Quantum Theory of Gravity - "QTG"

10. The  variability  of  the  “Universal   Gravitational Constant ”.  

The universal gravitational constant (G), with an official value of 6.6726 x 10^-11 and the strange units of m³.kg^-1.s^-2 (distance cubed divided by the product of mass by time squared), is the oldest constant in physics, but has proved to be the most difficult to determine. Most physical constants are precise to more than 8 decimal places, but values found for G differ shortly after the third decimal place and sometimes before. No precise value has yet been determined, and every time a new team of researchers sets out to establish it with new and modern equipment, different values are found.

We will now see how a range of experimental results or gravitational anomalies question the validity of Newton’s universal law of gravitation. This law states that the gravitational force between two bodies is proportional to the product of the two masses and inversely proportional to the square of the distance between them. To obtain the force of attraction between them, it is also necessary to multiply by G.

F.D. Stacey and G.J. Tuck’s 1981 study, “Geophysical evidence for non-Newtonian gravity” (Nature, v. 292, 1981, pp. 230-232.), shows that measurements performed under the sea, in deep mineshafts and in similar locations give results up to 1% higher than the official value, and that the deeper the location, the higher the value of G. According to Newton’s formulation, the force attracting the spheres was greater according to the increased depth.

See also http://prola.aps.org/abstract/PRD/v33/i12/p3487_1.

From the QTG, we have two reasons for the greater attractive force between the spheres measured by the torsion balance. Firstly, the variation in the frequency of the time between measurement locations, and secondly, the lower tension in the cable supporting the spheres on the balance.

In the first case, we know that the greatest gravitational intensity is recorded on the surface of the planet, which causes atoms there to generate less gravity there than, for example, in the depths of a mine.

This is a consequence of the different rate of time, which is faster at higher gravitational potential. A similar situation was shown in chapter 7 of the QTG, where space probes leave the solar system. This greater generation of gravity, beneath the surface of the planet, increases the attractive force between the spheres.

 
                It is easy to show why the gravitational potential is greater within a planet. For the gravitational potential on the surface, we have:

               

                We know that the Earth’s mass is equal to its volume multiplied by its density:

                For the potential, we therefore have:

                For a location beneath the surface of the planet at depth x, we have the following gravitational potential:

 
                Comparing, we find:

             Simplifying, we have:

This shows that the gravitational potential is greater inside the planet, beneath the surface, just as it is greater above the surface.

                For the second case, we must take into account that, within the planet, we have heavier atoms, and that these have more electrons. It is known that for each electron there is an acceleration or gravitational vector, which follows it like a shadow, and that these vectors generate the gravitational field, as shown in chapter 8 of the QTG.

If we take into account the influence of the atoms surrounding the test spheres inside the planet (see Figure 1), heavier than those in tests on the surface (see Figure 2), we find the following:

Within the planet, we must take into account the additional influence of the gravitational vectors of all of the atoms above the experimental location (see Figure 1). It can be seen that the contrary gravitational force reduces the attractive forces of the spheres towards the centre of the Earth. This makes the spheres lighter in relation to the supporting cable of the balance, which is thus under reduced tension.

On the surface of the planet, the spheres will experience a greater gravitational force towards the centre of the Earth, as shown in Figure 2, because there is a greater concentration of vectors in this direction.

In a torsion balance, we must have ideal spheres, that is, they must be identical. These spheres are suspended by a cable that twists when other, larger spheres are brought close. The attractive force is determined by the measurement of the torsion angle of the cable, resulting from the attraction of the spheres.

As these spheres are suspended by a cable responsible for the measurements (see Figure 3), if the tension on the cable is reduced as a result of reduced weight, it will show a higher torsion angle, indicating a greater attractive force, resulting in a higher gravitational constant.

The greater the depth at which the experiment is carried out, the lighter the spheres and, as a result, the lower the tension on the torsion balance cable, through which a greater attractive force between the spheres will be recorded.

Charles F. Brush’s 1924 study, “Some new experiments in gravitation” (Proceedings of the American Philosophy Society, v. 63, pp. 57-61.) with its extremely detailed photographic analysis, shows that metallic bodies with heavier, denser atoms tend to fall more rapidly or with greater gravitational force than do bodies of the same mass but with lower density or lower atomic number.

Chapter 8 of the QTG shows that atoms with many electrons generate a more uniform gravitational field, which also confers a greater attractive force, because the lighter the atom, the less uniform the gravitational field generated by the inertia vectors associated with the electrons. In the hydrogen atom, this generation is unilateral and lacks geometric equilibrium, which may be one of the reasons for it being difficult to manipulate. This case certainly reveals a very subtle gravitational difference, but one sufficiently large for Brush to be able to detect it with photons.

In 1798, Henry Cavendish published an experiment in Philosophical Transactions that has been challenging the world of physics for over 200 years. Using a sensitive torsion balance to determine the gravitational constant, he discovered that heating the spheres produced a considerable increase in the attraction between them (see Stephen Mooney, “From the cause of gravity to the revolution of science”, Apeiron, 1999, pp. 138-141). Since then, the experiment has been repeated countless times, in high vacuum chambers, using the most modern measuring equipment. Despite the powerful arsenal of contemporary physics, efforts to explain the phenomenon have been unconvincing.

We know that heated metals radiate electromagnetic waves or photons, and that this is accompanied by electrons changing orbits or an increase in free electrons that lodge in the crystalline structure of the metal, as in the case of a tungsten filament conducting an electric current. Each time an electron is dispersed, as shown in chapter 8 of the QTG, it leave a space in the atom, increasing the imbalance between the nuclear forces. The electron remains nearby, maintaining the electrical neutrality of the material, but, for this short period of time, we find an increased coulomb force in the atomic nucleus, which generates more gravity. The QTG shows that we must consider the time reference in relation to the nucleus.

Each year, further examples of gravitational anomalies appear to challenge Newton’s laws, mainly in astronomy, such as the complex orbits of the outer planets or Saturn’s thousands of controversial rings. Whenever an experiment suggests a slight disparity with the expected value, the scientific community attributes the difference to experimental error, so as not to compromise the sacred and conservative laws of Newton.

Experiments for measuring G are carried out on the surface of a sphere with billions and billions of atoms, which we call Earth, whose dimensions are gigantic in relation to the bodies used in the studies, with the result that there is a tiny margin for experimental detection of the gravity generated by them. The experimental bodies simply suffer the implacable action of that gigantic gravitational field.

This disproportion of planetary dimensions has delayed an understanding of the true nature of gravity for over 250 years. As can be seen, the gravitational effects of the Newtonian theory and those of the new theory, the QTG, are very similar, because the proportional difference between them is almost imperceptible. In the first, gravity is a consequence of the mere presence of mass, while in the second it results from the relative difference of the nuclear forces generated by the electrons associated with the atoms.

In fact, the number of electrons involved in the QTG is proportional to the amount of mass in the Newtonian model. Bearing this in mind, we find a subtle difference only under very precise experimental conditions.

The principle of equivalence, which is the basis of the general theory of relativity, shows that a homogeneous gravitational field is exactly equivalent to a uniformly accelerated point of reference. This same equivalence is accepted between gravitational mass and inertial mass, but this equivalence is only apparent: differences exist, but are well hidden from us.

On the other hand, adopting the new origin of gravity, as shown in  chapter 7 of the QTG, it is seen that these differences are accentuated in the case of large distances where the time reference is significant.

                See also: http://www.npl.washington.edu/eotwash/gconst.html