Session X10: Alternative Gravity II

Curvature, vacuum energy and the quantization of gravity

On technical grounds pertaining the quantization of gravity we argue for the convenience of taking the metric and the connection to be independent. Then we point out that some important logical implications of this assumption have not previously been considered enough or at all. Among the latter is the existence of a second curvature tensor written, not in terms of the connection, but of the metric. The use of this term enables the construction of a Lagrangian that has a much a much more benign high energy limit than Einstein's theory, while at the same time is identical in the low-energy limit to that theory. In the high energy limit the Lagrangian becomes very similar to a Yang-Mills theory. Of course, the different behavior in these two widely separated limits requires the introduction of an energy scale. This very large scale is conveniently supplied by the vacuum energy of quantum fields. As a fringe benefit the vacuum energy from the quantum fields cancels out automatically no matter its value.   

Dark Energy and the Age of the Universe

Most attempts to explain the nature and behavior of Dark Energy propose some scalar field to supply the energy, such as a cosmological constant, quintessence, phantom energy, tracker, and other scalar fields. The work described in this talk takes an entirely different tack, using a semi-classical approach to derive the dark energy from a previously unnoticed consequence of quantum mechanics on a cosmic scale. Because the age of the universe is finite, it follows that each quantum level in the universe is increased by a miniscule amount, 3*10$^{-33}$ eV. The total effect of this small increment of energy is cumulative over all the quantum numbers in the universe. An estimation of the net sum of all the universe's quantum numbers (which overwhelmingly arise from gravity) is $\sim $4*10$^{122}$, and the product of these values yields the total extra energy arising from this quantum mechanical effect. The result is close to the accepted value for the universe's Dark Energy content. With the additional assumption that time-dependent perturbative changes in the energy levels convert into matter, the value of the quantity of matter in the universe and the coincidence paradox are also resolved.   

Newtonian Gravitation and General Relativity as Possible Classical Corresponding Theories to Quantum Gravity

There are many traditional methods used by theoretical physicists to create a comprehensive theory of gravity that works on both the macroscopic and quantum scale. One common idea has been to unify the theory that works for gravity on the macroscopic scale, namely general relativity, with quantum mechanics, the theory that is used in modeling the behavior of entities on the micro scale. However, we propose the possibility that both the theory of general relativity and Newtonian Mechanics may be viewed as classical analogues to gravity's true quantum nature. In the same manner that the harmonic quantum oscillator mirrors the classical one (at high $n)$, the manner in which both theories treat gravity as a continuous potential that changes inversely with distance with respect to its source may indicate a similar correspondence, implying an underlying quantum characteristic of gravity. This also implies that both general relativity and Newtonian Mechanics are successful theories (on the large scale) by virtue of the fact that they were created specifically to model gravity on the macroscopic scale.   

Quantized Gravitation of Electromagnetic Waves as a Possible Solution to the Pioneer Anomaly

Analysis of radiometric data from the Pioneer 10 and 11 probes indicate that they are begin slowed by an anomalous constant acceleration with an average magnitude $a_{P} \quad \sim 8\times 10^{-8}cm/s^2$oriented with respect to the sun. We propose that the nature of the acceleration is due to a curvature of the space-time continuum caused by the suns light, which is predicted by G.R. We describe the acceleration as a quantized effect that depends on the frequency of the light and not the intensity, a kind of photo-gravity effect analogous to the photoelectric effect. The acceleration can be described by the equation: \[ a=[h]\nu c \] The constant used is equal to Planck's constant and is placed in brackets to indicate it is dimensionless: \[ [h]=6.626068\times 10^{-34} \] Although we associate the acceleration with the photons emitted by the Sun, we attribute the actual anomalous acceleration to gravitons associated with these photons. Any change in an emitted photon's energy is accompanied by a change in the energy of its associated graviton. We attribute the observable (acceleration) to the energy of the graviton. A photon's graviton's energy changes independently of its own, so we treat it as a separate variable, in the same manner that charge, spin and mass may be separate characteristics of the same particle. Separating the magnitude of the acceleration from the energy of its photon effectively shows why the anomalous acceleration is not seen in the planets. The planets, through their gravity fields, attenuate the acceleration associated with the photons by changing their energy through gravitational red-shift. Photons approaching the planets experience an increase in energy, but a decrease in graviton energy, or acceleration. Subsequently, planets alter the degree of perturbation to their trajectories by the acceleration. As the mass of the planets are much larger than the mass of the probes, they are able to effectively mask the anomalous acceleration detected in the Pioneers.   

Coherent and conventional gravidynamic quantum 1/f noise

Quantum 1/f noise is a fundamental fluctuation of currents, physical cross sections or process rates, caused by infrared coupling of the current carriers to very low frequency (soft) quanta, also known as infraquanta. The latter are soft gravitons in the gravidynamic case with the coupling constant g= pGM2/Nch considered here -- soft photons in the electrodynamic case and soft transversal piezo-phonons in the lattice-dynamical case. Here p=3.14 and F=psi. Quantum 1/f noise is a new aspect of quantum mechanics expressed mainly through the coherent quantum 1/f effect 2g/pf derived here for large systems, and mainly through the conventional quantum 1/f effect for small systems or individual particles. Both effects are present in general, and their effects are superposed in a first approximation with the help of a coherence (weight) parameter s" that will be derived elsewhere for the gravitational case. The spectral density of fractional fluctuations S(dj/j,f) for j=e(hk/2pm)$\vert $F$\vert $2 is S(F2,f)/$<\vert $F$\vert $2$>$ = S(j,f)/$<$j$>$2 = [4ps"/(1+s")]GM2/pfNch = 4.4 10E9 M2/(pfNgram2). Here s" = 2N'GM/c2=N'rs, where N' is the number of particles of mass M per unit length of the current, rs their Schwarzschild radius, and s" is our coherence (weight) parameter giving the ratio of coherent to conventional quantum 1/f contributions.   

Probabistic Aspect of Gravity

We postulate that every particle has a Planck size quantum mouth it stretches to interact with other particles, making all interactions between quantum mouths and the probability of an interaction between two particles is inversely proportional to the square of the statistical number of Planck lengths separating the particles [1], linking entropy, fine-structure constant and cosmological constant, explaining quantum tunneling, dark energy and some other issues consistent with some great minds. This was presented at the ``Concepts of Entropy and Their Applications'' conference in Melbourne, Australia on Dec 29, 2007. The natural logarithm connects the statistical entropy to thermodynamic and makes it consistent with the observed expansion of the universe with Hubble constant. [1] http://www.arXiv.org/physics/0210040   

A Quantum Theory of Gravity

Research unexpectedly uncovered a single vector cross product potentially unifying gravity with the electromagnetic field. It has been long established the Poynting vector cross products S = EXH was responsible for inertial mass in early eras from the high-intensity cosmic radiant density background, and photons of the EH field intensities mediate the electromagnetic force. However, pursuing further, Frank Keeney, president of Particle Physics Research Co,, recalled that D and B fields were also carried by photons, being uniquely inseparably connected with E and H by proportionality coefficients eo and $\mu$o, permittivity and permeability of space respectively, governing the speed of light equated as c = $1/({\epsilon}o {\mu}o)1/2$. However, incorporating these factors yields a second Poynting vector cross product S = c2DXB producing matter in which D represents the electric flux density and B the magnetic flux density of the photon. Of significance, he found inspection of the cross product DXB possesses units of momentum density per unit volume filling the immensity of space. Being a non-electrostatic field, embedded in all matter and filling space as a scalar boson, Keeney postulates this long-sought governing field of gravitation, in effect unifying these two force fields. Newton's universal constant G is shown to comprise the identical momentum flux density filling space. The field structure of the spin-2 graviton is unveiled, and taking advantage of an Einstein suggestion, theorizes our cosmic background to be a vector-displacement-tensor field which defines what is ``curved'' in relativity's ``curvature of spatial geometry'' are matter displacement volumes to this specific density.   

Our Static Universe

There are two astronomical cause of redshift; motion, which leads to the Big Bang Theory, and the presence of an ubiquitous gravity field, which leads to a Static Universe Theory. Our position in the universe, which is considered to be at its center or in a null vector condition, where the net vectors of all the gravity field components equal zero, having no or undefined direction, is not related to the concept of potential energy. If there were no mass in the universe there would be no redshift. Herein lies the secret of redshift; the wavelength or frequency of light is altered by time dilation while traveling great distances from the emission source through 3-directional strained or deformed space, C-space. The gravitational field intensity inside a geometrical sphere of homogeneous matter is directly proportional to the radial distance (R) from its center and is at maximum at the outer surface. We remotely collect the light at the surface or outer shell of the sphere where the remote light source is at the center. The mass-distance ratio, with the increasing distance, to the resulting increasing mass (M), where redshift is directly proportional to M/R, is demonstrated mathematically by the gravity redshift formula: z = G M /cR. I.e. z = 0.202 for Hydra with distance of 3.2 billion light year. Thus, the estimated constant density of our universe is 7.4 x 10--29gm/cu/cm. or where omega equals 1.