A unified field theory; atomic, gravitational orbitals as anti-photons

Transcription

1 (plankmomentum.om) A unified field theory; atomi, gravitational orbitals as anti-photons Malolm Maleod malem@plankmomentum.om In this essay I propose an alternate interpretation whereby partiles may be linked, not by the 4 fores, but by physial orbitals; that nulear, atomi, moleular and gravitational orbital wave-funtions are atually photons albeit of inverse phase (anti-photons or orbitons) that have been trapped to form standing waves. In this ontext a gravitational orbit would be the sum of these gravitational orbitals, the moon would therefore not be orbiting the earth, rather it would be propelled by these orbital momenta. Likewise there is no empty spae within the atom or nuleus, instead partiles are entangled via these physial anti-photon orbital links. As orbitals have different energy densities, movement between orbitals requires a hange in energy density, a quantum buoyany. As suh, if we move the IPK kg referene bar to a different loation (with a different g), then we will hange its orbit and so its orbital mass density. Introdution This is an outline of an orbital model where, instead of the 4 fores linking partiles, there are orbitals, referred to here as nulear, atomi, moleular and gravitational. These orbitals appear to be anti-photons, photons albeit of inverse phase (i.e.: E photon + E anti photon = E zero ). At the atomi level they may be desribed by atomi and moleular orbital theories, although they are physial waves of momentum rather than mathematial wave-funtions. I have denoted these anti-photon orbitals as orbitons in order to differentiate from the ommon onepts of both antiphotons and atomi orbitals. In this model there is no empty spae within the atom and the eletron is linked to the nuleus, not by an eletrostati fore, but by a physial standing wave (aka partile in a box) orbital (orbiton). Furthermore, what we typially onsider as a gravitational orbit around the earth is atually the sum of many gravitational orbitals, standing waves around the earth that derive from moleular orbits. As suh, the term orbit itself is misleading for it suggests an objet traveling through an empty medium around another objet aording to an abstrat fore. In this model, the moon does not orbit the earth, rather the moon is pulled along its orbit path by the momentum of these gravitational orbitals; they are both the trak and the loomotive. As these orbitals urve around the earth, the motion of the moon is the sum of their vetor momentum. Consequently, if they are unaligned, the moon will fall to the earth with a onstant aeleration. If they are all perfetly aligned, the moon will follow them at orbital veloity. We all these states potential energy (unaligned) and kineti energy (aligned). The atual motion observed is a measure of the degree of the alignment (and the orbital mix). This however leads to the urious observation that, as these orbitals are standing waves, the frequeny and so energy of a gravitational orbital around the moon is higher (E=hv) than that of a orresponding gravitational orbital around the larger earth, ie: the smaller the objet, the shorter the wavelength (irumferene), and so the lower the frequeny. As the energy density of an orbital is less than the density of spae (E orbital < E zero ), we may antiipate a orresponding mass-defiit. Movement between orbitals is a funtion of orbital buoyany, for example, a submarine may travel aross the oean at a fixed depth (i.e. 000m) via propeller motion (a motion within the 000m orbital), but to hange from this equilibrium depth (the orbital itself) to rise to the surfae or sink further, it must hange its mass density (add or ejet ballast). And so, while it is this gravitational momentum whih keeps the satellite following its orbit, it is this bouyany mass-defiit whih keeps the satellite (and us) from floating off into spae. kg is defined as the mass of the International Prototype of the Kilogram (IPK), a platinum alloy ylinder stored near Paris. If this bar were orbiting the earth, it would gain relativisti mass aording to its (motion through spae) veloity (mass > kg). To lift the bar froaris into spae, we must add veloity (momentum) to ompensate for the mass density differene. We find that the veloity (momentum) required to inrease its bouyany mass is equal to esape veloity. Esape veloity is that veloity required to ahieve the orret mass density just as the submarine takes on extra water to sink lower. And so, if we move this bar from its vault in Paris to the top of the Eiffel tower, we may have a new kg. Experiments to determine the gravitation onstant G may give different results depending on whether onduted on the st floor or the top floor of the physis department and so we may require both a onstant v and a onstant g to define our mass. The third omponent of a gravitational orbital is the rotation of the orbital itself, not only is the earth orbiting the sun, but that earth-sun orbit itself is also rotating like a dis. This is notieable with elliptial orbits. At the atomi level, when an inoming photon strikes an eletron in an atom for example, it does not ause the eletron to jump between orbitals, rather the original orbital (antiphoton) is deleted and then replaed with the new orbital (anti-photon) via a simple wave addition and subtration. Photons are thereby means by whih the information of Introdution

2 (plankmomentum.om) the universe is exhanged. The eletron itself doesn t move, however its orbital boundary has been hanged. The energy of an atomi orbital derives from the momentum of the orbital around the nuleus, the spin of the orbital itself and rotational momentum of the entire orbital; analogous to the spin of the earth, the orbit of the earth around the sun and the disk-like earth-sun orbital rotation (notieable with the Merury-Sun orbit). This energy is refleted in the frequeny of the atomi orbital. 4 Nulear orbits a a = α 3 n 4 λ a (5) T a = πα n 3 λ a E n = m ev a (6) (7) m nu = m p + m n (8) Bohr model (n orbits): The Niels Bohr model depits the atom as a small positively harged nuleus surrounded by eletrons that travel in irular orbits around the nuleus similar in struture to the solar system, but with eletrostati fores providing attration, rather than gravity. Although onsidered inorret by physiists; it does give orret results for seleted systems. It was later replaed with a more useful wave model (depiting the eletron and proton as waves). Nevertheless, for ertain simple orbits, the Bohr model was extremely aurate and still no one knows why. The basi Bohr model depited these orbits as fixed, only ertain orbits were allowed ( partile in a box ). In its most elementary form, it inorporates 4 values: the speed of light, the Sommerfeld fine struture onstant alpha α , the prinipal quantum number n and eletron wavelength λ e. Partiles exhibit a wave-partile duality. This model presumes that (modified) Bohr formulas may be applied to the partile state and so are also appliable to the gravity-mass state. Of priniple disussion in this artile are these partile states of the nuleus and of gravity for the simplest n orbitals as these are suffiient to illustrate the priniples. Bohr as relates to atomi orbitals has reeived muh onsideration in the literature over the past 00years and need not be repeated here. 3 Eletri orbits Key: λ a = λ p + λ e (redued mass equivalent) R a = Bohr radius v a = orbital veloity a a = aeleration (hypothetial) T a = orbital period m redued = λ a = λ e + λ p = l p m e m em p m e + m p = () m e + m p + l p m p = l p m redued () R a = αn λ a (3) v a = αn (4) λ s = λ p + λ n 4 = l p m nu (9) r 0 = αλ s (0) R s = αλ s () v s = α E = m nuv s () (3). Gravitational binding energy (µ): The gravitational binding energy is the energy required to pull apart an objet onsisting of loose material and held together only by gravity. µ = 3GM (4) 5R G = l p (5) R = (α)r 0 = αλ s (6) M = µ = 3m nu 5α µ = 3m nuv s 5 Average GBE in the nuleus = 8.MeV/nuleon (7) (8). Strong binding energy (SBE): Nulear binding energy is the energy required to split a nuleus of an atom into its omponent parts. The omponent parts are neutrons and protons, whih are olletively alled nuleons. The eletrostati oulomb onstant; a = 3e 0πɛr 0 (9) e ɛ = 4πl p α (0) a = 3l p 5αr 0 () 4 Nulear orbits

3 (plankmomentum.om) S BE = (α)a () S BE = 3l p 5 αr 0 (3) S BE = 3m nu 5α S BE = 3m nuv s 5 Average SBE in the nuleus = 8.MeV/nuleon 3. Fermi term: The density of nuleons in a nuleus: E f = 5 Gravitational orbitals n = 3 4πr 3 0 (4) (5) (6) h 4π m nu.( 3π n )/3 (7) E f = l p m nu.( 9π 8 )/3. r 0 (8) E f = m nu α.(9π 8 )/3 (9) E f = m nu v s.( 9π 8 )/3 = 3.5MeV (30). Gravitational wavelength = Shwarzshild radius r S λ g = G(m a + m b ) = l p.m a + l pm b = r S a + r S b (3) R g = αn λ g (3) v g = a g = αn (33) α n 4 λ g (34) T g = 8π α 3 n 6 λ g (35) n = ( E n = mv g (36) T 3 (α)4παµ ) /3 (37) Example - Earth surfae orbit (see on-line alulator []): µ earth = λ earth = µ earth / = r S =.00887m n = 90; R g = km a g = 9.8m/s T g = s = 84.4mins v g = m/s n = 9; R g = 6380km a g = 9.79m/s T g = 507.4s v g = 7904m/s. Gravitational potential energy between orbits where r = radius... As Plank units... Rydberg (gravity)... δ.µ GPE = GMm r r = αn λ g r = αn λ g GMm = l p Mm r n h = παn λ M+m R = πr ( ) = n n f = R( n GMm r (38) (39) αn λ M+m Mm m P παλ M+m ( n Mm E tot = h f m P N graviton = Mm m P E graviton = hr( n i (40) ) (4) n ) (4) n (43) (44) ) (45) n f E tot = E graviton N graviton (46) Example (see on-line alulator []): Earth mass M = 5.97x0 4 kg Satellite mass m = kg Earth surfae n = 90 (r = 6374km) Geosynhronous orbit n = 5890 (r = 469km) f graviton = n 90 orbit n 5890 orbit f graviton = = 6.354Hz E graviton = 0.4x0 3 J N gravitons = M.m/m P = 0.6x04 E total = E graviton. N gravitons =.53x0 8 (J/Kg) 3 5 Gravitational orbitals

4 (plankmomentum.om) Note that /7.485Hz = 40050km orresponds to the irumferene of the earth, and so gravitational orbitals are standing waves that enirle the earth. The formula for N gravitons (i.e.: the total number of gravitational waves = orbitals) suggests that every atom in the satellite is linked to every atom in the earth, as suh gravitational orbitals may be seen simply as extensions of moleular orbitals. If these 0.6x0 4 orbital waves of momentum are all unaligned as they irumnavigate the earth, the net result of summing their vetors of motion is that the satellite will appear to fall (aelerate) downwards, if they are all aligned, the satellite will follow them in orbit. Potential energy and kineti energy beome measures of this degree of alignment. 3. Gravitational time dilation Gravitational time dilation is the differene of elapsed time in regions with different gravitational potential. The lower the gravitational potential (the loser the lok is to the soure of gravitation), the more slowly time passes. v esape v orbit GM r g Cirular orbits: v esape = r S r g = r S αn r S = v esape = αn (47) v g = αn (48) + v orbit = αn + αn = 3 αn (49) Example: n=90 (R=6374km): v orbit = = m/s (50) αn v esape = 4. The lassial tests of relativity i) Perihelion preession of Merury s orbit semi-minor axis: b = αl λ g semi-major axis: a = αn λ g Radius of urvature: = 83.5m/s (5) αn L = b a = al4 λ g n (5) 3λ g L = 3n (53) αl 4 Using n=378, l=374, Merury orbit = days 3n / = (54) αl4 preession = ar ses (per 00yrs) Number of orbits required to omplete ar ses: N orbits = αl4 3n = If l = n, we find the formula for irular orbits eq.49; Rotational veloity (l=n): Rotational period (l=n): 3n αl 4 = 3 αn (55) v rotate = T rotate = 3 (α)αn 3 (α)4πα n 5 λ Suggesting the lassial merury-sun orbit is itself rotating. ii) Gravitational redshift iii) Defletion of light r star = r g 3 (56) (57) z approx = GM r g = αn (58) r S star r star = αn (59) 5. Elliptial orbits As a gravitational orbit is the sum of many individual orbitals, we need an additional term. The semi-major axis R a an be alulated from T (period of gravitational orbit) []; µ sun = [] λ sun = µ sun / = 953.5m Merury: µ merury = 03 T = days * 86400se a o = km (wikipedia) a k = km (kepler) a n = km (n = 378) v g = m/s (47.87) Venus: µ venus = T = 4.65 days * 86400se a o = km (wikipedia) a k = km (kepler) a n = km (n = 57) v g = 35.06m/s (35.0) 3R a = R g ( + T T g ) (60) 4 5 Gravitational orbitals

5 (plankmomentum.om) Earth: µ earth = T = days * 86400se a o = km (wikipedia) a k = km (kepler) a n = km (n = 608) v g = 9.784m/s (9.78) Mars: µ mars = 488 T = days * 86400se a o = km (wikipedia) a k = km (kepler) a n = km (n = 750) v g = 4.45m/s (4.077) 6. Gravitation formula (r s = Shwarzshild radius) r S = l pm (6) GM R g = l p M αn r S = (6) αn 7. Gravitational fore as a funtion of Plank fore F = M am b G R F p = E p l p (63) = r S ar S b F p 4R g = r S ar S b F p 4α n 4 λ g a) If r S a = r S b, the objet mass is not required F = b) If r S a >> r S b, the relative mass is used F = (64) F p 6α n 4 (65) r S bf p 4α n 4 r S a (66) and so the fore formula redues to F g = m b.a g a g = F. = r S a.r S b a g F p r S a + r S b F = l pm b α n 4 (r S a + r S b ) 8. Gravitational energy (m ob jet << M earth ) E graviton = h f = (67) = r S ar S b a g F p r S a (68) r S b = l pm b (69) a g E p l p = m ba g (70) h πr g = l p r g = l p αn λ earth = v g M earth (7) energy per graviton to reah esape veloity E ev = v s M - earth as blak hole; n =, E =.35e-6eV earth surfae; r = km, n = 90, E =.69e-3eV - moon as blak hole; n =, E =.64e-4eV moon surfae; r = 737.km, n = 0735, E =.9e-eV - M =.46e8kg (i.e.: a small planet); (7) M = α m e =.46e8 (73) m P v s E ev = αm P /m e The number of orbitals per orbit; E tot = E ev.n redues to N earth = M earthm m P N moon = M moonm m P = m e = 3.6eV (74) α E tot = mv g = mv s =.6e4 (75) =.55e39 (76) (77) And so, as noted earlier, esape veloity is not proportional to the mass (of the earth or the moon), but instead to n. V earth = =.83km/s (78) α90 V moon = =.386km/s (79) α Moleular Orbitals Moleular orbitals are the sum of atomi orbitals as desribed by the standard moleular orbital model although in this ontext they are physial orbitals and not wave-funtions. Listed here for referene are some dissoiation energies for homonulear diatomi moleules as approximate geometrial terms. Li-Li (.ev) F-F (.6eV) B-B (3.0eV) Li Li = m ev a 5 F F = 3m ev a 5 B B = m ev a 9 =.09eV (80) =.63eV (8) = 3.0eV (8) 5 6 Moleular Orbitals

6 (plankmomentum.om) H-H (4.5eV) Inoming photon (+λ) = (+λ i ) - (+λ f ) H H = m ev a 3 = 4.54eV (83) (+λ) = (+) 4πα n i λ a (+) 4πα n f λ a (89) O-O (5.eV) Change of orbitals from n = i to n = f : Positronium O O = 3m ev a 8 = 5.0eV (84) (+λ i ) + ( λ i ) = 0 (90) 0 (+λ f ) = ( λ f ) = ( ) 4πα n f λ a (9) N-N (9.8eV) (+)e ( )e = m ev a N N = 8m ev a 5 7 Atomi orbital transitions = 6.8eV (85) = 9.8eV (86) Aording to onsensus, an inoming photon hits the atom and an eletron jumps to a higher orbital. How this instantaneous proess ours and what onstitutes empty spae in the atom (whih is perent of the atom) remains a mystery. Here I have proposed that the orbital is a physial entity, a photon albeit of opposite phase that has been trapped to form a standing wave and whih I denote as an anti-photon. Analysis of the Rydberg formula suggests the inoming photon is atually photons; the first photon orresponds to the present eletron orbital, the nd photon orresponds to the new orbital. If so, then the orbitals are themselves photons, albeit standing waves of inverse phase (ie: anti-photons) whereby photon+antiphoton = 0. And so the inoming photon (+λ) does not ause the eletron to jump between orbitals, rather it deletes the present n = i orbital and replaes it with the new n = f orbital. The Rydberg formula re-written as photons; (+λ) = R n i R n f (inoming) photon (+λ) = (+λ i ) - (+λ f ) antiphoton (standing wave) orbital = (-λ i ) photon + antiphoton = (+λ i ) + (-λ i ) = 0 then 0 - (+λ f ) = (-λ f ) = (+λ i ) (+λ f ) (87) From this wave addition followed by subtration, we have simply replaed the n = i orbital with the n = f orbital. The eletron has not moved, however the boundary of its orbital has hanged. In moleular orbital theory, the terminology used is bonding and anti-bonding orbitals, nevertheless the priniple is the same, i.e.: the moleular bonding orbital is an anti-photon (E < 0), the anti-bonding orbital is the inverse photon (E > 0). When summed, the moleular bonding and anti-bonding orbitals anel (E = 0). 8 Disussion: I have desribed here a mehanism that replaes fore exhange with physial links - the orbitals themselves. Movement within the orbital ours aording to the orbital momentum, movement between orbitals requires a hange in momentum, akin to buoyany. The same priniple applies to nulear, atomi, moleular and gravitational orbitals, the primary differene being that gravitational orbits are the sum of multiple orbitals, onversely in the atom there is only orbital linking eah eletron with the nuleus. Likewise ionization energy, esape veloity, nulear binding energy... are essentially the same. The Bohr orbital model presented here relates to the partile state (of wave-partile duality), as the wave state in the atom is more predominant, the Bohr model has limitations, however these are less apparent in the gravitational orbitals as these may be treated statistially. Nevertheless the underlying priniple linking the 4 orbital types an be seen. Referenes. NASA planetary fatsheet Online orbital alulator For an n = i orbital, orbital wavelength = λ a ( λ i ) = ( ) 4πα n i λ a (88) 6 8 Disussion: