Quantum Mechanics and General Relativity: Creation Creativity. Youssef Al-Youssef, 2 Rama Khoulandi. University of Aleppo, Aleppo, Syria

Transcription

1 Quantum Mechanics and Geneal Relativity: Ceation Ceativity Youssef Al-Youssef, Rama Khoulandi Univesity of Aleppo, Aleppo, Syia Abstact This aticle is concened with a new concept of quantum mechanics theoy depending upon the two components: matte and anti-matte. The aticle also links quantum mechanics and geneal elativity. Linking the two theoies has been a long-pused attempt by many scientists. The aticle gives the eade the chance to undestand the micoscopic and macoscopic wolds by the two theoies linked by one equation. Quantum mechanics and geneal elativity ae the eye of science by which we look at the univese. Quantum mechanics is concened with micoscopic level and geneal elativity is concened with macoscopic level. Many scientists have attempted to link the two theoies but in vain. The following papes descibe the way in which one can have a scientific explanation of the univese with one theoy called the Ceation Theoy. Keywods: Quantum Mechanics, Geneal Relativity, Ceation Ceativity. olume: 0 Issue: 0 Date of Publication: Jounal: To physics Jounal Website: This wok is licensed unde a Ceative Commons Attibution 4.0 Intenational License. 8

2 Quantum mechanics theoy: In the cuent theoy of quantum mechanics known as standad model - atom consists of components. But it has been discoveed that atom consists of two components: matte and anti-matte; atoms contain electons, potons and neutons. To claify the point, adioactivity should be mentioned. Atoms emit fou types of adiation: Alpha, beta minus, beta plus and gamma. In alpha adiation the atom eleases two potons and two neutons. In beta minus the atom eleases an electon. In beta plus the atom eleases a positon and gamma ays ae high enegy photons. We ae inteested in beta minus and beta plus adiation. In beta minus, a neuton emits an electon and tuns into a poton. In beta plus a poton eleases a positon and tuns into a neuton. Howeve, if we look at the two equations that descibe these adiations, we find that the inteest is in chage and not in mass. Since a poton emits a positon and tuns into a neuton, this means that chage is what impotant hee. Fo a poton to elease a positon and tun into a neuton which is heavie is not possible if the inteest is in mass. This leads us to the conclusion that the poton consists of electons and positons but has one exta positon and neutons ae composed of equal numbe of electons and positons. i.e., matte and anti-matte. Fo claification, this is a table of atom components: poton Mass:.769 *0-7 kg Chage befoe emission: *0-9 Coulomb Type of emission: positon Chage afte emission: neutal neuton Mass:.6749 *0-7 kg Chage befoe emission: neutal Type of emission: electon Chage afte emission: *0-9 Coulomb Thus, the electon emits an electon and tuns into a poton and the poton emits a positon and tuns into a neuton. This means that potons and neuton ae composed of electon and positons; of matte and antimatte. This needs anothe table to show the popeties of similaities and diffeences between the two: Matte / electon Mass: * 0 - kg Chage: * 0-9 Coulomb Anti-matte / positon Mass: * 0 - kg Chage:.60766* 0-9 Coulomb Chage type: negative Chage type: positive If atom is bombaded with a photon with enegy equal to two electons accoding to Einstein equation, an electon and a positon ae ejected out of the atom. This is called double poduction. But quickly they collide and tun into two photons with one electon enegy each. This leads us to question what pevents matte and anti-matte fom destoying each othe inside the atom. To answe this question, one has to figue out how the atom is balanced. 8

3 Heisenbeg stated that what distinguishes the electon is the uncetainty pinciple. But Boh showed that electon moves in cicula paths aound the atom. Boh dew the atom in two dimensions and this led to misundestanding him that the atom in itself is two-dimensional. Boh did not mean this; what he meant is that electons move in cicles aound the nuclei. When examining the electon fequency, one can find out that fequency is connected to a cicle cicumfeence and this is an enough poof that the electon movement is cicula and that Einstein was coect when he objected to Heisenbeg's notion of uncetainty in declaing that " God does not play dice.'' Fequency has been found to be equal to speed divided by cicumfeence in geneal tems: f = c whee c is the speed of light, π is the cicle cicumfeence and con is a constant equal to π con By applying this equation, one can calculate the electon fequency and confim that its movement is v n cicula and its speed is equal to the speed of light. On the fist obit the equation becomes: whee v is velocity of electon and n is the obit numbe. On the othe obits the equation becomes: π con v π n con In the final equation the obit numbe is multiplied by the squaed constant. The constant has poved many popeties in the atom accoding to enegy adius of electon and mass: - h con = m neuton and equals to x 0-7 kg. whee h is Planck constant and is equal to x0-4 m kg /s. - con 0 = mc con x.8 x 0 5 = 5.9 x0 This numbe is Boh adius of the fist electon obit. If we think of the equation: K QQB = fh and the equation: BKπn = f we find that h = QQ Q 8n con con Qn4 = π con obit numbe. 4πn 4π con and we have h = by equating the second side of the fist equation to the second side of the second equation we find: whee is obit adius, Q is electon chage and con is a constant and equals to and n is 4- mc con x =.6 and this the electon enegy accoding to Boh. 5- c = v con n whee v is electon velocity, c is speed of light and n is the obit numbe. 6- m electon= h x con x0 Whee m is electon mass h is Planck constant f neuton = x.6 Whee f neuton is neuton fequency and f electon is electon fequency. f electon con m electon Q con = mc Whee m electon is electon mass and Q is electon chage. 9- I = Q C n con Whee I is cuent, Q is electon chage, n is obit numbe and is the obit adius. 0- I = π n This is cuent equation concening the obits. But the cuent equation inside the nucleus is: - I = π con - M neuton E electon = E neuton M electon whee M neuton is mass of neuton, E electon is electon enegy, E neuton is neuton enegy and M electon is electon mass. Bɛ - 0 = mv whee ɛ 8πn 0 is pemittivity of fee space and equals x 0 - m kg - s 4 A, B is magnetic field, n is obit numbe, m is electon mass, v is electon velocity and is electon obit adius. 8

4 8πcon 4- µ B = k QQ whee µ n B is Boh magneton and equals *0-4 joules/ tesla, con is a constant and equals to n is obit numbe, k is Coulomb constant and equals to 9 x 0 9, Q is electon chage and is electon obit adius. 5- B = 4πcon n Whee B is magnetic field, con is a constant and equals to and n is obit numbe. 6- BKnπ = f Whee B is magnetic field, K is Coulomb constant and equals to 9 x 0 9 n is obit numbe and f is electon fequency. 7- KQ Q = mv Whee k is a constant and equals to 9 x 0 9 Q and Q ae the same and equal to electon chage, is electon obit adius, M is electon mass and is electon velocity. 8- If we take the equation: KQ Q enegy ( KQ Q = mv and De Boglie s equation hf = mv we find that potential ) equals (hf) which can be eaanged in the following equation: hf = KQ Q. Thus, the electon is subjected to an attactive foce by the positon which is balanced by the wave popety of the electon. The wave popety of the electon is caused by the chaged electon being in movement. And accoding to Einstein, if chaged paticles move, electic field is tuned into a magnetic field. This means that we have an electomagnetic wave being fomed because of electic and magnetic fields. At the same time, the positon is static in its position because of the balance between wave popety and potential enegy; the positon has an electic field and is unde the influence of the magnetic field fomed by the electon movement. This means that fo the positon, it is also tue that hf = KQ Q 9- If we go back to the equation KQ Q K Q Q = mv. = mv and divide the two sides by the adius we get: Since = K Q mv, this equation can be eaanged to become: QE =. If we substitute E accoding mv = we find that the equation QB = is coect fo the electon movement. Whee Q is to the equation E B electon chage, is electon velocity and B is magnetic field. Accoding to this equation, what causes the cicula movement of the electon is the magnetic foce. 0- µ B Bn = K Q Q whee µ B is Boh magneton and it is a constant which equals *0-4 joules/ tesla. B is magnetic field, n is obit numbe, K is coulomb s constant and equals 9*0 9, Q and Q ae electon chages. This law shows how magnetic field is tuned into an electic field. This electic field is attactive in ode to countepat the epulsive field caused by the electons to each othe. G6π - = K Q Q whee G is gavitational constant and equals x *0 - m kg - s -, C Cn is speed of light and n is obit numbe. QCµ - 0 = K Q Q whee Q is electon chage, C is speed of light, µ 4πn 0 is pemeability of fee space and equals 4π x 0 7 newton/ampee, n is obit numbe, K is Coulomb constant and equals 9x0 9 newton mete coulomb - Gµ 0 n π = k QQ whee G is gavitational constant, µ 0 is pemeability of fee space and n is obit numbe. µ 4- B ε 0 = k QQ whee n ε0 is pemittivity of fee space and equals to x 0- m - kg - s 4 A µ B is Boh magneton and equals to *0-4 joules/ tesla and n is electon obit. 84

5 5-8πnKµ B Bε 0 = k QQ. Thee is anothe equation which can be substituted hee: Bɛ 0 = mv This equation 8πn is simila to anothe one: QB = mv By equation the two sides we get: ε 0 = 8πnB. If we substitute this into equation: 8πnKµ B Bε 0 = k QQ We get: 64π n kµ B QB = k QQ. It was found that 64π n kµ B =. The final equation becomes: QE = QB. Now since this is in quantum mechanics, this gives us an insight of how the electon is stable on its obit: Ceato ceated matte and antimatte. Due to the pesence of an electic field, thee existed a magnetic field. Both fields poduced the electon wave which is equal to electic and magnetic field. Due to the balance between thee foces the electic, the magnetic and electomagnetic wave the electon obited the nucleus with no poblem. 6- GQ = m(π )(π + ) If we substitute Q fom the pevious equation into the equation QC = G, we get: π G = mcπ(π )(π + ) And calculations diffeences concening the equation QC eveal that these calculation diffeences appoximately equal to G = mcπ(π + ) (π ) so the final equation becomes: whee m is electon mass and C is speed of light. = G π 7- speed. con = v whee con is a constant and equals to 6.606, is electon obit adius and v is electon 8- fh = K QQBn whee f is fequency, h is Planck s constant, K is Coulomb s constant, Q is poton chage, 4π B is magnetic field, n is obit numbe and is obit adius. This equation explains nuclea enegy inside the atom: it is fomed because of electic and magnetic enegy. 9- h = Q 8n con con this is Planck s constant being calculated fom the atom. H is Planck s constant, Q is electon chage, is obit adius, n is obit numbe and con is a constant and equals to inside the nucleus, the equation becomes: h = Q con. Geneal Relativity: 8 This theoy is concened with macoscopic level. Accoding to Einstein, gavity is caused by the cuvatue of space-time. And accoding to Wheele: "space-time tells matte how to move and matte tells space-time how to cuve.'' What makes celestial bodies move is the enegy obtained fom time. When time is pesent, times gives enegy to celestial bodies so they move in space at cetain speed. Einstein field equation that links spacetime cuvatue to enegy and mass distibution is: G uv = 8πG c 4 T uv Whee G uv is space-time cuvatue, π is the mathematical constant equals to.4, c is speed of light and equals to m. s - G is gavitational constant and equals to *0 - m kg - s - and T uv is enegymomentum tenso. Hee the components have been colo-coded to help claify thei physical intepetations. 85

6 enegy density, which is equivalent to mass-enegy density; this component includes the mass contibution,, the components of momentum density,, the components of enegy flux The space-space components of the stess-enegy tenso ae simply the stess tenso fom classic mechanics. Those components can be intepeted as:,,,,, The components of shea stess, o stess applied tangential to the egion,, The components of nomal stess, o stess applied pependicula to the egion; nomal stess is anothe tem fo pessue. (Quantitively) Now since the moon o sun ae objects that have mass and because paticle popeties ae: density, mass and velocity, we will eaange the above matix to suit the paticle o celestial bodies in geneal: The equation that govens the eplacement is: T uv = D M u v whee D is moon o sun density, M is moon o sun mass and is velocity. T uv = DMC DM C DM C DM C DMC DM DM DM DMC DM DM DM DMC DM DM DM Now in ode to solve the matix, one can find that whateve the solution of the matix accoding to the law of matix solutions, it will be equal to 0. And if - in cetain cases the matix deteminant is not 0, thee is no way to find, and except if they ae in the fom: ( ) + ( ) + ( ) whee the equation equals. Theefoe, the above matix accoding to special elativity and the pevious equation has the following solution: (DMC ) + (DM + DM +DM ) + (DMC x DM C) + ( DMC x DM C) + (DM C x DMC ). This elation can be simplified to be: DMC + DM(( ) + ( ) + ( ) ) +DMC (( ) + ( ) + ( ) ) now by eplacing instead of ( ) + ( ) + ( ) we get: DMC + DM + (DMC). D stands fo density which is mass divided by volume and volume of moon o sun is the same as the volume of sphee: by volume and we get: 4MM π C + 4MM π + ( 4MM π ) C In ode to calculate T, we will mention some values: The adius of moon is 77 km. the mass of moon is x 0 kg. The adius of moon obit is km. 4 x x0 44 π x x x x 0 44 π x x π 4 We substitute D with Mass divided + ( 4 x x 0 44 π x ) x x = x

7 If we manipulate numbes, we get the following fomula: T uv x π mv c = mc Whee is the adius of the moon obit, v is velocity of the moon, m is the mass of the moon and c is the speed of light. I- Linking the two theoies: If we apply the pevious equation on micoscopic level, we get anothe impotant equation: T uv = (n ) 4 T uv (n ) 4 Whee T uv is enegy of electon on the fist obit and T uv is enegy of electon on the second obit accoding to the pevious equation. n is the numbe of obit and hee it is the second obit and n is the numbe of the fist obit. If we go back to the equation T uv x π = mc and manipulate it a bit we get: T mv c uv = mc4 mv π Einstein s equation G uv = 8πG T c 4 uv we get: G uv = mv 4mG if substituted in In quantum mechanics, we have anothe equation: 64π GQ = m c 4 whee G is gavitational constant and equals *0 - m kg - s -, Q is electon chage and equals.60766*0-9 coulomb, m is electon mass and equals *0 - kg and c is speed of light and equals m s -. Anothe equation that links the two theoies is Gµ B n = hmc whee G is gavitational constant ( *0 - m kg - s - ), µ B is Boh magneton and squaed. µ B equals *0-4 joules tesla -, n is obit numbe, h is Planck constant and it equals *0-4 m kg s -, m is electon mass (9.0985*0 - kg), c is speed of light squaed and is electon obit adius. Anothe equation that links the two theoies is: T uv G4πn 4 = mc Whee T uv is enegy and mass distibution accoding to Einstein equation, G is gavitational constant, n is obit numbe, m is electon mass and c is speed of light. Anothe equation that links quantum mechanics and geneal elativity is: 6 T uv con = mv I f we substitute T uv fom the pevious equation and the equation: T uv G4πn 4 = mc we get: = 0 7 π n con Whee T uv is enegy and mass distibution tenso, con is a constant and equals to 6.606, m is electon mass, v is electon velocity and is electon obit adius. I = Q C n con so B = Q C n con 4π 4π x 0 7 anothe equation fo magnetic field is B = 4πcon n when equating the second side of the fist equation to the second side of the second equation we get: = Qn4 thus, con = cµ 0 π con Qc x0 7 = 4πcon n now : µ 0 ε 0 B get: = mc Substituting the equation: = cµ 0 and substituting Bɛ con 0 accoding to the equation Bɛ 0 8πn con mv = mc If we substitute mv fom equation 6 T uv con = mv we get: T uv8π con con = mv 8πn we 87

8 If we substitute T uv accoding to equation T uv x π = mc we get: mv = con con If we substitute fom equation = 0 7 π n and fom equation = mv c 64cn 4 con cµ 0 we get: mv = π (), 8c n mv = K QQ (), µ B Bn = K Q Q () Fom equation numbe () and equation numbe () we find: µ B Bn = mv (4) and fom equation numbe () and equation numbe (4) we have: µ B = (5). 64con c If we substitute T uv fom equation T uv x π mv c by equating the fist side of the equation to the second side of the equation: = mc into the equation T uv G4πn 4 = mc we get: mv = now Gc n 4 mv = con con 64cn4 we find that = Gc x con con by equating the fist side of the last equation to the second side of the equation = cµ 0 con we find: G x con = µ 0 whee G is gavitational constant, con is a constant and equals to and µ 0 is pemeability of fee space and equals to 4π x 0 7 newton/ampee It can be seen that quantum mechanics and geneal elativity ae now linked togethe. This long- pusued attempt of linking the two theoies has finally succeeded! Refeences:. Quantitative Intoduction to Geneal Relativity. /7/06. L Annunziata Michael (06) Radioactivity fom the Quantum to the Quak. Amstedam: Elsevie.. Bot David (08) Quantities Intoduction to Geneal Relativity. 4. Staumann Nobet (004) Geneal Relativity with Applications to Astophysics. Belin: Spinge. 88