Rodolfo Sergio González Castro. HAL Id: hal v2

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1 Equation of the force of gravity resulting from the Planck Energy/Area and wavelength of De-Broglie without using the Universal Gravitation Constant Newton. Rodolfo Sergio González Castro To cite this version: Rodolfo Sergio González Castro. Equation of the force of gravity resulting from the Planck Energy/Area and wavelength of De-Broglie without using the Universal Gravitation Constant Newton <hal v2> HAL Id: hal Submitted on 19 Feb 2014 (v2), last revised 25 Mar 2014 (v8) HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 Equation of the force of gravity resulting from the Planck Energy/Area and wavelength of De-Broglie without using the Universal Gravitation Constant of Newton. Rodolfo Sergio González Castro Research Institute, University of Tijuana CUT, Av. Lucrecia Borja 1010, Col. Altamira, Tijuana, Baja California, Mexico. CP BA in Psychology, MSc. Administration General (MBA), MSc. Education, PhD candidate in Education, Theoretical Physicist Autodidact. Abstract In this paper I show that it is possible to calculate the force of gravity deriving an equation of the Planck Energy/Area and wavelength of De-Broglie associated with particles or massive objects in gravitational interaction without use the universal gravitational constant of Newton (G). OAI: hal.archives-ouvertes.fr:hal PACS: Kd Newton Keywords: physics, particles, gravity, gravitation constant, 1. INTRODUCTION The mathematical physicist Sir Isaac Newton in 1687 published his book "Philosophiae Naturalis Principia Mathematica" where he presented the law of universal gravitation empirically derived to describe and calculate quantitatively the mutual attraction of each particle and massive objects in the universe. In that document, Newton concluded that the attraction together two bodies is proportional to product of their masses and inversely proportional to the square of the distance that separates them. However, these must be adjusted proportionalities by introducing a constant called Universal Gravitation (G) with an approximate value of N m2 kg-2 units in the International System. Without the introduction of this constant, the equation, lose their rationality and is impractical to calculate the force of gravity without it. For Newton, gravity is considered a force exerted on a remote Instant. Moreover, when the gravity force is exerted by two or more bodies extremely mass, Newton's law has serious limitations and then must resort to the Theory of Relativity General stated by Albert Einstein in 1915, who says that gravity is not a force exerted to distance but a contraction of Space-Time produced by the presence of matter (1). However in the final formulation of the equations of the universe, to make it compatible with the law of conservation of energy and principles of general covariance and minimal coupling, Einstein included mathematical concepts such as the Ricci Tensor and scalar, but mainly the energymomentum tensor, but fails to integrate into

3 said Energy-Momentum Tensor the constant Universal Gravitation Newton, as this is finally out in the second member of the equation. While Einstein equation establishes the relationship between gravity, energy and geometry distortions spacetime, it does not define the origin of the relationship. Subsequently in 1995 Jacobson linked the laws of thermodynamics to the Einstein equation and the equation of state correlates with entropy the energy sector flow (2). Erik Verlinde published on January 6, 2010, his work "On the Origin of Gravity and the Laws of Newton" (3), which proposed that gravity is a reality entropic force emerging space. In its formulation, includes reduced Planck's constant, N as a Screen of information bits of space, adds a new constant called G, which ultimately Accounts found to be equivalent to the Universal Gravitational Constant. On that basis, Verlinde forecast to gravity as a fundamental force. In March 2010, Jae-Weon Lee, Hyeong-Chan Kim and Lee Jungjai published a paper in which suggest that the Einstein equation can be derived from the principle of Landauers on the Elimination of information causal horizons, and conclude that gravity has its origin in quantum information (4). From then such work is also supported by Jacobson linking between thermodynamics and the equation Einstein, as well as on the work of Verlinde entropic force. Thus, we already have a strong linkage between energy, heat, laws of thermodynamics, theory general relativity, perturbation of the geometry of space-time, entropy and quantum information, but somehow linking gravity and electrostatic force has been fails to integrate in all this work to finally derive the Einstein equation and the gravitational constant universal. From my point of view, crucial to successfully solve the equations of gravity aspect is the distribution of Plank area, and both invariance in all particles and massive objects in the universe, as discussed in this paper. Derive a gravity equation that eliminates the universal gravitational constant and link strength gravity with the electrostatic force requires on the one hand make Planck area invariant, and include in the equation the length of De Broglie wave. I.-GRAVITATIONAL ENERGY DERIVED FROM PLANCK ENERGY/AREA Newton's equation establishes the relationship between mass and gravity, while the equation Einstein relates the Energy-Momentum Tensor with the modification or distortion of space, which is more proper perspective proposed here, including in the case of particles resting or non-relativistic speeds. For particles at rest, Einstein's equation defines the Energy-Momentum tensor in the coordinate time (t). I mean, you have a single source of tension, so the above equation requires the universal gravitational constant outside the tensor. This work is based on the priori hypothesis that particles resting actually have two sources of tension at different times (t) with different effects in terms of pressure on space. The first source of tension generated electrostatic force, while the second source of tension is the cause of the gravitational force. To explain this I have to consider the existence of a hypothetical particle whose Plank energy

4 distribution in space is the area of a perfect square: Y = = = 1, E-34 m X = = = 1, E-34 m electrostatic effects and Gravity effects are "visible" to outside observers. In other words, the ratio of Planck Area is invariant in all of the particles and objects mass of the universe when they are at rest or non-relativistic speeds. Here graphically proportional representation of an electron according to Planck Energy/Area: Y = = 4, E-57 m Both the axis (X) and the axis (Y) corresponding to the Planck length. Both faces of the square axes exert pressure on space, or in terms of Einstein, Energy-Momentum produce tensor. In the Axis (X) the Energy- Momentum tensor is exactly the same as Einstein or first source of tension, but for axis (Y) still corresponds to second source of tension or gravity source. However, in the case of the hypothetical Plank particle, because both axes or faces have equal length, and in the case of (Y) perpendicular pressure is negative and therefore, the two pressures or two source of tension cancel each other. In terms of the De Broglie wavelength to be exactly equal in length and amplitude but opposite to each other, they cancel each other, so that an external observer can t capture the presence of the Planck particle in electrostatic or gravitational terms. It is then a "Null particle" or "Space Empty". By the law of conservation of the area, or a hypothetical "law of conservation of space, an electron or any other particle in the universe always retain the same area of Plank. if the (X) axis is lengthened, then proportionally axis (Y) will be shortened. But also at the time at which the lengths (X) and the lengths (Y) are different, they stop cancel each other and the X = = = 2, E-12 m Note: The graph of the rectangle is not exactly proportional to the scalar quantities for obvious reasons. As will be seen, in the electron, because (X) is too extension with respect to the length of Planck, then (Y) is proportionally shortened and wavelength being excessively small but sufficient to generate gravitational effects of the electron. In other words, the particles are like strings or threads whose extension in the X axis is much longer compared to the Planck length, but the width, height or thickness (Y axis) is very short. In this sense, the present work of the a priori hypothesis that all the specific objects universe and all clusters of material occupying a particular area of space, whether electrons, protons, atoms, planets, stars and galaxies, all can be considered as "particles" whose distribution of energy per occupied space area, rigorously meet the total Planck energy distributed in the Planck area or area of the particle according to the following equation: = (1.1)

5 Where Ep is Planck's energy and N is the ratio of the rest energy of any particle or object mass and the Planck energy given by the equation: (1.2) Substituting N into Equation (1.1) then the energy distribution in an area Planck is given by: (1.3) In this case (E) corresponds to the rest energy of any known particle or massive object, while (Eg) in equation described below corresponds to the "Gravitational Energy" not known so far (Virtual, dark, pop, entropic or whatever you want to call) existing in the area occupied by a visible particle or massive object, which although is not observable or detectable until now, its possible existence is the source of gravitational attraction. (1.4) Both the rest energy (E) as the gravitational energy (Eg), both have a wavelength according to the associated de Broglie postulates given by the familiar equation: That in the case of the gravitational energy, the corresponding equation is: The product of two wave lengths, corresponding to the wavelength of Planck: ( 1.5) Where h is Planck's constant and c is the speed of light, and where is the wavelength of Broglie energy at rest and is the gravitational wave length. 2. GRAVITATIONAL COUPLING Because the two wavelengths originate almost "simultaneous", the Wavelength gravitational be coupled to the wavelength of the rest energy, Generating a factor of coupling to the gravitational force given by: (2.1) Where is the factor of gravitational coupling. For the electrostatic force, value coupling is considered constant (Fine Structure), but, in the case of gravity, said coupling depends on the ratio of both wavelengths (and thus Energy) as shown in the equation THE EQUATION OF GRAVITY FORCE WITHOUT CONSTANT GRAVITATION Thus if we have defined or calculated the "Gravitational Energy" derived from the Planck Energy/Area, the De-Broglie wavelength associated Gravity and Gravitational coupling factor, we can then stating a priori an equation for the gravitational attraction between two particles or massive objects identical to or have the same amount of mass: = (3.1) And for the case of two different particles or objects mass: (1.6) = (3.2)

6 Then comes to be a general equation for calculating the force of gravity without the use of the gravitational constant of Newton and based on Planck Energy/area, and Wave length De Broglie. Moreover, due to the existence of a constant in this equation, it is possible to reduce it further. In this case the product of the energy (E) for its associated wavelength is constant: E-25 joules per meter (3.3) Which in turn we reduce as in the case of Planck's constant: E-26 joules per meter (3.4) Thus we can write a new equation for calculating the gravitational force between two equal mass particles or objects: = = (3.5) And for the interaction between two particles or different massive objects: = Thereupon (3.6) = (3.7) It is my final general equation for calculation of the force of gravity between two particles or objects mass. 4. DERIVATION OF EQUATION OF CALCULATION OF FORCE ELECTROSTATIC About the same arguments above, the calculation of the electrostatic force between two particles is still simpler due to electrostatic coupling constant or fine structure. In this case, we carried a broad general shall term a priori constant Electrostatic Universal Constant: per meter E-27 joules (4.1) No matter how much rest energy of the particle, the electrostatic force is always the same and will vary only based on the distance. That is, the calculation of the electrostatic force between two identical or different particles is given by the general equation: = = (4.2) Where E is the energy at rest, the wavelength of de Broglie, coupling constant or Fine structure, d is the distance between the two particles. But it is possible to reduce it to eliminate (2 Pi) in the equation: = (4.3) That is my general equation for calculating the electrostatic force between two identical particles or different. This equation is equivalent to Coulomb's law: = For the case of two particles in load electrostatic interaction. = = =

7 Again, I must point out here that the develop equations for calculating the force of gravity are for particles or massive objects at rest or in non relativistic speeds. My next job will be related to cases of relativistic velocities integrated into the Einstein Tensor. 5. CONCLUSION Having proven naturally and clean that gravity is possible to calculate from the Plank energy/area and De Broglie wavelength without using the gravitational constant Newton, paves the way for a unified theory of everything, and in that sense can assert a priori: 1.-That to calculate the electrostatic force of gravity in terms necessarily need to include the concept of "Gravitational Energy" derivative of the Planck energy/area. 2.-That the electrostatic force and the force of gravity can be calculated from the Planck Energy/area. 3.-That because the wavelength of the energy at rest and the wavelength of the "Energy Gravitational" originate form virtually "simultaneously" because this, the wavelength Gravity be coupled to the variable length of electrostatic wave form, which so far had hampered their electrostatically calculation. 4.-Developed here that the equation for the calculation of the force of gravity, is actually an equation electrostatic force, instead of using the fine structure constant, must use the variable gravitational coupling due to the argument of the previous paragraph. 5.-And I can finally conclude a priori, due to the equations presented here that the force of gravity It is also modulated by the variable electrostatic force of gravitational coupling. REFERENCES 1. Wald RM. General Relativity. University of Chicago Press; Available from: ISBN= Jacobson T. Thermodynamics of Spacetime: The Einstein Equation of State. arxiv.org. 1995;Phys. Rev.(qr-qc/ v2): Verlinde E. On the Origin of Gravity and the Laws of Newton. 2010;(arxiv: v1): Lee J, Kim H, Lee J. Gravity from Quantum Information. 2010;(arXiv: v2).