The great enigma
Other publications
About this site
At the dawn of the third millennium, it would seem the right time to pull down an old wall, which, standing as it has for centuries between science and faith, has prevented unity of understanding.
The world of physics, that impregnable branch of science, is at the point of examining the ultimate, and therefore essentially significant, nature of matter; at the same time, the Christian faith would finally succeed in plumbing its own depths if it were to reply positively to a fundamental question which still remains unanswered.
The question: If Adam had not sinned, would the Incarnation have taken place? is said to be an open question, because the Church has not resolved it, one way or the other. So, the Thomists could say: no, and the followers of Duns Scotus: yes, basing their arguments upon the revelation and glorification of God, to which we will here add the creation of the world, the final cause of which would logically be the Incarnation.
The concept of a creative Incarnation is revolutionary. It is, in effect, the redemptive Incarnation which is the foundation of Christianity, and which completely eclipses the creative Incarnation, both having the same Person as their moving force, in the same place and at the same time: the moment of the conception of Jesus. The fact that this moment occurred well after the creation of the world does not preclude the idea that the Incarnation is creation's final cause. The question merits examination.
Before the world was formed out of the void, the triune God alone existed, and so the process of creation must be sought in Him.
According to Catholic dogma, the Father is the principle, that is to say, the origin, of his end: the Son, whom he engenders inhis image (Col 1, 15; Cor 4, 4; Jn 14, 4).
The Father thus gives paternity to the Son, forto be the image of the Father is to be able to do what the Father can do,the1 st principle of the Son,in other words.
A strange but logical state of affairs, the Son can bethe principle and so the end in himself.
Ad intra, as far as the Trinity is concerned, the Son is, with the Father, the principle of the Holy Spirit and not of himself. Butad extra, as far as creation is concerned (and this is the source of the creative power of God), the Son is principle and end in himself: he was such by incarnating.
St Paul, speaking of the Son, described the process: "He is the image of the invisible God, the firstborn of all creation; for in him all things in heaven and on earth were created, things visible and invisible...all things have been created through him and for him.for in him the set fullness of God dwells bodily." (Col 1, 15-16; 2, 9).
Why does the Incarnation create a visible universe and an invisible universe? This duality stems from the fact that the Son is,ad extra, principleand end. As principle, He creates the invisible universe, as end, He creates the visible universe and, as man, He joins spiritual nature with bodily nature, his invisible soul being the principle of his end: the visible body, as is the case for all mankind.
It is imperative here to distinguish between the active Incarnation and the passive Incarnation. The first is the joint work of the three Persons whoeffected incarnation, the second is the work of the Son alone, since He alonewas incarnated.
The Son, therefore, has a double role as creator: as God He is, together with the Father and the Holy Spirit, the first cause of the Incarnation of which, as God made man, He is the final cause.
The active Incarnation has been intended from all eternity. For God is immutable: it is not a question of Him wishing at first not to incarnate, then wishing the opposite. He has always wished it. The passive Incarnation has also been desired from all eternity, but takes place in time, which the Incarnation itself creates.
In effect, the Son could not incarnate into a universe which did not yet exist. That is why his future coming created an environment to receive Him. Between the creation of the environment and the Incarnation there is an interval of time in which the events related in the Old Testament take place. Mary'sFiat starts off a new time period, taken to be from the Incarnation to the End of Time, which is predicted by Scripture.
The Incarnation therefore creates time and divides it into two periods: before and after Jesus Christ. The Christian calendar takes up this schema, and so provides a meeting point between science and faith, both of which make use of this same method of measuring time. Far more importantly, they both think seriously about the final cause of the universe.
Out of the infinite number of possible worlds, the universe we know is, from a scientific viewpoint, the only one which combines all the necessary conditions for the appearance of intelligent life, for if any of the elementary constants had been even slightly different, the appearance of mankind would have been impossible.
This is why some cosmologists have developed the Anthropic Principle, stating that the universe evolved in order that mankind might appear.
The metaphysical implications of this concept have aroused suspicion amongst scientists, probably concerned about possible parallels being drawn between their discipline and faith; and a faith which, more precisely, believes that the universe did not evolve for the sake of mankind, but for the sake of one particular man: Christ.
A logical explanation of the process of creation must include an examination of the motive.
"The world was created for the glory of God" is a dogma of the Catholic Church (Vatican 1, ConstitutionDei Filius, can. 5).
In the Philosophical Dictionary, under the word Glory, Voltaire refers to God: "...men, having no expression suitable for describing him, use the expression which most flatters them.". But how could the poor human language express the divine and ineffable? The term used by the apostle John (God is love: 1 John 4,8) is undoubtedly the most appropriate.
Falling back on this definition and using what is outlined above, one can describe the creative impulse as follows: infinitely good, God wanted to express his generosity by communicating it to creation through an independent action, which is the Incarnation. He therefore created the world, both for Himself and for his creatures. By the same token, it is his infinite generosity which created the world we know rather than any other world.
For God contains in his limitless mind, and from all time, not only the world which was brought about in time, but also, in a virtual state, all the possible worlds which will never be made real.
Sole reality, sole being before the creation, God would not be able to create if He were one person; his triune nature, however, allows Him to send his Son on a mission involving his Incarnation and transmission to the chosen virtual world his own reality, his being, "his life" as Jesus says.
And because God is infinitely good, He certainly created the best of possible worlds, despite its tragic aspects. He knows how to draw a greater good out of evil. For example, if Adam had not sinned, mankind would have been destined for a happy, natural life in the Earthly Paradise; whereas, thanks to his redemption through Christ's sacrifice, mankind is destined for blessed, supernatural life, eternal life, which will be and is already, a participation in the life of God Himself. And mankind will experience this eternity in the best of worlds: the heavenly Jerusalem, described at the end of St John's Revelation.
God created man in his image (Gn 1, 26), but the matter of the cosmos must also reflect the divine form, even the simplest particle of the visible universe bearing a faithful representation.
God can only create starting from that which He knows, and He knows only Himself, unique substance in its three intratriune relationships: Father, Son and Holy Spirit, equal, distinct and consubstantial, each residing in each of the two others. This reciprocal indwelling of the three Persons is known as circumincession.
The essential particle which constitutes matter should therefore show the same characteristics. If that were the case, science and Christian faith, addressing the same subject, would be reunited in the same understanding. We will try, here, to prove that this is the case.
A theological discourse should not impose a mathematical or physical makeup on God. In what follows there is certainly mathematical and physical content, but only in order to examine and make comparisons between what is already known from God's Revelation and from science.
The material universe is an ensemble of indivisible particles. This self-evident logic - this refusal to believe in matter which is infinitely divisible - had already been adopted by ancient Greek and Latin philosophers who called the basic particle of matter 'atom', which means 'indivisible'. But was there only one kind of basic particle, or several?
Physics took this problem on board. Having discovered several kinds of atoms, physicists realised that they were all made up of common particles, and particle physicists set about tracking them using quantum chromodynamics, thus named by analogy with quantum electrodynamics.
Quantum electrodynamics studies the two electrical charges, positive and negative. Quantum chromodynamics studies three 'coloured' charges, labelled as such because they join together as do colours. We will here give them the names of the primary colours: red, yellow and blue, which together make white.
In its quest for the indivisible particle, quantum chromodynamics has accumulated 48 candidates: 24 elementary particles and 24 corresponding antiparticles. We are therefore a long way off from the simplicity of a trinity: are we at a dead end?
Group theory, which plays a major role in particle physics, enables us to instill order into this multiplicity, as we will do here, by classifying the elementary particles in a table of 48 compartments which represent subdivisions of the set made up of the three basic coloured charges {red, yellow, blue}.
Therefore, all the elementary particles and antiparticles result fromone single tripartite entity,in threedistinct coloured charges because the three colours are different,equal because the three colours have the same functions, andconsubstantial because, as we said earlier, the three colours join together to giveonesingle and same white result: this last point needs elucidation.
In mathematics, when the order of the parts of a set is significant, the set is said to be ordered and is put into brackets.
Therefore, the set (red, yellow, blue) is ordered: the red is before the yellow, the yellow before the blue. But if we replace the brackets by a brace, as we did three paragraphs above, this indicates that the colours {red, yellow, blue}are not ordered. The parts, in this case the coloured charges, are necessarily written in an order, but the order is rendered insignificant by the brace.
If the three coloured charges are not ordered, they each necessarily occupy the same space at the same time: so each is inside each of the other two, and they give rise to one single and same consequence. This state of affairs copies circumcession and characterises the photon which, as we shall see, is behind the table with 48 compartments.
Group theory makes it possible not only to describe the role of the photon, but also to take a major step toward understanding elementary particles and antiparticles, which may be defined very simply in terms of their relationship with the three coloured charges, according to whether they contain one, two, three or none of them. There are therefore four kinds of elementary particles: the quark (one coloured charge) the antiquark (product of two coloured charges) the electron (product of three coloured charges) and the neutrino (no coloured charge).
There are, accordingly, four kinds of elementary antiparticles. Their rotational sense is the opposite of that of their corresponding particles. For example, an electron which started to rotate in the opposite sense would become its antiparticle: the positron.
Thanks to the equilateral triangle representing group G3, we are even able to visualize a geometrical arrangement of all the electrical charges: those of the electron and positron or sub-set , and those of the quark and the antiquark.
The electrical charges are here created by the rotations which, in the diagram, do not affect the equilateral triangle, centre 0, with its apices of red, yellow and blue charges. A complete rotation creates a set electrical charge, two-thirds of a rotation creates an electrical charge two-thirds in value, and one-third of a rotation creates an electrical charge of one-third. The electrical charges are positive or negative according to the rotational sense.
During the rotation, each charge takes the place of one of the two others, and so each of the three occupies the same place successively and not simultaneously as with the photon. We also find permutations between coloured charges in non-elementary particles such as the proton. This phenomenon must therefore have a profound significance, perhaps tripartite, because, by demonstrating the identical nature of their functions, it shows the identical nature of the coloured charges.
All the same, in order that these strange and novel features may be seen as credible, we must justify them in purely mathematical terms, without reference to the tripartite context. We will try to express this briefly and simply, starting with a definition of the G3 group which we have mentioned.
G3 is the group of six permutations of the set E with its three sub-sets, here the coloured charges which, for simplicity, we will represent by their initials. So E = (r, y, b). Each of the six permutations gives a different aspect of E, and so we find six combinations of the three coloured charges: (r, y, b) (r, b, y) (y, r, b) (y, b, r) (b, r, y) (b, y, r).
The six combinations are thus divided into three families of two branches each. The families are characterized by the coloured charge which comes first in each of their two combinations. For example, (r, y, b) (r, b, y) is the red family, which consists of one particle (r, y, b) and its antiparticle (r, b, y), as can be seen if we apply the three charges to the apex of the triangle already described and whose rotation in the sense rby is the opposite of that in the sense ryb. The same goes for the yellow family and the blue family.
Each of the six combinations is a set consisting of three parts; however, each set, with its three parts, has eight sub-sets, and so there are in total six times eight, or 48 sub-sets for the six combinations of coloured charges. We have thus come back to the 48 indivisible particles: they are set out in a table with six bands and eight columns.
In order to interpret the table, we will use a mathematical model of three abstract symbols, as follows: E =(a,b,c), when the sub-set are (a), (b), (c), (b,c), (a,c), (a,b) (a,b,c) Ø.
The last symbol is the empty set, named as such because it contains no particle; the sub-set preceding it is the set (a,b,c) itself because each set is a sub-set of itself.
So we have, from left to right: three sub-set with one particle, three sub-set with two particles, one sub-set with three particles, and one sub-set which is empty.
In the first line of the table, we replace the letters of the mathematical model by the initials of the coloured charges of the set (r, y, b), giving ( r ), ( y ), ( b ), ( y,b ), ( r,b ), ( r, y ), ( r,y,b ), ( a ).
So, from left to right, we find: three quarks each bearing a different coloured charge, three antiquarks bearing the product of two coloured charges, one electron bearing the product of three coloured charges, and one neutrino bearing no coloured charge, and so represented by (a), the initial of 'ater' (black in Latin): absence of colour.
The second line contains the same particles as the first, but the rotation of the electron is reversed: rby instead of ryb; and so it is now the antiparticle, the positron, whose rotation determines that of all the particles in the line. Thus, the neutrino becomes an antineutrino.
The following lines adopt the same arrangement, but the electron-positron pair is replaced by muon-antimuon pairs and then tau-antitau. These are heavy particles and antiparticles, whose creation requires the activation of a large quantity of energy, hence their late discovery.
The disintegrating photon gives rise, as experiments show, to the six pairs of particles and antiparticles, whose sub-set constitute the table of 48 indivisible particles.
To date, physics does not acknowledge the presence of coloured charges apart from quarks and antiquarks enclosed within baryons and mesons, and does not consider the electron to be a coloured particle.
The baryon is not an elementary particle because it contains three quarks, in other words three sub-set: ((r), (y), (b)). The meson is not an elementary particle because it contains a quark and an antiquark, in other words, two sub-set: ((r), (y,b)). The electronis an elementary particle because it constitutes one single sub-set: (r, y, b). Its coloured charges are not three quarks but have one single product: white. In the same way, the antiquark (ry) does not consist of two quarks, but of two coloured charges, red and yellow, the product of which is orange.
Despite the shortcomings of such a schema, we can visualise the particles and antiparticles in the table by means of a single regular tetrahedron, a pyramid with each of its three faces the colour of a coloured charge, while the base, without colour, will be black.
If the pyramid turns on its axis like a spinning top, it appears to be white, through the effect of the spinning, which blends the three colours, resulting in white: this is, for example, how an electron appears. If the spinning is in the opposite direction, we see the white aspect of the antiparticle, the positron.
If we rotate the pyramid vertically through 180 o , we see its base, which is black, and so colourless: this is the aspect of the neutrino or the antineutrino, according to the rotational sense of the pyramid.
As for the quark, we see it if we observe a single face of the pyramid, while on the other two faces the corresponding antiquark wil be found, bearing the corresponding anticolour. For example, juxtaposed with the red quark face we will see the two complementary faces: yellow and blue, blending together with the rotational effect to produce green.
To sum up, modern physics has discovered 24 elementary particles of matter and divided them into three families, each with two branches, into which are allotted - with the help of group SU5 - both the coloured elementary particles, quarks and antiquarks, and the colourless elementary particles: leptons, whether charged or not, including the electron and the neutrino.
All the elements of the puzzle have therefore been brought together, but the meaning is not clear, especially with 24 elementary antiparticles adding further to the complexity of the problem.
However, the extraordinary fact is that faith has set out the 24 elementary particles and the 24 elementary antiparticles in a single table, and is offering science the key to its decoding: a photon with three coloured charges.
The three coloured charges of the photon are, through their six permutations, what lie behind the table; and, as we saw earlier, they determine the characteristics of the 48 particles, the sub-set of the six permutations, according to whether they contain one, two, three charges or none and whether they rotate in one direction or the opposite, this last feature being that which distinguishes matter from antimatter (cf table below).
Therefore, faith is suggesting that science should unite the photon, the elementary particles and antiparticles, in other words energy: matter and antimatter.
Of course, a theory based on an analogy between the photon and the Trinity has no chance of being accepted by a science which relies on experiment and not on faith, but which, in an unexpected way, thus gives faith an opportunity to convince it, as we shall see.
Having defined the natural world and brought to mind the purpose of the visible universe, we reunited matter and antimatter in one set whose origin is the photon, made up of three coloured charges.
Faced with the logic of this hypothetical reasoning, based on the group G3, we suggest that science should set out to verify its accuracy by research into whether the photon, or, more conveniently, the electron, carries three coloured charges; for the electron, one of a pair with the positron, is a stem from the photon. If the electron were coloured, this would prove that its coloured charges existed already in the photon.
If the experimental result were decisive, faith, which has indicated the tricolour nature of the photon, and science, which would have acknowledged this nature, would unite in a common conception of the elementary universe.