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Modified Einsteinian Dynamics(MOED): Discovery of a new waveform that unifies Relativity and Q.M. Jason cole [email protected] Abstract There exist a new type of wave that is the key to quantizing relativity. Traditionally when we think of waves we think of 2d sine waves. There exist a higher form of waves called spherehyperboloid waves that has all the wave properties of 2d but in a 3d form. This new waveform is the key to quantizing Relativity, give insight into quantum gravity, expansion of our universe and the flat rotational curve of galaxies. In which Relativity and cosmology is dominated by this new form of sphere-hyperboloid wave mechanics like the quantum world is dominated by wave mechanics. MOED (Modified Einsteinian Dynamics) is expressing Einstein’s Special and General Relativity based on this new type of wave mechanics that is compatible with the wave physics of quantum mechanics. MOED is essentially Quantum Relativity wave mechanics. An experiment is proposed in this paper to test this theory. The applied applications of MOED is condense matter physics because it will allow you to explore different wave pattern phases of matter. 1. Introduction to Q.R. wave mechanics When we think of wave we think of sine waves and the waves associated with quantum mechanics. However, up to this point it didn’t appear if wave mechanics played a role in Einstein’s Special and General Relativity. Relativity and quantum mechanics have been incompatible. With the discovery of this new wave pattern the big and small scale can now use the same type of wave mechanics physics as the basis for unification. MOED(Modified Einsteinian Dynamics) is expressing Einstein’s Special and General Theory of Relativity in terms of a new form of wave mechanics. MOED in a nutshell is quantum Relativity wave mechanics based on the discovery of a new waveform. 2. The discovery that waves can come in two forms: Figure 1. A particle is actually part of a sphere-hyperboloid wave. All we see is the peak(amplitude) of the wave due to constructive interference but the hyperboloid exist as the particle move through space over time. The groundbreaking idea is that the spherical particles we see are actually traversing like a wave. All we see is the peak (spherical particle) but don’t see the hyperboloid trough part. Essentially there is no such thing as particle-wave duality. It is all waves! The spherical particles are actually apart of a sphere hyperboloid waveform. The implications are enormous. As a mass particle move it is actually propagation like a wave (E.g. Electromagnetic wave). The mass particle itself is oscillating between sphere and hyperboloid shapes as it propogate. Just as wave constructive and destructive interference applies to traditional 2d waves so does the spherehyperboloid waves. Also these are fermion waves unlike the boson massless waves. We may be seeing the sphere part of the sphere-hyperboloid due to constructive interference (being in phase). We don’t see the trough part because we are not in phase. The implication of this mass wave propagation implies mass (physics as a whole) is propagating between maximum states and minimum states. Electric field, gravitational field, etc associated with spherical particles represents its maximum field strength energy state. However, as it propagates it has cycles of minimum gravity, electric field strength, etc. along with maximum strength levels. Just as their is a EM spectrum from radio to gamma rays the same applies to the mass sphere-hyperboloid wave spectrum. This new interpretation of oscillating mass changes the makeup of Special and General Relativity The wavelength is the peak (top part of the sphere) to the next peak of the sphere. The figure above is a transverse sphere-hyperboloid wave. A sphere-hyperboloid standing wave would be different because the sphere-hyperboloid will oscillate were the sphere will change into a hyperboloid and hyperboloid will change into a sphere. This can give new insight into the electron standing wave around an atom. An spherical atom orbit it not only can be represented as the traditional 2d wave but now the 3d spherehyperboloid standing wave pattern. Also as atoms move the Spherical nucleus is transforming into a Hyperboloid particle shaped nucleus. Going from spherical to hyperboloid. The following gives an illustration of how the atom and nucleus look in the negative oscillation cycle. As atoms move its geometry is oscillating from spherical and Hyperboloid shapes. Below are classical description of atoms. First show the normal atom based on spherical particles and second show the hyperboloid shaped atom in its negative oscillation we can't see. Figure 2. Image above shows spherical description of the atom in positive oscillation and image below show its negative oscillation. Figure 3 The illustration above is a graphical representation of an atom as it oscillate in negative cycle. The electron may only orbit around the curved side of the hyperboloid and not the open ends On a cosmological scale picture a neutron star. As it moves in time it is oscillating between periods of maximum strength(spherical neutron star) states and minimum strength or negative maximum hyperboloid neutron star states. The sphere particles are the amplitude of the wave. We are only seeing the amplitude. In between sphere and hyperboloid are the equilibrium or rest positions. we are only seeing the crest where it represents the maximum amount of positive or upward displacement. The trough is the maximum amount of negative or downward displacement. I am amusing we can only see the crest(particles) because it has positive values and can’t see the trough because it has negative values. It’s interesting because based on this wave model all we see is the crest. We don’t see the trough part of it. We are in phase with the crest part and not in phase with the trough. It's possible that for each crest(sphere) for this wave model the individual peaks(crest or spheres) can be in phase with other crests(particles) causing us to see it and interact with it. For the trough (hyperboloid) we can't see it or interact with it because we are not in phase with it. In which the individual crests or troughs can be in phase separately with other corresponding crests or trough but not the whole wave with other whole was like Boson EM waves. We only see the positive phase and not the negative phase in sphere-hyperboloid waves. It’s like taking a 2d wave graph and erasing the troughs were you only see the crests not the troughs but you know the troughs must exist, otherwise it couldn’t form waves. From our perspective spherical particles are appearing and disappearing and then reappearing like crests on a wave. We don't see the trough. The frequency of oscillation may happens so fast we don't notice it. The oscillation frequency may be shorter than Planck Time! 3. Special Relativity wave mechanics According to Special Relativity when a object approaches the speed of light, time slows down, length contraction (object becomes thinner) and more massive. This is a perfect analogy to the electromagnetic spectrum. Going from lower to higher wavelength the wavelength becomes shorter and the energy becomes higher. Special Relativity from a wave perspective was doing more than just describing the electrodynamics of moving bodies to describing the electrodynamics spectrum of moving bodies. The following gives the mass spectrum oscillation pattern of particles approaching the speed of light. At light speed time stops but beyond light speed the reverse is taking place. Lorentz transformation stops at 2(c). In reverse lorentz transformation the 2(c) will be the end of transformation because it will be equivalent to v=0 for objects slower than the speed of light. It is the mirror image of objects approaching C. Figure 4. As objects approach the speed of light mass is oscillating like a EM spectrum from radio waves to gamma rays. Beyond c, mass is approaching the speed of light from a different starting point. Just as electromagnetic spectrum oscillates and produces a wave pattern so is mass itself. It’s not the de broglie wavelength but literal the spherical particles are oscillating(waving) between spherical shapes and hyperboloid shapes as it moves through time. Because the figure of above is a perfect correlation of the EM spectrum (2 mirror image EM spectrums), the Special theory of Relativity can be expressed as wave mechanics. Keep in mind these are a new type of Fermion mass wave oscillation and not exactly the same as the Boson EM spectrum wave oscillation waveform. Neither the less, the Special Relativity can be quantized because it shares properties to EM spectrum such as E=hf where there is a planck constant for the electrodynamics spectrum of moving bodies. The following shows acceleration due to gravity in a gravity well. As objects fall it is doing so within maximum and minimum cycles of gravity strength. Figure 5. When objects fall into a black hole they form a gravity well spectrum pattern analogous to EMS spectrum of going from a radio wave to a gamma wave. If the pull of gravity keep going beyond the black hole then it would produce a mirror image gravity well. It would be a mirror image reflection gravity well. Their both approaching the same singularity but from different starting points. That mutual inflection point leads to a new idea. That idea is that the inflection point(black hole) is the ground state for gravity systems. 4. QFT and the ground state of gravity When viewing the mirror image gravity wells it appears that they share a mutual point of inflection. This leads to the idea that the black hole is the ground state for gravity. It may sound counter intuitive but a gravity well in some regards will be a U shape graph similar to the EM field-strength graph. Just as the base of the U shape graph represents the ground state, the bottom of the gravity well represents the ground state for gravity. In some waves it makes sense. If you look at a atom and how the outer wider orbits represents higher energy states the same applies to gravity well concept. Away from the ground gravity state of a black hole space is wider like the wider orbits or space of the atomic orbitals. Based on this concept the physical curvature of spacetime may correlate to the U shape graph of the EM field-strength graph. The dipple in space time is actually the nearest grounds state for gravity. it’s not so much objects are falling in due to inward curvature of space, objects are drawn towards the lowest ground stable state. The gravity well of GR may actually be a macro system for the gravity field-strength like the U shape graph is for the EM field strength. This gives a new definition of gravity where the curvature of spacetime is actually the manifestation of a U shape gravity field-strength model to cause mass to go into it’s lowest ground state. Like the quantum state objects only go into higher energy levels if excited. Otherwise it will naturally tend to go into it’s most stable state. Likewise, the heat causes mass to expand to into higher energy state, but mass will nature go towards it’s lowest and ground energy state. Gravity U shape energy-field strength model that correlate to the U shape EM field strength is a structure picture of quantum gravity. The physical curvature of spacetime is from a quantum mechanical perspective the manifestation of a U shape gravity-field graph model where objects want to go into it’s lowest ground gravity state like quantum mechanical objects. Higher energy states in the U shape gravity field strength model is heat. The absolute ground state of gravity is the black hole. For example as you approach black hole time slows down and eventually stop. Space flows stop. Essentially a black hole is the ground state of gravity. It is a neutral zero state. From a mirror image gravity well the black hole would also be its ground state. The geometry of the ground state would be new also. Just as matter falling into the gravity well has a sphere-hyperboloid wave pattern, when it gets to the singularity point(ground state), the geometry will be neutral like a cylinder. Space flow stop. Because a black hole is at the center of every galaxy the flat rotational curve of the galaxy can be attributed to the cylinder manifold. Space is neither flowing but is at a stand still. Due to frame dragging by the spinning black hole it is causing space itself to rotate like a ferris wheel. Just like the toy animals on the ferris wheel are not moving but the ferris wheel itself that is how the stars are moving. The stars and objects are not flowing or moving but space is. Because the zero state (ground state) can also be represented as two parts (e.g. 2+-2=0) it can have both flowing gravity and backwards flowing gravity cancelling each other out like a subatomic neutron particle has a total electrical neutral charge. The positive matter in the galaxy near the black hole is attracted to the positive part of the ground state and the matter in the mirror image universe is attracted to the backwards flowing gravity. Essentially a galaxy is a structure where the black hole is the ground state of the gravity system. Up and out of the perimeter of the black hole is the higher energy(heat) states. Figure 6. Quantum mechanically what Einstein was describing for gravity was a Gravity fieldenergy(heat) model analogous to a EM field-energy model. The longer the gravity well(from the black hole) the higher the field strength of gravity like the EM field-energy model graph. The ground state of the gravity is a black hole. time stop,Just like water stop flowing space stop flowing. The flat rotational of curve of galaxies can be explained as planets, stars not moving due to the ground state of the black hole but it is space itself moving due to frame dragging by the spinning black hole. Because the ground state can be forward and backwards flowing ground that cancel out, the positive mass in the galaxy is attracted to the positive part of the ground state and spiral in. The backwards part of the ground state is associated with the mirror image gravity well. We see that Einstein’s Special theory of Relativity can be expressed as the “Electrodynamic Spectrum of Moving bodies” rather than Electrodynamics of moving bodies because as mass travels towards C it is doing so like a EM spectrum wave propagation formation. Second, the General Theory of Relativity can be expressed as a quantum mechanical field-energy (heat) U graph for gravity like the U shaped graph for the EM field-energy. In which the literal curvature of spacetime for the gravity system is the literal correlation of the U shape graph for the EM field-energy model. The ground state for gravity is a black hole like the valley of U shape graph for the EM spectrum is the ground state for that graph. The ground state of a black hole is like “Neutral pressure” in the context of Einstein’s Field Equation. It is a composite of compressing pressure and negative pressure resulting in a static holding in place pressure. It is this neutral gravity field that is holding galaxies in place preventing them from flying apart. In which if you expand the pressure state of Einstein’s GR you won’t need Dark Matter nor MOND(Modified Newtonian Dynamics). The two opposing pressures from the mirror image gravity wells meeting at black hole is resulting in an overall neutral pressure. That causes a static gravity field. Imagine the 3 pressure states of GR like orbits. You have orbits that spiral in and spiral out and spiral in a circle(fixed orbit). Einstein’s GR can be expanded to include Neutral pressure, along with Negative and Positive pressure. Because neutral pressure(static gravity) is a composite pressure like a subatomic neutron particle containing both positive and negative charge, the surrounding matter around the black hole is attracted to the positive part of the black hole. The mirror image gravity well is associated with the negative(or reverse) pressure part of the black hole. By defining the black hole as the ground state for gravity can serve as the foundation for a Quantum Field Theory of Gravity. Based on this model one can get quantized states of gravity(geometry of spacetime) like the quantized states of the EM field-energy U graph model. 5. Sine wave model of universe (Quantum cosmology) The universe on a cosmological scale is governed by wave mechanics. A explanation of the missing antimatter is that it formed a different wave formation alongside regular matter. In which it formed a complex conjugate wave universe like the positron is a complex conjugate wave pair of the electron. The overall wave function of antimatter is different from the overall wave pattern of regular matter like the two different wave functions of Paul Dirac equation describing the electron and positron wave function. Just as you have traditional Q.M. 2d waves and spherehyperboloid wave propagation patterns, the overall universe is also waving in a cosmological wave formation pattern. We see from the quantum, Relativistic and cosmological scale that wave mechanics govern the laws of physics. On a cosmological scale it’s not Dark Energy but wave energy. The matter and antimatter universe may be quantum entangled as one overall system. Figure 7. Matter and antimatter universes have different wave functions as complex conjugate pairs like the electron and positron wave function in Paul Dirac wave equation. They are mirror images. Matter and antimatter universe have equal and opposite wave patterns like opposite charges. If you combine the waves they would make a destructive interference pattern. If you plot a complex point and its complex conjugate they would be in different quadrants. Mirror images but different quadrants. Matter and antimatter couldn't have annihilated because they are separated in different quadrants on a coordinate plane. Mirror image wave functions. Each complex conjugate pair wavelength represents a different universe and their can be an infinite number of different wavelengths. it’s not one continuous wave but waves created in parallel like a superposition of many states. The big bangs big crunches are equilibrium or positions of rest between the waving universes. We see quantum mechanical phenomena on a cosmological wave mechanics scale. That is the essence of this Quantum cosmology where the universe can be expressed as wave equations and also be described as E=hf where their is a planck constant for this cosmology wave model system. Aside from the matter-antimatter waving universes it’s possible on the vertical axis that the start and end time of the universes are one and system. It’s atoms are cylinder in shape because time is zero (it’s unchanging with time). There can exist an infinite number of universes on the vertical axis). Normally when we think of a wave we think of one over time were it has a beginning and end. What if the beginning and end were one and the same. Rather than mass waving like sphere-hyperboloid the mass particles would be unchanging with time and have a cylinder shape. The cylinder universes (cylinder atoms) exists on the imaginary axis while the sphere-hyperboloid universe exist on the real axis. The sum of complex products will be a real number but for the cylinder universes it is pure imaginary. The parallel universe model can be viewed as one super universe analogous to individual computers making up a supercomputers. In which the parallel universes operate as one over universe system. It is still one universe but in a supercomputer one universe structure. Based on the matter-antimatter of the universe it’s possible that if objects go FTL it will become antimatter and not Tachyons. In which Antimatter is simply approaching the speed of light from a different starting point. With respect to an observer at light speed their trying at the same speed but from different starting point. Likewise in the big bang, matter and antimatter universe become physically separated and formed mirror image universe wave patterns were they are complex conjugate pair wave universes like in Paul Dirac wave equation of electron and positron complex conjugate wave function. Their is no such thing as Tachyons. What a relief! Keep in mind that the math of Relativity and QM are different. With Relativity if objects travel FTL it is considered imaginary. However, for QM it uses complex coordinate plane where everything is imaginary(complex points) if you take it literally. Tachyon from Relativity is due to a disparity in the mathematics between Relativity and Q.M. Based on this paper if an object goes faster than light it will turn into antimatter and be a mirror image of regular matter. The antimatter is part of an antimatter universe with a mirror wave function like electron-positron are complex conjugate wave pairs. It is a perfect mirror image and the speed of light is the mirror. For example the gravity well has a mirror image gravity well (antimatter will produce regular gravity). It is a reflection of the gravity well much like a person looking into a mirror. In this case the speed of light is the mirror itself between matter and antimatter. Antimatter isn’t actually travel 2(c) and traveling down to see it is a mirror image traveling at the same speed as normal matter but just coming from opposite starting points on the coordinate plane. Just like matter and antimatter annihilate it leads you the idea that they have mirror or opposite wave. If those wave patterns meet they would undergo destructive interference. We don't see anti matter because it has a mirror image sine wave path based on Figure 7. They have a equal and opposite wave pattern like equal opposite charge. When matter and antimatter wave universe recombine in a annihilation big crunch then they will have a destructive interference wave pattern. A possible reason on why we only see spherical particles not the hyperboloid part may be related to the overall crest of the universe. The overall universe is propagating like a wave. Its possible the spherical sub atomic particles are in phase with the spherical crest big bang to big crunch universe. We don't see or experience the hyperboloid part(physics) because it is not in phase with our crest wave universe. However, in the negative cycle of the overall universe the hyperboloid part of the atoms will be in phase with the overall negative trough of the universe based on figure 7. The negative maximum physics of the atoms will be in phased with the negative cycle of the universe and influence its behavior while the spherical crest will be out of phase. If this is true then the antimatter universe is in the negative trough and will exhibit negative maximum hyperboloid physics because it is in phase with the overall negative trough of the antimatter universe causing its physics to be mirror image. The physics will be negative mirror image. Objects are approaching the speed of light from a opposite start point of 2(c) slowing down towards light in reverse physics. An alternative explanation may be put forth such as all spherical particles are created in one cycle and then in the next universe cycle all the hyperboloid particles are created. That would mean the frequencies of the subatomic particles last for the life of the universe. To make one quantum oscillation it would mean it would take 50 billion years(life of the universe) to make the crest of the wave and then in next big bang take the life span of the universe can create the trough. What we've seen with QM waves they oscillate in time very quickly. The particle wave duality shows electron particles are actually part of a Sphere-Hyperboloid wave formation. We only see the sphere part(crest) of the Sphere-Hyperboloid wave. In either case whether a particle oscillate very quickly or takes universe cycles to oscillate it still forms a Sphere-Hyperboloid wave patterns over time. 7. Experimental proof The question is if mass itself is oscillating in shapes between sphere-hyperboloids then why don’t we ever see the hyperboloid? The answer is phase coherence. The spherical (peak waves) reinforce and we see the other peak waves. However, we can’t see or experience the minimum hyperboloid particle physics due to wave decoherence (destructive interference). Also our universe is positively curved and the spherical matter is in phase with the positively curved universe. It's not the the hyperboloid don’t exist it is just were not in phase to experience it. In other words constructive and destructive wave interference still applies to sphere-hyperboloid waves like traditional 2d wave physics. Even though mass (physics as a whole) is waving through cycles of maximum strength and minimum strength we only experience and see the physics of the maximum (spherical) part of the wave due to constructive interference. The only way to experience the minimum physics of the universe(e.g. minimum gravity strength) is by being in phase with the hyperboloid part of mass. You will need to be in phase and when you do you’ll reinforce and be able to experience the minimum phase state of the universe. The same applies to the ground state were if you can cause the maximum and minimum wave state to destroy each other like wave destructive interference then you would be able to experience the ground state physics of the universe(e.g. space stop flowing, zero inertia, zero gravity field were not lorentz transformations due to acceleration). It's a new and weird concept but keep in mind that the sphere-hyperboloid wave operate under similar type of wave interference patterns like traditional 2d waves. Like the difference interference patterns you can be in phase with peak waves if you have similar wave structure or in phase with trough waves if you have trough waves or have a destructive ground state wave if you can be in phase with it. If all the mass in the universe is oscillating between maximum and minimum states like a wave then the minimum state of the universe must be prove. For example gravity is actually going through maximum and minimum state. The gravity field we see and experience is the maximum state of gravity but over time as mass move gravity goes through minimum state. It is due to wave interference as to why we only see and feel the maximum peak (sphere) part of wave mass and not the trough hyperboloid shape. Electromagnetic experiment The following shows different dipole pairs to enable you to be in phase with the different states of the universe to being in phase with it’s unique physics. Figure 8. Above are the 3 types of dipole configurations coinciding with the 3 phases of the universe. Sphere-Sphere is the maximum(normal phase). Sphere-Hyperboloid is the ground state destructive interference phase and the Hyperboloid-Hyperboloid is the minimum phase of the universe. Each phase has different physics states of our universe. A. Traditional EM radiation with the spherical dipoles causes you to be in phase with the normal universe. That is the maximum strength(positive maximum) side of the universe B. Theoretically if you have hyperboloid shape dipole it will oscillate and put whatever's in the vicinity of the radiation within the emission to cause it to become in phase with the minimum (negative maximum) matter physics of the universe. Like wave interference the hyperboloid emission is enabling you to become in phase with the minimum state(negative maximum) of the universe. You can orient the dipole vertically or horizontally. Experimentation is needed to determine correct orientation. C. A hybrid dipole pair consisting of a sphere-hyperboloid will have a destructive interference pattern that will cause you to be in phase with the destructive phase ground state of the universe. D. It comes down to phase interference. The difference dipole configuration emissions is intended to enable you to be in the minimum phase or destructive interference (ground state) phase of the universe. The EM radiation from the dipole doesn’t have any new physics. It is enabling you to be in phase with the minimum phase(e.g. minimum gravity or negative maximum gravity) or ground phase state(e.g. neutral static gravity were no inertia from acceleration) of the universe to access it’s unique physics state for new technological applications. For propulsion EM magnets can be placed around the dipole for a control system. E. A main different between Sphere-Hyperboloid waves to traditional waves is that the individual crests(spherical particles) can reinforce with other spherical particles but not the entire Sphere-Hyperboloid wave like in classical two dimensional waves were the entire wave has either constructive interference or destructive interference. Likewise, the Hyperboloid trough can only be in phase with the troughs of other hyperboloid particles. In each case the individual maximum or minimal states would be constructive interference and not the entire Sphere-Hyperboloid waveform as a whole as in classical 2d waves. It appears a sphere crest particle would have destructive interference with a hyperboloid particle making a ground state. The individual crest particle wouldn't feel the effects of minimum phase or ground destructive interference phase because it can only experience maximum phases. F. The following gives another example of the interference patterns of the spherehyperboloid waves in 2d representation. It’s a weird concept to think of particle spheres as literal waves but the sphere-hyperboloid has all the type of wave interference properties as traditional 2d waves. Figure 9. Above is a reminder that the sphere-hyperboloid waves are waves like 2d waves and subject to same type of interference patterns. It's possible that fermion and Boson Sphere-Hyperboloid waves behave differently. 8. New condense matter physics We see that matter can come in three different phases: spherical particle phase, Hyperboloid phase and ground state phase. The EM dipole configuration will enable you to be in phase with the different matter wave states to explore new technological applications. 9. Conclusion MOED(Modified Einsteinian Dynamics) in a nutshell is expressing Einstein’s theory of Relativity in wave mechanics language based on the newly discovered sphere-hyperboloid waveform.It shows that on the quantum and Relativitic scale everything is covered by wave mechanics in some form. Whether it’s the traditional wave functions of Quantum Mechanics of the Sphere-Hyperboloid wave function of Quantum Relativity. It’s amazing to know that mass and physics as a whole is waving through periods of maximum states and minimum states. Through EM experimentation it’s possible to become in phase with minimum or ground wave state of our universe to experience the unique physics associated with that state. In which the EM dipole configurations in itself isn’t doing anything new. What it is doing is enabling you to be in phase with the minimum or ground wave state of the universe(constructive wave interference) to access the corresponding unique physics along with that state for new technological applications. The dipole are like keys to the car enabling you to be in phase with the minimum(negative maximum) and ground state phase (physics) of the universe for new technological applications. This is like a new form of condense matter physics where it is allowing us through EM radiation(dipole) to be in phase with the negative maximum or ground state of matter. References 1. Einstein A. (1916), Relativity: The Special and General Theory (Translation 1920), New York: H. Holt and Company 2. Jump up^ Planck, Max (1906), "Die Kaufmannschen Messungen der Ablenkbarkeit der βStrahlen in ihrer Bedeutung für die Dynamik der Elektronen (The Measurements of Kaufmann on the Deflectability of β-Rays in their Importance for the Dynamics of the Electrons)",Physikalische Zeitschrift 7: 753–761 3. Jump up^ Miller, Arthur I. (1981), Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911), Reading: Addison–Wesley, ISBN 0-201-04679-2 4. Jump up to: a b Einstein, Albert (November 28, 1919). "Time, Space, and Gravitation". The Times. 5. Jump up^ Greene, Brian. "The Theory of Relativity, Then and Now". Retrieved 2015-09-26. 6. Jason Cole. The Imaginary Mass Lambda-CDM Model. American Journal of Modern Physics. Vol. 5, No. 1, 2016, pp. 1-14. doi:10.11648/j.ajmp.20160501.11 7. Jason Cole. Modified Einsteinian Dynamics (Moed) Cosmology: Expanding GR to Include Neutral Pressure to Explain Dark Matter.viXra:1602.0111 8. Jason Cole. Modified Einsteinian Dynamics (MOED).viXra:1602.0103