## STEPS TOWARDS A THIRD QUANTIZATION

Having its essence in the union of time and space, matter carries the seal of both. (Arthur Schopenhauer)

The objective of this work is to contribute, in the field of the ideas, to a more unified vision of nature.

We'll begin our explanation with a question presented by the physicists Carlos Pinheiro (UFES) and Gentil O. Pires, on 1966:

"We have to ask the following: is gravitation a quantizable theory? Or is it a metric theory that is indifferent to the appeals of Quantic Mechanics? Or is it that we have to make a change in the Quantic Mechanics, as R. Penrose insinuates in his book 'The Emperor's New Mind', so that we may really incorporate Einstein's gravitation theory inside Gauge theory and, therefore, to obtain the so much dreamed and desired Quantum Theory of Gravitation consistent with the other proposed theories for the fundamental interactions and in perfect harmony with General Relativity?"

Well, according to our vision, we have to make changes on both theories. Let's see: English physicist Petter Higgs has postulated, 40 years ago, the existence of the so-called 'God particle' (Higgs boson), without which the basic physics theory – the standard model – lacks a crucial element, because it doesn't explain how other subatomic particles, like quarks and electrons have mass. Now, to want to discover so essential particle before the empirical confirmation of others, supposedly less important, is like, keeping in sight the differences, to want to discover the neutrino before the electron.

The particle called Higgs boson is really the quantum of one of the components of Higgs field. Since the Higgs field is a scalar field, Higgs boson has spin zero. That means this particle has no intrinsic angular momentum and that a collection of Higgs bosons satisfies Bose-Einstein statistics. The standard model do not predict the exact Higgs boson mass nor this mass has been experimentally measured. It is expected among the physicists that the Larger Hadron Collider (LHC) confirms or denies the existence of Higgs boson. The confirmation of that particle, in the manner I suppose, will make the necessary changes possible, as we'll see ahead.

But, before that question, we have the problem of the graviton. In the classical gravitational field theory described by General Relativity, metrics has a crucial role. In order that we build a model in which gravitation works as a Gauge Field, similar, therefore, to electromagnetism, gravitation will have to be mediated by a "quantum", that is, dynamics will not reside in the space-time geometry, but in a field that is able to create and destroy particles of the graviton type. According to Steven Weinberg, the change of these gravitons will produce the same gravitational effects predicted by the General Relativity. However, such hypothetic mediator particle – graviton – has not yet been detected.

Having made these considerations, we we'll formulate two propositions that will imply in changes on the two theories under discussion:

1st
proposition: The particle which will be confirmed by LHC will have zero mass.
As it is implicit that this particle has spin zero, since Higgs Field is a
scalar one, we believe that what will be found is a graviton. We agree with the
thesis defended by physicist Mario Novello that the graviton with spin of value
2 has very low mass but not zero. At a seminary of IAG (Astronomy, Geophysics
and Atmospheric Sciences Institute of Federal University-São Paulo), at the end
of his presentation Mario Novello has said: "So, to end, as I know astronomers
love numbers very much, I'll let you with a number: 10^{120. }This
gigantic number, according to Novello, represents the thing that exists in the
biggest quantities in the universe: gravitons. Attributing this number for
gravitons, Novello has proposed a solution for a mystery that one of the great
physicists of modern times, Nobel prize Steven Weinberg, of Texas University,
called 'the cosmological constant puzzle'; Novello linked that number with the
hypothesis of gravitons with mass.

What has difficulted the detection of this fact was a double mistake (or correctness?) made by Einstein when, discovering, on 1916, that his equations predicted an expansion or a contraction of the universe (which was correct), he introduced, on 1917, one more parameter in his equation, that is, "Lambda", also called cosmological constant, in order to harmonize his equations to his concept of a static universe. On 1929, when American astronomer Edwin Hubble discovered, via observation, that the galaxies were all moving away one from the others at a great speed, Einstein has repudiated the change he made on 1917 (second mistake?). Today, however, this "Lambda" is used to explain the dark energy – a mysterious power that makes the universe expand on accelerated rhythm and, according to Novello, "Lambda" may very well represent the value for the the graviton mass. Now, we have two gravitons: the frst one (graviton1) with spin of value 2, but low mass, and the second (graviton2) with spin zero and zero mass.

2nd Proposition: Because of the introduction of spin zero graviton, we have to make changes also in the Theory of Relativity. We will have to introduce a scalar component in Einstein's field equations, because the new graviton has spin zero and, therefore, is a generator of a scalar field. Thus, the Theory of Relativity would have two components: graviton1, giving support to the tensorial part of the field, and graviton2 giving support to the scalar part. Considering that the tensorial part is now sustained by a graviton with low mass (as predicted by Novello), its reach would be limited, and could not be applied to the whole universe. The part that we can apply to the whole universe is the scalar part, which would oblige necessarily a graviton without mass, which is the characteristic of graviton2.

Therefore, it's clear that the theory here presented depends on the confirmation of the existence of graviton2, which has zero mass, and also that graviton1 has low mass. However, the confirmation of Higgs boson does not imply the inexistence of graviton2.

Now we'll discuss about our cosmological model.

The General Theory of Relativity is on the basis of the cosmological model that predominates today, which is known as the "standard model" or commonly as "The Big Bang Theory". It has introduced the revolutionary conception of an essentially symmetric relation between space-time and matter-energy, that is, the presence of matter-energy determines a curvature of the space-time, which determines the movement of this matter-energy.

The singularity which is associated to the Big Bang is a direct consequence of a static entity, enclosed in itself, which constitutes Einstein cosmology. Thus, as already said, General Relativity, which is the heiress of the Newtonian theory, does not confer sense to irreversibility nor does it explain the enormous production of entropy which marked the birth of our universe.

Thus, our model will include some thesis defended by Ilya Prigogine e Isabelle Stengers in their book "Between Time and Eternity", with some modifications. The initial singularity of the standard model is replaced by a creative instability, simultaneously of matter and entropy of our universe. Therefore, the universe is the product of a symmetry break between space-time and matter-energy. It's not necessary to deal with energy separated from the particles, since the quantic theory teaches us that light is constituted by zero mass and zero electric charge particles known as photons.

The change that we introduce in our model is that we do not need to take separately space-time and matter-energy, which means that the nature of space-time is the same nature of matter-energy. At this point, we need to make some considerations in order to give continuity to our cosmology. As we did in the beginning of this article, we will put one more questioning formulated somewhere:

"Are there, really, some elementary entities which are particles and others which are field excitations (quanta)?"

If we defend a separation between genuine particles and field quanta, we can distinguish fermionic matter made of particles from bosonic power fields. However, some doubts may arise, considering that fermions can mediate interactions between bosons. So, fermions are, in a certain way, connected to power.

In our model we reject any distinction between genuine particles and field quanta. Thus, in our vision, there is not any duality wave-particle, but only duality of models. In relation to this, there is much talk about the "second quantization", when Quantum Theory of Fields is expanded to everything and not only to electromagnetism.

Now, a
quantic field is not a quantized wave function. For instance, Maxwell Field,
obviously, is not a wave function of photon. In a relativistic theory, wave
function is a functional of fields and not a function of the particle
coordinates. In our model, we consider quantic fields as the basic ingredients
of the Universe, and all the *observables* are constructed from them, even
if the fields are not necessarily measurable. The particles are only
excitations of the quantic fields, energy packs of these fields.

Hence, in our model, space-time is the gravitational field itself, which exists independently of matter and has intrinsic curvature, and the presumed particles that arise only reinforces locally (Einstein Theory) the primary field which created them. Paraphrasing the authors cited above, the purely geometric Universe represents a state which entropic creation of matter has destroyed. What marks the difference between an "empty" Universe and our "material" Universe is not energy but entropy. Thus, we have to go not towards the infinitely small but towards the infinitely hot in order to discover what existed in the first instants of the Universe. In our vision, only photons existed.

Let's see. The existence of antiparticles is a direct mathematical consequence of quantic mechanics and the restrict relativity principles. According to Steven Weinberg (The First Three Minutes: The Story of Our Universe), it's possible to create any particle-antiparticle pair from the collision of a pair of photons, depending on the energy employed, which is given by the product of temperature of radiation vs Boltzmann Constant. Our model, then, coadunates with the theoretical exigencies: the creation of matter and antimatter in the same proportion is a result of collision between photons.

The beginning of the Universe is thus with light and sound, as predicted by Ramana Maharshi (Hindu sage and philosopher): light of photons and sound of background noise of microwaves at 3ºK. The so-called "initial explosion" was, thus, produced by the collision between photons at very high temperature and density, and the explosion occurred simultaneously in every part, filling the entire space from the very beginning and not from a definite center, as stated by Steven Weinberg (The First Three Minutes: The Story of Our Universe). Therefore, we are making of the origin of the Universe a true object of science, differently from the "Big-Bang", which escapes from our physics theories.

As explosion continued, temperature lowered because of the expansion, gradually reducing the energy employed on the collisions and consequently creating all known particle-antiparticle pairs. The idea of the birth of the Universe is thus associated to a spontaneous quantic fluctuation of the "vacuum", which caused a creative instability simultaneously of particles (photons) and entropy.

During this creative phase, density at first grows until it reaches a regime value, when the Universe enters in expansion of exponential type of constant density (inflationary phase "de sitterian"), followed by adiabatic expansion described by the standard model. In other words, at the birth of the Universe, the gravitational field energy diminishes (becoming more negative), "irradiating" photons (positive energy), having as a consequence an increase of space-time curvature. The presumed singularity is no more necessary. What is necessary is the instability of an Universe essentially empty (excited state), of which the space-time curves itself, irradiating photons. Something like an excited atom, which emit photons too.

To end this part, we would say that the gravitational field and matter (excitation of that field) have a common property when excited: to irradiate photons.

Another question not solved by the standard model is the enigma of antimatter. Following several reasoning, Steven Weinberg and other theoretical physicists have concluded that the Universe should contain equal amounts of matter and anti-matter and that, after temperature has reached a specific value, the Universe would be divided in domains of pure matter and pure anti-matter. Thus, the question arises: why nobody observes an appreciable amount of anti-matter in any part of the Universe? According to a hypothesis, with which we agree, developed by Pedro Livio Sande Vieira, Electrical Engineer graduated on UFBA (Federal University of the State of Bahia) that occurs because of a very simple fact: all anti-matter existent today is now in the form of black holes, and thus we cannot see it. It's obvious that anti-matter could never be dispersed together with matter, because then there could be no material Universe. Therefore, anti-matter has to be necessarily concentrated, and, according to this postulate, in the form of black holes, true elements of universal cohesion.

Luiz Humberto Sande Vieira

Salvador- Bahia - Brasil

*Autor: Luiz Vieira*

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