J s = J s s the interaction law between FPs of static BSPs (Coulomb) follows the cross prouct between longituinal angular momenta J e1 J s = J e1 J s sin β = J n of the FPs, cross prouct which is zero for the istance = 0 between BSPs because of β = π/. In Fig. the ifferential linear momentum p at BSP is generate by pairs of oppose angular momentum J n of regenerating FPs. BSP proviing regenerating FPs () 1 r r1 l J v e 1 v r J ( s) J n s r r s 1 R e 1 J s 1 () ( ) R ' J r r () BSP proviing regenerating FPs rr 1 s J ' e 1 ' v r x ' v e 1 J ( s) n p Figure : Generation of angular momentum J n at regenerating funamental particles of two static basic subatomic particles at the istance Fig. 3 gives the linear momentum between two BSPs as a function of the istance. The variable r o represents the raii of the focus of the BSPs, which are constant for non relativistic spees. 4

5 Nucleons are compose of electrons an positrons which are concentrate in the range of 0 γ 0.1 of the curve of Fig. 3 where the attractions an repulsions between them are zero. 1.4 x 10 3 p stat // // / r o Figure 3: Linear momentum p stat as function of γ = /r o between two static BSPs with equal raii r o1 = r o Electrons an positrons of a nucleon migrate slowly into the range of 0.1 γ 1.8 polarizing the nucleon, an are subsequently reintegrate with high spee when their FPs cross with FPs of the remaining electrons an positrons of the nucleon because of β < π/ (Neutron 1 at Fig. 4). Oppose linear momenta p a an p b are generate at BSPs a an b. The movement of BSP b generates the H n fiel shown in Fig. 4, fiel that is passe to the static BSP p of neutron accoring the inuction law of sec. 1. The final result is that neutron 1 moves with the linear momentum p a an neutron with the oppose linear momentum p p. The mechanism is inepenent of the sign of the interacting BSPs explaining the attracting force of gravitation. It is important to note that as BSPs a an b generate oppose H n fiels that are passe to BSP p of neutron, the fiel of BSP b is closer to BSP p an has a higher probability to be passe to BSP p. 5

6 p 1 p p a p b ( ) ( ) Figure 4: Transmission of momentum p b from neutron 1 to neutron 3 Gravitation force. To calculate the gravitation force inuce by the reintegration of migrate BSPs, we nee to know the number of migrate BSPs in the time t for a neutral boy with mass M. The following equation was erive in [6] for the inuce gravitation force generate by one reintegrate electron or positron F i = p t = h νo mp 4 K Grav with Grav =.466 (8) with m p the mass of the resting electron, h the Planck constant an h ν o = E o where E o is the energy of the resting electron. Also it is t = K r o r o = m an K = s/m (9) The irection of the force F i on BSP p of neutron in Fig. 4 is inepenent of the sign of the BSPs an is always oriente to the reintegrating BSP b of neutron 1. For two boies with masses M 1 an M an where the number of reintegrate BSPs in the time t is respectively G1 an G it must be F i G1 G = G M 1 M with G = (10) As the irection of the force F i is the same for reintegrating electrons G an 6

7 positrons + G it is G = G + + G (11) We get that or G1 G = G 4 K M 1 M h νo mp Grav (1) thus G1 G = M 1 M = γ G M 1 M (13) The number of migrate BSPs in the time t for a neutral boy with mass M is G = γ G M with γ G = kg 1 (14) Calculation example: The number of migrate BSPs that are reintegrate at the sun an the earth in the time t are respectively, with M = kg an M = kg G = an = (15) The power exchange between two masses ue to gravitation is P G = F i c = E p t = c h νo mp 4 K G1 G The power exchange between the sun an the earth is, with = m Grav (16) P G = F G c = G M M c = J/s (17) 4 Dark matter an ark energy. In the previous sections we have seen that the inuce gravitation force is ue to the reintegration of migrate BSPs in the irection of the two gravitating boies. When a BSP is reintegrate to a neutron, the two BSPs of ifferent signs that interact, prouce an equivalent current in the irection of the positive BSP as shown in Fig. 5. As the numbers of positive an negative BSPs that migrate in one irection at one neutron are equal, no average current shoul exists in that irection in the time t. It is 7

8 Neutron 1 Neutron Migrate BSP M 1 p p FR FR p Migrate BSP p M Migrate BSP Migrate B SP i m1 1 i m Figure 5: Resulting current ue to reintegration of migrate BSPs R = + R + R = 0 (18) We now assume that because of the power exchange (16) between the two neutrons, a synchronization exists between the reintegration of BSPs of equal sign in the irection orthogonal to the axis efine by the two neutrons, resulting in parallel currents of equal sign that generate an attracting force between the neutrons. Thus the total attracting force between the two neutrons is prouce first by the inuce force an secon by the currents of reintegrating BSPs. F T = F G + F R with F G = G M 1 M an F R = R M 1 M (19) To obtain an equation for the force F R we start with an equation that was euce in [6] for the linear momentum when bening electrons through a crystal, equation that is base on the Ampere law of sec. 1 for the interaction of parallel currents. with p b = c h ν o l n (0) ν o = s 1 l = m o t = s (1) 8

9 The force for one pair of parallel BSPs (n = 1) is given by F R = p b o t = K Dark with K Dark = 1 h o t = Nm () The total force is F R = R1 R F R = R1 R K Dark = R M 1 M (3) We get or R1 R = R K Dark M 1 M (4) R1 R = γ R M 1 M with γ R = R K Dark (5) The number of currents in the time t for a neutral boy with mass M thus is The total attraction force gives F T = F G + F R = R = γ R M (6) [ G + R ] M 1 M (7) For sub-galactic istances the inuce force F G is preominant, while for galactic istances the force of parallel reintegrating BSPs F R preominates, as shown in Fig. 6. The transition istance between sub-galactic an galactic istances we get making F G = F R resulting gal = G R (8) 4.1 Flattening of galaxies rotation curve. For galactic istances the force of parallel reintegrating BSPs F R preominates over the inuce gravitation force F G an we can write eq. (7) as F T F R = R M 1 M (9) The equation for the centrifugal force of a boy with mass M is 9

10 F G F R 1 F G G R gal 3 m kg s Nm kg m F R 1 subgalacti c gal galactic Figure 6: Gravitation forces at sub-galactic an galactic istances. F c = M v orb with v orb the tangential spee (30) For steay state moe the centrifugal force F c must equal the gravitation force F T. For our case it is We get for the tangential spee F c = M v orb = F T F R = R M 1 M (31) v orb R M 1 constant (3) The tangential spee v orb is constant an inepenent of the istance what explains the flattening of galaxies rotation curves. Calculation example With the following calculation example we will etermine the value of the constant R an the transition istance gal. For the Sun with v orb = 0 km/s an M = M = kg an a istance to the core of the Milky Way of = m we get a centrifugal force of F c = M v orb = N (33) With the mass of the core of the Milky Way of M 1 = M an an with F c = F T F R = R M 1 M we get R = Nm/kg (34) 10

11 F G = F R we get gal = G R = m (35) justifying our assumption for F T F R because the istance between the Sun an the core of the Milky Way is gal. We also have that If we compare with γ G = very small. R γ R = = kg 1 (36) K Dark kg 1 for the inuce force we see that γ R is Note: The flattening of galaxies rotation curve was erive base on the assumption that the gravitation force is compose of an inuce component an a component ue to parallel currents of reintegrating BSPs an, that for galactic istances the inuce component can be neglecte. 4. Dark Energy: We have assume in sec. 4 about Dark Matter that because of the power exchange (16) between the two neutrons, a synchronization exists between the reintegration of BSPs of equal sign in the irection orthogonal to the axis efine by the two neutrons, resulting in parallel currents of equal sign that generate an attracting gravitation force between the neutrons. We now assume that the synchronization of the reintegrating BSPs in the orthogonal irection of the two neutrons is between parallel currents of oppose sign, generating a repulsive gravitation force between the two neutrons. The repulsive gravitation force between matter is known as ark energy. 5 Quantification of gravitation forces. In sec. 8.1 from [6] Inuction between an accelerate an a probe BSP expresse as close path integration over the whole space the elementary linear momentum p elem is erive which with gives t(v = 0) = o t = s an k = < 1 (37) p elem = m c k = h c o t k = kg m s 1 (38) 11

12 The elementary linear momentum p elem is now use to quantize the two components of the gravitation force. 5.1 Quantification of the inuce gravitation force. From sec. eq. (8) we have that the gravitation force for one aligne reintegrating BSPs is F i = h νo mp 4 K Inuction with which we can write with o t = K r o an p elem = m c k as F i = N i ν o p elem with N i = r o 4 k Inuction Inuction =.466 (39) Consiering that G 1 G = γ G M 1 M we can write for the total inuce gravitation force between M 1 an M (40) F G = F i G 1 G = N G ν o p elem with N G = N i G 1 G (41) Finally we get F G = N G (M 1, M, ) ν o p elem with N G = M 1 M (4) The frequency with which aligne reintegrating BSPs interact in space is ν G = N G (M 1, M, ) ν o = M 1 M (43) For the earth with a mass of M = kg an the sun with a mass of M = kg an a istance of = m we get a frequency of ν G = s 1 for aligne reintegrating BSPs. 5. Quantification of the Ampere gravitation force. From sec. 4 an eq. (0) we have for a pair of parallel reintegrating BSPs that F R = p b o t = c h ν o o t l (44) with 1

13 ν o = s 1 l = m o t = s (45) an which we can write as F R = N ν o p elem with p elem = m c k an N = k l (46) force For R1 an R parallel reintegrating BSPs we get for the total Ampere gravitation F R = F R R1 R = N R ν o p elem with N R = N R1 R (47) an with R1 R = γ R M 1 M we get F R = N R (M 1, M,, l) ν o p elem with N R = M 1 M l (48) The frequency with which parallel reintegrating BSP interact in space is ν R = N R (M 1, M,, l) ν o = M 1 M l s 1 (49) For the Earth with a mass of M = kg an the Sun with a mass of M = kg an a istance of = m we get a frequency of ν R = s 1 for parallel reintegrating BSPs. The frequency ν G for aligne reintegrating BSPs is nearly 10 6 times grater than the frequency for parallel reintegrating BSPs an so the corresponing forces. 5.3 Quantification of the total gravitation force. The total gravitation force is given by the sum of the inuce force between aligne reintegrating BSPs an the Ampere force between parallel reintegrating BSPs. F T = F G + F R = [N G (M 1, M, ) + N R (M 1, M,, l)] p elem ν o (50) or with l = m F T = F G + F R = p elem ν o [ ] M 1 M (51) We efine the istance gal (Fig. 6 ) as the istance for which F G = F R an get 13

14 gal = = m (5) 5.4 Gravitation an the Cosmic Microwave Backgroun raiation. We have seen in sec. that gravitation is generate by the reintegration of electrons an positrons to neutrons an protons of their atomic nucleus. Due to the acceleration, transversal angular momenta are generate on the regenerating FPs of the reitegrating electrons an positrons, transversal angular momenta that comply with the requirements to generate linear momenta (oppose H fiels). The oppose pairs of transversal angular momenta are passe to electrons an positrons of neutrons an protons of another atomic nucleus, generating on it linear momenta in the same irection they first generate at the neutron or proton of the atomic nucleus where the reintegration took place. Atoms are forme of an atomic nucleus with neutrons an protons an the level electrons. When protons an neutrons of a nucleus reintegrate migrate electrons an positrons, the generate oppose H fiels are also passe partly to the level electrons of another nucleus shifting temporarily the electrons to a little higher energy level. When these electrons return to their original energy level they emit photons in the range of micro waves which are etecte by the etector. The main ifference between linear momenta generate by gravitation an photons is, that gravitation generates linear momenta that are all oriente in the same irection, while photons generate alternate linear momenta. What follows is a calculation comparison with the intention to show that the apparent CMB raiation is really raiation that is prouce inirectly by gravitation. CMB raiation is measure at a temperature of.7 K uniformly from all irections in space. Accoring Wien s law we get for the maximum of the raiation curve λ max = 898 T µm = µm or ν max = s 1 (53) From sec. 5.3 we have that the total gravitation force is [ F T = [ν G + ν R ] p elem = + ] ν o M 1 M p elem (54) We now calculate the gravitation force on the small microwave etector in the center of the COBE satellite which has a mass of 840 kg. The small etector has a 14

15 mass of approximately 3.0 g. The mass of the satellite aroun the etector we assume is equivalent to a concentrate mass at a istance =.0 m of the small mass of the etector. For the small istance of =.0 m the secon term of eq. (54) can be neglecte an we have ν G = ν o M 1 M (55) We now make calculations for the COBE satellite with the mass M C = M 1 + M = 840 kg where M 1 = 3.0 g an M = 840 kg 3.0 g. We get a gravitation frequency ν G = s 1 which is very close to the frequency ν max = calculate for the thermal raiation with.7 K. If we now assume that the intensity of the thermal raiation at.7 K is much smaller than the intensity of the raiation inuce by gravitation, we can explain easily the measure isotropy of the apparent CMB raiation. s 1 6 Resume. The work is base on particles represente as structure ynamic entities with the relativistic energy istribute over the whole space on FPs, contrary to the representation use in stanar theory where particles are point-like entities with the energy concentrate on one point in space. Funamental parts of the mechanism of gravitation are the reintegration of migrate electrons an positrons to their nuclei, an the Inuction an Ampere laws between FPs of BSPs. The gravitation force has two components, one component ue to the reintegration in the irection of the two gravitating boies an one component ue to the reintegration in the irection perpenicular to it. For sub-galactic istances the first component, which is inverse proportional to the square istance, preominates, while for galactic istances the secon component, which is inverse proportional to the istance is preominant. The secon component explains the flattening of galaxies rotation curves without the nee of aitional virtual matter (ark matter). The secon component also explains the repulsive forces between galaxies without the nee of aitional virtual energies (ark energy). The two components of the gravitation force are quantize with the help of the elementary linear momentum euce for the reintegration of migrate electrons an positrons to their nuclei. 15

16 Finally the hypothesis is mae that the apparent CMB raiation is a raiation inuce by the gravitation mechanism explaining the isotropy of the raiation. 7 Bibliograpy. 1. Albrecht Linner. Grunkurs Theoretische Physik. Teubner Verlag, Stuttgart Benenson Harris Stocker Lutz. Hanbook of Physics. Springer Verlag Stephen G. Lipson. Optik. Springer Verlag B.R. Martin & G. Shaw. Particle Physics. John Wiley & Sons Max Schubert / Gerhar Weber. Quantentheorie, Grunlagen un Anwenungen. Spektrum, Aka. Verlag O. Domann. Definition of a space with funamental particles with longituinal an transversal rotational momentum, an euction of the linear momentum which generates electrostatic, magnetic, inuction an gravitational forces. June