Chapter XXIV


Quantum theory of Gravity




"It is at night that it’s beautiful to have faith in light."

- Edmond Rostand -


      Unifying Forces! Where is the formula for a Unifying Force?

      As we all know, all physicists do like formulas!

      Oh yes ... the formula! The truth is, I must confess, I did not found the formula. This formula has already been discovered by the contemporary physicists, but they still do not know that they have already found it!

      What all physicists do wish to achieve is the official unification of the Quantum Theory with a Gravity Theory.

      It is practically impossible to marry the classical Theory of Gravity with a Quantum Theory of everything else ... how many times did I have already heard this sentence! It seems impossible to join these two theories together. Perhaps that is so because, maybe, they do not wish to get marry! If that is their will, let them stay single but happy!

      The Standard Model works very well for all the other three forces of Nature, except for the Force of Gravity. The reason why this problem remains is because we are still looking at these four forces as having the same origin and nature.  Considering these four forces as being all original of the Cosmos, but what we have here, if we look more closely, is a clear problem of perspective!

      It is true that we see four forces, but the subtlety is to realize that not all of them are original forces of the Cosmos. One of them is a secondary force, only three of them are really quantum forces, because Gravity, as I said before but I will say again, is not an original force of the Cosmos but a consequence, a side effect. Of which can be concluded that what we call Gravity is an atomic force and so it is not a quantum force, as such, it cannot be included in the Standard Model.

      This debate which aims to unify the three pattern forces of Nature: the Weak Force; Strong Force; and Electromagnetic Force with a fourth one: the inconvenient Gravity, is now eliminated!

      This scientific speech which has continued and persist for years; this scientific saga which physicists have carried for a long time is then resolved.

      And maybe the search for a Unified Formula is just to mislead. Perhaps it does not exist such a formula for this unification.

      The only unification which I can present is the one of the current Standard Model. But this unification which unites three Forces:  Strong; Weak and Electromagnetic, physicist already have it … or almost. The unification is still pending in the Strong Force and the Electroweak Force.

      Making a vain analogy, I would say that physicists have first discovered the developments of Maxwell Equations before they even find the formula of the Electric Field. Which is, actually, much more difficult to accomplish. But, somehow, they have succeeded. The two formulas of this unification are very complicated, there is still missing a final rearrangement and a simplification.

       The theory of Electroweak Force is studied by the Quantum Electrodynamics, short known as QED, whose formula is:


ElectroWeak Formula


     The theory of the Strong Force is studied by the Quantum Chromo-dynamics, short known as QCD, whose presentation in the language of Physics is:


Strong Force Formula


      As you can see, the expressions which describe these interactions are horribly complicated, but they do show a mathematic consistency which is in full agreement with the experimental predictions and, therefore, among its main protagonists, some were reward with the Nobel Prize.

      But there is a possibility for a simplification ...

      First, the Strong Force is, with no doubt, the most complex force of Nature and the most difficult to simplify.

       We know that the Strong Nuclear Force acts trough protons and neutrons inside the nucleus, keeping them together and preventing the electromagnetic repulsive force between protons to manifest. However, it would be more accurate to say that this force acts, not quite between protons and neutrons but rather between their most fundamental constituent particles, inside the level of its internal constitution: the quarks. The Strong Force joins protons together but also joins neutrons inside the nucleus, because it’s a force between quarks. In a way, we can ignore that there are protons and neutrons in the nucleus and consider that within this system there are only quarks.

      Inside this system there is a significant degree of complexity that arises when ever we want to study the physical behavior of this force.

      While in the electromagnetic force we only have to consider one photon as the mediator particle of this force, with the strong force we must considered eight gluons particles mediating this strong interaction. These different categories of gluons can occur randomly and with an additional feature. Again, making an analogy with the electromagnetic force, the photons are electrically neutral particles, and therefore they do not interact with each other. But with the Strong Force that does not happened. We can say that these gluon particles can also feel the strong force, and therefore they interact with each other. Under these conditions, the treatment for this force is a little more demanding and exigent. And that is why it comes the complexity of the equations.

      Without wishing to move towards the complex details of Quantum Chromo-dynamics, I can say that this is a science that has just started to make their first steps, because its deeper knowledge still escape and eludes our understanding.

      Essentially, we can say that the fundamental particles of the whole matter are quarks and leptons. We have seen that leptons and quarks always form duplets and also that they react in a similar way to the Weak Force. However, leptons and quarks appear to behave quite differently to in the presence of the electromagnetic force and the strong force. Since the quarks feel the strong force and leptons don’t. Moreover, once quarks have a fractional charge of + 2/3 or -1/3 and leptons ( electrons and neutrinos ) have a whole charge number of -1 or 0, the power of participating in a electromagnetic field varies from one to another but only in a quantitative manner, because the electromagnetic properties expressed are, in fact, identical. Both quarks and leptons feel the electromagnetic force.

      There is a triangle that must be accomplish and that means that all forces have to work together, which suggests once again that these forces are not as distinct and independent as we think.

      Until very recently it was thought that these forces had no relationship between them, since they act in a very different way and also with quite different intensities.

      The power of intensity of these forces is an interesting measure which allows us to make a relationship between them and, as we know, the intensity of these forces differs from each other. Even the intensity of the forces varies, depending of the environmental energy, it is therefore not a constant value but a function of temperature.

      In the cold Universe of today, these intensities are well defined and can be related through the Fine Structure constant.

      The Fine Structure constant is a very special constant in Physics, and characterizes and describes the intensity and magnitude of the Electromagnetic Force. It is defined as α = 1 / 137. This alpha arises from the unification of three fundamental constants …


α =  __e2_ _    ≈    _1_

       2 ε0 h c            137


  ... The electric charge, the permittivity, the Planck constant and the speed of light. These constants represent and combine different components from different areas of Physics:


c = relativistic component;

h = quantum component;

e = component of the electromagnetic interaction

ε0= component related with the charged particles of vacuum.


      This constant is actually extremely important.  If our Universe is the way it is today, that only happens due the value of this precious fine structure constant. If, by any chance, this constant were modified, making it a little stronger or a little lower, if alpha had a different value, even minimum ... the essential characteristics of our Universe would no longer be the same and everything would change.

      Disturbing this constant involves changing the energy levels of the atom; meaning that the values of the atomic energy connections would be different ... implicating a major modification in the whole atomic process! This would mean, in practice, that we would get a new Universe!

      The coupling constant that defines the electromagnetic force is the reason to be of everything around us.

      The Standard Model aspires to obtain a unification of the various coupling constants in a high energy environment.

      The Grand Unification Theory requires that the natural forces and the particles on which they act, produce, in a high energies environment, a uniformity that is obscured at low energies. So that, it is briefly concluded that these forces act in a similar way in a remote past in the form of a single Unifying Force.

      The introduction of this idea allows the high energy physicists deduce that there is a similar behavior between the main forces of Nature when they are exposed to very high energies, in the order of 1015 GeV and, therefore, they consider that there was a primitive unification at a time when our Universe was still very hot and young.

      The Unification presented is, as such, a function of the scales of energy involved. The theory provides a different evolution with distinct intensities for each force of Nature, according to the increase of temperature, as described in the following graph:



- Unification of coupling constants α –


      The development of this evolution seeks to identify a magic point in time, the point which would unify and change all Forces of Nature into one!

      The idea of unification does have some meaning. It is clear that Particle Accelerators show us new processes of mutation and disintegration of particles that can only happen in high energies levels. However, even agreeing that the intensity of forces converge into higher energies, how can we be so secure that their properties and characteristics also change and converge to a single unified force?

      According to the current Model of Unification it is consider that there are several steps in the liberation process of the four Forces of the Universe. First it is considered that the four forces of Nature were join together in one single branch and that the spread branches of the forces happens in a partial and gradual process. With this process of ramification results that the Force of Gravity was the first force to get separated and to emerge from this Grand Unified Force, however, as we have seen before, it is exactly the opposite that happens. The Force of Gravity is the last to emerge and it is, therefore, the youngest force of the Universe!

      And for the following ramifications it would be necessary to clarify a little better the reasons and justifications for this process.

      In my point of view, there is no unification. There is, quite simply, evolution. And very hardly the forces would change their properties as if they were the same substance in a phase transition ... I do not think that it is reasonable to treat the Forces of Nature as liquid water, ice and water vapor ...

      As we saw earlier, the justification is simple and it is withdraw from the cosmological evidence.

      We can notice that all forces of Nature have a common characteristic, which is to unify, and as such the Electromagnetic Force, the Strong Force, and the Force of Gravity respect the symmetry. However, there is a force that does not share this characteristic of unification, because its main function runs exactly in the opposite direction. Its power is to disunify and it is, therefore, a force of imbalance and instability.

      We can consider that the Weak Force is within the origin of all forces of Nature, once this is the only force which breaks the symmetry. As so, it is from this dissymmetry that evolves and emerges all the other three forces that surround us.

     Thus, we can simplify the development and evolution of the forces of Nature, proposing a more balanced and symmetric branching:



- Evolution of the Forces of Physics -


      With this structure in mind, we can emphasize that it was not the temperature that has conditioned all these physical processes. The external factor of greater relevance which more conditioned these circumstances is according to a natural process of Evolution and its influence is predominant and crucial ... the external agent more effective in this process was ... the Time!

      I must remind you that the Particles Accelerators cannot reproduce all forces … and time is definitively ... a huge force!

      Time is a great force but given its extraordinary subtlety and discreet nature of its activities, it’s a force which nobody notices ...

      But this force acts constantly, cleverly, without being noted. It is an actor that hides its true nature and identity, by showing, or to be more accurate, by hiding behind their actions among things.

      It is with its actions that we must count on, in order to draw a complete perspective of the Evolution of the Universe, it is with this action that we must conceived the whole History of the Cosmos.

      Time is also a Force … always forgotten …

      The simple structure, functional, harmonious and beautiful of our Universe is due to the complementarities and interactions of all these forces.

       Returning to the theory of unification, it is possible to compare the magnitude of the forces with each other and thus obtain a relative magnitude.

      The main relationship is made from the fine structure constant.

      Usually the magnitude of the Electromagnetic Force is stipulated as having a value of  1/137  and this force is considered to be 137 times weaker than the Strong Force;

      The Weak Force is by its turn 106 times weaker than the Strong Force;

      And the Gravity Force is the weakest of all, in the order of 1040 times weaker than the Strong Force.

      With these data we can establish a relationship, in which the more intense force is the Strong Force and we match it to the unit 1:


Strong Force = 1

Electromagnetic Force = 1 / 137

Weak Force = 1 / 106

Gravity Force = 1 / 1040


           We can also adjust these equations by multiplying the intensity of all forces by 137. And we began to define the coupling constant, not according to the Strong Force but in order of the Electromagnetic Force:


Strong Force = 137

Electromagnetic Force = 1

Weak Force = 137 x 10-6

Gravity Force = 137 x 10-40



      With this definition, there are several relationships which can emerge from this structure, as for example:


FE = 1 x FE

FS = 137 x FE

FW = 137 x 10-6 x FE

FG = 137 x 10-40 x FE


       Other equivalences can also be deducted. Transforming the equation and considering that FEM = 1 / 137 x FS, appear as:




FE = α  FS

FS = α-1 FE

FW = α-1 x 10-6  FE

FG = α-1 x 10-40  FE


      With the exception of the Material Force, about which we know very little, this is our alternative for the unified and simplified formulas of Electromagnetic Force, Strong Force, Weak Force and Gravitational Force. Thus avoiding to present these equations through extremely complicated developments.

      Considering that we know the relationship of alpha 'α' as also the formula of the electric field FE, it is possible to obtain a decomposition and resolution of these forces.

      However, the theoretical physicists wish to facilitate the calculations and, therefore, they would like to obtain one single Unified Force ... but if the forces are exactly these ones, then, there is nothing else to simplify ... there is no Unifying Force!

      At this point I am reminding me of the classification for the scientific system according to the physicist John Barrow: 'Every time a new idea is presented and notice in the scientific community it necessarily has to get through three steps: 1st It does not worth anything, we do not even want to hear about it; 2nd It is not wrong, but it probably has no relevance; 3th It is the greatest discovery of all time and we were the ones who found it first. And by then there will be many more candidates claiming the priority of the discovery. "

      It is unfortunate that some scientists never deviate from what is already known, always choosing to follow the safer trail. They do not even risk crossing the berm, transgressing the trail, or even give any chance to an alternative theory.

      It is their responsibility to expand the frontiers of Physics and open new horizons.

      Clearing new trails and discovering something completely new is fascinating! What's more magic in Science is the ability to go and get lost in the jungle of the unknown.

    "The most beautiful experience is the encounter with the unknown." - Einstein-.

      Science is above all a human activity very rewarding. Perhaps the most purest of all in a world far from perfection ...

      Only scientists feel very deeply what they do and only they feel real passionate in what they seek.

    "In the Universe no one has more fun than us." - João Magueijo-.