Chapter XXVIII

 

DEDUCTION OF THE GRAVITACIONAL CONSTANTE G

 

"Something it is only impossible until someone doubts

and proves the opposite."

- Albert Einstein -

 

      According to the model presented to our Gravitational Force, we believe that the component of attraction between bodies, the part that attracts and unites the atoms and matter together, is not based in the classical and traditional source of Gravity produced by masses. As so, we assume that this new kind of attraction has no source in masses at all.

      As mentioned earlier, this constant of attraction between bodies is not directly related to the quality of mass but is rather related with another characteristic of matter, more precisely with a magnetic component, whose source is in the magnetic spin moments which all particles have.

      Despite the strength of this gravitational-magnetic force is clearly small, in the order of magnitude of 10-40, this force of attraction can reach long distances in space and go through all the Universe; since we consider that there is a transfer of the magnetic moment to the macrocosms through the classical way of the Electromagnetic Force. If in Classical Physics the kinetic angular moment can be transferred, than we can also assume that the magnetic moment of a particle can also be transferred.

      The clear evidence of the emission of this double radiation to the interstellar space (an electromagnetic force and a gravitational-magnetic force) is always present in the unfolding and decomposition of the Hydrogen spectrum, which always gives us two distinct stripes instead of one single line. Understanding the origin of this radiation and the meaning of these double stripes belongs to the area of Spectroscopy, a science which studies the interaction of electromagnetic radiation with matter, in which, in  this case we also have to include the origin of this gravitational-magnetic radiation.

      Spectroscopy is nowadays in the great development of current science. From Chemistry to Astrophysics, this new science is revealing new concepts and new possibilities for the interpretation of the Electromagnetic Spectrum; new information previously unknown to us.

      As we know, all atoms emit electromagnetic Radiation. The emission of this radiation, of photons, can be produced by various and different subatomic particles such as protons and electrons in motion.

     Radiation can have various kind of manifestations and be produced in several ways, such as: Ultraviolet, Visible light, Infrared, Radio waves, etc.. The origin and processing of these different types of radiation is not yet fully understood and the initial explanations and investigations are now beginning to happen, producing major developments in the understanding of the electromagnetic spectrum, showing the reason to be for all this rich interaction between light and matter.

      In general, we can say that the emission of electromagnetic waves is related to changes in the energy levels of atoms. For example, the absorption and emission of Visible Light has a direct relationship with transitions between energy levels of the valence electrons ( the electrons more distant of the nucleus ). The energy of light, and consequently the frequency, and therefore the color, is directly related to the energy difference involved between the two states of the electron transitions in these two energy levels. In the Hydrogen atom this radiation is associated with the Balmer Series.

      However, the issue from various sources of radiation is not directly related to the transitions of the energy levels of the electrons!

      The diversity of this phenomenon is dependent on the variation of the energy of the atom itself. Every time the atom gains or losses energy, radiation is involved. The condition of the frequency of Bohr tells us that:

 

f = (Ei - Ef)/ h

 

 <=> ΔE = h.f

 

      It is the transformations and energy transitions of the atom which are on the origin of the emission of different kinds of frequencies, allowing a contribution to the wide range of the entire electromagnetic spectrum.

      Several factors may contribute to the variation of the internal energy of the system, thus mean, the atom. Basically, what we assist is that there are changes in the values of the Kinetic Energy and Electrostatic Potential Energy, which can be expressed by several changes, such as: translational motion; rotational motion; vibrational motion; transitions of the electronic levels of the electrons;  and changes in the orientation of Spin, nuclear and electronic, of different particles. The phenomena involved in the origin of these different forms of radiation are always distinct.

      The contribution to the total energy of the system, of the atom, takes several variables and can be considered as follows:

 

Etotal = Etranslation+ Erotation + Evibration + Eelectronic levels +

 

+ Eelectronic spin orientation + Enuclear spin orientation

 

      We have for example, the absorption and emission of Infrared radiation as a result of quantization of the vibrational energy of molecules. Molecules present vibrating movement around their centers of mass. These normal modes of vibration may be present in the direction of the chemical link (distention and elongation) or perpendicular to the chemical connection (bending or deflection angle). As a consequence of this disturbance, of this vibration, the atom is accompanied by a change in its dipolar moment. Only molecules that produces changes in the dipole moment can produce spectrum of IR (Infra-Red).

      Other changes in the energy values of atoms can occur and thus produce other forms of radiation.

      It is known that the emission of Micro-wave is related to the transition of the rotational energy levels, thus mean, with the rotation of the molecule or atom, and consecutively with the change of the electronic spin orientation.

      The emission of Radio waves is related to the transition of the spin energy levels within the core. This radio wave is directly related with the change of the direction of particles spin within the nucleus, such as protons and neutrons (nuclear spin).  The way this radio frequency is processed is really interesting …

      Summarizing, any atom or molecule alone has a certain amount of energy associated with the Kinetic Energy and Electrostatic Potential Energy which arises from the state of motion of electrons; and also other smaller quantities of energy associated with the positions and orientation of particles in relation to the centers of mass of the atom or molecule considered. Only certain frequencies, vibrational amplitudes, and certain rates of rotation are allowed for an atom or molecule in particular. Each possible combination of electronic levels, vibrations, rotations, and spin orientation defines a particular level of energy and a very specific frequency, and therefore an emission / absorption of the electromagnetic spectrum.

      Only certain discrete energy changes are allowed. As provided by the quantum theory, a certain amount of energy is associated with a corresponding emission of a photon radiation.

      Most of the absorption lines are associated with orbital transitions (change of electronic distribution) and within this process we can include: the X-ray, Ultraviolet and Visible radiation. Vibrational changes are usually associated with the Infrared. Rotational changes are usually assigned to the Microwave region. Finally, the emission of Radio waves is related with the change of orientation of the nuclear spin. However, the electromagnetic spectrum does not end here, it still continues and shows us another form of radiation …

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

- Electromagnetic spectrum and its origins /

 Natural sources of the emission of Radiation -

 

           Within this process the variation of the ranges of energy becomes smaller as the wavelength increases and, consecutively, the energy of the photon irradiated is also lower.

      

 

- Variation of the energy levels according to

 the different manifestations of radiation -

 

    In certain types of molecules it can occur a simultaneous transition of vibration and rotation. This continuous movement allows the spectrum of absorption show clusters of very close lines, instead of a unique defined transition with a very clear frequency. The existence of these sub-levels of vibration and rotations represent the various possible transitions of energy around a fundamental and center frequency, which is reflected in the absorption spectrum.

                      

               

- Relationship of the Frequency with the Spectrum of Absorption -

 

      However, a more careful analysis of the spectrum of Hydrogen atoms shows the existence of two well-defined lines.

      In my point view, the reason to be and the explanation of this phenomenon – the double frequency - remains unsatisfactory. The Hydrogen spectrum shows that there are two levels of absorption/emission of two distinct energies, very well defined ...

      We can say that without rotation, the electrons and protons only have an Electric Force produced by their own electrical charges. But because these particles have a movement of rotation around themselves, a Spin movement, a bit like a pivot that rotates around a vertical axis, these particles acquires a new force, a Magnetic Force, created by a magnetic dipole that installs and involves the particle, also called as a magnetic moment; or intrinsic angular moment; or more simply spin. The electronic spin moment and the orbital angular moment of the electron in motion around its orbit on the atom are combined together to contribute to the total angular moment of the atom.

      However, the core of an atom behaves as if it has an independent nuclear magnetic moment. Since each particle of the nucleus produces nuclear magnetic interactions with the environment around them.  We cannot forget that protons and neutrons also have spin and that they interact to a contribution for the nuclear spin.

     Another interesting characteristic is the intrinsic magnetic moment of the subatomic particles, which when placed under the action of an external magnetic field B0, it only has two possible orientations: plus and minus: ½, which correspond to the two only possible values of the magnetic potential energy. The two alignments of nuclear spins are, therefore, manifestations of different energies, according to their orientations. These spin directions are classified as follows:

 

Spin  -½  aligned against the field ( anti-parallel );

 

Spin  +½  aligned with the field ( parallel ).

 

 

- Orientation of the magnetic moment of Spin μs -

    

     A chemical species that emits radio frequency, thus mean Radio Waves, is the atom of Hydrogen 1H, the simplest atom of the Periodic Table and, coincidentally, the most abundant type of atom in the Universe.

      Each atom of Hydrogen has one proton and one electron in its constitution, and both particles revolve around their axes and have spin. The direction of the spins of these two particles can only have two possible orientations: the proton's spin is parallel to the spin of the electron and both operate in the same direction, or each particle spins is in opposite directions and the spin is anti-parallel.

      The state of lowest energy of the Hydrogen occurs when the spin of the nucleus (proton) is opposite to the spin of the electron. However, the atom of 1H can receive external energy and with it produce a parallel spin alignment of the proton and the electron. Since the Hydrogen atoms are continuous moving from the parallel configuration (maximum energy) to the anti-parallel configuration (lowest energy level), the excess energy acquired is released in the form of radiation: Radio Waves.

      The characteristic wavelength of this emission is about 21 cm, and with a frequency equal to 1.4 Gigahertz. There is a predominance and a preference for the parallel || orientation, but the difference is very small, only an excess of 10 in a total of 106 nuclei is presented in the state of spin of higher energy.

      The atom of Hydrogen vacillates and constantly oscillates between these two states and the strength of energy it gets comes from the application of its own external magnetic field, produced by the orbital motion of the electron. The absorption of energy occurs when the magnetic field of the nucleus B' (proton) is aligned with the external magnetic field B0 (of the electron). This nucleus aligned with the field absorbs extra energy, changing its spin orientation into the opposite direction.

 

 

- Parallel orientation of the spin magnetic field B' (or H') -

 

      Usually a macroscopic magnetic field is defined by the quantity vector B (Tesla), also known as magnetic induction. However, when referring to magnetic fields at a microscopic level we can use another scale which relates the intensity of the magnetic field, defined as H ( Ampere / Meter).

      All nuclei have a characteristic spin ( designated by a ’I’ letter ), depending on the number of protons and neutrons that enter into their constitution. Thus, some nuclei have fractional spins: I = 1/2, 3/2, 5/2 ... others have integer spins: I = 1, 2, 3 ... and some do not have any spin at all: I = 0, since the contribution of the nuclei, with a pair number of protons and neutrons, produces coupled spins with a total spin zero.

      Nuclei containing an odd number of protons and neutrons (an unpaired number of nucleons) have a quantized spin, as so, they have a magnetic moment. Examples of chemical nucleus with a magnetic moment associated are: 1H, 13C, 19F, 31P, etc. . To highlight again the Hydrogen! The most abundant chemical element in the Universe contributes to a significant nuclear magnetic moment …

      When we refer to molecules we must considered that, besides the interaction with B0, the nuclear spins can also feel the presence of other spins in the molecule. If a molecule has got several atoms in its constitution, this condition leads that the atmosphere of a single magnetic spin is also depending of the orientation of other magnetic spin moments neighboring the molecule. Spins do interfere with each other.

      The magnetic characters of these nuclei and of these atoms are naturally weak and we could think that this low magnetism would not have any magnetic influence with other particles more distant in space. However, if the magnetic fields of each nuclear spin is presented in a regular and orderly position in a certain moment in time, if these domains stay all aligned during a short moment, then, as it happens at the Magnetization phenomenon we may say that these single magnetic spins spread through the Universe may feel other spins from far away atoms quite distant from each other. And, this would be the process which would lead to a standardized and universal spin magnetic alignment, consisting of the same direction and orientation. In this state of Resonance the magnetic flow becomes higher and, consecutively, this represents a gain of extra energy for the atom which, afterwards, it will immediately release this extra energy into space in the form of electromagnetic  emission or … Gravitational Radiation!

      There is a moment in time when it occurs a synchronized alignment between all the magnetic moments; as so, we can imagine the existence of a specific coupling where all spins are in phase … the presence of a Universal Spin!

      These magnetic interactions are a quite complex. When considering a single atom of Hydrogen, what we have, in this case, is a single electron, unpaired, associated with an atomic nucleus which has a considerable magnetic moment. Therefore, this electron will feel not only the external magnetic environment produced by other atoms in its neighborhood and from himself but also it will feel the magnetic field emitted by the core, thus mean the nuclear proton.

      We know that the component of the magnetic orbital moment of the electron ( translation movement ) contributes to the total magnetic moment of the atom and it is related with the classical Electromagnetic Force. However, we cannot ignore that there is another subatomic magnetic component. The existence of an individual magnetic component ( the spin magnetic moment due to the movement of rotation ) which all particles have, contributes to the magnetic field of each particle, creating a new magnetic field, smaller and independent of the Electromagnetic Force. This new field - when considering a nuclear particle of the atom and not the atom itself - is related to the classical Gravitational Force, let's see how:

      In a general standard we can consider that the magnetization of an atom is equal to the magnetic moment per unit of volume. The resulting magnetization is directly related to the total magnetic field inside the atom ( of the constituent particles of the atom ), and it is also depending on the external magnetic field which is being applied ( of the orbital motion of the electron ). So, the total magnetic field (B) produced by an atom depends on the contributions of the orbital magnetic moment of the electron (μL) and also of the magnetic spin moments (μS) of its constituent particles.

      In a similar analogy, when considering a region of space where there is a magnetic field B0 produced by a wire conductor crossed by an electrical current; and if we fill this region with a magnetic substance, the total magnetic field B produced in this region will be according to the following expression:

 

B =  B0 + Bm

 

      Where B0 is the field introduced and Bm is the field caused by magnetization of the substance, and this is directly dependent on the magnetization vector M:

 

Bm = μ0 M

 

      We believe that our total field B depends on the contribution of two different magnetic fields: B0 and Bm.

      We can draw this analogy to our atoms; considering that the total magnetic moment is dependent of two different magnetic moments: the angular or orbital moment μL and of the spin magnetic moment μS.

      In our case concerns us, particularly, the field produced and induced by the magnetization process, thus mean, Bm.

      Given that all the vast region of the Universe is mostly filled with atoms of Hydrogen; and according to data provided by the Critical Density, we can consider that the average density of the Universe is about 6 atoms of Hydrogen per unit volume. As we know, these atoms of Hydrogen have in its constitution one electron and one proton. Both particles contribute with their own magnetic moments: the spin magnetic moment S for the proton and the electron, and the angular magnetic moment L for the orbital electron. All these moments contribute to the resulting magnetic moment of the atom. The maximum magnetization occurs according to the vector sum of all these magnitudes. Imagining that in a certain moment in time all these vectors have the same orientation, the resulting magnetic moment μr will be given by the following equation:

 

μr = √ (  μSe2 + μSp2 + μLe2)

 

μr = 1,313 x 10-23 J/T

 

      Where we have:

      Spin magnetic moments of the electron and proton μS = - gsmsμB:

 

     μSe = 9,285 x 10-24  J/T

     μSp = 1,410 x 10-26  J/T

 

      And the orbital angular magnetic moment of the electron, also known as Bohr’s magneton μB = -e/(2ml) L:

 

     μB  = μLe = 9,285 x 10-24  J/T

 

      The maximum magnetization or the saturation magnetization is obtained through the following expression:

 

M = n.μr

 

      Where n defines the number of atoms per unit of volume and μr the resulting magnetic moment.

      Considering that our sample corresponds to the entire Universe, we will consider as a reference the critical density, which corresponds to 6 atoms of 1H by m3

 

M = 6 x ( 1,313 x 10-23 )

 

M = 7,878 x 10-23 A/m

    

      Returning to our expression to obtain the magnetic field Bm induced by the magnetization process and considering μ0 as our magnetic constant, is that:

 

Bm = μ0 M

 

Bm = ( 4π x 10-7 ) . ( 7,878 x 10-23 )

 

Bm = 9,9 x 10-29 T

 

      According to the classic formula, a Magnetic Force is obtained through the next equation:

 

Fm = Q.v.B senθ

 

      This force is maximum for θ = 90 °, thus mean sen90 ° = 1, and simplifying:

 

Fm = Q.v.B

 

      Making the substitution of the values in this equality, and considering the average speed of action as v = c/137 = 2,2 x 106 m/s, it comes that:

 

Fm = ( 1,6 x 10-19 ).( 2,2 x 106 ).(9,9 x 10-29 )

 

Fm = 3,48 x 10-41 N

 

      Most curiously, the order of magnitude of this magnetic force that arises is framed in the same order of magnitude of the Gravitational Force!

      Very interestingly …

      Considering the possibility that the gravitational force ( Fg ) is a magnetic force ( Fm ) and matching both equations, is that:

 

Fg = Fm

 

G.m2/r2 = Q.v.B

 

G = Q.v.B.r2

      m2

 

            G = Fm .r2. m-2         N. m2. Kg-2

 

      Thus, one can evaluate another evidence in our 'Gravitational Constant', which are the units that appears in the relationship between the gravitational force and magnetic force, because they do match perfectly!

      In this way, the Gravitational constant G arises as a Magnetic Constant!!

Considering ‘r’ as the atomic radius of Hydrogen ( rH = 25 pm ); and the total mass ‘m’ as the contribution of the mass of the electron and the mass of the proton: m = ((1,672 x 10-27)+(9,109 x 10-31 )) ó m = (1,673 x 10-27 ) kg; and replacing the values in the equality, we have:

 

G = __( 3,48 x 10-41 ).(2,5 x 10-11 )2_

       (1.673 x 10-27)2

 

 

G = __( 2,175 x 10-62 )_

       (2.799 x 10-54)

 

 

G = 7,77 x 10-9      N.m2.Kg-2

   

    This would be the G reference value for an interstellar space filled mostly by vacuum and in accordance with the data supplied to the critical density (average of 6 Hydrogen atoms per m3).

     The magnetic moment of the Hydrogen is indeed immense. Since the proton has a very significant magnetic moment and the highest of all the fundamental particles. Thus, in interstellar clouds composed of gas, dust and other materials, it is among these chemicals substances that begins the first gravitational attractions and the formation of the first aggregations of matter. Mother Nature gives priority to the formation of these clouds of Hydrogen, made up mostly of atomic and molecular Hydrogen (H2).

     With the passage of time, the clustering of this Hydrogen mass is gradually compressed by action of its own Gravity Force. Being constantly and successively compressed, the density and temperature slowly increases, gradually warming this giant molecular of mass and forcing it to revolve faster and faster on its own. When the gas heats up enough and the core temperature reaches 107 Kelvin, begins the nuclear reaction that causes the fusion of Hydrogen into Helium. At this time, nuclear fusion occurs and the protostellar cloud becomes into a new born star.

     The interstellar environment and the formation of these nebulae is of extreme importance in the evolution of the cosmos. These are prolific areas par excellence. It is in this interstellar space which is born all the new generations of stars which exist in our Universe.

     However, the measurement of the gravitational constant is dependent on several factors. As we have seen previously, when we referred to the experience of Cavendish, we saw that the influence of temperature has a decisive role in the outcome of the G constant. As a final result and as a consequence, is that this gravitational constant must reach very big values in stars.  Similarly, the rotation speed of the star is also very important when measuring this constant. Therefore, the final conclusion is that, this constant must therefore reach the highest values in neutron stars and pulsars.

     Returning to Planet Earth and when we refer to planets in general we should consider other chemical elements more complex and more dense which participate in its formation, such as iron (26Fe) for example, constituent of the Earth's core ( which contributes, at least, with one electron  with an unpaired spin ); among many other chemical elements with specific characteristics and very particular proprieties. Considering that these elements have different atomic radius, whose value is also influenced by external conditions such as pressure and temperature, but in general we can consider that the average radius of an atom is in the order of magnitude of 10-12 m.

     Among the atomic radius of Iron; the average Bohr radius; and the Compton wavelength, we can begin to consider, for example:

 

r = 2,31 x 10-12 m

 

        With this small change in the atomic radius it gives us a substantial difference in the gravitational value, the G constant:

 

G = Fm .r2

          m2

 

G = __( 3,48 x 10-41 ).(2,31 x 10-12 )2_

           (1.673 x 10-27)2

 

 

G = 6,6 x 10-11      N.m2.Kg-2

 

     And so we get the average value of G at the surface the earth!

     In fact, the accurate measurement of this constant must require a highly complex process ... since this constant is always inconstant in each location.

     But the fact is that this constant can be influenced by two decisive factors:

     - By the variation of the atomic radius (r);

     - And by the rate of change/intensity of the external magnetic field (v)

       ( the speed variation of the magnetic field is influenced by the speed of rotation of the star and  temperature).

     Therefore, the universal constant G is a magnetic constant and a variable constant!!

 

     While everyone thinks that the origin of Gravity hides no secret ... When everyone 'knows' that the source of Gravity comes from the quality of mass; this simple feature so much 'clear' for us in Nature ... It's at the obvious that no one notices and that no one doubts, and it is exactly in that propriety, in this particular characteristic, that Nature surprises us completely!

     After all, it was nothing like the way we had imagine, it was nothing like the way we were thinking ...

 

RADIATION / SPECTRUM

 

ORIGIN OF THE PHENOMENON

 

ENERGY BY PHOTON ΔE

 

FREQUENCY f

 

WAVE LENGTH λ

Cosmic

 Ray

Nuclear reaction ( production of electron-positron pairs )

>  1,022 MeV

1023 Hz

Ionizing Radiation

(10-13 m)

Neutron Radiation

Nuclear reaction  ( free neutrons penetrating into the nuclei causing radioactivity )

 

Ionizing Radiation

 

Gamma

 Ray

 Nuclear transitions

( excited nucleons  – reorganization of the  nucleus)

10-12 J

( 5 MeV )

1021 Hz

Ionizing Radiation

Picometros (10-12 m)

Beta

 Ray

Nuclear Mutation

( neutron-proton mutation – emission of an internal electron )

Depending of the radioactive isotope

Ionizing Radiation

 

Alpha

Ray

Nuclear Fissions

( Helium nuclei positively charged)

Depending of the radioactive isotope

Ionizing Radiation

 

X Ray

Electronic Transitions (reorganization of the electronic layers – electron transition from a highest to a lowest level )

10-15 J

1018 Hz Ionizing Radiation

Nanometerss (10-9 m)

Ultraviolet

Electronic Transitions

( Energetic transitions of the valence electrons)

6x10-17 J

 ( 3,7 eV )

1017 Hz

 10-8 m

Visible Light

Electronic Transitions

( Electronic  transitions of the valence electrons)

10-18 J

1015 Hz

Micrometers (10-6 m)

Infrared

Vibrational Transitions  (alterations of the energy levels by molecular vibrations  - variation of the dipolar moment )

10-21J

( 0,37 eV )

1012 Hz

Millimeters (10-3 m)

Microwave

Rotational Transitions

(alterations of the energy levels by molecular rotations – electronic spin variation )

10-24 J

(0,0037 eV)

109 Hz

Meters (100 m)

Radio Waves

Nuclear Transitions

(alteration of the energy levels of the core/atom - nuclear spin variation )

10-27 J

106 Hz

Kilometers (103 m)

Gravitational Waves

Nuclear transitions  (alteration of the energy levels of the core/atom – nuclear spin alignment with the universal spin and resonance )

10-40 J

10-6 Hz

Kilometers (1014 m)