Quantum Theory of Gravity - "QTG"

22 – The Graviton ?

                Theoretically predicted but never observed, this hypothetical particle with no electric charge and no mass is supposed to be responsible for the gravitational interaction between matter and energy.

                The following summary will show how its existence can be predicted and why we can eliminate it from the new theory of gravity.

                Its existence has traditionally been justified by the need for an element responsible for gravitational mediation, to carry out the transmission of energy between objects or particles, because physics does not accept the conversion of force into energy. It is presumed that the graviton disappears and is converted into energy when it acts on an object or particle.

                We know that when a force acts on a particle, its energy is altered, and that this energy is quantised in multiples of h (Planck’s Constant), as established by quantum theory and confirmed experimentally. We can thus analyse the following relations between force and energy.

                Force is equal to change in momentum over change in time.

                We therefore have: F = ΔP/ΔT     [N or (kg.m) /s/s].                                       (22-1)

                Force is also equal to change in energy over change in distance.

                We therefore have: F = ΔE/Δx      [N or (kg.m²)/s²/m].                                    (22-2)

                Where: ΔE = (E2 – E1)       [(kg.m²)/s²]                                                       (22-3)

                When a force acts on an object or particle, its energy is changed, which is to say that work is done. This work is a change in energy, with the same units as the energy itself, thus:

                W = ΔE = E2 – E1= F.Δx      [Joules or N.m or (kg.m²)/s²].                   (22-4)

                From 13-4, we can see that, as work is a change in energy, and as this energy is quantised, we can state that the work must also be quantised. If one is quantised, the other must also be.

                Returning to 13-2, the force must therefore also be quantised, assuming that any change in distance is a continuous quantity.

                We can now ask whether the distance is indeed continuous, which we cannot state with absolute certainty. It may be theoretically possible to always find a new point between any two given points, but quantum mechanics shows that the shortest measurable distance is Planck’s length (Lp).

                Using the gravitational energy of an isolated mass given here:

                Eg @ 3/5.Gk.m²/r      [Joules or N.m or (kg.m²)/s²],                                     (22-5)

                we can deduce Planck’s length (Lp) as follows:

                Lp = (¬. Gk/c3)^(1/2)       [m].                                                                  (22-6)

                This Lp could theoretically generate the lowest quantised work (Wq), and this could be used to define the lowest quantum of gravitational force (Fq). Here is the graviton.

                It was shown in chapter 7 of the QTG that the Universal Gravitational Constant (Gk) is not entirely constant, but was calculated for this part of the universe and could assume different values depending on the presence of objects or masses that could modulate the frequency of the local time reference. We can thus conclude that Lp will also vary from place to place, which will be of significance later.

                As gravity is the weakest force, the graviton would theoretically be its elementary unit. In this case, it would be a quantum of work by Planck’s length (Lp), and the graviton would have the following force:

                Fq = Wq/Lp      [N or (kg.m /s/s)].                                                                  (22-7)

                From 13-7, we can see that this quantum of gravitational force (Fq) has the units of force [N], while gravity has the units of acceleration [m/s/s]. As force is classically the product of mass and acceleration, we have:

                F = m.a      [N or (kg.m /s/s)].                                                                           (22-8)

                It was strategically determined that the graviton should have zero mass:

                m = 0      [kg],

                We should therefore theoretically have a lowest quantum of gravitational force equal to zero:

                Fq = m . 0 = 0      [N ou (kg.m /s/s)].                                                             (22-9)

                For this to occur, convention determined that this quantum of gravitational force be magically converted into inertia. In chapter 6 of the QTG, it was shown that this artifice is unnecessary, with the demonstration that a difference in the relative forces of the atom results in a force without mass or inertia, thereby respecting all the laws and postulates of the classical theories of physics.

                In chapter 2 of the QTG, it was shown that gravity is generated only when an atom is found in a gravitational field, without which there can be no temporal reference, this being defined by the presence of at least one other atom, and that the gravity generated also depends on the intensity of the gravitational field. We can conclude that it is not a force that generates gravity, but the presence of a gravitational field. That is to say, we do not have the conversion of force into energy, but the conversion of the influence of a gravitational field into gravitational energy, because, as shown in chapter 8, “gravity gravitates”.

                To complement and to verify how difficult it is to quantized the gravity, we can still calculate the variation of the force among two atoms of hydrogen, initially moved away by the distance of one millimeter or 6,18x10³¹ Planck’s length (Lp), in the inter-stellar space, we will see that when this distance be reduced of one Planck’s length (Lp), the increase resulting of the classical gravitational force is around 6x10^-90 N, certainly something very smaller of that that would represent a quantum of gravitational force (Fq).