Gravity
Gravity
The Standard Model of non-gravitational forces provides a quantum-mechanical description of particle physics. In it, the effect of electromagnetic and nuclear fields on elementary matter particles are described in terms of elementary force particles. Gravity and its interaction with mass stand outside the standard model. To simplify the discussion of gravity and spacetime, it is normal practice to focus on a region small enough for the gravitational force to be considered constant throughout. It then becomes an inertial reference frame in which physical experiments will give standard results. It is a region in which the standard model and special relativity hold true. In such an inertial reference frame the acceleration for the short period in which it is crossed can be considered constant. This is familiar in our calculations near the surface of the earth. We assume the gravitation force is the same at the top of a building as at the bottom, with everything falling at one-g from top to bottom. That is the sort of assumption being made here.
Special relativity applies to observation of masses moving at uniform speeds. But we can also apply special relativity to observation of a mass undergoing a constant acceleration. It is a matter of using the instantaneous velocity of the mass at a given time in an inertial reference frame when applying the relevant equations. Then we get an indication of the shrinking of space and time for the velocity at that particular instant. A series of calculations will show a progressive shrinkage as the acceleration produces higher velocities over short increments of time within the period we examine. When the gravitational field increases, we have to observe events over a smaller interval for the equations we use to be true.
We can look at this another way, by using Einstein's equivalence principle, which also is accurate only over the small region of space constituting an inertial reference frame. Einstein found that in such a frame it is not possible to distinguish between an acceleration and a gravitational field. Thus, the shrinkage in dimensions taking place due to an acceleration can be equally well attributed to a gravitational field. This does not surprise us because we are used to thinking of acceleration being caused by a gravitational field. So we conclude that the effect of a gravitational field is to shrink spacetime quanta dimensions in the direction of the acceleration we observe.
In short we find that when mass creates a gravitational field, the field shrinks spacetime quanta in the direction of increasing field. But we may equally well assume that the shrinkage in spacetime quanta causes mass to accelerate in the direction of shrinkage. That is, as Einstein postulated in his general theory of relativy, mass distorts spacetime and the distortion of spacetime governs the path of mass.
This actual distortion of the lattice goes counter to the initial assumption that there is an absolute minimum to length and time that gives rise to a uniform lattice. Therefore, as in special relativity, this assumption has to be replaced by the more fundamental assumption that in the presence of gravity the speed of light remains constant, even as the effective Planck length and Planck time decrease. That is, the ratio of Planck length to Planck time remains constant. The universal constants are ratios that govern the relationships between physical quantitites like space, time, mass and energy.
Mass particles move under the influence of a gravitational field. if you will pardon the tautology, as if they were rolling down hill. The effect is realized in the lattice by movement of particles in the direction of contraction of the spacetime quanta. In a sense, the particles move in the direction they have less distance to travel. The effect is illustrated when a small body like a rock falls to Earth. The mass of the planet creates a very large gravitational field compared to that of the rock. So the rock sees a contraction of spacetime in the direction of the Earth and moves in the direction of the contraction. The Earth sees an extremely small contraction in space time at the rock, due the smallness of the mass of the rock, and moves an infinitesimally small distance towards the rock. The distortion of the lattice by the Earth's gravity also causes composite assemblies in space, such as spacecraft, to move as a whole towards the Earth. A long object that extends beyond the short region under discussion, the inertial reference frame, will actually be physically distorted by differential shrinkage in the stronger part of the gravity field. The motion of the body will then be more complex, as the distortion is both part of the motion and of further distortion of the gravitational field.
In intense, non-uniform gravitational fields, the differential shrinkage will cause space itself to become curved. It could curve so much that the shortest distance across a circle could become an arc in three-dimensional space. In this case, the extra length of the arcs in a circle can change the ratio between the circumference of a circle and its diameter, so that the value of pi is no longer constant. When this occurs the increase in the diameter is a measure of the curvature of space [14].
Gravitationally Collapsed Objects
For a composite body to maintain its integrity, its internal forces must resist the distortions of the spacetime lattice caused by mass. In an active star, the resisting force comes from the outward pressure of energy released by nuclear fusion. But when the fuel for fusion is exhausted, the internal distortion of space by the mass of the star causes it to fall inward on itself. If it has sufficient mass it will form a collapsed object that distorts the spacetime lattice so strongly that it prevents the escape of light, radiation, and matter. The surface where this occurs is termed an event horizon.
A qualitative description of what happens to the spacetime lattice at an event horizon like this can be gained by considering an object called a Schwarzchild black hole (spherically symmetric and stationary, [15]). Contours of the intensity of the field around the spherical object will become increasingly close together as the horizon is approached. Consequently, the spacetime quanta spheres around the object will become progressively distorted the closer they are to the event horizon. In two dimensions, which are easier to visualize, the contours of gravitational field strength will be concentric circles spaced closer and closer together as the event horizon is approached, with the added complexity (not accounted for here) that pi is changing as space curvature in three dimensions intensifies.
The effect of the field is to compress the spacetime quanta in the radial direction of the event horizon, reducing the Planck length and time. Suppose an external observer outside of the field has a space probe with a light clock whose bounce time is relayed to her by a flash of ultra-violet radiation. , The probe moves slowly towards the collapsed object, relaying the time of light clock flashes as it does so. It moves slowly to avoid a change of frequency by the Doppler effect.
As measurements are made closer to the event horizon, the period between flashes increases – the onboard clock is slowing down. From the observer's point of view, the time interval of each quantum is decreasing. This is comparable to the time shrink of quanta a ground observer envisions when a clock appears to slow down in a spacecraft moving at constant speed. The gravitational slowing, however, is a real effect. It is an experimentally verified prediction of general relativity. Clocks do slow in a gravitational field (16).
At the same time, the frequency of the transmitted flash decreases. It too is a clock. The light moves down the spectrum from ultraviolet to the visible region, to the infrared, to radio wavelengths, to an infinite wavelength at the event horizon. The observer is seeing time slowing down in the gravitational field. Eventually, the light is extinguished when it reaches the event horizon. The time dimension of the quantum in the direction of the event horizon has gone to zero. In synchronism with this, the delay between flashes has become infinite: the light clock in the space probe has stopped. Throughout this train of events, the size of an inertial reference frame has been shrinking, so that it too has gone to zero at the horizon. The principle of equivalence does not hold true. We can no longer consider that a gravitational field and an acceleration are indistinguishable when the absence of space and time invalidates the concept of acceleration.
As the Planck time goes zero, the Planck length does likewise There are no quantum dimension in the radial direction: the next length interval never comes. For the external observer, time at the event horizon has stopped and space in the radial direction has gone to zero. The spherical symmetry of the gravitation field has turned the spacetime lattice at the event horizon into a spherical shell of two-dimensional spacetime quanta. Unlike the slowing and contraction in special relativity, which varied with the velocity of the observer, this is a real physical effect. It creates a spherical shell of zero thickness. Here is a form of the two-dimensional eternity mentioned in the introduction.
The spherical Planck volume of a spacetime quantum in the lattice has become the fundamental, circular Planck area. This is an indication of its fundamental nature, in comparison with the Planck length. Planck areas cover the event horizon of a gravitational shell. The interstices between the Planck areas continue to contain formless energy. In addition, this interstitial energy has been squeezed into the ”interior” of the spherical event horizon. As this energy is in atemporal and aspatial eternity, it is difficult to describe it as "interior", except as viewed from outside the shell.
Within the shell there are no dimensions in space or time. Furthermore, as argued previously, it has no mass. All of the collapsed-object mass is on the surface of the spherical event horizon. So is all the mass subsequently attracted to the shell. Mass does not fall through the event horizon to meet an unknown fate at a singularity. There is no hole to fall through. The full gravitational field is at the horizon. We may view the gravitational shell as that awesome object described by Pascal and the gnostics -- a sphere whose circumference is nowhere and whose center is everywhere.
To have achieved this form, the event horizon would have collected initially as a spherical seed that expanded as incoming material fuzed into radiation piled on top of it, sending a shock wave back radially, blowing off the outer material of the star while a flow of spacetime quanta and interstitial energy continued inward, compressing as they go. The infinite compression of the lattice shell collapses objects held together by non-gravitational forces. They undergo fusion into radiation that spreads throughout the two-dimensional array of spacetime quanta at the event horizon.
Gravitational Shell Temperature
To gain some impression of the quantitative implications of a gravitational, or black, shell, consider its predicted temperature at the spherical horizon. The calculation is shown in Figure 3.
For comparison, equation 1 gives the Schwarzchild radius [15] of the horizon of a black hole of mass M, where G is the gravitational constant and c is the speed of light.
Equation 2 gives the corresponding area of a black shell at the horizon over which its mass is distributed.
Equation 3 takes the area of the shell and divides it by the Plank area, Ap, to give the number of Planck areas, Np, over the black shell, bearing in mind that the interstitial energy between the touching circles has no area.
Equation 4 yields the mass in each spacetime quantum, Mp, by dividing the black shell mass by the number of Planck areas.
Equation 5 yields the energy per Planck area, Ep, by multiplying the mass Mp by the square of the velocity of light. Mp is far smaller than the mass of any known particle, so the energy will be in the form of radiation.
Equation 6 shows the formula for the Planck area, Ap, in terms of universal constants, where h is the Planck constant.
Equation 7 shows the energy per Planck area in terms of universal constants/
Equation 8 shows the conversion factor to go from energy to temperature, T, using the Boltzmann constant, k. As discussed in relation to entropy, there is only one degree of freedom.
Equation 9 displays the expression for temperature of the Planck area, Tp , and so for the black shell as a whole, TBS when the Boltzmann conversion factor is applied.
Equation 10, for comparison, shows the currently accepted expression, for the temperature of a black hole, TBH.
For a gravitational shell the size of the Moon, the expression yields a temperature of 1.7 K. A solar-mass gravitational shell would have a temperature of 6.2 x 10-8 K.
Entropy
The derivation of the entropy of a gravitational shell is shown in Figure 4.
The black shell entropy S is equal to the amount of hidden information on the shell, which amounts to the number of Plank elements on the event horizon, since there is none "inside" the shell. This is found by dividing the Planck area, equation 11, into the area of the horizon, equation 12.
The formula for calculating black shell entropy then becomes that shown in equation 13.
For comparison, the corresponding equation that has been derived for a black hole is shown in equation 14. The difference may be related to the entropy of the material that is assumed to arrive at a singularity (a region where the laws of physics no longer hold) said to reside at the center of a black hole.
The approach to spacetime proposed here indicates that the mass of a gravitationally collapsed object is on the event horizon. Contrary to theories that assume the mass is located inside the event horizon and can be considered to be at the center of gravity of a spacetime sphere, this theory indicates that an astronaut would not fail to notice her arrival at the event horizon of a black shell with the mass of several million suns. There would be no safe passage to the interior. The spacetime quanta containing her particles would be flattened and added to the shell, expanding it. She would be fused into radiation on her own little patch on the horizon. Time having come to a stop, there is no motion on the horizon.
From the point of view of eternity theory, what is called a black hole is a actually a black shell. Its event horizon is pierced by the formless energy of the interstitial medium, which also fills the spherical region created by the two-dimensional spherical event horizon. To the extent that there is anything in a gravitational shell, it is energy existing in aspatial, atemporal eternity. This has no spacetime dimensions. There is no there there.
1/12/2016