The Concept of Mass as Interfering Photons, and the Originating Mechanism of Gravitation D.T. Froedge

Transcription

1 The Conept of Mass as Interfering Photons, and the Originating Mehanism of Gravitation D.T. Froedge V04 Formerly Auburn University Abstrat For most purposes in physis the onept of mass partiles and photons are treated as though they are ompletely separate and distint entities having little onnetion aept through ollision interations. This paper explores the onept of a mass partile being viewed as a pair of trapped photons in a mass-less box demonstrating proper relativisti dynamis, Lorentz ovariane, and gravitational properties. The mehanism of trapping of the photons in the partile is not herein defined; however the lak of suffiient spin to properly onstitute a photon would be a ontainment fator. Although this presentation is primarily foused on eletrons, presumably it would be appliable to any partile with primary onstituents onsisting of partiles that travel at light speed along null vetors. This illustrates the onept of the equivalene of mass and energy, and why mass veloity annot exeed the speed of light. It is asserted and illustrated; that the gravitational effet on partiles and photons an be an be effetuated by a simple gradient in the speed of light. This allows the assertion that gravitation is a loal alteration of generated by the presene of matter and ould be a QFT effet. Introdution The speial theory of relative, through the Lorentz transformations, yields the energy veloity relation for photons and partiles, one through a shift in frequeny, the other through a shift in mass. Considering these partiles as different forms of energy, however, bestows a distintion between the forms of energy that is possibly unwarranted. The Lorentz transforms applied to a pair of loalized photons an be shown to yield the same results as the transforms applied to a mass partile. A photon onstrained to a point as the result of annihilation by the emission of a virtual photon by its opposite going ompanion, is just the three-dimensional interferene of two photons that are somehow spatially onstrained to their enter of mass, and the properties math very well the dynamis of real mass partiles. One may not subsribe to the details of this, but it does give a useful perspetive regarding mass, rest mass, energy, and gravitation.

2 I Momentum Consider a thought experiment, in whih two photons are plaed in a perfetly refleting massless ontainer. Presuming that if the two photons are not aligned in the given frame, there has to be some sub-light speed frame of referene, in whih the photons are aligned, and in opposite diretions, as well as having equal energy and frequeny. This frame is thus the rest frame for the enter of mass for the two photons Using the momentum for the photons to be: h P M, () where we an designate an energy equivalent mass for the photon to be M h /. The momentum of the ontainer with respet to a moving frame of referene with veloity v is then: P M M v. () From the perspetive of the individual opposite-going photons the momentum is: P P P h h h h. (3) B The wavelength of the differene in the frequeny here, or the beat frequeny, is just the simple debroglie wavelength. The total energy, whih is the sum of the energy of the photons, and thus sum of the frequenies, yields the simple Compton wavelength: E E h h h. (4) C Using the above noted designation for mass we an write for the total mass :, (5) M h h / T Defining a mass for photons is not a unique onept and has been used by others [4] The momentum is then:

3 . (6) P M v M M T Solving for veloity: v M M M M. (7) This is notably just the veloity for the enter of mass for two opposite going photons. Sine for a partile: v M0 M. (8) Putting in M, and v / and solving gives: T. (9) 0 M M M M M 4M M So the square of the rest mass of the partile is four times the produt of the mass of the individual photons. II Doppler This same piture an be viewed from the standpoint of the Doppler shift, on the transformation of veloity oordinates for the two photons. The relativisti Doppler shift of the photons from one veloity frame to another is: v v ' ' v v, (0) or using the above noted onventions for energy equivalent mass: v v M ' M M ' M v v, ()

4 Multiplying the two relations gives: M 'M ' MM ons tan t, () and simple math gets: and: M M M M M M, (3) 4 v 4M M M 0 M M M, (4) whih is the same as the above relation, found for onformane to relativisti kinematis, the model thus transforms properly. III Four Momentum Defining the photon mass as in Eq.(5), moving along null vetors in the opposite diretion the null four-momentum of two opposite going photons previously defined for the partile in the geometri algebra matrix form is: P m k 0 k P m k 0 k Presuming these two photons are o-loated, the square of the sum of the two null vetors is neessarily onstant and is: (5) (6) 0 m m m m 4m m m (7)

5 The magnitude of eah of these null four-momentum is zero for ovariane, and the sum of two suh moments must be onstant. Thus m0 must be invariant fixed quantity assoiated with the pair of opposite going photons. If this is defined as a rest mass then it is easy to identify: m m m, (8) T as the total mass. Fatoring the total mass from Eq.(7), gives: Noting that: m m m m m m m 0 m m m m (9) (0) is the ratio of the veloity of eah photon to the veloity of the enter of mass. m m v m m () This makes Eq.(9), the relativisti energy equation for a mass partile. v m m 0 () It an thus be asserted that two light speed photons, or other onfined zero rest mass partiles, have the property of a mass partile, with mass energy equivalent to the energy of the individual partiles. IV Eletron-Positron Annihilation The above relations give the proper Mehanial result for the eletron-positron annihilation. That is, as two partiles merge the veloity of eah inrease to and beome two opposite going photons. In a simplisti desription as the pair merge, the left going photons in the two

6 partiles, and the right going photons in the two partiles, onstrutively and destrutively interfere giving two opposite going free photons. V Gravitation The paper [] on a theory of gravitation with loally onserved energy shows a theory in whih the total energy of a partile in a gravitational potential is not hanged. The kineti veloity inreases at the expense of the rest energy but the total energy remains the same. The dependene of the rest mass on the gravitational potential is: ml0 m0 r, (3) where m0 is the rest mass of a partile in free spae and ml0 is the loal rest mass of that partile in the gravitational potential at a distane r. putting Eq.(3), into Eq.(9), gives: or m m m m m. m m 0 v M M 0 r r (4) (5) From that paper and [] the loal speed of light in a loally onserved gravitational field is dedued from Eq.(3), to be: 0 r (6) 0 is the speed of light in free spae and is the loal value. This is slightly different from the GR equivalent expression for flat spae whih is is just the first two terms, [4]. Inserting this into Eq.(5), gives:

7 v m m m 0 0 (7) If a partile is falling in a onservative field the total energy remains onstant, and if the initial value of the veloity is zero, then the mass remains equal to the initial rest mass. i.e.: m m m (8) 0 From Eq.(7), the rest mass in terms of the masses of the individual photons is: Eliminating m in Eq., by use of Eq., gives: (9) 4mm m0 0 (30) 4m m0 m m0 0 Solving for the mass of the mass of one of the single photons, m gives: m mm0 m0 0, (3) 4 0 The quadrati solution of this is: m m0 0 (3) Sine the initial mass of the total partile m 0, is twie the initial mass of the m photon then the mass hange in the internal photon is: or: m0 m 0, (33) m 0 0 m m, (34) 0 0

8 Eq.(5), is the relation between the onstant total mass, whih is the same as the rest mass. Eq.(34), is the hange of the mass from one internal photon to another inside the partile as a funtion of the hange in the speed of light. From Eq.(4), it is lear that it represents a hange in the veloity of the partile without a hange in energy. The in-going photon has the + sign and the outgoing is the sign. Origin of Gravitation The above expression, Eq.(34), may not seem all that impressive, but does have profound impliations, the hange in the kineti energy of a partile is effetuated by the gradient of the veloity of light, but the total energy is not hanged. Coneptually, this seems simple aept that there is no work done on the partile as the partile enters the potential, no energy exhanged, and thus gravity is not a fore at all. The veloity has inreased at the expense of the rest mass. The hange in provides the mehanism by whih a onservative gravitational potential effetuates a hange in the veloity of a partile without ontributing energy. The effet of gravitation on a partile is thus, indued in the partile by the gradient in the speed of light. Newton s apple falls not beause of a derease in energy, but beause the speed of light at the branh is higher than the speed of light at the ground. It has long been known that a photon obeying Fermat s priniple, with a speed defined by Eq.(6), exhibits the proper trajetory [3], and from this development the same hange in indues the proper gravitational motion in partiles. The onept of gravitation thus redues to the presene of a gravitating mass, altering the veloity of light in its viinity, and is not a fore at all. It is asserted that Eq.(34), represents a ause-effet relation between partile motion and the speed of light that onstitutes the origin of gravitation. Impliations

9 If there is no energy exhanged by gravitating partiles, then there is, as pointed out earlier, no quantization of gravitational energy, and no gravitons or gravitational radiation. This is onsistent with the fat that despite exeptional effort there has been no detetion of gravitational radiation, and from this development it would be diffiult to envision how a gradient in ould be propagated. It is well known and experimentally verified, however that gravitating masses do lose orbital energy. If it is as asserted here, not possible for gravitational waves to arry the energy away from the system, then the searh for gravitationally transmitted energy should be onduted in the eletromagneti spetrum. QFT Origin of Gravitation? Consider a thought experiment in whih here is a avity with opposing mirrors. If photons are injeted and trapped between the mirrors, from the onservation of energy, the mass of the apparatus has inreased. It is not without preedent that photons osillating in a avity are noted as having mass [4]. The photons thus having mass, must originate gravitation, but being just photons bouning bak and forth from one mirror to another in a avity having no asribed interation, how does this result? It has been asserted here that gravity is generated by an alteration of the speed of light. The possible mehanism for this in the viinity of osillating photons is by mehanisms of quantum eletrodynamis. From the work of D. Kharzeeva, et.al, [5] it is shown that for an intense laser beam the QFT effets related to eletron positron loops indue vauum self-fousing whih an be interpreted as a slowing down in the vauum speed of light in the viinity of the beam. The photons refleting bak and forth in the here disussed partile, onstitute an intense repetitive beam orders of magnitude greater than a laser, and as suh have path ation that an find the photons having a path probability far outside the trapped zone [6]. It is asserted that this slow down of in proximity of osillating light speed partiles, ould be the mehanism that generates the effet of gravitation between massive partiles. If the redution in in the viinity of photons osillating in a massless box an be found by methods of QFT to be:

10 0 G 4 r (35) then the gravitational onstant is alulated, and the riddle of gravitation is solved. It ould be argued that the photons are not observed outside the massless box, and thus unable to affet, but as in the ase of the Aharonov Bohm effet the underlying oupling of the eletromagneti potential with the omplex phase illustrates the effet of the probability path ation of a partile is non loal and present outside the loal area even if the partile presene is shielded [7]. Conlusion The onurring points of similarity of the opposite going photons in a massless box model and the partiles are onsistent with: ) The debroglie wavelength. ) The Compton wavelength 3) The zero veloity rest mass 4) The total energy 5) Veloity transforms 6) Loal onservation of Gravitation Using a refleting ontainer is somewhat artifiial, but as in the ase of the transformation of momentum between veloity frames, the gross mehanis do not depend on the internal struture. All of the real internal onstraints suh as spin, energy, et, whih may be important to the atual mehanis of holding a partile together are not neessary to understand the onept. The dynamis of the enter of mass of the two photons is the same whether the photons are onfined or not, and it is easy to understand from this model why mass partiles do not exeed the speed of light. A mehanism for produing the effets of gravitation on suh a partile has been offered that ould lie within the sope of the effets generated by QFT. Referenes:

11 . DT Froedge, Salar Gravitational Theory with Variable Rest Mass,V0094, DT Froedge, The Veloity of Light in a Loally Conserved Gravitational Field, V094, 3. Roger Blandford, Kip S. Thorne, in Appliations of Classial Physis, (in preparation, 004), Chapter Alex KruhkovBose-Einstein ondensation of light in a avity 5. D. Kharzeeva, K. Tuhinb, Vauum Self Foussing of Fery Intense Laser Beams, arxiv:hep-ph/0633v 6. Feynman, Hibbs, 965, Quantum Mehanis and Path Integrals MGraw-Hill pp 4, 7. Chambers, R.G. (960). "Shift of an Eletron Interferene Pattern by Enlosed Magneti Flux". Physial Review Letters 5: 3 5.Bibode:960PhRvL C (