Ten Minutes for Physics Number 8 The Proton Joseph M. Brown Basic Research Press Ten Minutes for Physics Number 8 The Proton (c) 2001 Copyright owned by Joseph M. Brown ISBN: 0-9712944-0-2 Published by Basic Research Press 120 East Main Street Starkville, MS 39759 United States of America www.basicresearchpress.com Ten Minutes for Physics Number 8 The Proton We describe here the proton structure as derived from the kinetic particle theory of physics. The postulates of the theory are that everything is made up of one type of Newtonian particle. The particles have no force fields and they interact only by a repulsion when they contact each other. The particles make up a gas that pervades all the universe. In most of the universe the gas is uniform, but in a good proportion of the universe there are stable inhomogeneous assemblages of these particles. The homogeneous gas has a particle number density which is uniform over space, has velocities whose directions are distributed uniformly over a sphere, and has speeds which are distributed as given by the Maxwell-Boltzmann (bell-shaped) curve. The arithmetic mean of the speeds is vm. The square root of the speeds divided by the number of particles, i. e., the root mean square or rms speed, is vr. With the Maxwell - Boltzmann speed distribution distribution the rms speed is greater than the mean speed; their ratio is vr/vm. The stable inhomogeneous assemblages are vortex-like structures which vary in "mass" (i. e., energy divided by the square of their speed) over many orders of magnitude, which develop a large propulsive force making them translate at the speed of light, and which have angular momentum which is a constant value independent of their mass. These assemblages are the neutrinos. A proton consists of a single neutrino which, when the proton is at rest, orbits in a circular path. The proton is formed of the single neutrino. The orbit of this neutrino must produce the same angular momentum that the original translating neutrino had and the orbit radius must be so that the centrifugal force balances the neutrino propulsive force. There is one, and only one, mass of neutrino which satisfies these constraints. That neutrino has the mass of the proton. The dominant type of neutrino has a solid core, which is made up of background basic gas particles that were taken from the background and aligned but with their speed unchanged, then squeezed together so that they all move at the same speed. In this final compression process if the total particle energy remains constant the flow velocity must increase from the mean speed, vm, of the background particles to the rms speed, vr; an 8% increase. To increase this speed a longitudinal force must be applied to the periphery of the particle core assemblage. The total assemblage then translates at a speed vr-vm which, of course, means that the speed of light "c" is vr-vm. The propulsion mechanism of the neutrino depends upon the rate at which particles come into the core and not on the size of the core, i. e., the propulsive force is independent of the size of the neutrino as measured by its "mass" (i. e., the neutrino energy divided by the square of the speed of light) is directly dependent upon how many background gas particles have been collected in the core. Everything observed in the universe is a direct result of the neutrinos with their variable sizes and with their constant propulsive force. The propulsive force of the neutrino is now computed. Force is the time rate of change of linear momentum. Thus, the force is the particle mass inflow rate times the momentum imparted per unit mass (i. e., the velocity change). The inflow is assumed to reach the mean speed of the background gas at a radius equal to 2.2 times the mean free path, and further, the local density at the mean free path distance from the neutrino center is assumed to be the same as the background density. Mass flow is (Av, where ( is the density, A is the area, and v is the velocity. The increase in velocity from the entrance into the neutrino, which is a spherically symmetric flow and thus has no net longitudinal flow velocity, to the exit is vr-vm (i. e., the velocity increase). The neutrino propulsive force thus is In this expression (o is the background mass density and "" is the mean free path. If the background mass density and the mean free path were known then the propulsive force could be determined. The gas condensation mechanism of the neutrino also produces another all-pervading phenomenon. During condensation it is not possible for the gas to take a straight-line path into the core. It is necessary that the gas take a spiral path. As a result of this spiraling and the final condensation into the hard core the neutrino has a particular amount of angular momentum-i.e., mass times velocity times the radius of curvature. This angular momentum depends upon the flow rate which is a constant for all size neutrinos and thus has a constant value for every size neutrino, just like the propulsive force. Since everything observed in the universe is a result of neutrinos, everything has an angular momentum that is an integral value of this basic angular momentum. (The multiple can be zero since a particle could have two neutrinos with their angular momentum each in opposite directions.) In computing the angular momentum of the neutrino we assume that the angular momentum of the solid core is negligible and that the angular momentum is the outflowing mass at the flow speed vr (flowing in the opposite rotational direction) and all this occurs inside the volume defined by the radius equal to the mean free path. The mass of inflowing particles inside the sphere with a radius of the mean free path is the inflow rate times the time required to reach the core, which is . The outflowing mass is the same. The angular momentum is computed by assuming all the mass is rotating at . With these assumptions, and knowing that the angular momentum of the neutrino is , where is Planck's constant, we have (since vr-vm=c). From this we have Let us now come to the simplest matter particle--the proton. A proton consists of just one single neutrino. The proton is formed when a neutrino that has the same mass as the proton is impacted by another massive neutrino and knocked into a circular orbit. Once in this circular orbit the correct mass neutrino (i.e., neutrino with the same mass as the proton) will remain in that configuration. This configuration is extremely stable. Since each neutrino has a propulsive force it should be possible for a neutrino to take a circular path with the propulsive force directed inward toward the center of rotation. This propulsive force should be able to just balance the centrifugal force. The neutrino always moves at the speed of light so that for any given mass neutrino there is a certain radius at which the centrifugal force would exactly balance the fixed value of propulsive force. However, recall that the original translating neutrino had a fixed angular momentum that must remain the same if it were placed into a circular orbit. With the constraints that the neutrino move at the speed of light (in orbit), that the centrifugal force balance the propulsive force, and that the angular momentum remain the same as for the translating neutrino (remember the basic law of conservation of angular momentum), there is precisely one value of neutrino mass that will meet all these conditions. This mass is the mass of the proton. The neutrino making up the proton thus must have the mass of the proton. The great mystery of why the proton has just one value of mass is solved by this mechanism. A neutrino in orbit is what makes matter. When we speak of mass we most often mean the mass of matter. However, linearly translating neutrinos have mass-but they are not matter. Every bit of matter in the universe is constructed out of orbiting neutrinos just like the proton. From this mechanism of matter construction it is clear why matter can not move at a speed greater than the speed of light. In order for matter to move it is necessary for the orbiting neutrinos (which make up all matter) to take a spiral path. The path must always be such that the centrifugal force and the fixed propulsive force balance each other. As the proton neutrino takes its circular path (i. e., for the proton at rest) it stirs up the background. This background disturbance is essentially a spherically symmetric phenomenon at a distance of a few proton radii. This disturbance is the electrostatic "field" of the proton. We now compute the mass of the proton. The centrifugal force of the proton is Where Mp is the proton mass and rp is the proton orbital radius. This is balanced be the neutrino propulsive force. Thus . From this The angular momentum is from which Substituting rp from the above into the equation for the proton mass gives or Thus, knowing the parameters characterizing the basic postulated gas the proton mass can be determined. The equation for the proton mass also can be solved for the unknown constants characterizing the kinetic particle universe as . From the basic angular momentum equation (for the neutrinos) we have Equating (o from the above from the above two equations gives This gives the mean free path "" as Substituting , and m/s gives m Further =0.0498 x 1.054 x 10-34/(3.00 x 108 x 10-64) = 2.87 x 1016kg/m3 We note that the mean free path is in the order of the sizes of the fundamental particles. We also note that (o is an extremely large number. There are other approximate approaches for obtaining these quantities ("" and (o). The resulting analyses give results in the order of these quantities. We have done calculations which indicate that the basic particle diameter may be the Planck length, i. e., where G is the universal gravitational constant From this the basic particle radius rb is given by We now can find the mass of the particle. The particle number density is The basic particle mass "mb" is given by As a check on these numbers we can compute the radius of the (assumed spherical) core of a neutrino with a "mass" equal the electron mass. The neutrino core radius r( is given by Where 1.2 is the assumed packing density of small spheres packed into a large sphere and N is the number of basic particles. Thus The number of basic particles in an electron is given by Now The cross sectional area A( of this assumed spherical core is This quantity is not greatly at variance with measured scattering cross sections of neutrinos. This is one of the reasons we anticipate that the basic particle diameter may be the Planck length. 1 1