i The Deadbeat Universe ii iii The Deadbeat Universe by Lars Wåhlin Colutron Research Boulder, Colorado iv Copyright © Colutron Research 1997 ISBN 0-933407-03-3 Second Edition Revised 2003 v Preface We always thought of ourselves as being at the center of the Universe and at rest It was not until very recently that Copernicus explained how our Earth is orbiting the Sun and that the Sun, not the Earth, is at the center of our solar system Today’s theories such as Einstein’s special and general relativity, still believe that we and our galaxy, are at the center of the Universe In fact, relativity with its “cosmological principle” claims that any observer on any galaxy in the Universe can consider him or herself at the center and at rest In other words, everything is relative and there is no preferred or absolute point in space to relate our location or frame of reference to, thus the term “relativity” This view creates certain problems Imagine how difficult it was for astronomers before Copernicus’ time, to set up mathematical equations for planetary orbits with the Earth at the center and at rest and how difficult it is today to deal with a Universe that has more than one center in which we are motionless and at rest It is understandable why we tend to believe that we are at rest since the star studded sky seems motionless relative to us and we have no feeling or conception of velocity or acceleration For example, we cannot feel that we are hurling through space around the Sun fifty times faster than a rifle bullet at an orbital velocity of 30 km/second (18 miles/second) Nor we feel our velocity around the center of our galaxy which is ten times higher or our velocity relative to the rest of the Universe which is still another thousand times higher and which equals c, the velocity of light There is no doubt that a clever mathematician can construct mathematical equations that will describe planetary orbits with the Earth at the center or equations that will work for a Universe where we assume ourselves to be at rest and everything else moving relative to us To build a good conceptual theory on such equations is difficult if vi not impossible The problem is that by accepting the theory of relativity we deal only with relative motion and denounce the existence of absolute motion Why not accept both? For example, if we are part of a large system in which everything is moving about in an organized fashion, then there will obviously exist both relative motion between bodies as well as absolute motion, with respect to a common center of the whole system The fact that we are moving at a velocity of c with respect to the rest of the Universe and still subject to a minute cosmic acceleration of a towards its center, is what this work is based on One can compare our galaxy and the rest of the Universe to a swarm of bees in which all members are moving relative to a common average point In our Universe, where all matter is subject to a mutual gravitational attraction, such a point is the center of mass of the system or the point to which everything is attracted Knowing our absolute speed c and gravitational acceleration a in such a system makes it possible to create exact mathematical solutions which can pinpoint parameters such as mass, size, age and temperature of the Universe to mention a few To date there are no such solutions obtainable for distances beyond the solar system Most equations in this book are based on the harmonic motion of the Universe and will accurately describe the contracting-expanding Universe The outcome implies that we are part of a “deadbeat” or a one cycle Universe that is in a state of contraction and the most compelling evidence for this type of cosmology are the equations describing atomic orbits in Chapter section 6.3 It will also be shown that the observed cosmic 2.76 K microwave temperature is a direct result of collective or thermolized radiation from all stars and matter in the Universe The lifetime of our galaxy is about million, million years and the cosmic model described promotes both evolution and continuous creation (Chapter section 7.4) It is not the intention of this book to reject Einstein’s work since many of his basic equations and discoveries are used throughout It is merely to point out that the conceptual explanation of his relativity needs to be changed and that further progress can be made if we add vii the idea of absolute and relative motion, as well as absolute and relative energy It is not the first time a great theory has to be modified For example, Isaac Newton, the father of modern physics, had his theories modified by Einstein himself and Einstein’s model of a static Universe had to be altered by contemporary science to a dynamic expanding-contracting Universe We are still far from a perfect theory that will explain everything The field of natural science is like a labyrinth where progress is made in small steps and where each step usually ends up at a dead end and considerable time passes before a new path can be found There are two ways to derive a scientific theory One is by logical reasoning where a theory has to be both conceptually and mathematically sound The other is by mathematical modeling where equations are structured to fit observations and where conceptual explanations are often missing or misleading The theory of electric current in solid conductors is one example, where mathematical reasoning requires current to flow from positive to negative, when in reality the opposite is true One of my favorite subjects is mathematics I believe mathematics to be a wonderful manmade tool and there is no doubt that mathematical physics has had much success, but I also think that page after page of abstract Picasso mathematics might scare off many potential new scientists I therefore like to add that it is important to remember that the laws of mathematics must obey the laws of physics and not the other way around Mother Nature does not know of numbers or digits She behaves more like an analogue computer rather than a digital computer This book is written for anyone intrigued by the subject of basic physics and cosmology, and even though it contains numerous equations, only a limited knowledge of algebra and trigonometry is required In fact, I believe most of the equations can be skipped since numerical solutions are already provided and the purpose of the equations is merely to prove a point, or to describe a scientific statement in rigid mathematical terms L.W Boulder Colorado, 1997 viii ix Table of Content Page CHAPTER HISTORICAL BACKGROUND 1.1 Early Developments 1.2 Later Developments 1.3 Present status quo 14 1.4 Problems 16 CHAPTER THE HARMONIC UNIVERSE 21 2.1 Harmonic Motion 21 2.2 The Contraction 25 2.3 Gravitation 29 2.4 Energy and Time 29 2.5 The motion of the Universe 33 CHAPTER VELOCITY, ENERGY AND ACCELERATION 35 3.1 Velocity-Energy relationship 35 3.2 Inward acceleration 42 CHAPTER COSMIC DISTANCE AND MASS 49 4.1 Our position x0 relative to the center 49 4.2 Total mass within x0 53 4.3 Mass density 54 4.4 Potential energy of matter 54 4.5 Mass and Energy 55 154 THE DEADBEAT UNIVERSE APPENDIX C 155 APPENDIX C THE PROBLEM WITH E = mc In 1905 Einstein concluded that the energy of a mass m is equivalent to mass × velocity of light squared According to the literature (Pais (1982)) Einstein’s proof is as follows: “If a body gives off the energy L in radiation, its mass diminishes by L / c ” This links energy with the velocity of light or the propagation of electromagnetic waves, and the conclusion drawn was that energy of mass must be related to the speed of light so that L = mc Today, nearly 100 years later, the equation has seen no change except that the symbol for energy L is usually replaced by E There has never been any doubt about the accuracy of the equation as long as the speed of light remains constant However, recent advances in space science and satellite technology suggest that there are changes in both the speed of light and the rate of time, which poses the question: is energy of mass really proportional to the speed of light squared and how can we test the validity of Einstein’s proof? This essay provides such a test, and the result is quite contradictory since it will show that energy of mass in Einstein’s equation is not proportional to the velocity of light squared, but is proportional to a universal gravitational potential or gravitational tension φ univ The Problem with E = mc Einstein’s equation E = mc suggests that energy stored in mass is proportional to the velocity of light squared In fact, the opposite is true Energy stored in mass is inversely proportional to the velocity of light squared For example, if energy of mass is proportional to the velocity of light squared, then energy of mass will be less in situations where velocity of light is slower, e.g at the surface of the Sun or near a 156 THE DEADBEAT UNIVERSE massive black hole where light is believed to slow down to zero preventing it from escaping the black hole’s strong gravitational field This is an example of how mathematics can sometimes give a correct numerical answer but a misleading physical picture The problem is that c in Einstein’s E = mc has always been associated with the speed of light, when in reality c in Einstein’s equation has a different meaning than the speed of light Although the numerical value and the physical dimensions of c are the same as those of the speed of light squared, its function is quite different For example, the distance between New York and Albany has a totally different meaning from the same distance squared, which describes surface area Another example is the amount of potential energy per unit mass required to lift a mass to a certain height h above the Earth’s surface under the influence of the Earth’s gravitational acceleration g E / m = gh (meter/second) , ( l / t ) (146) where the answer is velocity squared, even though the physical process described does not involve velocity In reality, c in Einstein’s equation and velocity squared in the above equation represent gravitational potential or gravitational tension φ Einstein’s energy equation should therefore be written as E = mφuniv , where φuniv = GM univ / Runiv ≡ c (147) Here φuniv is the cosmic gravitational tension, or the amount of Energy per unit mass E/m generated by the Universe (Wåhlin ( 2002)) at Runiv , the distance to Earth from the center of mass of the Universe, and M univ is the mass of the Universe within Runiv G is the universal gravitational constant Note that φuniv includes both the Earth’s and the Sun’s gravitational tension a location on Earth The Sun’s gravitational tension at Earth is 100 million times weaker than φuniv and the Earth’s own gravitational tension at its surface is an additional 14 times less The cosmic gravitational tension φuniv APPENDIX C 157 determines the rate of time The gravitational tension φuniv also establishes the speed of light and therefore acts as a propagation medium for electromagnetic waves which means that any change in the cosmic gravitational tension changes the speed of light The ratio of change in time and rate of clocks and physical processes is φuniv and φuniv + Δφ φuniv φuniv − ∇φ , (148) where Δφ represents an increase in gravitational tension and ∇φ a decrease in gravitational tension relative to an observer For example, when a clock progresses one second on Earth the same clock on the Sun’s surface would read tsun = tearth φuniv φuniv + Δφ = 0.99999788 sec , (149) where Δφ = Gmsun / rsun is the gravitational tension of the Sun added to φuniv and neglecting the influence of the Earth’s gravitational tension The slowdown of solar time has been measured by Snider (1972) A reduction in gravitational tension, on the other hand, will speed up clocks or physical processes and the propagation of light A clock raised to any height above ground would therefore run faster because of the decrease in the Earth’s gravitational tension ∇φ with altitude The rate of a clock at height h above ground relative to a clock on the Earth’s surface is theight = tearth φuniv φuniv − ∇φ , (150) which has been verified by many experiments (Pound and Rebka (1960)) including the Mössbauer effect involving very sensitive measurements of atomic frequency spectra However, the change in the propagation of light caused by changes in the cosmic gravitational tension is twofold First, light is subject to the same slowdown in time as observed for clocks and physical processes described above Second, THE DEADBEAT UNIVERSE 158 it is also subject to the change in the tension of the propagating medium The result is that the speed of light is affected twice, i.e vlight ⎛ φuniv ⎞ ⎟⎟ = c⎜⎜ φ φ + Δ ⎠ ⎝ univ 2 and vlight ⎛ φuniv ⎞ ⎟⎟ = c⎜⎜ φ φ − ∇ ⎠ ⎝ univ (151) These equations are in agreement with experimental data One such experiment involved the timing of radar waves bouncing off Venus (Shapiro (1971)) while crossing the gravitational field of the Sun The change in velocity and time by gravitational fields is often referred to as gravitational red shifts when generated by Δφ and blue shifts when produced by ∇φ The velocity of light remains constant whenever the cosmic gravitational tension φuniv is constant Since gravitational tension φ represents energy per unit mass, there are other processes that can increase or decrease the energy of mass, e.g kinetic energy A fast-moving jet aircraft will generate a level of energy per unit mass of v , where v is velocity of the jet This will raise the gravitational tension of the jet aircraft by 12 v , (nonrelativistic) thus slowing clock s and physical processes accordingly, so that the clock rate onboard the jet would be t jet = tearth φuniv φuniv + 12 v (non-relativistic) (152) This is true only if the change in gravitational tension due to the jet’s altitude is not considered Experiments involving clocks on board jet aircraft (Hafele (1972)) verify Equation (152) Also, an increase in the half-life of decaying cosmic particles has been observed, which has been attributed to the high velocities of the particles as they enter the Earth’s atmosphere The time change due to velocity is known as time dilation APPENDIX C 159 Orbiting satellites are subject to both time dilation and gravitational blue shifts, which compete against each other, as shown in the following equation tsat = tearth φuniv φuniv (non-relativistic) − ∇φ + 12 v (153) Both ∇φ and v can vary due to the position of the satellite relative to the Sun’s, Moon’s and Earth’s gravitational tensions The orbital velocity v of a satellite is determined relative to the fixed stars Clocks on a GPS satellite (Ashby (2003)) orbiting at an altitude of 26500 km will run faster by about 4.92 × 10 −10 second per second and clocks onboard the space station, which orbits at the much lower altitude of 380 km above Earth, will run slower by 2.88 × 10 −10 second per second compared with clocks on the Earth’s surface, ignoring the effect on clocks on Earth caused by the Earth’s own rotational velocity For relativistic velocities we need to replace the Newtonian 12 v with φrel = φuniv φuniv φuniv − 12 v − φuniv (154) Another interesting consequence of Equation (153) is Einstein’s twin paradox, where a twin traveling in a space ship will age more slowly than the twin remaining on Earth, so that on the return from the voyage the returning twin will be younger than the one on Earth Here ∇φ in Equation (153) can be replaced by the square of the escape velocity ( vesc = Gmearth / rearth ) required for the space ship to leave the Earth's gravitational field and v equals the square of the velocity of the space ship when traveling through space Conclusions Replacing velocity of light squared in Einstein’s equation E = mc with φuniv has several implications, two of which are mentioned below THE DEADBEAT UNIVERSE 160 The slow-down of light in strong gravitational fields according to Equation (151) offers a simple explanation for the bending of light near gravitating bodies such as the Sun The index of refraction n according to Snell’s law or René Decartes’ law is n= Δv Δ(sin α ) c sin α ' = and = c sin α ' v sin α " (155) where c and v represent the speed of the incoming and retarded light respectively and α ' and α " are the angles of incidence and refraction respectively Since the mean incident angle of light penetrating the Sun’s gravitational equal-potentials is 45° then the total angle of refraction becomes α bend = 2{α '− sin −1 [sin α '−Δ(sin α ]} = 1.75053023 arc second (156) for light grazing the Sun’s surface The factor “2” is necessary since light has to pass through two refractive indices, one at the entrance to and one at the exit from the gravitational field The outcome of Equation (151) also casts serious doubt on the existence of black holes, since the equation shows that light cannot slow to zero in order to be prevented from leaving a black hole’s gravitational field no matter how strong the gravitational field REFERENCES REFERENCES References 162 Page Allen, C W.: 1973, Astrophysical Quantities, Athlone Prem, London 70 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Aristarchus, 2,6 Aristotle, 2,3 Ashby, 159 B Background radiation, 51 Bagge, 71 Bending of light, 13,59,139,159 Berkeley, George (Bishop), 11,13 Big Bang, 14,16,18,29,50,96 Birch, 67 Black holes, 64,91 Black-body radiation, 16,99,100 Black-body temperature, 72,99,28 Blue shift, 18,59,99 Boltzmann’s constant, 87,145 Bondi, 29,101 Bremsstrahlung, 46 Burbidge, 51,53 C Cavendish, Sir Henry, 59 Centrifugal force, 11,13,22 Charlier, 33 Clausius, 113 Collapsing Universe, 2,18,29,38, 41,46,48,68,83,86,96,101 Columbus, Coma cluster, 43,46,115 Compton red-shift, 86, Compton wavelength, 44,145 Continuos creation, 29,101 Copernicus, 3,5,6,7,79 Cosmological Principle, 2,5,17 Crommelin, 60 Curvature of space, 13,105,115,117 166 D Davisson, 83 Deceleation parameter, 50 de Broglie, Loius, 82,83,150 de Vaucouleurs, 46,97 Descartes, 8,61,160 Desclaux, 86 Digges, Thomas, Dirac, P.A.M., 86,108 Dirac-Fock correction, 86 Doppler shift, 14,43,73,93-96 E Ether, 10,12,57,89,121 Eddington’s magic number, 104, 106,145 Eddington, 60,104,106,107,108, 118,119 Einstein, Albert, 12-16,2932,37,39,47,59,84-86,104, 115,122,138 Electron, Electron's electromagnetic radius, 46,103,145 Emissivity, 71 Energy self enegy, 55,58,77,86,104 Energy density of matter, 100 Energy density of radiation, 29,100 Energy, 1,15,35 Energy, kineteic, 31,35,113,123, 128, 139 Energy, potential energy, 24,28,38, 42,54,58 Eratosthenes, Equivqlence principle, 138 F Fitzgerald, 122 Fixed stars, 11,13 Force constant, 67 Force, 1,9 Fujii, 107 167 THE DEADBEAT UNIVERSE G Galileo, 7,136 General Relatively, 12, 60 Germer, 83 Gilbert, William, Giordano Bruno, God, Gold, 29,101 Gravitational constant, 10,28,32, 105,107,113,130,145 Gravitational potential, 56 Gravitational red-shift, 93 Gravitational tension, 13,31,49, 56,64,87,90,122,135,140,156 H Hafele, 158 Harmonic motion, 21 Heisenberg, 15,26 heliocentric, 2,8 Heraclides, Hipparchus, Hooke, Robert, Hoskin, M., Hoyle, Sir F., 29,101 Hubble’s law, 43,51,105,134 Hubble, Edvin, 14,42 Huchra, 70 I Inertia, 8,11,30,31 Infinity, 5,13,16,17 Inhalation, 112 Jupiter, 10,56 J K Källen, 86 Karachentsev, 46 Kazuaki Kuroda, 107 Kembhavi, 101 Kepler, 7,9,18,19,65,87 Kiang, 33 L Landsberg, 73 Lanzerotti, 71 Large number ratios, 103 Lebach, 63 Light year, 42,145 Long, 107 Lorentz, 12,122 Lorentz-Fitzgerald conraction, 122 Lovell, M Mach, Ernst, 11,13 Mach’s principle, 11 Mass density, 27,50,54,89,100, 105,113,117,120,134,145 Maxwell, 89,119 Michelson, 12,121 Michelson-Morley experiment, 12,121 Microwave radiation, 16 Missing mass problem, 50,53,115 Mohr, 86 Momentum, 15,44,83 Morley, 12,121 Munitz, Mössbauer effect, 157 N Narlikar, 51,101 Newton, Isaac, 9,31,35,39,59, 84,85,110,121 Nicholas (Cardinal) of Cusa, 5,13,17 O Olbers’ paradox, 99 Olbers, Heinrich, Wilhelm, 99 Ozernoy, 46 P Pair production, 29,101 Pais, 155 INDEX Penzias, 16,51 Photon, 87 Plank’s constant, 15,28,44, 46,80,145 Planck, Max, 15,74 Plank’s wavelength, 44 Poincaré, 12 Posidonius, Pound, 157 Q Quantum, 80 Quantized, 70 R 168 T Temperature, 16,27,72 Thales, Thomson, Sir, G.P., 83 Time dilation, 30,32,94,158 Time universal constant s, 32,145 Time, 30 Twin Paradox, 32 U Uehling, 86 Uncertainty Principle, 16,26 Radian, 22,66 Radiation, 79 Radio polarization, 67 Recession velocities, 16,38,43,49, 96 Red shift, 14,16,26,28,38,42, 59,86,93 Ritz, 122 Rutherford, 149 V Vacuum polarization, 86 van den Bergh, 46 velocity 1,22,26,35 Velocity of light, 12,89,145 Velocity of ligth in gravitational field, 63 Virgo cluster, 97 Virial theorem, 53,113 S Saslaw, 33 Satelite, 158 Segal, 46 Shapiro, 158 Simple harmonic motion, 21 Slipher, 42 Smoot, 73 Snell’s law, 61, 159 Snider, 157 Soldner von, Johann Georg, 59 Soneira, 46 Space station, 159 Special Relativity, 12,39 Spin, 152 Stacey, 107 Star aberration, 10,64 Stefan's law, 72, 87 Stephan Boltzmann's constant, 52,72,87,118,136,145 Stewart, John, 104,118 W Wå hlin, 18,27,43,156 Wavelength of particles, 82 Weight, 8,30 Weyl, Herman, 103, Whittaker, 119 Will, 59 Wilson, 16, 51 X-ray, 46 X Z Zero point energy, 46,70 Zwicky, F, 48, 115 ... work on the 10 THE DEADBEAT UNIVERSE Earth's and the planets' motion around the Sun Hooke was convinced that the force holding the planets in their orbits around the Sun was the same as the gravitational... such a fashion that the original center, the center of the primeval explosion, occupies the periphery of the Universe and that the periphery of the Universe is at the center of the expansion This... is obvious that the Earth does not move, neither does it lie anywhere but at the center of the Universe. " The belief that we are at the center of the Universe is shared by many theoreticians even