Frank Znidarsic COMMENTS: 8 PAGES ASCII TXT FILE. NEW ENERGY PROJECT, Submitted to the Canadian Journal of Physics, July 94 resubmitted Jan 95 Texted in the DOS editor. REPORT-NO: SPECIAL ENERGY PROJECT ABSTRACT Present quantum theory is very exact in its representation of atomic and nuclear interactions. This theory represents matter as a series of superimposed zero energy probability waves. This superposition of component waves is known as a Fourier addition.1 Wave propagation is a fundamental property of all simple harmonic motion. The waves of matter, like all other waves, should propagate into space. According to present theory the propagation of the wave states of matter is inhibited by the Fourier addition of an infinite number of component waves. 2 This addition of component waves localizes the wavefuctions of matter. This author questions if an infinite number of states can exist within a finite universe. Louis deBroglie believed that matter waves are real and as such contain energy. This author also questions the reality of a zero energy probability wave. It has not been possible to reconcile gravity with the current model of matter. This author has added a new ingredient to the current models of matter. This ingredient is force. This author's model will show that the matter waves contain energy and that this energy is localized by a reflection at the potential well of matter. The modified model requires no infinities, probability waves, or special reconciliation with gravity. The fundamental postulate of the new model requires the production of a gravitational field. 3 INTRODUCTION Present theory identifies matter as a source of gravitational and inertial mass. Einstein's General Theory of Relativity demonstrates that an applied force also produces a gravitational field. Photons have no rest mass. According to existing theory photons do, however, have a gravitational mass that is proportional to their rest energy. Present theory states that there are three sources of gravitational mass. These sources are: 1. Matter 2. Force 3. Photons (and all other energy flows) This author will show that there is only one source of mass. This one source is an applied force. It will be shown that at all inertial and gravitational mass is a direct result of an applied force. INERTIAL MASS An analysis will now be done that will describe inertial mass in terms of an applied force. Consider a photon trapped in a perfectly reflecting containment. (see fig. #1) ---------------------- | p \ | | 1 \ | A| / |B -------> X | p / | r | 2 | ---------------------- |-------- k ----------| FIGURE #1 This photon in a containment model is a simplistic representation of matter. The photon represents the matter wave function. The wavelength of the photon corresponds with the Compton wavelength of matter. The containment represents a potential well. This analysis considers only the momentum of the photon. The containment will be considered to be at rest. The photon is ejected from wall "A" of the containment, its momentum is p . The photon now travels to wall "B". It's 1 hits wall B and immediately bounces off. Its momentum is p . The photon now travels back to wall "A", immediately 2 bounces off, its momentum is again p . This process repeats 1 continuously. If the energy in the containment is carried by a number of photons evenly distributed throughout the containment, the momentum carried by this energy will be distributed evenly between the forward and backward traveling components. The total momentum of this system is given in equation #1. p =(p /2 - p /2) Eq #1 t 1 2 The momentum of a flow of energy is given by equation #2. p = E/c Eq #2 Substituting equation #2 into equation #1 yields equation #3. E = (E /2 - E /2) Eq #3 t 1 2 Given the containment is at rest. The amount of energy in the containment remains fixed, the quantity of energy traveling in the forward direction equals the quantity of energy traveling in the reverse direction. This is shown in equation #4. E = E Eq #4 1 2 Substituting Eq. #4 into Eq. #3 yields Eq #5. p = (E/2c)(1 - 1) Eq #5 t Equation #5 is the total momentum of the system at rest. If an external force is applied to the system its velocity will change. The forward and the reverse components of the energy will then doppler shift after bouncing off of the moving containment walls. The energy of a photon varies directly with its frequency. Given that the number of photons in the containment is conserved, the amount of reflected energy will vary directly with the energy of the reflected photons. This is demonstrated by equation #6. E = E (f /f ) Eq. #6 2 1 f i Substituting Eq. #6 into Eq #5. yields eq. #7. p = (E/2c)((f /f ) - (f /f )) Eq #7 t f i f i Equation #7 is the momentum of the system after all of its energy bounces once off of the containment walls. Equation #7 shows a net flow of energy in one direction. Equation #7 is the momentum of a moving system. The reader may desire to analyze the system after successive bounces of its energy. This analysis is quite involved and unnecessary. Momentum is always conserved. Given that no external force is applied to the system after the first bounce of its energy, its momentum will remain constant. Relativistic doppler shift is given by equation #8. 2 2 .5 (f /f ) = (1-v /c ) /(1 +- v/c), Eq #8 f i v = velocity with respect to the observer c = light speed f / f = frequency RATIO f i + or - depends on the direction of motion Substituting equation #8 into equation #7 yields equation #9 _ _ | 2 2 .5 2 2 .5 | E | (1-v /c ) (1-v /c ) | p = ---| --------- - ----------- | Eq #9 2c | (1-v/c) (1+v/c) | |_ _| _ _ | 2 2 .5 2 2 .5 | = E |(1+v/c)(1-v /c ) (1-v/c)(1-v /c ) | -- | -------------- - ----------------- | 2c |(1+v/c)(1-v/c) (1-v/c)(1+v/c) | |_ - _ _ | 2 2 0.5 | = E | (1-v /c ) (1+v/c-1+v/c) | -- | -------------------------- | 2c | 2 2 | | (1+v /c ) | - - Ev = --------------- 2 2 2 0.5 c (1+v /c ) 2 Substituting mass for energy, M = E/c Mv = ------------ 2 2 0.5 ( 1+v /c ) Eq #10 The result, equation #10 is the relativistic momentum of moving matter. This first analysis graphically demonstrates that inertial mass is produced by a containment force at the potential well of matter. A fundamental change in the frame of reference is produced by the force of containment. This contaimnment converts energy, which can only travel at light speed, into mass, which can travel at any speed but light speed. In 1985 Nick Herbert wrote in his book Quantum Reality", Pg 46 "The fact of the matter is that really knows these days how an electron, or any other quantum entity, actually possesses its dynamic attributes." This author will now show that matter's dynamic deBrogglie wavelength results from the application of a force. As stated, the original wavelength (L) of the photon represents the Compton wavelength of matter. L = h/Mc Eq #11 c c = (f)(L) Eq #12 Substituting Eq #12 into Eq. #11 converts wavelength into frequency yielding the Compton frequency f of matter. c 2 f = Mc /h c c A doppler shifted component of the original frequency was produced by the reflection at the containment wall. Classical doppler shift is given by Eq #13. f = f (1 +- v/c) Eq #13 2 1 A beat note is formed by the mixing of the doppler shifted and original components. This beat note is the de Broglie wave of matter. Given both waves are in phase at the containment wall. The beat note extends from the wall to the point at which the waves again come into phase again. Substituting equation #12 into equation #13 yields, equation #14, the length beat note. sin(f +6.28n) = sin((f )(1 + v/c)) Eq. #14 c c 2 2 sin(Mc /h + 6.28n)) = sin((Mc /h)(1+v/c)) Taking the arcsin of Eq #14 yields Eq #15. 2 2 Mc /h + 6.28n = Mc /h + Mvc/h Eq #15 6.28n = Mvc/h Eq #16 The right side of Eq. #16 is the quantumized frequency of the beat note produced by the mixing of the original wave and its doppler shifted reflection. This is the de Broglie frequency. Converting this frequency back into a wavelength by Substituting Eq #12 into Eq #16 yields Eq. #17 the de Broglie wavelength L of matter. d 4 L = h/(MV) Eq #17 d It has been shown that the dynamic attributes of matter result from an applied force. GRAVITATIONAL MASS Einstein's principle of equivalence states that gravitational and inertial mass are the same. 5 Gravitational mass then must be generated by the same mechanism that produces inertial mass. The reflection of the energy off of the walls of the containment must also generate the gravitational mass of the energy in the box. It is well known that the gravitational field can generate a force. This the gravitational force is given by equation #18. The force of gravity = mg Eq #18 It is less well known that the application of a force also induces a gravitation field. The application of a force must induce gravity in order to conserve a symmetrical relationship between the forces. For example, a changing magnetic field will induce an electrical field and conversely a changing electrical field will induce a magnetic field. Likewise the application of a force also 6 induces a gravitational field. The application of a force must also produce gravity in order to conserve momentum. If mass is pushed into the established field of other mass time is required for the gravitational field of pushed matter to reach the other mass. To conserve momentum during this interval an induced gravitational field is required. The relationship between the induced gravitational field and the force of acceleration as demonstrated by General Relativity is given by equation #19. 7 2 Field gravity = (G/(c r))(dp/dt)*i Eq #19 i = unit vector in direction of the force of acceleration G = the grav constant r = the grav radius dp/dt = Force Each time the photon strikes the wall of the containment it produces a gravitation field according to equation #19. An exact mathematical analysis of the gravitational field produced by the photon in the box will now be undertaken. k = The dimensions of the box p = momentum t = the time required for the photon to directly traverse the box t = k/c r = The distance to point X The far gravitational field at point X is the vector sum of the field produced by the impacts on walls A and B. Field = 1/r field from wall A - 1/r field from wall B (at X) 2 2 = (G/(c (r+k))) dp/dt - (G/(c r)) dp/dt Eq #20 2 2 simplifying = -(G/c )(dp/dt)(k/(r +rk)) Taking the limit to obtain the far field. 2 2 2 2 lim -(G/c )(dp/dt)(k/(r +rk)) = -(G/c )(dp/dt)(k/r ) as r>>k Substituting for dp/dt in the box model. dp/dt = /\ p / /\ t = (2E/c)/(k/c) = 2E/k In order to remain consistent with the first argument only half of the energy will be considered to be impacting on wall "A" of the containment. The other half of the energy will be considered to impacting on wall "B" of the containment. A factor of 1/2 is introduced as a result of this qualification. 2 2 Field = 1/2(G/c )(2E/k)(k/r ) (at X) 2 Substituting mass for energy, M =E/c 2 Field = -GM/r Eq #21 (at X) The result, equation #21, is Newton's formula of gravity. 8 This second analysis clearly shows that gravitational mass is produced by the force of containment at the potential well of matter. PHOTONIC MASS A photon has no rest rest mass therefore the source of the gravitation mass of a photon cannot be mass. The source of the gravitational mass of a photon will now be demonstrated. Hubbles' constant expresses the expansion space in units of 1/time. Ordinarily, the effects resulting for the Hubble expansion are quite tiny. At great distances and at high velocities significant effects do, however, take place. As a photon travels through space at the high velocity of light it red shifts. This red shift may be considered to be the result of an applied force. This force is produced by the acceleration given in equation #19. Acceleration = Hc Eq #22 H = Hubble's constant, given in units of (1/sec) c = light speed To demonstrate the gravitational relationships of a photon the principle of the conservation of momentum will be employed. According to this principle exploding bodies conserve there center of gravitational mass. Mass M ejects a photon while over the pivot I. (Ref fig #2) |----S -----|------- S ----------------| 1 2 mass photon _________________________________________ ^ I PIVOT FIGURE #2 The gravitational center of mass must remain balanced over the pivot point I. Mass M is propelled to the left velocity at v and the photon travels to the right at velocity c. The 1 product of the velocity and time is the displacement S. Setting the products of the displacements S and the gravitational masses Mg equal yields equation #23. Note the gravitational mass of the photon is determined by force (the right side of equation #23) Mg S = Mg S Eq #23 1 1 2 2 2 2 GMS /r = (G/c ) (force) S /r 1 2 2 2 GMS /r = (G/c ) dp/dt S /r 1 2 2 GM(v t) = (G/c ) dp/dt (ct)r 1 2 Substituting, dp/dt = Ma = MHc = (E/c )Hc = EH/c 2 G(Mv )t = (G/c )(E/c)Hctr 1 Setting momentums equal p = p = Mv = E/c 1 2 1 Gp t = G/cc p Hctr 1 2 c = Hr Equation #12 The result, equation #12, shows that the gravitational mass of a photon is produced by the it force it experiences as it accelerates through Hubble's constant. The result is true only under the condition where the speed of light is equal to the product of Hubble's constant and the radius of the universe. The gravitational radius of the photon is the radius of the universe. These qualifications are essentially consistent with the known cosmological constants. CONCLUSION It has been shown that the application of a force is the exclusive mechanism by which all inertial and gravitational mass is generated. A reflection takes place at matter's potential well. This force produced by this reflection induces the gravitational field of matter. This reflection, like all reflections, is a result of a change in the product of a substances elasticity per unit of mass. This author believes that there is an elastic limit associated with free space. As this elastic limit is reached the elasticity of 9 free space changes producing reflections. A new model of 10 matter has been developed that shows that acceleration of energy at matter's potential wall is the source of the gravitational and inertial mass of matter. This model is so simple that once it is seen it appears to be almost self evident. The gravitational mass of a photon was shown to be produced by the acceleration of the photon through Hubble's constant. This analysis shows that there is a relationship between the speed of light, Hubbles's constant, and the radius of the universe. A profound, yet simple, model has been developed. This model demonstrates the mechanism though which all gravitational fields are generated. It also demonstrates the mechanism underlying the dynamic deBroglie wavelenght of matter. The scope of the symmetrical relationship that exists between force and gravity has been exposed. This author believes that this new understanding will lead to the development of gravitational technologies. 11 NOTES 1. Joseph Fourier showed that any wave can be written as a sum of sin waves in the 19th Century study "La Theorie analytique de la chaleur." 2. E. Schrodinger referred to such a localization as a "Gaussian wave packet." 3. Gilbert N. Lewis demonstrated the relationship between external radiation pressure and momentum. Gilbert N. Lewis, Philosophical Magazine, Nov. 1908 4. French aristocrat Louis de Broglie described the electrons wavelength in his Ph.D. thesis in 1924. De Broglie's hypothesis was verified by C. J. Davisson and L. H. Germer at Bell Labs labs. The mechanism through which elementary particles can possess dynamic attributes, such as the de Broglie wavelength, has been a central mystery in the field of quantum physics. 5. Einstein's principle of equivalence was experimentally confirmed by R.v. Eotos in the 1920's R.v. Eotvos, D. Pekar, and Feteke, Ann. d. Phys 1922 Roll, Krotkov and Dicke followed up on the Eotvos experiment and confirmed the principle of equivalence to an accuracy of 10EXP in the 1960's R.G. Roll, R. Krotkow & Dicke, Ann. of Physics 26, 1964 6. Danish physicist Han Christian Oersted first discovered that and electric current produces a magnetic field in 1820. English scientist Michael Fariday demonstrated that a changing magnetic field produces an electric current in 1831. 7. A. Einstein, Ann. d. Physics 49, 1916. 8. Sir I. Newton, PHILOSOPHICA NATURALIS PRINCIPIA MATHEMATICA (1687) 9. For leptons this elastic limit is equivalent to -24 3.42 x 10 Farads. This author believes that capacitance in a non-local phenomena. 10. Puthoff has also introduced force into a model of matter. "Gravity as a zero point fluctuation force" Physical review 11. The discovery of the symmetrical relationship between the electric and magnetic fields by Oersted and Faraday is the basis of our current electro-technologys.