icarus2

Dear pantheory, I’m very sorry. I apologize for my poor English. My assertion is that 1. Space does not expand. (I agree that Universe is expanding.) 2. Hubble's law is a dynamical result from the movement of galaxies in space. 3. [math]R = \frac{1}{z}[/math] is derived from assumption that space is expanding. R=1/(1+z) is wrong because of that space does not expand. But, two equations show similar results in close galaxies(z<2). ... --Icarus2

Hello! I apologize for my poor English. New proof of Hubble's law. Is space really expand? ---------------- I. Introduction ~~~~ 3. We have never observed the expansion of space. 4. Expansion of the universe and expansion of space are not the same concept. The fact that the universe expands shows that distance between galaxies become further. This can be explained from the expansion of space between galaxies, but this can be explained even when galaxies have +r direction initial speed in condition where space doesn't expand. II. Proof of Hubble's law through dynamics 1. After accelerating expansion(such as inflation) of early universe has almost finished, particles started to have some velocity. This velocity distribution naturally has higher velocity when it is further away from the center of the universe and has lower velocity when it is closer to the center. A. Big bang simulation in the zero energy universe [Video for Big bang Simulation] Fig.1.Velocity distribution of galaxies at early universe. Red arrows show the velocity vector of particles. It can be known that the magnitude of velocity vector is bigger as it become further from the center. Even if the velocity of particles is zero in the early universe, there are particles with higher velocity in further areas from the center and particles close to the center have relatively low velocity by inflation. When positive mass gravitationally contracts to form a galaxy, momentum must be conserved, so higher initial velocity continues to exist as it becomes further away from the center of universe. B. Natural distribution of velocity in the 3D space Thinking in another way, 3 dimensional space can be divided into 3 areas (from the center) to far, middle, and close area. Even if the velocity of the far area is lower than the middle area, middle area particles exceed far area particles when time passes because the velocity of middle particles are higher. As a result, velocity distribution of particles shows that the velocity of far areas is highest, middle area is second, and the close area becomes third. C. Velocity distribution when some kind of anti-gravitational source exists If some kind of anti-gravitational source in 3 dimension exists, M exists with even density, the above velocity distribution can exist. [math]m\vec a = + \frac{{G(\frac{{4\pi }}{3}r^3 \rho )m}}{{r^2 }}\hat r[/math] [math]\vec a = + \frac{{4\pi G}}{3}\rho r\hat r[/math] If anti-gravitational source is evenly distributed in accelerating expansion time like the inflation of early universe, a bigger acceleration a exists as r becomes larger and velocity distribution has a higher velocity as the radius of the universe becomes larger. As a result, higher velocity exists for particles of far area from the center of the universe after inflation ends. The 3 explanations shown above mean that higher velocity for larger R(distance from the center of universe) after inflation in the early universe isn't a peculiar phenomenon. If speed in small area in the early universe distributes from 0 to c and if some time passes, velocity distribution will be in order as above. 2. Derivation of Hubble's law in space without expansion A. Decelerating expansion time First to look into the possibility of this model, let's look into the case in which the direction of Va1 and Vb1 is the same. Va1 = Va0 + ( - a1t1 ) Vb1 = Vb0 + ( - a1t1 ) Va0, Vb0: It is the speed in which A and B galaxy has when inflation ends. - a1: It is the acceleration of decelerating expansion because decelerating expansion seems to have taken place in the early universe. It is actually a function of time. To make the problem simple, we plan to solve the problem making it as a constant. t1 : Total time of universe decelerating expansion. [math]R_{a1} = R_{a0} + V_{a0} t_1 - \frac{1}{2}a_1 t_1 ^2[/math] [math]R_{b1} = R_{b0} + V_{b0} t_1 - \frac{1}{2}a_1 t_1 ^2 [/math] The above equations are equations of speed and distance when acceleration is constant. B. Accelerating expansion time After decelerating expansion ends, there was a time of accelerating expansion. Acceleration is given as a2 this time and the duration time is set as t2. [math]V_{an} = V_{a1} + a_2 t_2 = (V_{a0} - a_1 t_1 ) + a_2 t_2 [/math] [math]V_{bn} = V_{b1} + a_2 t_2 = (V_{b0} - a_1 t_1 ) + a_2 t_2 [/math] [Van,Vbn is the now speed of galaxy a and galaxy b. [math]R_{an} = R_{a1} + V_{a1} t_2 + \frac{1}{2}a_2 t_2 ^2 = R_{a0} + (V_{a0} t_1 - \frac{1}{2}a_1 t_1 ^2 ) + (V_{a0} - a_1 t_1 )t_2 + \frac{1}{2}a_2 t_2 ^2[/math] [math] = R_{a0} + V_{a0} (t_1 + t_2 ) - a_1 t_1 t_2 - \frac{1}{2}a_1 t_1 ^2 + \frac{1}{2}a_2 t_2 ^2[/math] [math]R_{bn} = R_{b0} + V_{b1} t_2 + \frac{1}{2}a_2 t_2 ^2 = R_{b0} + (V_{b0} t_1 - \frac{1}{2}a_1 t_1 ^2 ) + (V_{b0} - a_1 t_1 )t_2 + \frac{1}{2}a_2 t_2 ^2[/math] [math] = R_{b0} + V_{b0} (t_1 + t_2 ) - a_1 t_1 t_2 - \frac{1}{2}a_1 t_1 ^2 + \frac{1}{2}a_2 t_2 ^2[/math] C. Deriving Hubble's law (when direction is the same) [math]V_{rel} = V_{bn} - V_{an}[/math] is the relative speed of galaxy a and galaxy b. [math]V_{rel} = V_{bn} - V_{an} = (V_{b0} - a_1 t_1 ) + a_2 t_2 - (V_{a0} - a_1 t_1 ) - a_2 t_2 = V_{b0} - V_{a0}[/math] [math]R_{rel} = R_{bn} - R_{an} = R_{b0} + V_{b0} (t_1 + t_2 ) - a_1 t_1 t_2 - \frac{1}{2}a_1 t_1 ^2 + \frac{1}{2}a_2 t_2 ^2 - [R_{a0} + V_{a0} (t_1 + t_2 ) - a_1 t_1 t_2 - \frac{1}{2}a_1 t_1 ^2 + \frac{1}{2}a_2 t_2 ^2 ][/math] [math]R_{rel} = (R_{b0} - R_{a0} ) + (V_{b0} - V_{a0} )(t_1 + t_2 ) \cong (V_{b0} - V_{a0} )t[/math] Because the galaxies or particles in the early universe were concentrated in a very close distance, it can be set as [math](R_{b0} - R_{a0} ) = 0[/math] [math]t = t_1 + t_2[/math] This is the age of the universe. Deriving the relation between Vrel and Rrel, [math]V_{rel} = V_{bn} - V_{an} = V_{b0} - V_{a0} = \frac{1}{t}R_{rel} = HR_{rel}[/math] It can be known that Hubble's law comes out. Especially, the Hubble constant is H=1/t and this is a result that the Hubble constant in Hubble's law corresponds to the reciprocal of the age of universe. Considering decelerating expansion and accelerating expansion and movement of relative particles, the actual age of the universe is 0.993tH. It is very close to 1. Therefore, the above model contains simple equation, but has possibility. Thus, the recession velocity and Hubble's law between galaxies don't come from some vague concept (unknown concept without empirical experience) of "expansion of space" and shows possibility that it comes from a simple movement equation called [math]R = V_0 t + \int {\int {a(t)d^2t} }[/math] In [math]R = V_0 t + \int {\int {a(t)d^2t} }[/math], if a(t)(acceleration) is small, this is because a [math]V_{rel} = \frac{1}{t}R_{rel} = HR_{rel}[/math] shape Hubble's law comes out. D. The observation of "all galaxies become further from us and all galaxies have recession velocity from Hubble's law" isn't from the expansion of space, it is result of dynamics that galaxies show. Fig.2.Hubble's observation of all galaxies receding with Earth in the center It is assumed that interpretation issues of observation results above applied most in physicists and astronomers introducing expansion of space. When observed from Earth, it is observed that all galaxies recede from Earth and the recession velocity also follow all relations of [math]\vec V = H\vec R[/math]. To explain this, if position of the Earth is the center of expansion, namely if position of the Earth is the center of universe, this issue can be simply solved but it can be clearly known that Earth isn't the center of the universe from the observation of the universe until now. It is because Earth isn't the center of the solar system, but is clear to be just a planet and that the solar system isn't the center of the galactic system either. Therefore, physicists and astronomers had to find a way to explain this and as this couldn't be explained by dynamics, a new concept that "space expands" was introduced. To explain more specifically, it is assumed that the stereotype that Hubble's observation isn't valid in places where isn't the center of expansion had influence. [ Derivation of Hubble's law ] Fig.3. Hubble's law doesn't result from the expansion of space, but is a dynamical result from the movement of galaxies in space. Set as [math]|\vec a_{E1} | = |\vec a_{\alpha 1} | = |\vec a_{\beta 1} | = |\vec a_{r1} | = |\vec a_{\delta 1} | = a_1[/math][math]|\vec a_{E2} | = |\vec a_{\alpha 2} | = |\vec a_{\beta 2} | = |\vec a_{\gamma 2} | = |\vec a_{\delta 2} | = a_2[/math] [math]\vec V_{E1} = \vec V_{E0} - \vec a_{E1} t_1[/math] [math]\vec V_{\alpha 1} = \vec V_{\alpha 0} - \vec a_{\alpha 1} t_1[/math] [math]\vec V_{En} = \vec V_{E1} + \vec a_{E2} t_2 = (\vec V_{E0} - \vec a_{E1} t_1 ) + \vec a_{E2} t_2 = ((V_{E0} - a_1 t_1 ) + a_2 t_2 )\hat x[/math] Set as x-axis. [math]\vec V_{\alpha n} = \vec V_{\alpha 1} + \vec a_{\alpha 2} t_2 = (\vec V_{\alpha 0} - \vec a_{\alpha 1} t_1 ) + \vec a_{\alpha 2} t_2[/math] [math]= (V_{\alpha 0} - a_{\alpha 1} t_1 + a_{\alpha 2} t_2 )\cos \theta \hat x + (V_{\alpha 0} - a_{\alpha 1} t_1 + a_{\alpha 2} t_2 )\sin \theta \hat y [/math] [math]= (V_{\alpha 0} - a_1 t_1 + a_2 t_2 )\cos \theta \hat x + (V_{\alpha 0} - a_1 t_1 + a_2 t_2 )\sin \theta \hat y [/math] [math]\vec R_{En} = \vec R_{E1} + \vec V_{E1} t_2 + \frac{1}{2}\vec a_{E2} t_2 ^2 = (\vec V_{E0} t_1 - \frac{1}{2}\vec a_{E1} t_1 ^2 ) + (\vec V_{E0} - \vec a_{E1} t_1 )t_2 + \frac{1}{2}\vec a_{E2} t_2 ^2[/math] [math]= (t_1 + t_2 )\vec V_{E0} - t_1 t_2 \vec a_{E1} - \frac{1}{2}t_1 ^2 \vec a_{E1} + \frac{1}{2}t_2 ^2 \vec a_{E2}[/math] [math]\vec R_{En} = [(t_1 + t_2 )V_{E0} - t_1 t_2 a_1 - \frac{1}{2}t_1 ^2 a_1 + \frac{1}{2}t_2 ^2 a_2 ]\hat x[/math] [math] \vec R_{\alpha n} = \vec R_{\alpha 1} + \vec V_{\alpha 1} t_2 + \frac{1}{2}\vec a_{\alpha 2} t_2 ^2 = (\vec V_{\alpha 0} t_1 - \frac{1}{2}\vec a_{\alpha 1} t_1 ^2 ) + (\vec V_{\alpha 0} - \vec a_{\alpha 1} t_1 )t_2 + \frac{1}{2}\vec a_{\alpha 2} t_2 ^2[/math] [math] = (t_1 + t_2 )\vec V_{\alpha 0} - t_1 t_2 \vec a_{\alpha 1} - \frac{1}{2}t_1 ^2 \vec a_{\alpha 1} + \frac{1}{2}t_2 ^2 \vec a_{\alpha 2} [/math] [math] \vec R_{\alpha n} = [(t_1 + t_2 )V_{\alpha 0} - t_1 t_2 a_1 - \frac{1}{2}t_1 ^2 a_1 + \frac{1}{2}t_2 ^2 a_2 ]\cos \theta \hat x + [(t_1 + t_2 )V_{\alpha 0} - t_1 t_2 a_1 - \frac{1}{2}t_1 ^2 a_1 + \frac{1}{2}t_2 ^2 a_2 ]\sin \theta \hat y[/math] [ Relative Velocity ] [math]\vec V_{rel} = \vec V_{\alpha n} - \vec V_{En} = [(V_{\alpha 0} \cos \theta - V_{E0} ) + ( - a_1 t_1 + a_2 t_2 )(\cos \theta - 1)]\hat x + (V_{\alpha 0} - a_1 t_1 + a_2 t_2 )\sin \theta \hat y[/math] [ Relative Distance ] [math]\vec R_{rel} = t\{ [(V_{\alpha 0} \cos \theta - V_{E0} ) + \frac{1}{t}( - t_1 t_2 a_1 - \frac{1}{2}t_1 ^2 a_1 + \frac{1}{2}t_2 ^2 a_2 )(\cos \theta - 1)]\hat x[/math] [math]+ [V_{\alpha 0} + \frac{1}{t}( - t_1 t_2 a_1 - \frac{1}{2}t_1 ^2 a_1 + \frac{1}{2}t_2 ^2 a_2 )]\sin \theta \hat y\}[/math] 1) When Θ is zero. [math]\vec V_{rel} = (V_{\alpha 0} - V_{E0} )\hat x[/math] [math]\vec R_{rel} = t(V_{\alpha 0} - V_{E0} )\hat x[/math] [math]\vec V_{rel} = \frac{1}{t}\vec R_{rel} = H\vec R_{rel} [/math] Therefore, Hubble's law is valid. 2) When Θ is small. [math]\vec V_{rel} \simeq (V_{\alpha 0} - V_{E0} )\hat x + (V_{\alpha 0} - a_1 t_1 + a_2 t_2 )\theta \hat y[/math] [math]\vec R_{rel} \simeq t\{ [(V_{\alpha 0} - V_{E0} )\hat x + [V_{\alpha 0} + \frac{1}{t}( - t_1 t_2 a_1 - \frac{1}{2}t_1 ^2 a_1 + \frac{1}{2}t_2 ^2 a_2 )]\theta \hat y\}[/math] Hubble's law is valid for the 2 following cases. i) VE0,Vα0 >> -a1t1 + a2t2 :When initial speed is much larger than speed change by deceleration and acceleration : * Because there is high possibility that there was a time of inflation of the early universe, particles gained high speed after inflation and the galaxy composed by these particles also had high speed, so the above supposition has validity. * -a1t1 + a2t2 ~ 0 : When the effects of deceleration and acceleration are offset by each other ========== Considering decelerating expansion and accelerating expansion and movement of relative particles, the actual age of the universe is 0.993tH. It is very close to 1. Namely, our universe has a state of -a1t1 + a2t2 ~ 0 ========== **Ref : Bradley W. Carroll, Dale A. Ostlie. Introduction to Modern Astrophysics. ** * Zero Energy Universe : In principle, the total energy is zero. So deceleration and acceleration terms are small. [math]\vec V_{rel} \simeq (V_{\alpha 0} - V_{E0} )\hat x + V_{\alpha 0} \theta \hat y[/math] [math]\vec R_{rel} \simeq t[(V_{\alpha 0} - V_{E0} )\hat x + V_{\alpha 0} \theta \hat y][/math] [math]\vec V_{rel} = \frac{1}{t}\vec R_{rel} = H\vec R_{rel}[/math] Therefore, Hubble's law is valid. ii) Hubble's law is valid in t1 = t2 ,a1 = 3a2 condition. Because the term of decelerating expansion and accelerating expansion is almost similar from the current observation, it can be set as t1 = t2. [math]\vec V_{rel} \simeq[(V_{\alpha 0} (1 - \frac{{\theta ^2 }}{2}) - V_{E0} ) + a_2 t_2 \theta ^2 ]\hat x + (V_{\alpha 0} - 2a_2 t_2 )\theta \hat y[/math] [math]\vec R_{rel} \simeq t\{ [(V_{\alpha 0} (1 - \frac{{\theta ^2 }}{2}) - V_{E0} ) + a_2 t_2 \theta ^2 ]\hat x + (V_{\alpha 0} - 2a_2 t_2 )\theta \hat y\}[/math] [math]\vec V_{rel} = \frac{1}{t}\vec R_{rel} = H\vec R_{rel}[/math] Therefore, Hubble's law is valid. 3) When Θ is big. [math]\vec V_{rel} = [(V_{\alpha 0} \cos \theta - V_{E0} ) + ( - a_1 t_1 + a_2 t_2 )(\cos \theta - 1)]\hat x + (V_{\alpha 0} - a_1 t_1 + a_2 t_2 )\sin \theta \hat y[/math] [math]\vec R_{rel} = t\{ [(V_{\alpha 0} \cos \theta - V_{E0} ) + \frac{1}{t}( - t_1 t_2 a_1 - \frac{1}{2}t_1 ^2 a_1 + \frac{1}{2}t_2 ^2 a_2 )(\cos \theta - 1)]\hat x + [V_{\alpha 0} + \frac{1}{t}( - t_1 t_2 a_1 - \frac{1}{2}t_1 ^2 a_1 + \frac{1}{2}t_2 ^2 a_2 )]\sin \theta \hat y\}[/math] i) VE0,Vα0 >> -a1t1 + a2t2 [math]\vec V_{rel} \simeq (V_{\alpha 0} \cos \theta - V_{E0} )\hat x + V_{\alpha 0} \sin \theta \hat y[/math] [math]\vec R_{rel} \simeq t[(V_{\alpha 0} \cos \theta - V_{E0} )\hat x + V_{\alpha 0} \sin \theta \hat y][/math] [math]\vec V_{rel} = \frac{1}{t}\vec R_{rel} = H\vec R_{rel}[/math] Therefore, Hubble's law is valid. When initial speed is much larger than velocity change from deceleration and acceleration, Hubble's law is valid is a very wide area. Also this initial speed is the velocity gained from the inflation process. ii) If t1 = t2 ,a1 = 3a2 [math]\vec V_{rel} = [(V_{\alpha 0} \cos \theta - V_{E0} ) - 2a_2 t_2 (\cos \theta - 1)]\hat x + (V_{\alpha 0} - a_2 t_2 )\sin \theta \hat y[/math] [math]\vec R_{rel}= t\{ [(V_{\alpha 0} \cos \theta - V_{E0} ) - 2a_2 t_2 (\cos \theta - 1)]\hat x + (V_{\alpha 0} - 2a_2 t_2 )\sin \theta \hat y\}[/math] [math]\vec V_{rel} = \frac{1}{t}\vec R_{rel} = H\vec R_{rel}[/math] Therefore, Hubble's law is valid. E. Direct meaning of proof 1) Hubble's law is valid is a very wide area in 3 dimensional space when the initial speed of galaxies is much larger than the velocity change by deceleration and acceleration (in the same meaning, when velocity change by deceleration and acceleration is smaller compared to initial speed). 2) Even though initial velocity isn't much bigger than the effect by deceleration and acceleration, Hubble's law can be valid in some specific condition. For example, t1 = t2 ,a1 = 3a2 3) Even though Earth isn't the center of the universe, the belief(something not experienced such as "expansion of space”) isn't necessarily needed to explain the reason all galaxies recede from Earth. III. Meaning including proof Hubble's law isn't a matter only explained by special condition such as "center of the universe" or a new concept that we haven't experienced such as "expansion of space." Hubble's law is a result of dynamics valid in almost all areas when change of acceleration is small in the universe. 1. Even if -a1(t) and + a2(t) is a function of time, Hubble's law is always valid when the effect of decelerating expansion and accelerating expansion is smaller than initial velocity. To derive the Hubble's law, we presumed decelerating expansion in the early term and accelerating expansion of the later term. -a1 and +a2 was set as a constant in this process. However, more closely speaking, -a1 and +a2 is a function of time. Fig.4. Hubble's law is a dynamical result from the movement of galaxies in 3D space. Two situations are same. 4. Therefore, red shift comes from the Doppler shift of light and implies that the existing equation of red shift should be revised. Existing equation : [math]z = \frac{{R_{obs} }}{{R_{emitted} }} - 1[/math] R is scale factor. Doppler shift :[math] z = \sqrt {\frac{{1 + \frac{V}{c}}}{{1 - \frac{V}{c}}}} - 1[/math] The two equations show similar results in close galaxies(z<2), but show difference in far galaxies. In condition of z<2, difference of distance <5%. By the way, distance in z=2 is over 11Gly. ** Maybe, this result derived from the model [math]\Lambda=0[/math] ** **Ref : Bradley W. Carroll, Dale A. Ostlie. Introduction to Modern Astrophysics. ** When we did not have verifiable ability about two models, we decided the final model. Because of the fixed idea that Hubble's observation isn't valid in places where isn't the center of expansion. Therefore, should be given the opportunity of review to non-expandsion model of space(or the movement of galaxies through space). On Inflation - expansion faster than light To explain the flatness and horizon problem, expansion faster than light (inflation) was assumed. However, positive energy and negative energy are cancelled in the zero energy universe. So zero energy universe is flat. Therefore to explain flatness, there is no need to assume expansion faster than light. The horizon problem occurs from the wrong Hubble radius which is derived from the assumption that space expands. If particles don't have velocity faster than light, all areas in the early universe will be inside the area of light(radiation) and are all causally connected. Therefore, thermal equilibrium takes place. We don’t know(or observe) velocity of distant galaxy. We observed only redshift and then, we estimate the scale factor, velocity, distance…. Key point of problem, [math]R = \frac{1}{{z + 1}}[/math], it is derived from assumption that space is expanding. (R is scale factor) If space does not expand, R=1/(1+z) is wrong. Therefore, existing velocity and distance derived from redshift eq. are also wrong. In my opinion, Horizon problem doesn't occur and expansion faster than light isn't needed. Space doesn't expand. New proof of Hubble's law and Center of the universe http://vixra.org/abs/1203.0044

Almost Yes! Simulation program made by other person. As examined with Newton dynamics of negative mass, attraction works between positive mass, and they have attractive effect, so they gradually clusters each other, and then make massive mass like planet or star. On the other hand, attraction works between negative mass, but they have repulsive effect, so they cannot make massive mass structure like star or galaxy. Negative masses will be distributed all over space because it cannot form large mass structures like stars. Negative mass within the galaxy is cancelled out by attraction from large positive mass during the galaxy formation process. Furthermore, the space, other that the galaxy, will maintain the distribution state of negative mass. **Characteristics of the negative mass **Centripetal force effect in the galaxy from dark matter(negative mass) halo out of the galaxy http://www.bautforum.com/showthread.php/105870-Video-of-the-motion-of-negative-mass-dark-matter-dark-energy?p=1765927#post1765927

Hello, I'm soorry. I can't English well. Refer to abstract [Abstract] Gravity is the force conquering the structure of the universe. By recognizing the components of the universe, we are estimating the quantity of components composing the universe through size of gravity and gravitational potential energy (GPE). In this paper, it is being shown that the universe can be born and expanded through pair creation of positive energy (mass) and negative energy (mass) from zero energy condition. Also, GPE is composed by 3 units of U++, U--, and U-+ when negative and positive energy exists, U-+ (GPE between negative mass and positive mass) has positive values and is the component that makes repulsive gravitational effect. U-+ corresponds with the inner energy of the system and can be interpreted as dark energy. Also, situations in which U-+ has much higher value than |U--| + |U++| depending on the distribution of negative mass and positive mass is possible. This doesn't mean that 72.1% of dark energy independently exists, but means that explanation from GPE occurring from 4.6% of negative energy, which is the same as 4.6% of positive energy, is possible. Moreover, 4.6% of negative energy is the energy which is inevitably required from zero energy, which is the most natural total energy value in the universe. This discovery implies that our belief that size of gravitational effect and size of components of the universe would always 1:1 correspond was wrong. We set up each model from the birth of universe to the present, and calculated GPE using computer simulation in each level. As a result, we could verify that “pair creation model of negative mass and positive mass” explains inflation of the early universe and decelerating expansion, and present accelerating expansion in time series. ---Icarus2

I apologize for my poor English. I had a new computer simulation. We set up each model from the birth of universe to the present, and calculated GPE using computer simulation in each level. As a result, we could verify that “pair creation model of negative mass and positive mass” explains inflation of the early universe and decelerating expansion, and present accelerating expansion in time series. This simulation is showing incredible results. It not only explains the total energy of the universe, flatness, and the essence (Total zero energy, pair creation of negative energy and positive energy) of the process of birth of the universe, but it explains inflation, decelerating expansion in the early stage, accelerating expansion in the late stage, and dark matter through the only term, negative energy. Moreover, this negative energy is one that is essentially required by the law of energy conservation. Please see to below link! Simulation 1. Dark energy - Accelerating expansion of distant galaxy due to negative mass Simulation 2. Inflation, decelerating expansion and accelerating expansion with pair creation of negative mass and positive mass 3. Paper: The change of Gravitational Potential Energy and Dark Energy in the Zero Energy Universe. http://vixra.org/abs/1110.0019 A. Birth of the universe from zero energy state 1) computer simulation Fig14. m+=+1 (1,000ea), -m-=-1 (1,000ea), U++ = -5190.4707907, U-- = -5308.0373689, U-+= 10499.2712222, U_tot = 0.7630625 Total rest mass energy is zero. Total gravitational potential energy ([math]U_{tot}[/math]) is +0.763. [math]|\frac{{U_{tot} }}{{U_{ - + } }}| = 0.0000726[/math], so [math]U_{tot}[/math] is almost zero. We could not make GPE 0 for there were too many particles. Therefore, we simulated dividing the value of [math]U_{tot}[/math] (total GPE) into two parts which are when it is little bit bigger than 0 (+0.76306) and when smaller than 0 (-0.53277), and we could gain almost similar results. (Attached 1, 2) 2) Accelerating expansion of the universe (inflation) It can be confirmed that even though the total energy starts with 0, the universe expands and positive masses combine one another due to attractive interaction among themselves, while negative masses can not form massive mass structure because of repulsive interaction. The pair creation model of negative mass and positive mass explains “energy conservation” in times of the birth of the universe and “expansion after the birth” naturally, and it does not need institution of new mechanism or field like inflaton or inflation itself, and it explains this effect with only gravity. 3) Change of GPE Figure15-a.The ratio of negative GPE to positive GPE of the early universe. We can confirm that as the universe expands, (+GPE/-GPE) ratio decreases, and [math]U_{tot}[/math] gets to be negative value. Figure15-b. Total GPE of the early universe. Figure15-c. [math]U_{tot}[/math] of the early universe and GPE related with positive mass. It looks almost like a straight line for the size of [math]U_{tot}[/math] is relatively small. The graph above is that the change of GPE related with positive mass and [math]U_{tot}[/math] drawn through graph. As we have observed activities of only positive masses, “GPE related with positive mass ([math]U_{-+} + U_{++}[/math])” has a significant meaning. a) Nevertheless the value of [math]U_{tot}[/math] changes from 0 to negative value, the universe expands for GPE related with positive mass has + value. b) Note that nevertheless the total energy is 0, GPE related with positive mass has very big positive value, and this value approaches to 0 very rapidly. This explains the dramatic expansion like the early universe inflation and the finish of this inflation mechanism. c) The thing we can notice by this and the next simulation is that if time goes bit more, [math]U_{tot}[/math] and GPE related with positive mass both have negative values, and the universe is converted to the decelerating expansion stage. d) In order to explain the flatness of the universe, typical researchers assume the inflation mechanism and explain it using this. But Zero Energy Universe does not need institution of new field for it guarantees flatness itself, and additionally, the simulation above means that the accelerating expansion of the early universe can be explained with gravity without instituting new field. 4) Change of GPE related with positive mass and [math]U_{tot}[/math] in three initial value Fig16-a. Total rest mass energy=0, [math]U_{tot}[/math](initial value)= +51.79 / +0.76 / -0.53. Time scale=0.5, Step scale(+51.79,-0.53)=200, Step scale(+0.76)=250, Fig16-b. Change of GPE related with positive mass in three cases GPE related with positive mass has very big positive value, and this value approaches to 0 very rapidly. B. GPE among distant galaxies and accelerating expansion 1) When positive mass is spread through relatively large area Fig17.Distant galaxy – The structure that negative mass surrounds galaxy composed of positive mass. [math]m_+[/math] = (1 X 500) + (1 X 500) = + 1000, center1(-1000,0,0), center2(+1000,0,0), R=150, [math]-m_-[/math] = (-1 X 500) +(-1 X 500) = - 1000, negative mass distribution : [math]- 250 \le (x \pm 1000),y,z \le + 250[/math]. We simulated having it has unit mass of positive mass and negative mass. After the birth of the universe, positive masses bind together by attractive interaction. Meanwhile, negative masses are being almost uniformly distributed because of repulsive interaction. Negative masses are gravitational bounded to massive positive masses (Galaxy or Galaxy cluster) for massive positive mass has attractive effect on negative mass. Figure18-a.The ratio of +GPE to –GPE of distant galaxy. Figure18-b. [math]U_{tot}[/math] and GPE related with positive mass on distant galaxy. Note that GPE value related with positive mass changes from positive value to negative value, and to positive value again. This represents acceleration expansion [math]->[/math] deceleration expansion [math]->[/math] acceleration expansion of the universe. a) The ratio of +GPE to –GPE of distant galaxy i) Early status is that positive GPE is smaller than negative GPE, and the [math]U_{tot}[/math] has negative value. This negative GPE status results from gravitational binding of positive masses. ii) As time goes by, binding of positive mass increases due to attractive interaction, and the absolute value of negative gravity potential reaches maximum. iii) The absolute value of negative GPE decreases due to positive mass has a gravitational binding and negative mass does gravitational contraction and [math]U_{tot}[/math] is converted to positive value as a result. Center of gravitational contraction of negative masses is galaxy or galaxy cluster. iv) [math]U_{tot}[/math] and GPE related with positive mass both are converted to positive value. Therefore, the universe gets to an era of accelerating expansion again. v) On the simulation above, we can confirm that +GPE increases 200% the value of –GPE, and for we deduce the universal components through GPE, we will guess that repulsive dark energy increases 200% the value of attractive mass energy (matter + dark matter, as a general deduction). b) [math]U_{tot}[/math] and GPE related with positive mass on distant galaxy i) In the early universe, GPE related with positive mass had very big + value, but this value gets smaller as positive masses binds together and comprise of galaxy structure. On the simulation above, it still has positive value, and so it is in the status of accelerating expansion. ii) We can notice that [math]U_{tot}[/math] and GPE related with positive mass both are converted to negative value by gravitational binding of positive masses. Therefore, the universe gets to an era of decelerating expansion. iii) GPE related with positive mass is converted to positive value due to negative mass does gravitational contraction around massive positive mass(Galaxy or Galaxy Cluster). Therefore, the universe gets to an era of accelerating expansion again. iv) The decelerating expansion and accelerating expansion is naturally explained through “pair creation model of negative mass and positive mass”, and the conversion from accelerating expansion to decelerating expansion and from decelerating expansion to accelerating expansion is explained in sequence. v) The conversion from negative value to positive value shall be done more smoothly than the graph above for there exist thousands of billions of galaxies in our universe. Figure19-a.The change of distance and relative speed among distant galaxies. Figure19-b. GPE related with positive mass and negative mass. c) The change of distance and relative speed among distant galaxies Massive positive mass is given a birth from the 8th stage due to gravitational contraction. We calculated distance between the two massive positive masses (corresponding to the galaxy or galaxy cluster) and relative speeds of the two from then. We can notice that there exits positive acceleration, and it corresponds to accelerating expansion. d) GPE related with positive mass and negative mass Positive mass and negative mass have different GPE value each other, therefore their movements are different each other. D. Gravitational contraction due to positive mass and negative mass 1) When positive mass does gravitational contraction The structure that negative mass surrounds galaxy composed of positive mass. fig24. [math]-m_-[/math]= (-1 X500)+(-1 X500)= -1000, negative mass distribution: center1(-1000,0,0), center2(+1000,0,0), within R=220~250. [math]m_+[/math] = (+1X500) + (+1X500)= +1000, positive mass distribution : center1(-1000,0,0), center2(+1000,0,0), within a)R0-R200, b)R0-R150, c)R0-R100, d)R0-R50 It is shown that as positive mass does gravitational contraction, [math]U_{tot}[/math] and GPE value related with positive mass both gradually smaller (negative value). This means that our universe is converted from accelerating expansion (inflation) in the early universe to decelerating expansion. 2) When negative mass does gravitational contraction fig25.[math]m_+[/math] = (500 X1) + (500 X1)= 1000, positive mass distribution: center1(-1000,0,0), center2(+1000,0,0). [math]-m_-[/math] = (-1X500) + (-1X500)= -1000, negative mass distribution : center1(-1000,0,0), center2(+1000,0,0), within a)R50-R250, b)R50-R200, c)R50-R150, d)R50-R100 It is shown that as negative mass does gravitational contraction around massive positive mass, [math]U_{tot}[/math] and GPE value related with positive mass both are bigger. This means that our universe is converted from decelerating expansion to accelerating expansion (Dark energy effect). E. Distant six galaxies fig26. Distant six galaxies. [math]m_+[/math] = +100 X 6 = +600. Each +100 at (±1000,0,0),(0,±1000,0),(0,0,±1000). [math]-m_-[/math] = (-0.4 X 250) X 6 = - 600 center(±1000,0,0), center(0,±1000,0), center(0,0,±1000) negative mass is spread within [math] -250 \le x,y,z \le + 250[/math] fig.27 1) The ratio of +GPE to –GPE and GPE related with positive mass on six galaxies [math]U_{tot}[/math] and GPE related with positive mass both have a positive value. Therefore, expansion of universe is accelerating. fig.28 2) The change of distance and relative speed among six galaxies We can notice that there exits positive acceleration, and it corresponds to accelerating expansion. F. The change of GPE in the whole time of the universe fig29. The change of [math]U_{tot}[/math] of universe according to time. Refer to Figure15-b, 16-a, 18-b, 21-b, 21-b, 23-c, 27-b. 2) The change of [math]U_{tot}[/math] of universe according to time. a) GPE approaches to 0 at last as universe gets larger for it is in proportion to 1/r. b) [math]U_{tot}[/math] can have diverse values in the early universe. But it is assumed that it would have similar graph as time goes. c) It seems that [math]U_{tot}[/math] more likely has 0 or positive value. The homogeneous distribution of negative energy and positive energy makes [math]U_{tot}[/math] have positive value (red line). Although the total GPE starts with 0 or positive value in the early stage, it change to negative value as time goes by, and positive masses forms galaxies binding themselves, and as negative mass does gravitational contraction, it is converted to positive value. This provides natural explanation about accelerating expansion of the early universe, decelerating expansion in the first half, and accelerating expansion in the second half. fig30.The change of [math]U_{tot}[/math] and GPE value related with positive mass according to time. The reason of dark energy seems to be constant, is that our universe pass this section (slope) lately 5~7Gyr. Refer to Figure15-b,c,16-a,b,18-b,21-b,23-c,27-b. 3) The change of [math]U_{tot}[/math] and GPE value related with positive mass according to time. In early universe, Even if the total GPE is 0, the universe can expand in acceleration. The typical matter we observe in the universe is positive mass, and this is because there are two GPE categories related with positive masses. Although [math]U_{tot}[/math] and GPE value related with positive mass can have values that have large difference in the early universe, as time goes by, [math]U_{tot}[/math] and GPE value related with positive mass have values and shapes similar to each other. ============ HSS(The High-z Supernova Search) team : Brian P. Schmidt, et al : http://arxiv.org/abs/astro-ph/980520114P, 26~29lines. If Λ=0, Ω_m = - 0.38(±0.22) : negative mass density SCP(Supernova Cosmology Project) team : S.Perlmutter et al. http://arxiv.org/abs/astro-ph/98124737P If Λ=0, Ω_m = - 0.4(±0.1) : negative mass density ============ Paper: The change of Gravitational Potential Energy and Dark Energy in the Zero Energy Universe. http://vixra.org/abs/1110.0019

Is dark energy constant? Currently, dark energy is being observed as though it has a constant value. Generally, density of subjects that have local energy distribution should change to [math]1/r^3[/math], so this model is difficult to explain the constant value. Therefore, it is easy to consider it as a wrong model. Where [math]R_0[/math]=200, it is the situation where the radius has increased in double to R=400 when the distance of the particle pairs has decreased to [math]1/30[/math]. It is the result randomly producing 1000 particle pairs and finding gravitational potential energy value. Looking into the above results, the [math]\rho _{ - + }[/math] value that corresponds to the repulsive gravitational potential energy density (dark energy density) is almost being maintained as a constant even though the volume was increase to 8 times. In the above mechanism, particle A (positive mass) and particle B (negative mass) is evenly distributed, and particle A and particle B do change by [math]1/r^3[/math], but any physical quantity that comes out of their relation is possible by constant value. Of course, dark energy in my model is a variable that essentially depends on time.

Paper : Important Report on the Dark Energy and Gravitational Potential Energy http://vixra.org/abs/1110.0019 <== Paper ---Icarus2

Hello I’m sorry. I can’t English well. My native language is not English. Important Report on the Dark Energy and Gravitational Potential Energy [Abstract] Gravity is the force conquering the structure of the universe. By recognizing the components of the universe, we are estimating the quantity of components composing the universe through size of gravity and gravitational potential energy (GPE). In this paper, it is being shown that the universe can be created and expanded through pair creation of positive energy (mass) and negative energy (mass) from zero energy condition. Also, GPE is composed by 3 units of [math]U_{++}[/math], [math]U_{--}[/math], and [math]U_{-+}[/math] when negative and positive energy exists, [math]U_{-+}[/math] (GPE between negative mass and positive mass) has positive values and is the component that makes repulsive gravitational effect. [math]U_{-+}[/math] corresponds with the inner energy of the system and can be interpreted as dark energy. Also, situations in which [math]U_{-+}[/math] has much higher value than [math]|U_{ - - } + U_{ + + }|[/math] depending on the distribution of negative mass and positive mass is possible. This doesn't mean that 72.1% of dark energy independently exists, but means that explanation from GPE occurring from 4.6% of negative energy, which is the same as 4.6% of positive energy, is possible. Moreover, 4.6% of negative energy is the energy which is inevitably required from zero energy, which is the most natural total energy value in the universe. This discovery implies that our belief that size of gravity and size of components of the universe would always 1:1 correspond was wrong. I. Introduction Gravity is the force conquering the structure of the universe. By recognizing the components of the universe, we are estimating the quantity of components composing the universe through size of gravity and GPE. In estimating some kind of unknown energy quantity of universe components, gravity has been a crucial part. For example, if the universe is composed of some materials and these materials are always moving in equal velocity, unknown repulsive energy to offset this attraction was needed and it was assumed that the size of this energy is the same as the size of the energy of materials and the direction should be the opposite. From the observation on accelerating expansion of the universe in 1998, we assumed that a repulsive energy bigger than the total energy of visible matter need to exist and called this dark energy. Also, this dark energy has been accepted as an independent energy different from matter or dark matter We have trusted the above analysis on gravity and GPE had clear validity. However, through current numerical computation, we found that there was possibility of severe errors in this analysis through gravitational effect. Negative mass is stable at the state of high energy. So the “problem of the transition of the energy level of minus infinity” does not occur, and thus positive mass and negative mass can exist in the same space-time In this paper, we show that the universe led to the current structure of the universe, if we assume pair creation of positive energy and negative energy in the early universe. We looked for size of GPE when negative and positive energy (mass) both exist and try to explain this GPE value regarding to the current size of dark energy. II. Birth of the universe from zero energy state This is a computer simulation that shows you that the universe led to the current structure of the universe with pair creation of positive energy and negative energy from the zero energy state. III. Significant characteristics of dark energy and gravitational potential energy A. Simulation background and method 1) Physical background a)Initial energy value of the universe It looks more natural when an initial energy value of universe is 0. Therefore, negative energy is needed to offset positive energy of matters. If there was pair creation of positive and negative energy in the beginning of the universe, it is estimated that the total value of all positive energy will totally offset the total energy of all negative energy. If we consider only rest mass energy and GPE, the relation below will be valid. [math]E_T = 0 = ( + E) + ( - E) = 0 = \sum {( + m_ + c^2 ) + } \sum {( - m_ - c^2 ) + } \sum {U = 0} [/math] [math](m_ + > 0,m_ - > 0)[/math] b) [math]m_- = m_+[/math] The size of [math]m_+[/math] and [math]m_-[/math] can be a different during pair creation but this paper has purpose in showing possibility of various GPE values depending on the placement of particles which are pair produced, so the case in which [math]m_+[/math] is equal to [math]m_-[/math] will be looked into. c) Gravitational Potential Energy (GPE) If negative mass and positive mass coexist, GPE consists of the below three items. [math]U_T = U_{ - + } + U_{ - - } + U_{ + + }[/math] [math]U_T = \sum\limits_{i,j}^{i = j = n} {( - \frac{{G( - m_{ - i} )m_{ + j} }}{{r_{ - + ij} }})} + \sum\limits_{i,j,j > i}^{i = j = n} {( - \frac{{G( - m_{ - i} )( - m_{ - j} )}}{{r_{ - - ij} }})} + \sum\limits_{i,j,j > i}^{i = j = n} {( - \frac{{Gm_{ + i} m_{ + j} }}{{r_{ + + ij} }})}[/math] [math]U_T = \sum\limits_{i,j}^{i = j = n} {( + \frac{{Gm_{ - i} m_{ + j} }}{{r_{ - + ij} }})} + \sum\limits_{i,j,j > i}^{i = j = n} {( - \frac{{Gm_{ - i} m_{ - j} }}{{r_{ - - ij} }})} + \sum\limits_{i,j,j > i}^{i = j = n} {( - \frac{{Gm_{ + i} m_{ + j} }}{{r_{ + + ij} }})} [/math] GPE between positive masses are negative value. [math]U_{ + + } = \sum\limits_{i,j,j > i}^{i = j = n} {( - \frac{{Gm_{ + i} m_{ + j} }}{{r_{ + + ij} }})} [/math] GPE between negative masses are negative value. [math]U_{ - - } = \sum\limits_{i,j,j > i}^{i = j = n} {( - \frac{{Gm_{ - i} m_{ - j} }}{{r_{ - - ij} }})} [/math] GPE between positive mass and negative mass are positive value. [math]U_{ - + } = \sum\limits_{i,j}^{i = j = n} {( + \frac{{Gm_{ - i} m_{ + j} }}{{r_{ - + ij} }})} [/math] When the number of negative mass is [math]n_-[/math], and the number of positive mass is [math]n_+[/math], total potential energy is given as follows. [math]U_T = (n_ - \times n_ + )U_{ - + } + (\frac{{n_ - (n_ - - 1)}}{2}U_{ - - } + \frac{{n_ + (n_ + - 1)}}{2}U_{ + + } )[/math] For example, two pairs exist. [math]U_T = (U_1 + U_2 + U_3 + U_4 ) + (U_5 + U_6 )= 4U_{ - + } + 1U_{ - - } + 1U_{ + + }[/math] Gravitational potential shows significant characteristic when negative mass and positive mass both exist. While [math]n^2[/math] positive gravitational potential is produced above, [math]n^{2}-n[/math] negative gravitational potential are produced. Therefore, total GPE can have various values. d)Vacuum Energy Vacuum energy value which is currently known is an energy value that is too big. If this vacuum energy exists, it is difficult to explain why it isn't easily found around us. In the hypothesis of the pair creation of negative mass and positive mass, Vacuum energy will become exactly 0 because vacuum is the space in which pair creation and pair annihilation of positive and negative energy occurs. e)Characteristics of the negative mass For characteristics of the negative mass, refer to below video. 2)Simulation Program To look into the characteristic of GPE, we used the simulation program named Gravitation3D made by Roice Nelson. 3)Simulation setting a)Definition of parameter A few parameters were needed to be defined for simulation. Distance between pair creation negative energy and positive energy(distance of 1 pair) : [math]d_0 [/math] Minimum distance between particle pairs for density modification during pair creation : [math]d_m [/math] Radius of pair creation range : [math]R_0 [/math]=500 Particle number of pair creation : [math]N_0 [/math]=2000ea (1000 pair) b)Finding mean value Through Gravitation3D program, 1000 particle pairs (total 2,000ea particles) were produced by random and one mean value (GPE) of each distance value was found 5 times each. c)Verification on program To check if the calculated results of the program were correct, we calculated the GPE when 1, 2, and 3 pairs (consist of 15ea potentials) of particles existed by hand and confirmed that this value corresponded to the calculated results of the program. B. Results of simulation 1) Distance=0.01 It was found out that [math]U_{ - + } [/math] value having positive value could be much higher than [math]|U_{ + + } + U_{ - - } |[/math]. Thus, even though the size of positive mass and negative mass was equal, it could be known that repulsive GPE could be much higher than attractive GPE. 2) Distance =0.10 We will describe that an unknown repulsive energy [math]U_{ - + } [/math] higher that attraction of visible matter exists for the energy value of above. 3) Distance =0.19 According to the observance result of WMAP, it is predicted that current dark energy, dark matter, and matter is approximately 72.1%, 23.3%, and 4.6%, respectively . Dark matter and matter correspond to negative gravitational potential because they have attractive gravitational potential and dark energy correspond to positive gravitational potential because it produces repulsive effect. Therefore, observation ratio of current universe is 72.1/27.9 = 2.584. Is shows similar condition to 2.63 which was found above. If conditions are changes, ratio of negative gravitational potential and positive gravitational potential can have various conditions close to 2.58. 4) Distance =1.00 Particle pairs show to overlap (in the process being expressed in visible size) because of distance between negative mass and positive mass composing singular particle pairs are relatively close. Overlapping is unrelated to the calculation of GPE. It can be known that distance between singular particle pairs are much smaller compared to the distance between other particle pairs. One particle pair corresponds to the cluster of galaxies in the universe structure. From movement characteristic of negative mass and positive mass, galaxies and cluster of galaxies have clustering structure of negative mass in the outside of the galaxy. 5) Distance =10.00 C. Accelerating expansion of the universe Expansion of the universe means increase of the distance between cluster of galaxies or the galaxy while the sizes of individual galaxies are the same. Structure of galaxies or cluster of galaxies surrounding negative masses in the pair creation model of negative and positive mass is implied. In this simulation, d0, which is the distance between negative and positive mass, is maintained as a constant in this simulation, or the radius value of the size of the universe increases when d0 decreases. Change of potential energy by change of R radius Pay attention on the change of negative GPE and positive GPE ratio As R, which corresponds to the radius of the universe, increases, absolute values of GPE all decrease while the total GPE is mostly maintained. However, ratio of positive gravitational potential and negative gravitational potential increases as the universe expands and this is seen to mean that percentage of repulsive effect (Dark Energy) increases compared to the attractive effect of ordinary matter. F.Centripetal force effect in the galaxy from dark matter(negative mass) halo out of the galaxy If the negative mass is disposed at the outline, the test mass vibrates, and a kind of restoring force (This corresponds to the centripetal force when considering rotation of the galaxy) exists. This suggests that the halo, dark matter (negative mass) of the external Galaxy could get additional effects of centripetal force to the inner Galaxy. G.Observation value of WMAP 1)Pair Creation Assuming pair creation of negative and positive energy in the beginning of the universe, it is seen that law of conservation of energy should be valid for each pairs for law of conservation of energy to be valid. According to calculation of the previous paper, it is predicted that size of negative must bigger than size of positive. So [math]m_ - > m_ + [/math] 2)Some interpretation According to the observance result of WMAP, it is predicted that current dark energy, dark matter, and matter is approximately 72.1%, 23.3%, and 4.6%, respectively . Now, let's correspond to the GPE as follows. Matter = [math]U_{++} [/math] = Negative GP Dark Matter = [math]U_{--} [/math] = Negative GP Dark Energy = [math]U_{-+} [/math] = Positive GP In condition of [math] - m_ - = - 2.25m_ + [/math], results shown above were gained. This doesn't prove that the size of current negative mass is 2.25 times as positive mass. However, the above result implies that there is possibility to explain that the size ratio of the 3 predicted energy by using the "hypothesis of pair creation of negative and positive mass." The ratio above is valid between the 3 physical parameters. Case of this ratio being valid was found through simulation. H.Results of simulation 1) Even though negative and positive mass have the same size, total GPE can have +, 0, - values depending on the placement of each. 2) [math]U_{-+}[/math] value is higher as [math]d_0[/math] is smaller and the total GPE also have a high positive value. 3) Looking into the numerical calculation of B)-1)-B)-4), it can be seen that positive gravitational potential value [math]U_{-+}[/math] can have much higher values than negative gravitational potential values(138% - 3,201%). If we consider the distance of Planck length level, this value can have very high values enough to explain inflation. From the observation result of WMAP, we know that dark energy value, which generates repulsion, is 2.58 times the total of matter and dark matter. Until now, it is predicted that dark matter produces attraction. Closely look into numbers B)-3). 4) Because we judge components of the universe by gravity or GPE, it can be assumed that there is dark energy of 2.63 times or inner energy of 2.63 times regarding the situation of [math]U_{-+}[/math] value having approximately 2.63 times [math]U_{++}[/math] and [math]U_{--}[/math] values in number B)-3). There are several situations satisfying 2.58 times. 5) The above results show that 72.1% of dark energy doesn't exist independently, but implies that there is possibility that negative energy having the same size of positive energy can emerge. 6) This "increase of dark energy" doesn't come from a newly generated space, but shows feature of GPE which is made by negative mass and positive mass. IV. Conclusion From the simulation result of chapter II and accelerating expansion of the universe, there is possibility that our universe is composed of negative and positive energy (mass). From analysis results of chapter III, total GPE has 3 components and it is known that the total of this GPE can have positive and negative values. No one has seen dark energy or dark matter. We must remember that we only recognize it through gravitational effect. Because we judge components of the universe by GPE and gravity which is the slope of GPE, it is estimated that some unknown energy generates repulsive gravitational effect which is 2.63 times higher than the total quantity of matter and dark matter. This discovery shows possibility that content estimating dark energy quantity through gravitational effect we found can be different from the real fact. This discovery implies that our belief that size of gravity and size of components of the universe would always 1:1 correspond was wrong. Therefore, it is necessary to try to calculate and observe negative mass more strictly, laying aside the abstract aversion of negative mass. --- Icarus2

Refer to below link! Birth of the Universe from the Zero Energy state - Bigbang Simulation : Centripetal force effect in the galaxy from dark matter(negative mass) halo out of the galaxy :

For the Negative energy and Dark energy, Refer to below link! Hypothesis of dark matter and dark energy with negative mass : http://vixra.org/abs/0907.0015 Birth of the Universe from the Zero Energy state - Bigbang Simulation : Negative mass, Dark matter, Dark Energy, Antigravity-1 : Negative Mass is Stable at the State of High Energy : http://vixra.org/abs/1107.0052

Hello I’m sorry. I can’t English well. My native language is not English.... We are now living in the era of new revolution. Are we again treading on the process of huge revolution that occurred in the late 19th century and the early 20th century? The current observation of dark matter requires explanation on two important situations as the following. Situation 1: Denial of the gravitational (attractive) phenomenon Dark matter is five times more than the general matter, but it does not show macro-structure like the structure of galaxy or galaxy cluster, or micro-structure like fixed star or planet. The result of the current observation is that dark matter has attractive interaction with the general matter, but does not interact with the other dark matter. In other words, the observation or interpretation is that dark matters do not exert gravity(attraction) on each other. Situation 2: Denial of the fundamental phenomenon of physics that absorbs or emits photons It is not the level that dark matter has not interacts electromagnetically because it is electrically neutral, but the observation result is the level that dark matter does not emits or absorbs photons. From the several explanations above(refer to my old thread or my paper), Situation 1 shows that the essence of dark matter is negative mass, and that consequently they have the repulsive gravitational effect, so it can be explained. In regard to Situation 2, without giving that kind of characteristics of “the observation result that seems to be that it does not emit or absorb photons” from the first, can this kind of result be induced from other basic principle? A. Negative mass is stable at the state of high energy. Fig1. [math]\vec F = - m_ - \vec a[/math], [math]\vec a = - \frac{{\vec F}}{{m_ - }}[/math],([math]m_ - > 0[/math]). The acceleration of negative mass is opposite of the direction of force, and in case of negative mass, it does harmonic oscillation at the maximum point and is stable at the maximum point. B. The problem of transition from positive energy level to negative energy level Since we do not know clearly about the characteristics of negative mass yet, we do not know whether transition of positive mass at the positive energy level to negative energy level is possible or not. Fig2. Transition to the negative energy level However, for positive mass to enter the area of negative energy level, energy should have the negative value, and this means that it should have the characteristics of the negative mass. When considering the process of entering the domain of negative energy level from positive energy level, it must pass through the domain between 0 and [math]- \frac{1}{2}\hbar \omega[/math]. In case it follows the laws of negative mass because it's in the domain of negative energy, it cannot reach [math]- \frac{1}{2}\hbar \omega[/math],which is the first energy level of negative, because it is stable at the state of high energy, and it tries to have higher value of energy. It is because the energy level [math]0^ -[/math] is much higher than the energy level [math]- \frac{1}{2}\hbar \omega[/math]. That is to say that it shows possibility that the law of negative mass itself does not allow the situation where positive mass at the positive energy level succeed to the negative energy level. Even if it reaches [math]- \frac{1}{2}\hbar \omega[/math], the first energy level, at the negative energy level, it must follow the law of negative mass, it is stable at the state of high energy, and thus “the problem of the transition of the energy level of minus infinity” does not occur. As we have examined above, “the problem of the transition of the energy level of minus infinity” does not occur, and thus positive mass and negative mass can exist in the same spacetime. This is a very important result because it means that negative mass and negative energy can exist stably in our universe. (This finding suggests that “the problem of the transition of the energy level of minus infinity”, which we have had for eighty years regardless of whether negative mass exists or not, does not occur, and it itself has important meaning. Thus, it needs to be reflected in the teachings that are being performed when explaining the solution to negative energy, which the relativistic energy eq. suggests.) In regard to Situation 2, without giving that kind of characteristics of “the observation result that seems to be that it does not emit or absorb photons” from the first, can this kind of result be induced from other basic principle? Now, to think about this problem, C. Why dark matter does not emit photon? 1) The process of negative mass emitting photon [math]- E_ - - h\nu < - E_ -[/math] [math]- E_ -[/math]: Initial energy of negative mass, [math](E_ - > 0)[/math] [math]h\nu[/math]: Energy of photon The relational expression above means that if negative mass emits photon(with positive energy), then the energy after emitting gets lower than the energy before emitting. Negative mass is stable at the state of high energy, so the voluntary transition that negative mass emits photon and succeeds to the lower energy level does not exist. Therefore, negative mass explains the result of the current observation that dark matter does not emit photon from the fundamental principle. * The explanation on why dark matter does not emit photon is enough with this. In my paper, more various situations are set-up. ---Icarus2 Negative Mass is Stable at the State of High Energy http://vixra.org/abs/1107.0052 ================================================================= Situation 1: Denial of the gravitational (attractive) phenomenon 1. Dark matter is five times more than the general matter, but it does not show macro-structure like the structure of galaxy or galaxy cluster, or micro-structure like fixed star or planet. 2. Dark matter does not attractive interact with the other dark matter. Ex. Bullet Cluster From the several explanations above(refer to my old thread or my paper), Above situation shows that the essence of dark matter is negative mass, and that consequently they have the repulsive gravitational effect, so it can be explained. ============ The law of motion of negative mass and positive mass ----------- -[math]m_1 [/math]........... +[math]m_2 [/math] fig02. Negative mass -[math]m_1 [/math] and positive mass +[math]m_2 [/math] (initial velocity =0, [math]m_1>0[/math], [math]m_2>0[/math]) [math] -m_1 \vec a_1 = - G\frac{{( - m_1 )m_2 }}{{r^2 }}\hat r[/math] [math] \vec a_1 = - G\frac{{m_2 }}{{r^2 }}\hat r[/math] [math] +m_2 \vec a_2 = - G\frac{{( - m_1 )m_2 }}{{r^2 }}\hat r[/math] [math] \vec a_2 = G\frac{{m_1 }}{{r^2 }}\hat r[/math] Negative mass and positive mass : Negative mass is accelerated in the direction of positive mass, and positive mass is accelerated in the direction to be far away from negative mass. The direction of acceleration a1 worked on negative mass [math]–m_1[/math] is [math]-\hat r[/math], so [math]-m_1[/math] moves in the direction of reducing distance r, and the direction of acceleration a2 worked on positive mass [math]+m_2[/math] is [math]+\hat r[/math], so positive mass [math]+m_2[/math] is accelerated in the direction that distance r increases, namely the direction of being far away from negative mass If the absolute value of positive mass is bigger than that of negative mass, they will meet within finite time(attractive effect), and if the absolute value of positive mass is smaller than that of negative mass, the distance between them will be bigger, and they cannot meet(repulsive effect). The type of force is repulsion, so the potential energy has positive value. Let's take a look at the case where the absolute value of the positive mass is very bigger than the absolute value of the negative mass. [math] [m_2 > > | - m_1 |][/math] [math] \vec a_1 = - G\frac{{m_2 }}{{r^2 }}\hat r[/math] [math] \vec a_2 = G\frac{{m_1 }}{{r^2 }}\hat r \approx 0 [/math] The acceleration of the negative mass [math] - m_1 [/math] is [math]\vec a_1 = - G\frac{{m_2 }}{{r^2 }}\hat r[/math] . Yet, this is the same as the acceleration of the positive mass that has small size around a massive positive mass. In other words, if there is the minimalist negative mass on the surface of the earth, this means that it falls in the direction of the center of the earth like the positive mass. The motion of negative mass around the massive positive mass is very similar to that of the positive mass around the massive positive mass. If there is negative mass around a massive positive mass, then the negative mass gets affected by the attractive effect, and consequently, it becomes clustered around the massive positive mass. This characteristic seems to be related to the highly strange natures that the dark matter currently has. For more detailed information, refer to Chapter III-C. Refer to above video : time 2:00 ~ 7:02 ============= 3. Dark matter that is almost uniformly distributed By the repulsive effect among dark matter (negative mass), dark matter is distributed uniformly. 4. The problem of nonobservance of galaxy or cluster of galaxies consisted of dark matter The repulsive gravity (antigravity) effect among dark matter makes difficult for galaxy or clusters of galaxies, which are only consisted of dark matter, to form massive mass structure. 5. Low interaction among dark matter The repulsive gravity effect among dark matter is the cause. 6. The problem of nonobservance of dark matter 1) The fact that dark matter is unobserved earth or solar systems. 2) Dark matter does not exist in the center of galaxy. The result of observation that the black hole in the center of galaxy does not absorb dark matter and it will not absorb. 3) Dark matter does not exist in Galactic plane. 4) Dark matter does not exist in halo inside the galaxy. Dark matter made of negative mass is usually distributed outside the galaxy, so it can explain the nonobservance of it inside the galaxy. 7. Dark matter becomes clustered around galaxy. According to “The motions of negative mass and positive mass,” that we have examined above, when the absolute value of positive mass is bigger than that of negative mass, there exists the attractive effect between positive mass and negative mass, so the negative mass becomes clustered around the massive positive mass. Currently, negative mass is distributed usually around outside the galaxy, the clustering phenomenon (or Gravitational Lens effect) of negative mass (dark matter) occurs in galaxy or at the level of cluster of galaxies. The explanations above provide explanations about very strange characteristics related to those of dark matter. Dark matter that is consisted of negative mass usually spreads outside the galaxy, so it is observed that it becomes clustered around galaxy or clusters of galaxies that are consisted of positive mass. On the other hand, since it barely exists inside the galaxy, it doesn’t show becoming clustered around Earth, or any objects in the solar system and galaxy, and yet, we can know that it still generates the effect of additional centripetal force on objects within the galaxy. Negative Mass is Stable at the State of High Energy http://vixra.org/abs/1107.0052

Hello I’m sorry. I can’t English well. My native language is not English. [math]\begin{array}{l} TotalEnergy = 0 = Nothing = 0 = ( + E) + ( - E) = still - zero \\ = (\sum + m_ + c^2 ) + (\sum - m_ - c^2 ) + (\sum potential - energy) = 0 \\ \end{array}[/math] 0 = Nothing But, (+E),(-E), [math] (\sum + m_ + c^2 ) [/math] and [math] (\sum - m_ - c^2 ) [/math] are somthing. [birth of the Universe from “Nothing”] [ Birth of the Universe from the Zero Energy State ] 1)There was a pair creation of positive and negative energy in the early universe. 2)The total energy of universe is 0. Stephen Hawking and Alan Guth et al. argued that gravitational potential energy is negative energy, and that such gravitational potential energy can offset all positive mass energy during a period of inflation. 3) The acceleration in the expansion of the universe observed suggests the existence of positive energy out of mass energy, and alternatively, it corresponds to what the overall gravitational potential energy of the universe has positive value, indicating that gravitational potential energy will not able to offset positive energy. 4) Nothing but the gravitational potential energy doesn’t completely offset mass energy. And for the birth of the universe from “nothing” and energy conservation at the birth of the universe, “negative mass”, which corresponds to “negative energy”, is needed. 5)The basic principle of physics of “lower state of energy is stable!” is wrong. So it should be modified to “lower state of energy as far as positive mass is concerned and higher state of energy as far as negative mass is concerned is stable!”. 6)“Transition to the energy level of minus infinity”, which was used to deny the existence of negative mass, did not occur, whereas a. Relativistic energy eq., b. Dirac eq., c. field equation existed, suggesting the existence of negative mass. [ Void Structure results from~ ] 1)The presence of primitive void due to a pair annihilation of positive mass and negative mass. 2)The presence of void due to gravitational contraction between positive mass and repulsive effect between negative mass. [ Birth and Expansion of the Universe from singular point(or domain) ] 1)Even though all the mass of the universe come together in one small area on Big Bang, it does not have the same density as the black hole due to offsetting of density between positive mass and negative mass. Therefore it can be expandable. 2)The law of motion of positive mass and negative mass naturally explains that “expansion after birth” is the essential characteristics of the universe. 3)The expansion of the universe takes place in the state of total rest mass energy of “0” and, clusters of galaxies and the void structure can be achieved. 4)Energy conservation and momentum conservation exists without giving the initial velocity, and expansion of the universe occurs. 5)It does not require any other force except already known force, gravity. ---Icarus2 ========== Hypothesis of dark matter and dark energy with negative mass : http://vixra.org/abs/0907.0015 [simulation Video-1] Centripetal force effect in the galaxy from dark matter(negative mass) halo out of the galaxy!

Hello I’m sorry. I can’t English well. My native language is not English. [birth of the Universe from “Nothing”] [ Birth of the Universe from the Zero Energy State ] 1)There was a pair creation of positive and negative energy in the early universe. 2)The total energy of universe is 0. Stephen Hawking and Alan Guth et al. argued that gravitational potential energy is negative energy, and that such gravitational potential energy can offset all positive mass energy during a period of inflation. 3) The acceleration in the expansion of the universe observed suggests the existence of positive energy out of mass energy, and alternatively, it corresponds to what the overall gravitational potential energy of the universe has positive value, indicating that gravitational potential energy will not able to offset positive energy. 4) Nothing but the gravitational potential energy doesn’t completely offset mass energy. And for the birth of the universe from “nothing” and energy conservation at the birth of the universe, “negative mass”, which corresponds to “negative energy”, is needed. 5)The basic principle of physics of “lower state of energy is stable!” is wrong. So it should be modified to “lower state of energy as far as positive mass is concerned and higher state of energy as far as negative mass is concerned is stable!”. 6)“Transition to the energy level of minus infinity”, which was used to deny the existence of negative mass, did not occur, whereas a. Relativistic energy eq., b. Dirac eq., c. field equation existed, suggesting the existence of negative mass. [ Void Structure results from~ ] 1)The presence of primitive void due to a pair annihilation of positive mass and negative mass. 2)The presence of void due to gravitational contraction between positive mass and repulsive effect between negative mass. [ Birth and Expansion of the Universe from singular point(or domain) ] 1)Even though all the mass of the universe come together in one small area on Big Bang, it does not have the same density as the black hole due to offsetting of density between positive mass and negative mass. Therefore it can be expandable. 2)The law of motion of positive mass and negative mass naturally explains that “expansion after birth” is the essential characteristics of the universe. 3)The expansion of the universe takes place in the state of total rest mass energy of “0” and, clusters of galaxies and the void structure can be achieved. 4)Energy conservation and momentum conservation exists without giving the initial velocity, and expansion of the universe occurs. 5)It does not require any other force except already known force, gravity. ---Icarus2 ========== Hypothesis of dark matter and dark energy with negative mass : http://vixra.org/abs/0907.0015 [simulation Video-1] Centripetal force effect in the galaxy from dark matter(negative mass) halo out of the galaxy!

Centripetal force effect in the galaxy from dark matter(negative mass) halo out of the galaxy! I’m sorry. I can’t English well. My native language is not English. Negative mass(energy) can explain the dark matter and dark energy. In the simulation, When negative mass's shells exist at outline, collision time is shorter compared to existing only with positive mass's shells. This implies that there exist additional effects of centripetal force by the dark matter halo at the galaxy's outside in case of the galaxy having the axial symmetry. 1. Observation evidence for dark matter 1) Galactic rotation curves 2) Galaxy clusters and gravitational lensing 3) WMAP 4) Bullet cluster 5) Structure formation 2. In the Galaxy, No evidence for dark matter 1) At the Earth : non-observation(Xenon100, CDMS-II...) 2) At the solar system : non-observation 3) At the center of galaxies : no evidence Greedy Supermassive Black Holes Dislike Dark Matter http://www.universetoday.com/13091 Astronomers Find Black Holes Do Not Absorb Dark Matter http://www.universetoday.com/60422 4) At the galactic plane : no evidence "No evidence for a dark matter disk within 4 kpc from the galactic plane" http://arxiv.org/abs/1011.1289v1.pdf 5) At the galactic halo : no evidence Globular Cluster problem "Evidence Against Dark Matter Halos Surrounding the Globular Clusters MGC1 and NGC 2419" http://arxiv.org/abs/1010.5783 3. Negative mass hypothesis It is simply explained. Dark matter which has negative mass is clustered around galaxy. And centripetal force effect exist in the galaxy from dark matter halo out of the galaxy. =========== Additional effects of centripetal force exist from the previous simulation. Unfortunately, evidencing the effects of centripetal force in the negative mass has not been succeeded yet owing to my knowledge shortage. However, this simulation program was designed by other persons, and thus more trustworthy than me.;; If there is a person among readers of this report who can treat with classical mechanics(or general relativity) skillfully, please attempt evidences on the centripetal force’s effects having been made by the negative mass’s shell (having the axial symmetry or sphere one). ---Icarus2 ============= Hypothesis of dark matter and dark energy with negative mass : http://vixra.org/abs/0907.0015

I’m sorry. I can’t English well. My native language is not English. So, my expression is short and insufficient. ();; Again, I’m sorry. 1. How does your value and the mainstream cause the universe to expand outwards. fig10. caption : Expansion of the universe by negative mass distribution. The force, which is applied to the galaxy and galaxy cluster and located within radius R from the center of a 3-dimensional space, when assuming equal distribution of negative mass from repulsive effects between negative masses across space is valid. As considered the problem of the gravity at the point placed on arbitrary radius R of spherical object like the earth that mass is uniformly distributed, the gravity by mass distribution out of radius R is offset each other, and there is only the gravity effect by mass within radius R. If negative mass was born at the beginning of universe together with positive mass, it should be uniformly distributed in universe by repulsion between negative mass. Of course, there can be difference in negative mass density owing to the local distribution of massive positive mass. For the gravity effect that almost uniformly distributed negative mass has on positive mass(galaxy or galaxy cluster) located in radius R from the center of universe(3-dimensional center), negative mass within radius R only has the gravity effect on positive mass located within radius R, and at this time, positive mass is accelerated in the direction of begin far away from negative mass. The direction that positive mass becomes farther from negative mass is in keeping with the direction of cosmic expansion, and also negative mass continuously works the force, so finally positive mass is gradually accelerated. As examined in Chapter II, in the description of the force of positive mass and negative mass, the force is repulsion(the direction of +R), and integrated potential energy is positive value. Therefore, the assumption of the existence of negative mass can suggest the explanation of repulsive effect required for cosmic expansion, and the accompanying positive dark energy. "The hypothesis of dark matter and dark energy with negative mass" insists that dark matter is not different from dark energy each other, dark matter is the effect of centripetal force by negative mass out of galaxy, and dark energy is that positive potential term in total potential energy, and total potential energy has positive value at now. So universe has accelerating expansion. Accordingly, if we calculate the distribution and mean density of negative mass that describes rotation velocity within galaxy, and explain accelerating expansion of current universe with the size of potential energy that has positive value by this negative mass, we can prove the hypothesis that negative mass is the origin of dark matter and dark energy. ============= 1) Calculation by physicists. Refer to below paper : HSS(The High-z Supernova Search) team : Brian P. Schmidt, et al. : "Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant" http://arxiv.org/abs/astro-ph/9805201 14P, 26~29lines. If Λ=0, Ω_m = - 0.38(±0.22) : negative mass density SCP(Supernova Cosmology Project) team : S.Perlmutter et al.: "Cosmology from Type Ia Supernovae" http://arxiv.org/abs/astro-ph/9812473 7P If Λ=0, Ω_m = - 0.4(±0.1) : negative mass density From the observance of the HSS team and SCP team in 1998, they gained the mass density of the negative(HSS: Ω_M = -0.38( ± 0.22), SCP: Ω_M = -0.4( ± 0.1)), using field equations which do not have the cosmological constant.(It is inspected Field equation during 70 years.) In they thought, the quantity of the mass couldn't be negative value. So the value was discarded. We have to know that not the field equation has disposed the value, but our thought disposed that value. Also, negative mass is stable at the maximum point. Therefore the catastrophe to energy level of minus infinity never happens So, negative mass can be exist. 2) My calculation, refer to the first posting. http://www.scienceforums.net/topic/43190-dark-energy-dark-matter-fine-tuning-problem-negative-mass/page__view__findpost__p__509927 The value of observed dark energy has been proved in accordance with negative mass hypothesis. ρ_de = (0.201 ~ 5.02) X [math]10^{-47}GeV^4[/math] : Theoretical computation(Refer to recently paper ) ρ_obs = [math]10^{-47}GeV^4[/math] : Observed value ============== 2. How do you create negative mass? Initial energy value of universe 1) It looks more natural when an initial energy value of universe is 0. Therefore, negative energy is needed to offset positive energy of matters and in my opinion, only with negative gravitational potential energy, it is difficult to offset positive energy. - The present theory for the universe creation from nothing Argue that E_T = 0 = (+E) + (-E) = 0 = (Σ+mc^2) + (Σ-GMm/r) = 0 - But, in my opinion, (Σ+mc^2) > |(Σ-GMm/r)|, so (Σ+mc^2) + (Σ-GMm/r) ≠ 0 In my think, E_T = 0 = (+E) + (-E) = 0 = (Σ+ m+c^2) + (Σ - m_c^2) + (Σ U) = 0 (m+ : positive mass / m_ : negative mass / U : gravitational potential energy) 2) We observe the universe today. If we run all the particles positions backwards, they appear to be packed together at infinite density. Maybe, early universe has a density of black hole. In generally, particles cannot escape from the black hole. However, present theories have explains to the situations with ambiguous method. But, Assuming that negative mass(energy) and positive mass(energy) were born together at the beginning of universe, If we run all the particles positions backwards, they appear to be packed together at infinite density(each positive mass and negative mass). But, Universe has not a density of black hole. So universe can be expanded. The reason why we have not found negative mass on the earth until now is that negative mass exists as the state of mass when it was born without forming massive mass structure which can be easily measured owing to basic characteristics of negative mass(repulsive effect) as described above, and that negative mass is not observed because negative mass which exists around massive positive mass such as earth or the solar system receives attractive effect from massive positive mass, and it was disappeared long time ago when forming galaxy, even if it existed at the beginning of universe. Negative mass within the galaxy is cancelled out by attraction from large positive mass during the galaxy formation process. Furthermore, the space, other that the galaxy, will maintain the distribution state of negative mass.(view to the simulation video) I’m very sorry. I can’t English well. So I have a difficulty in English expression. ========= Negative mass, Dark matter, Dark energy, CC Problem! http://www.bautforum.com/showthread.php/105870 Hypothesis of dark matter and dark energy with negative mass : http://vixra.org/abs/0907.0015

modify the equation (97), (98) [math] v = \sqrt {(\rho _ + (r_ + ) + \rho _ - (r_ + ))\frac{{4\pi Gr_ + ^2 }}{3}} [/math] The mass density of collisionless isothermal sphere is given as [math]\rho ® = \frac{{\sigma ^2 }}{{2\pi Gr^2 }}[/math] in galaxy dynamics. [math]\sigma ^2 [/math] is velocity dispersion. [math] M_{dark} = M_{negative} = \int {\rho ®dV} = \frac{{2\sigma ^2 }}{G}r [/math] Motion of the negative mass and dark matter -1 Motion of the negative mass and dark matter -2 ========= Negative mass, Dark matter, Dark energy, CC Problem! http://www.bautforum.com/showthread.php/105870 Hypothesis of dark matter and dark energy with negative mass : http://vixra.org/abs/0907.0015

For the motion of negative mass, negative gravity and repulsive gravity I make simulation video of the negative mass. Refers to below the explanation and video, http://www.bautforum.com/showthread.php/105870

Thank you! cropduster23! ========== I’m sorry. I can’t English well. My native language is not English. [ Dark matter and dark energy come from one origin! ] I. Negative mass is stable at the maximum point! therefore the catastrophe to energy level of minus infinity never happens In the negative mass, F= - ∇U, F= - ma (m>0), a = - F/m ============= II. Dark energy is corresponding to the negative mass(energy) HSS(The High-z Supernova Search) team : Brian P. Schmidt, et al : http://arxiv.org/abs/astro-ph/9805201 14P, 26~29lines. If Λ=0, Ω_m = - 0.38(±0.22) : negative mass density SCP(Supernova Cosmology Project) team : S.Perlmutter et al. http://arxiv.org/abs/astro-ph/9812473 7P If Λ=0, Ω_m = - 0.4(±0.1) : negative mass density ============= III. Calculating centripetal force in galaxy from negative mass(Dark Matter) distributed out of galaxy fig11 caption : Revolution velocity of galaxy. The revolution velocity through the total quantity of matter that can be observed is A, while the actual observed value is B. We observed not positive mass but gravitation effect. This study mentioned the effect of centripetal force described previously, and the effect of centripetal force of negative mass with the description of dark matter. The researcher suggests that it is possible to prove the existence of negative mass with the comparison between observed value and revolution velocity of star according to the distance in galaxy which is calculated from negative mass distributed out of galaxy. fig12 caption : Negative mass effect on arms of galaxy. The actual observed spiral galaxy is on the left. Since repulsive effects occur between negative masses in Newton’s dynamics, negative masses will be distributed all over space because it cannot form large mass structures like stars. Negative mass within the galaxy is cancelled out by attraction from large positive mass during the galaxy formation process. Furthermore, the space, other that the galaxy, will maintain the distribution state of negative mass. - Please view to the simulation video-1,2 When negative mass is distributed uniformly, if we examine the area of galaxy diameter working the gravity on the basis of mass m for the analysis, there is no negative mass in the space of spiral space on the left, so negative mass can exist as much as the size of black and white on the right. negative mass on the right works the force on positive mass m on the origin to the left(positive mass moves after receiving the force that becomes farther from negative mass), and this direction will be in keeping with the central direction of gravity of real galaxy. [math] V®^2 = GM®/r [/math] [math] M® = M®_{visible} + M®_{dark} [/math] From the calculation of centripetal force in Newton dynamics, the important matters to calculate gravity effect of negative mass are the size and model of empty space of negative mass by real galaxy on the left, in case of spiral galaxy or oval galaxy, it may be close to oval if we consider the fact that most of mass is placed on galaxy core, the rotation of galaxy, and the gravitational radius of galaxy core, thus we regard empty space of negative mass as spherical or oval, and perform calculation to compare with observed value. fig13 caption : Effective negative mass. The negative mass distribution, where gravity is applied without cancellation of the oblique field located on the right side. [math] \frac{{mv^2 }}{{r_ + }} = \frac{{GM_ + (r_ + )m}}{{r_ + ^2 }} + \frac{{GM_ - (r_ - )m}}{{r_ - ^2 }} ---(103) [/math] ([math]M_ + (r_ + ) > 0, M_ - (r_ - ) > 0[/math]) Adding the term of centripetal force by negative mass to the term of centripetal force by positive mass as described above, we compare revolution velocity of star and the density of negative mass, then expand this to apply to other galaxies, and we can inspect if the interpretation of dark matter distributed out of galaxy is proper or not. The distribution of negative mass that remains without being offset in Fig12 & Fig. 13 is crescent-shaped, so it seems to be difficult to calculate, but 1)if we assume that the white empty space on the left is full with negative mass and positive mass at the same density, white empty space(0) = (+mc^2) + (-mc^2) = 0 2)here negative mass is uniformly distributed over the whole area, so the effect of negative mass on mass m is 0. Remaining positive mass is distributed over the white area on the left at the density of negative mass, and 3)the gravity that uniformly distributed positive mass(with same density to the negative mass density) works on positive mass m place on radius r is worked only by the distribution of mass within radius r. – Shell Theorem. fig14 caption : Equal to the degree of gravity that is applied on the equally distributed positive mass within the radius r of the left side. The gravitational effect from negative mass, which functions at mass m is equal to the gravitational effect from positive mass within radius r. Therefore, the effect of negative mass that remains out of galaxy without being offset can make it approximate to the gravity generated by the distribution of positive mass within the radius R in galaxy [math] M_ - = \rho _ - ®V = \rho _ - ®(\frac{{4\pi r^3 }}{3}) [/math] In equation(103) [math] \frac{{mv^2 }}{{r_ + }} = \frac{{GM_ + (r_ + )m}}{{r_ + ^2 }} + \frac{{GM_ - (r_ + ^{} )m}}{{r_ + ^2 }} [/math] [math] v = \sqrt {\frac{{G(M_ + + M_ - )}}{{r_ + }}} = \sqrt {\frac{{G(M_ + + \rho _ - (r_ + )V)}}{{r_ + }}} [/math] [math] v = \sqrt {\frac{{GM_ + }}{{r_ + }} + \rho _ - (r_ + )(\frac{{4\pi r_{_ + }^2 }}{3})} ---(107) [/math] The mass density of collisionless isothermal sphere is given as [math]\rho ® = \frac{{\sigma ^2 }}{{2\pi Gr^2 }}[/math] in galaxy dynamics. [math]\sigma ^2 [/math] is velocity dispersion. [math] M_{dark}=M_{negative}= \frac{{2\sigma ^2 }}{{3G}}r ---(108) [/math] Equation (107) is applied to arbitrary spherical or oval galaxy, and in case of normal shaped spiral galaxy, the distance which spherical approximation can be applied from the center of galaxy will be effective. So if we consider that the distribution of negative mass out of galaxy comes under isothermal, the effect of mass in galaxy by the distribution of negative mass out of galaxy is proportional to r as shown in equation (108 ), and this is in keeping with observed dark matter. Positive mass dark matter distributed in galaxy does not form the spherical distribution, and it is broken owing to the gravity of galaxy core, gravitational action with stars, and rotation of galaxy, if its shape is not very intentionally assumed. Furthermore, there are various heat sources in galaxy according to position, so it cannot be regarded as collisionless Isothermal. However, the effect of centripetal force that negative mass works from the exterior of galaxy can keep the spherical distribution of mass, and make the mass effect that increases linearly in accordance with distance r as seen above because it receives less influence from elements such as the gravity of galaxy core, or rotation of galaxy. Also ideal state of collisionless can be achieved by negative mass, because negative mass has repulsive effect each other. At the solar system, non-observation of dark matter(negative mass) is explained. In negative mass hypothesis, dark matter exists at the exterior of galaxy, so dark matter is not observed at the solar system. It described that the quantity of negative mass decided at the beginning of universe can explain the effect of centripetal force in galaxy(V-4), repulsion effect on cosmic expansion(V-3), decelerating expansion at the first half, and accelerating expansion(V-1) of universe at the second half(7 billion years ago) at the same time. Therefore, it is necessary to try to calculate and observe negative mass more strictly, laying aside the abstract aversion of negative mass. Please review to the fig12, fig13, fig14. And then, please understand that the gravitational effect from negative mass is equal to the gravitational effect from positive mass(with same density to the negative mass density) within radius r. Below problems explained by negative mass - Almost uniformly distribution of the dark matter, - Non-observation of the star and galaxy consists of dark matter, - Dark matter clumping around galaxy, - Rotation curve of the galaxy -Centripetal force effect, - Low interaction between dark matter when collision occurs between dark matter, - Collision of Bullet Cluster, - Non-observation of dark matter at the Earth and Solar system (Xenon100, CDMS II…) - Non-baryonic dark matter condition, - Observed value of the dark energy(10^(-47)GeV^4), - Repulsive force needed for accelerating expansion, - It is show that result of original field equation(Λ=0) of general relativity is right. ======== Hypothesis of Dark Matter and Dark Energy with Negative Mass : http://vixra.org/abs/0907.0015

Video of the motion of negative mass or dark matter I’m sorry. I can’t English well. My native language is not English. I make simulation video of the negative mass. Negative mass(energy) can explain the dark energy and dark matter. It is explain that Almost uniformly distribution of the dark matter, Non-observation of the star and galaxy consists of dark matter, Dark matter clumping around galaxy, Rotation curve of the galaxy -Centripetal force effect, Low interaction between dark matter when collision occurs between dark matter, Collision of Bullet Cluster, Non-observation of dark matter at the Earth and Solar system (Xenon100, CDMS II…) Nonbaryonic dark matter condition, Observed value of the dark energy(10^(-47)GeV^4), Repulsive force needed for accelerating expansion, It is show that result of original field equation(Λ=0) of general relativity is right. Motion of the negative mass or dark matter -1 Motion of the negative mass or dark matter -2 ======= Hypothesis of dark matter and dark energy with negative mass : http://vixra.org/abs/0907.0015

Thanks CaptainPanic ! Your calculation is right! It is roughly right!( about 458m/s = 1.34 X(velocity of sound)) It’s my mistake! A long time ago, I recognize to it. That sentence was translated 18 months ago. I have failure to check it! It’s my mistake! Though, the velocity is fast. But it is not impossible. Again thanks! Merged post follows: Consecutive posts mergedRefer to : ISS(International Space Station) docking speed : about 7,700 m/s On the earth, 458 m/s docking speed is ....

Hello! Few years ago, I tried to think on methods to transport freight and humans to space economically and safely. I thought at that time, moon elevator could be created if powerful cable can be produced from development of carbon nano-tube technology. Through moon elevator, space development of mankind, commercial travel to space and moon will become possible, and contribute enormously to development of human civilization. Please have a look at the following introduction of basic concepts, and compare relatively with "space elevator" and its feasibility etc [Moon Elevator] 【Brief explanation on Figures】 Figure 1 is structure diagram of moon elevator Figure 2 is plane figure seen from perpendicular of lunar orbit plane Figure 3 is structure diagram of multiple moon elevators 【Purpose of invention】 This invention is about transport method of freight and humans to space using rocket and space shuttle. More specifically, a cable is put on the moon toward the earth, so the moon acts as a ceiling with a cable hanging down. Although position changes at all time due to moon moving around the earth, using the property that this cable will always face toward the center of the earth because of earth gravity will allows an elevator to move on this cable. Currently the only method to go out to space from the earth is by using rocket or space shuttle, and since space shuttle uses exterior rockets to obtain propulsive force to go out to space, rocket is the only present method. However, escaping earth by using these rockets has many problems. First, solid fuel and liquid fuel etc that are used for rocket fuel are extremely high explosive materials. Little mistakes or problems while using these fuel types could lead to deadly accidents, as example, Challenger explosion accident or Columbia explosion accident etc. Second, in order for a rocket to head out to the space through self-propulsion, it takes off from launching pad with enormous amount of fuels. To increase efficiency of fuel, most of the fuels on the rocket are used at the initial stage of take off, thus maintaining very fast speed. However, because it passes through the atmosphere at very high speed, air friction and collision with outside material damages body of the rocket frequently and safety system in preparation for these damages causes problem of increase in weight and fuel amount of rocket body. Third, the most crucial problem is that current rocket launching cost is commercially too expensive. Because of its high cost, space exploration or moon exploration using rockets has become a project performed by nations, and due to high cost, the only nation that has accomplished landing on the moon is United States. These high costs are acting as an obstacle in moon development, space exploration and launching artificial satellites etc… 【Technical task achievement through invention】 The aim of this invention is to present safer and inexpensive transport method of freight and humans to space than existing rocket method and the goal is not only transporting freights needed for moon development but also transporting extracted resources from moon to earth efficiently. 【Invention structure】 Figure 1 is a diagram that shows the final outcome of this invention, a cable (103) is suspended from moon (100) toward the earth (101), elevator (102) is attached to the cable (103), and this elevator (102) operates from the earth surface to space or moon (100) to transport freight or humans to space. Composition elements of moon elevator (102) are solar power plant (105) that is constructed on the moon (100), motor (106) that pulls the cable (103), cable (103) that can withstand the weight of elevator (102) and freights and elevator (102) that can operate by obtaining power externally or internally. For power plant (105), solar power plant (105) or other fuel type power plant (105) can be installed to operate the motor (106), and electric power can be transmitted to moon when cable (103) connects the earth (101) and the moon (100) and this power can be stored for later use. Construct moon (100) base on the surface of the moon (100) where it is closest to the earth (101) and distance change between earth (101) and moon is the minimum, and construct power plant (105) to supply power and motor (106) to operate the cable (103). For case where elevator operates itself by power supplied, cable does not need to be operated by motor directly. Construct a structure underneath the moon (100) and after tying up one end of the cable (103) to the structure, launch the rocket with the cable so cable points toward the earth. From locations of earth surface where earth gravitation direction (201) of the cable (103) meets, construct earth base where accessibility is ease, affect on flight service of plane and weather is low and location is close to the moon (100). When cable (103) suspended from moon (100) reaches the earth base, install the elevator (102) located at the earth base. To maintain the cable in straight line, install weight and communication equipments for ground base etc at the end of the cable. On the elevator (102), embark freight and human that will be transported to moon (100) or space. Supply power to the elevator (102), transport freight and human to locations by ascending and descending the elevator (102) or by pulling the cable directly to pull up the elevator from the space base located at the middle. As seen in Figure 1, moon (100) performs as a ceiling (211), and although one end of the cable (103) is not tied up to the surface, cable (103) is pulled tightly in perpendicular due to gravity (213) on the cable (103), so the elevator(102) on the cable (103) is able to move upward. Similarly, even if the cable (103) is floating on air, it would perform similarly to cable(103) hanging on the ceiling (211) due to gravity from the moon (100) and the earth (101) and direction of the cable (103) rotates in 360 degree because the moon rotates around the earth, but due to characteristics of gravity, it will always point upward as the earth surface as base, so it can perform necessary role to head out to space from the earth surface. Figure 2 is a plane figure of this invention seen from perpendicular of lunar (100) orbit plane (205). Due to affect from rotation of the earth (101) and moon’s (100) revolution affect around the earth (101), it takes approximately 27.32 days for moon (100) to revolve around the earth (101) once. These revolution cycles of the moon (100) as to revolution-side of the moon (100) that meets with surface of earth (101) shows angle changes of approximately 13.36 degree a day, and in time unit, shows less than one degree per hour, 0.56degree/hour. Thus cable that is suspending from the moon stays on top of earth base for a certain time, providing enough time for the elevator to load and unload the freights. Of course the speed of cable on the earth surface due to revolution of the moon is relatively huge but expects embarking freight and passenger is technically possible. There is some distance difference between closest and farthest location because to be exact, the moon (100) rotates in oval orbit, not in circle. The most appropriate location to build earth base on the earth surface is where the moon is the closest or select location where revolution surface meets the earth surface with minimal obstacle elements and ease to access considering land features of circumference, accessibility, climate, plane operation situation etc, with location where moon is close by. At this point, earth gravitational direction of the cable suspending from the moon is necessary to consider. As seen in Figure 2, cable (103) and elevator (102) suspending from the moon (100) is affected by the earth (101) gravity so it is always perpendicular to the surface, whether the moon (100) is in three o’clock direction(303), six o’clock direction(302) or at ten o’clock direction(301). The mass of the moon (100) or mass of the earth (101) are much greater than the mass of elevator (102) or freight inside the elevator (102), so affect on moon (100) and earth (101) by the movement of cable (103) or elevator (102) and freight mass can be ignored. Figure of three o’clock direction (303) is when elevator (102) is located at the moon (100). Elevator (102) can transport freight or human from the earth (101) or transport extracted resources from the moon (100) to earth (101) using the elevator (102). Figure of six o’clock direction (302) is when elevator (102) reached the geostationary satellite orbit (206). Instead of firing up satellites from the earth surface, elevator (102) can be used to transport satellites to the geostationary satellite orbit (206) and these satellites can be placed on its proper orbit using self-propulsion fuel from geostationary satellite orbit (206). If satellites can be transported using moon (100) elevator (102), not only satellite can be transported to precise height but it will also extend the life span of the satellites by more couple of times than current method because it can be transported with enough fuel of its own. Figure of ten o’clock direction (301) is when moon elevator (102) reached the transport center, known as earth base (300) located at earth (101). At this moment, freight and human can be loaded or unloaded from the elevator (102) and supply power to elevator (102) and the moon (100). Communication equipment (208) is installed at the end of the cable (103) to communicate exact position and height etc information with earth base (300), and perform role as a weight. As shown, there is no danger of explosion using moon elevator (102), although it does have a possibility of fall, but it can escaped using parachute etc inside troposphere and also when emergency situation occur, it has some time to figure out the problem compared to explosion, so this is much more safer method compared to using rockets. Furthermore, to construct habitable space and live on the moon while developing moon and extracting resources, vast amount of materials are needs to be transported but using current rocket method has considerable constraint and cost problem. However using this invention, vast amount of materials can be transported to moon (100) inexpensively and also transport extracted resources from moon to earth easily. When exploiting resources like helium3 on the moon (100), transport method needs to be ready at all time, thus moon elevator (102) will be utilized very usefully for these development. Although there are high priced space-travel plans available now, if moon elevator (102) gets installed, cheaper space travel will become possible, achieving commercial success, and can also be utilized for uses like launching artificial satellite and various exploration vessels. Figure 3 shows an object produced by applying core concept of this invention. It is a multiple elevator (102) system that uses space base (107) that is connected with the moon. Unlike from previous space base, this invention does not exhaust fuel from rotating after when it is installed, ease in transporting material and human to earth, able to conduct various types of experiment by adjusting the position of the space base and is able to adjust height. Construct space base (107) as in this plan, install motor (133) inside the space base (107) to transport freight and human on earth to space, this is a bit more efficient compared to operating the elevator (102) by using the motor (106) installed at the moon (100). Suppose cable1 (131) is pulled by activating motor (106) located at the moon (100), entire cable (131,132) needs to be pulled but if motor (133) installed at space base (107) is operated, energy can be saved by only operating cable2 (132), from space base (107) to earth surface. Space base (107) can be used for space experimental lab and tourist uses etc. As mentioned before, if elevator can operate itself from self-power or transmitted power, it is better for the elevator itself to move rather than pulling the cable up. Construct numerous space bases, such as moon base, geostationary orbit base, 100km upper sky base etc by expanding multiple elevator system to transport human and materials between sections and use it for various uses (moon base- transport moon resources and commercial travel, geostationary orbit- space station and execute artificial satellite launch and commercial travel, 100km base- commercial travel etc). Movement between corresponding sections in the multiple elevator system can be operated by technically ease method, either pulling the cable directly to move the elevator or elevator itself can move up and down following the cable by self-power or transmitted power. 【Effect of invention】 As described above, this invention can install cables in air with no support put on the surface, and even though the earth rotates, this cable always maintain on top of the surface due to characteristics of gravity. This invention does not have danger of explosion and is considerably safe compared to methods that use rockets. Also it uses electric energy as source power so it is eco-friendly compared to fossil fuels. This invention can be applied to satellite launch and space exploration etc, which still has quite a lot of demand, and can be used as very useful tool for moon exploration and transporting resources located at the moon. And can provide cheaper method of commercial space travel and moon travel than previous method. My idea also has some drawbacks. Drawbacks are that distance between moon and earth is extremely far, and will it be possible to manufacture strong cable like carbon nano tube to reach other and will it have enough tensile strength? The key is if sufficient tensile strength is achieved through development of technology, length of the cable is not a big problem because it only needs funds, and I think the cost of development can be sufficiently supplied through resource exploit from the moon, executes artificial satellite launches, and commercial space travel demand etc. Although my idea has some drawbacks, I believe that my idea is much more stable, ease in technology, and can be used in multipurpose than space elevator. And it has a merit that only if cable related technology is achieved, moon elevator can be developed easily with current technology. Regardless of existing space elevator’s high possibility, it seems it has several drawbacks of instability elements, technical difficulty and increase in transportation cost etc. First, even though earth base is located where climate affect is minimum because the cable is always linked between space and earth base, enormous power is applied to the cable by the movement of the atmosphere and to keep the cable connected with space and earth base, couple more times of cable tension than normal connection is required and dangerousness will increase largely due to movement of the atmosphere. ==> Moon elevator technology: Cable is not tied up with earth base, so danger from atmosphere and tension increase of cable is relatively low because of flexible condition. Second, even though space base does not lose additional energy due to its location at geostationary orbit, cable connected from the earth base is continuously forced and in result, space base is forced downward pulling, so energy is exhausted continuously to propulsion the space base to maintain its orbit. Therefore, space base will require 24hour 365day supply of energy even if there are no transports of freight and personnel to space base, which will eventually increase the transportation cost. ==> Moon elevator technology: Space base is held by earth’s gravitation, and rotates due to revolution of moon so almost no additional energy is exhausted. Lowering the cable or elevator to earth only for transportation can cut down cost of operation. Third, it seems transmitting energy needed to operate the elevator that will move to the space base is considered to be sent through laser etc from earth base, but with current technology and near futures, it seems technically hard to possess energy transmitting technology to move the elevator to space base. ==> The key to moon elevator is whether able to manufacture cable that has enough tensile to be used on space elevator, than rest of technology difficulty are relatively low, such as lowering the cable using the motor or technology that moves elevator up and down through transmitted electric energy. Have a good time!

[ Dark matter ] Calculating centripetal force in galaxy from negative mass distributed out of galaxy fig11 caption : Revolution velocity of galaxy. The revolution velocity through the total quantity of matter that can be observed is A, while the actual observed value is B. We observed not positive mass but gravitation effect. That is, universe has not said that dark matter is positive mass. This study mentioned the effect of centripetal force described previously, and the effect of centripetal force of negative mass with the description of dark matter. The researcher suggests that it is possible to prove the existence of negative mass with the comparison between observed value and revolution velocity of star according to the distance in galaxy which is calculated from negative mass distributed out of galaxy. fig12 caption : Negative mass effect on arms of galaxy. The actual observed spiral galaxy is on the left. Since repulsive effects occur between negative masses in Newton’s dynamics, negative masses will be distributed all over space because it cannot form large mass structures like stars. Negative mass within the galaxy is cancelled out by attraction from large positive mass during the galaxy formation process. Furthermore, the space, other that the galaxy, will maintain the distribution state of negative mass. When negative mass(negative energy) is distributed uniformly, if we examine the area of galaxy diameter working the gravity on the basis of mass m for the analysis, there is no negative mass in the space of spiral space on the left, so negative mass can exist as much as the size of black and white on the right. negative mass on the right works the force on positive mass m on the origin to the left(antigravity;positive mass moves after receiving the force that becomes farther from negative mass), and this direction will be in keeping with the central direction of gravity of real galaxy. [math] V®^2 = GM®/r [/math] [math] M® = M®_{visible} + M®_{dark} [/math] From the calculation of centripetal force in Newton dynamics, the important matters to calculate gravity effect of negative mass are the size and model of empty space of negative mass by real galaxy on the left, in case of spiral galaxy or oval galaxy, it may be close to oval if we consider the fact that most of mass is placed on galaxy core, the rotation of galaxy, and the gravitational radius of galaxy core, thus we regard empty space of negative mass as spherical or oval, and perform calculation to compare with observed value. fig13 caption : Effective negative mass. The negative mass distribution, where gravity is applied without cancellation of the oblique field located on the right side. [math] \frac{{mv^2 }}{{r_ + }} = \frac{{GM_ + (r_ + )m}}{{r_ + ^2 }} + \frac{{GM_ - (r_ - )m}}{{r_ - ^2 }} ---(93) [/math] ([math]M_ + (r_ + ) > 0, M_ - (r_ - ) > 0[/math]) Adding the term of centripetal force by negative mass to the term of centripetal force by positive mass as described above, we compare revolution velocity of star and the density of negative mass, then expand this to apply to other galaxies, and we can inspect if the interpretation of dark matter distributed out of galaxy is proper or not. The distribution of negative mass that remains without being offset in Fig. 13 is crescent-shaped, so it seems to be difficult to calculate, but if we assume that the white empty space on the left is full with negative mass and positive mass at the same density, here negative mass is uniformly distributed over the whole area, so the effect of negative mass on mass m is 0. Remaining positive mass is distributed over the white area on the left at the density of negative mass, and the gravity that uniformly distributed positive mass works on positive mass m place on radius r is worked only by the distribution of mass within radius r. fig14 caption : Equal to the degree of gravity that is applied on the equally distributed positive mass within the radius r of the left side. The gravitational effect from negative mass, which functions at mass m is equal to the gravitational effect from positive mass within radius r. Therefore, the effect of negative mass that remains out of galaxy without being offset can make it approximate to the gravity generated by the distribution of positive mass within the radius R in galaxy [math] M_ - = \rho _ - ®V = \rho _ - ®(\frac{{4\pi r^3 }}{3}) [/math] In equation(93) [math] \frac{{mv^2 }}{{r_ + }} = \frac{{GM_ + (r_ + )m}}{{r_ + ^2 }} + \frac{{GM_ - (r_ + ^{} )m}}{{r_ + ^2 }} [/math] [math] v = \sqrt {\frac{{G(M_ + + M_ - )}}{{r_ + }}} = \sqrt {\frac{{G(M_ + + \rho _ - (r_ + )V)}}{{r_ + }}} [/math] [math] v = \sqrt {\frac{{GM_ + }}{{r_ + }} + \rho _ - (r_ + )(\frac{{4\pi r_{_ + }^2 }}{3})} ---(97) [/math] The mass density of collisionless isothermal sphere is given as [math]\rho ® = \frac{{\sigma ^2 }}{{2\pi Gr^2 }}[/math] in galaxy dynamics. [math]\sigma ^2 [/math] is velocity dispersion. [math] M_{dark}=M_{negative}= \frac{{2\sigma ^2 }}{{3G}}r ---(98) [/math] Equation (97) is applied to arbitrary spherical or oval galaxy, and in case of normal shaped spiral galaxy, the distance which spherical approximation can be applied from the center of galaxy will be effective. So if we consider that the distribution of negative mass out of galaxy comes under isothermal, the effect of mass in galaxy by the distribution of negative mass out of galaxy is proportional to r as shown in equation (98), and this is in keeping with observed dark matter. Positive mass dark matter distributed in galaxy does not form the spherical distribution, and it is broken owing to the gravity of galaxy core, gravitational action with stars, and rotation of galaxy, if its shape is not very intentionally assumed. Furthermore, there are various heat sources in galaxy according to position, so it cannot be regarded as collisionless Isothermal. However, the effect of centripetal force that negative mass works from the exterior of galaxy can keep the spherical distribution of mass, and make the mass effect that increases linearly in accordance with distance r as seen above because it receives less influence from elements such as the gravity of galaxy core, or rotation of galaxy. Also ideal state of collisionless can be achieved by negative mass, because negative mass has repulsive effect each other. At the solar system, non-observation of dark matter is explained. In negative mass hypothesis, dark matter exists at the exterior of galaxy, so dark matter is not observed at the solar system. It described that the quantity of negative mass decided at the beginning of universe can explain the effect of centripetal force in galaxy(V-4), repulsion effect on cosmic expansion(V-3), decelerating expansion at the first half, and accelerating expansion(V-1) of universe at the second half(7 billion years ago) at the same time. Therefore, it is necessary to try to calculate and observe negative mass more strictly, laying aside the abstract aversion of negative mass. Please review to the fig12, fig13, fig14. And then, please understand that the gravitational effect from negative mass(negative energy) is equal to the gravitational effect from positive mass within radius r. ======== Hypothesis of Dark Matter and Dark Energy with Negative Mass : http://vixra.org/abs/0907.0015

Thanks! Michel Good Lectures! At fourth files! The energy of gravitational field is negative! The positive energy of the false vacuum was compensated by the negative energy of gravity. The TOTAL ENERGY of the universe may very well be zero. At third files ( 3:55s ~ 4:23s ) Gravitational Repulsion! The combination of general relativity and modern particle theories predicts that at very high energy, there exists forms of matters that create a gravitational repulsion! Gravitational potential energy is negative energy. However, mass-energy equivalence says that negative energy has a negative mass. Therefore, we can say that gravitational potential energy has a negative mass. ======== http://www.scienceforums.net/forum/showthread.php?t=46362

I’m sorry, I can’t English well. Above wiki explanation is Gravitational binding energy=| ∑ gravitational potential energy |= [math]|\sum\limits_{i < j}^n {U_{ij} |} = - \sum\limits_{i < j}^n {( - \frac{{Gm_i m_j }}{{r_{ij} }}} )[/math] Namely, sign of the gravitational binding energy has an absolute sign of the gravitational potential energy. At wiki, gravitational binding energy is [math]U = \frac{{3GM^2 }}{{5r}}[/math] "The gravitational binding energy of a system is equal to the negative of the total gravitational potential energy, considering the system as a set of small particles." Above sentence means [math]U_{bindingenergy} = - U_{gravitationalpotentialenergy} = - ( - \frac{{3GM^2 }}{{5r}})[/math] In other words, They say that gravitational potential energy has a negative value. ========== To swansont, In SR, gravitational potential energy is gravity source. In my think That means, gravitational potential energy has a fixed value such as rest mass.(at proper frame) [math]E_T = M'c^2 = \gamma Mc^2 + ( - \frac{{GM_1 M}}{r})[/math] So, the reference is not purely a matter of convenience. Also, for the mass defect [math]U = - \frac{{GM_1 M}}{r}[/math] is correct. Therefore, Gravitational potential energy is negative energy. However, mass-energy equivalence says that negative energy has a negative mass. [math]E_T = M'c^2 = \gamma Mc^2 + ( - \frac{{GM_1 M}}{r})[/math] is E=A+B structure So, this equation can be explain by A+B or E Although total mass of the system has a positive mass, we can say that gravitational potential energy corresponds to the negative mass.

Thanks! Snail, Farsight, swansont, Amr Morsi From Amr Morsi’s explain, In SR, total energy is [math] E = mc^2 = \gamma m_0 c^2 + ( - \frac{{GMm_0 }}{r})[/math] For the consistency (refer to the first posting), [math]E = M'c^2 = \gamma Mc^2 + ( - \frac{{GM_1 M}}{r})[/math] [math]( - \frac{{GM_1 M}}{r}) = - m_ - c^2 [/math] ([math] - \frac{{GM_1 M}}{{rc^2 }} = - m_ - [/math] : Negative mass define (m_≥0)) So, [math]E = M'c^2 = (\gamma Mc^2) + ( - m_ - c^2 ) = (\gamma M + ( - m_ - ))c^2 [/math] If, c>>v, γ~1, [math]E = M^{'} c^2 = (M + ( - m_ - ))c^2 [/math] Mass deficit is happen, because of gravitational potential energy(It is a kind of binding energy) Semi-Classically, or SR Total Energy = ((γX rest mass) + (mass of the gravitational potential energy))c^2 =================================== In the chapter 2.7( Gravitation and Spacetime, Hans C. Ohanian and Remo Ruffini )) P116~118 Our Gedanken-experiment is less farfetched than it seems. The Earth is in continuous acceleration as it orbit the Sun, and action and reaction are in fact out of balance all the time. We can give a rough estimate of the difference between action and reaction. The force of the Sun on the Earth is GM1M/r^2, where M1 and M are the masses of Sun and Earth, respectively. The force of the Earth on the Sun differs from this by a term depending on the acceleration of the Earth. In the time r/c, the radial displacement of the Earth caused by the acceleration is [math]\Delta r \simeq \frac{1}{2}\frac{{GM1}}{{r^2 }}(\frac{r}{c})^2 = \frac{1}{2}\frac{{GM1}}{{c^2 }} [/math] [194] Hence, without the acceleration the Earth would have moved off tangentially and increased its distance by this amount. Fig. 2.8 shows the present position of the Earth and retarded position, that is, the position at a time r/c before the present position. The figure also shows the “extrapolated” position, or the position that the Earth would have reached if it had moved at constant velocity along a straight line beginning at the retarded position. This extrapolated position is nearly on the same radius as the present position, but the radial distance is large by the amount given by Eq. [194]. As a rough estimate for the force felt at the Sun, we take that force which the Earth would exert if stationary at the extrapolated position. This estimate for the force gives [math] \frac{{GM1M}}{{(r + \Delta r)^2 }} \simeq \frac{{GM1M}}{{r^2 }} - \frac{1}{2}\frac{{GM1}}{{c^2 }}(\frac{{2GM1M}}{{r^3 }}) [/math] [195] Of course, Eq. [195] is no more than an educated guess. Essentially, we are assuming that the force depends mainly on the velocity of the Earth at the retarded time, and that to this the acceleration contributes only some insignificant corrections (which have to do with the emission of gravitational radiation). If only the velocity is important, then the force exerted by the Earth is the same as that for a mass that moves with uniform velocity from the retarded position and reaches the extrapolated position at the present time. (For a mass moving with uniform velocity, the center of force will coincide with the position of the mass, as becomes immediately obvious if one asks for the force as seen from the rest frame of that mass. However, the transformation to the rest frame of that mass introduces relativistic corrections which are typically of the same order of magnitude as the extra term in [195]). The difference between action and reaction is then of the order [math](\frac{{GM1M}}{{rc^2 }})(\frac{{GM1}}{{r^2 }})[/math] [196] The inequality of action and reaction implies a violation of momentum conservation. The question is now; Where does the momentum go? There is only one place it can go—it must be stored in the gravitational field. What is conserved is not the momentum of the Earth-Sun system, but rather the momentum of the system of the Earth-Sun system, but rather the momentum of the system consisting of Earth, Sun, and gravitational fields. This interpretation is in accord with our estimate [196]. To see this, note that GM1M /rc^2 may be interpreted as the “mass” associate with the interaction energy (potential energy) between the Sun and the Earth. This energy is stored in the gravitational fields, and as the Earth orbit the Sun, so will this extra “mass.” To obtain the rate of momentum transfer to the fields, we must take the product of this “mass” by a characteristic acceleration. A reasonable estimate for the acceleration is GM1 /r^2, and the product then has the form [196] ======================================== From [195] [math]\frac{{GM_1 M}}{{(r + \Delta r)^2 }} \simeq \frac{{GM_1 M}}{{r^2 }} - (\frac{{GM_1 M}}{{rc^2 }})(\frac{{GM_1 }}{{r^2 }})[/math] [195] [math]\frac{{GM_1 M}}{{r^2 }} - \frac{{GM_1 M}}{{(r + \Delta r)^2 }} = (\frac{{GM_1 M}}{{rc^2 }})(\frac{{GM_1 }}{{r^2 }})[/math] [A] In the eq. [A] Below term is eq [196] [math](\frac{{GM_1 M}}{{rc^2 }})(\frac{{GM_1 }}{{r^2 }})[/math] = (mass of gravitational potential energy) X (acceleration) term From the gravitational potential energy [math]| - \frac{{GM_1 M}}{r}| = mc^2 [/math] --> [math]\frac{{GM_1 M}}{{rc^2 }} = m[/math] Generally gravitational acceleration term a = - GM1/r^2 ([math]\vec F = m\vec a = - \frac{{GM_1 m}}{{r^2 }}\hat r = = > \vec a = - \frac{{GM_1 }}{{r^2 }}\hat r[/math]) If [math]\vec a = \frac{{GM1}}{{r^2 }}\hat r [/math], Namely, if acceleration term is positive, it means antigravity. So, gravitational acceleration term [math](\frac{{GM_1 }}{{r^2 }})[/math] is absolute value of acceleration. So, strictly speaking eq. [A] is [math](\frac{{GM_1 M}}{{rc^2 }})(\frac{{GM_1 }}{{r^2 }}) = ( - \frac{{GM_1 M}}{{rc^2 }})( - \frac{{GM_1 }}{{r^2 }}) = - \frac{{GM_1 ( - \frac{{GM_1 M}}{{rc^2 }})}}{{r^2 }} = - \frac{{GM_1 ( - m_ - )}}{{r^2 }}[/math] --------------------------- [ Einstein said, "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". ] means that below shape [math] ma = - \frac{{GMm}}{{r^2 }} [/math] namely, a= - GM/r^2 (In the book "Gravitation and Spacetime") mass is not concerned it. --------------------------- From the eq[A] [math]\frac{{GM_1 M}}{{r^2 }} - \frac{{GM_1 M}}{{(r + \Delta r)^2 }} = - \frac{{GM_1 ( - m_ - )}}{{r^2 }}[/math] [C] [math] - \frac{{GM_1 M}}{{(r + \Delta r)^2 }} = ( - \frac{{GM_1 M}}{{r^2 }}) + ( - \frac{{GM_1 ( - m_ - )}}{{r^2 }})[/math] [math] - \frac{{GM_1 M}}{{(r + \Delta r)^2 }} = - \frac{{GM_1 (M + ( - m_ - ))}}{{r^2 }} = - \frac{{GM_1 M^{'} }}{{r^2 }}[/math] [D] ============== From the above in SR, [math]E = M^{'} c^2 = (M + ( - m_ - ))c^2 [/math] or [math]E = M'c^2 = (\gamma M + ( - m_ - ))c^2 [/math] So, we can explain that gravitational potential energy(or negative binding energy) has a negative mass. However, Negative mass is stable at the maximum point. Therefore the catastrophe to energy level of minus infinity never happens http://www.scienceforums.net/forum/showpost.php?p=529741&postcount=5 Therfore, In my think From the “mass and energy equvalance” 1) We can treat that gravitational potential energy has a negative mass. (Standard expression is "mass deficit") 2) Newton’s eq. of the negative mass is [math] - m_ - a = - \frac{{GM( - m_ - )}}{r}[/math] ([math]m_ - \ge 0[/math]) or [math]m_ - a = - \frac{{GMm_ - }}{r}[/math] ([math]m_ - \le 0[/math]) Two notational systems are same.