THE OCTET OF THE PHYSICALS BEINGS
Vacuum, the Class of Fermions and the Six Bosons Mediating Natural Forces
Luiz Sergio Coelho de Sampaio
April, 1998.
ee-001001.01[1](15/07/1999)



Since the electroweak synthesis attempts to encompass the 4 physical forces within an unified theory has not fully succeed. In order to overcome this blockage, we propose here an interpretative reformulation of the general frame of natural forces, admitting not 4, but 6, by simple aggregation of the hypothetical force of Higgs and of the old strong force (Yukawa’s force). Tree of these forces are considered simple and the other tree complex ones, whose set of six mediators, together with vacuum and the class of fermions, will form the octet of beings in physical world. Such reformulation clarifies the reasons for the failure of the currently accepted theoretical strategy, which should be henceforth replaced by a new one, aiming, not the unification of forces per se, but to establish a network of interdeterminations among forces. Furthermore, the use of this new strategy will allow new predictions about a variety of crucial problems of modern physics.


Physics is essentially determined by its desideratum [1] of reducing the phenomenal diversity of the world into three fundamental quantities: time (T), space (L) and matter (M). Such intent was firstly stated by Newtonian mechanics, which, however, considered all of them absolute entities: absolute time, absolute space and absolute matter.

The idea of absolute multiples [2] constitutes an evident oxymoron, a contradiction in its own terms. For this reason, the history of Modern Physics became a search for ways to conserve, and at same time, to "disabsolutize" the 3 quantities using the explicit determination of their reciprocal compromise. This is accomplished by the formulation of the so called non classic mechanics, which brings the idea of number of commitment, which is actually the essence of the well known universal constants.

Considering the existence of 3 fundamental quantities - T, L and M - there are three possibilities of combinations 2 to 2:

    T and L, a commitment already fully disclosed by the Special Relativity as a maximal velocity (c) for the translation of mass, energy or their effects;
    M and T, a commitment already fully disclosed by quantum mechanics as a minimal spin (h/4  c2) [3].

These two commitments, linked, constitute the most successful theory of Physics: the quantum electrodynamics (QED); L and M, a commitment expected to be disclosed by the General Relativity [4], has not been fully defined so far. This commitment will be represented by a new quantity, the cliname, whose dimension is ML-1 [5].

Taking into account the significance of the above stated compromises between the primary quantities (M, L and T), the set of fundamental quantities increases from 3 to 6: what was lost in autonomy by T, L and M was necessarily gained by LT-1, MT and ML-1.
Among the fundamental quantities there are tree dynamic ones (those bearing M in their dimensional formulas): mass, m (with dimension M), cliname, a (with dimension ML-1) and spin, s (with dimension MT). From dynamic quantities arise directly the family of physical quantities (mechanics) and also, by their combinations, the variety of physical beings (vacuum and particles, both fermions and bosons).
The families are sets of equivalent quantities, i. e., quantities differing for powers of a velocity (LT-1) [6]. So, each fundamental dynamic quantity engenders its particular family:

M family - mass, m (M), momentum, p (M x LT-1 = MLT-1) and energy, E (M x L2T-2 = ML2T-2);

ML-1 family- cliname, a (ML-1), "mass variation", A (ML-1 xLT-1= = MT-1) and force, F (ML-1 x L2T-2 = MLT-2);

MT family - spin, s (MT), static momentum, S (MT x LT-1 = = ML) and angular momentum J, (MT x L2T-2 = ML2T-1).

Considering the tridimensionality of space, there would be still two families related to ML-1: ML-2, a family with no great use, and ML-3

ML-3 family- density,  (ML-3), material flux intensity, j, (ML-3x LT-1 = ML-2T-1) and pressure, P (ML-3x L2T-2 = ML-1T-2).

Thus, each fundamental dynamic quantity has its own family of equivalent quantities. The equivalence mass/energy is a particular case of this general statement. The fundamental quantities will be named proper mode - rest mass and spin (angular momentum/c2) are good examples of that -; the proper mode multiplied by the dimensional of velocity (LT-1) generates the relative mode; and the latter again multiplied by the same dimensional generates a new global mode. The global mode is a natural synthesis of the two first modes. The relationship among these 3 modes will lead to a very common and characteristic kind of physical equation, exemplified by E2 = p2c2 + mº2c4 (about the dynamic quantity mass, M) and P = j.v +    v2 (about the dynamic quantity density, ML-3). [7

From the same set of dynamics fundamental quantities -m (M), a (ML-1) and s (MT) - , arise, by pure combination, the set of physical beings (vacuum and particles): {ø}, {m}, {a}, {s}, {m, a}, {m, s}, {a, s} e {m, a, s}. Table 1 shows the clear correspondence between these combinations and the set of physical beings. Only one true disagreements with previously established concepts in physics can be here detected: the graviton classification.

According to Table 1, the graviton is endowed with cliname, but not with a spin value. Conversely, in General Relativity it is considered to possess spin 2. Assuming spin 2 for graviton the perfect symmetry of the frame of natural forces proposed here would be disrupted, since there would be two particles with spin only (graviton and gluon) and none with cliname only. We believe that the attribution of spin 2 to the graviton is a formal consequence of the superabundant complexity of the General Relativity equations. A deeper study of these equations will show their inconsistency, independently of the spin ascribed to the graviton.

As already observed in Table 1 the fermions would be endowed with mass, spin and cliname. So it is necessary here to admit one exception: the neutrino the electron with a null mass [8]. In fact, this constitutes a real exception, impossible to be suppressed, but which is supported by a more than compensatory logical explanation, as shown below.

Particles endowed with only one fundamental dynamic quantity will be named mediators of simple forces and the particles endowed with two of them, mediators of complex forces. Naturally, all of them will be classified as truly bosons. Thus, on the one hand, there would be three simple forces: the Higgs force{m}, gravitational {a} and strong (gluonic interquarks [9]) {s}. On the other hand, there are three complex forces: electromagnetic {a, s} , weak {m, s} and the Yukawa force{m, a}, (the ancient internucleonic strong force mediated by pions). The six bosons, the mediators of the forces, plus vacuum and the class of fermions form the perfect octet of the physical beings, as showed in Figure 1.

Each simple force is responsible for the inner structure of the mediator of its complementary complex force. This happens because all simple forces are saturated (including the gravitational force below a specific distance). By being saturated, their characteristic quantities will not be present in the assemblage of quantities of their complementary complex bosons. For example, the weak bosons {m, s} - W+, W- and Zº - are deprived of cliname {a}, therefore, insensitive to propre gravitation. This happens exactly because the gravitational force is responsible for the inner structure of these complex bosons. As a necessary consequence, the radial lines of forces of the gravitational field will collapse at very short distances, with the gravity becoming a saturated force. Thus, the intensity of the gravitational force will increase up to the intensity of the remainders forces of nature [10]. With this new concept one opens a new pathway to solve the problem of gravity quantization, hitherto without solution.

In spite of an apparent disagreement, there is no major difference between the set of 6 forces proposed here and the set of 4 currently accepted in physics. Why 6 and not 4 forces? Firstly, it is necessary to consider the mechanism of Higgs as a true force, not only because it permits acquisition of mass by weak bosons, but more importantly, because that is the only way to provide mass in general. The particle of Higgs is endowed with a single attribute, mass (m) and it is an authentic boson. Thus, not counting it as a force is non-sensical [11].

As for the sixth force, the natural candidate is the old strong force, theoretically deduced by Yukawa in 1935. It will be thus named force of Yukawa. Despite the existence of gluons, the nucleons go on changing pions. The new strong force does not suppress the old one, but simply provides an explanation on how it works, i.e. , how pions and nucleons are structured (undoubtly, a strong suggestion as to the existence of simple and complementary complex forces). In order to disqualify the force of Yukawa we would need to suppose that nucleons are endowed with epistolary intentionality, i. e., that it is able to change gluons, though it previously envelops them within pions. This case is completely different from that of the discovery of the electromagnetic force, in which inter and intra-atomic interactions were explained by the same force. All these considerations lead us to admit not four, but six as the actual number of natural forces. What reasonable meaning could now have the expression "unification of forces"?!

Finally, the expression grude in parentheses following gluon (Table 1) means that the present model for quarks is transitory. We believe that in the near future it will be replaced by a new model simultaneously accounts for the extra and inner structure of quarks (as electromagnetism operates both at inner and extra atomic levels) , the gluons being then replaced by grude, a boson with the same features as gluons, i.e., endowed only of spin 1.

It is easy to verify that only the mediators of complex forces have been empirically discovered so far. This is the case of photon,  , weak bosons, W+, W- and Zº, and pions, pi° , pi + and pi -. In contrast, no simple boson has been hitherto artificially produced. This happened because the simple forces are more "elementary", or more deeply rooted. Consequently, their bosons have a greater proper energy than their complex partners.

Which meaning could we attribute to the expression primordial particles? From a construtivist point of view, primordial particles would be those able to engender all other fundamental particles by themselves. Therefore, primordial particles have to meet the following conditions:

  1. They must at least include one fermion and one boson, otherwise it would be impossible to start a constructive process;

  2. They have to conjointly embrace the tree fundamental dynamic quantities, otherwise these (m, a and s) would not be able to come to light in the route of the constructive process; for symmetry or for aesthetics considerations [12], it would be desirable that each quantity appear only once;

  3. As a decisive test, it would be necessary to show, on the basis of the present physical knowledge, how to construct all fundamental particles, in a rather elegant and exclusive manner.

The six possible combinatory options are shown in Figure 2. Options in which bosons are endowed with s have to be dismissed because if they had zero or whole spin numbers, they would not be able to engender fermions with fractional spins. Thus, options III, IV and V are immediately discarded. The quantity m cannot participate in a primordial fermion, otherwise it would be impossible to engender particles with null mass as the electron-neutrino, gluon, graviton and photon. Hence, options IV, V and VI must be rejected too. Actually, this is the logical justification for the existence of a fermion without mass, as noted above. Only options I and II remain possible. However, the primordial boson cannot present two fundamental dynamic quantities because by doing so, it would become impossible to engender any simple bosons; if this is accepted, options I, III and V should also be removed. Finally, only option II is preserved, in which the fermion is endowed with quantities a and s and the boson with m only. Therefore, the former could not be other than the electron-neutrino and the latter, the particle of Higgs (Figure 2) [13].

It should be reinforced that the logical overdetermination of the primordial particles is not sufficient yet. The consistence of the choice for option II - electron-neutrino and the particle of Higgs - must be now empirically validated, as established above. Figure 3 shows by itself, albeit succinctly, the scheme of construction of all fundamental particles (construction is used here as the equivalent expression for reverse of decay). Arrow heads in full lines represent the direction towards which particles are constructed. Dashed lines indicate a new force (yet not present in the engendered particles) intervening in the construction of the pointed particle.

The position of tau could be equally occupied by nucleons: proton and neutron. This happens because in the inner structure of tau there is one neutrino of tau, which could be replaced by a electron or an electron-neutrino at a lower energetic level, leading to particles with similar structure but much more stable.

We should now proceed to confront the standard model (SM) with the one proposed in Figure 3 (M3). Table 2 below provides a summary gives a resumed presentation of both models. The following disagreements are self-evident:

  1. SM only presents the particles while M3 not only presents them but also shows their logical process of construction. The 3 levels or families of elementary particles in SM can only be empirically justified, while in M3, those levels are provided with a logical character;

  2. In SM bosons are set aside of the central frame since 4 sets of bosons could not find correspondence in a table with 3 lines; in their places 6 quarks are shown. In contrast, M3 presents the 6 boson sets corresponding to the 6 natural forces in two columns, one for simple and other for complex bosons. It is important to note that quarks d and u are both implicit in pions, as well as in tau , since tau decays as  «­»  t . Thus, there would be no reason for d and u to appear twice in SM, once isolated and again implicit in tau. There is also a multiplicity of appearances implicit in M3. However they occur coherently according to the logic of their own constructive scheme;

  3. All quarks in MS - d, u, s, c, b e -, although not present in M3, can be "constructed" with their twelve elements, showing that M3 is more general than MS. It is also demonstrated why MS works, despite their conceptual deficiency. [14]

  4. In M3 there are a perfect symmetry between bosons and fermions, whereas this is not true for MS.

The present interpretative reformulation of the general frame of forces gives rise to a series of inferences, some necessary, others highly probable, about a variety of crucial problems of modern physics. Among them:

  1. The electron-neutrino will necessarily have null mass. Therefore, the problem of the deficit of solar electron-neutrino fluxes must not be explained by its "transformation on flying" into other kinds of neutrinos. In addition, electron-neutrino could not be responsible for the presumed dark mass of Universe;

  2. The graviton will be endowed with cliname only and its spin will be zero. This statement points to the need to proceed, sooner or later, to a reformulation of General Relativity;

  3. The current strategy of unification of physical forces will not work and will need to be replaced by a strategy of articulation, as QED is the best example. By simply considering the mediators of electromagnetic {a, s} and weak {m, s} forces, both complex, it would have been easy to predict that their unification by means of the formal absorption of the latter by the former would cause the emergence of a force endowed with the quantity, mass (m), i. e. , the force of Higgs. Thus, it becomes obvious that the current unification of complex forces is a very bad strategy, as seen in the present case. The process starts with two forces and also finishes with two: symbolically, electromagnetic + weak = electroweak + the force of Higgs. Unification of forces is still a bad strategy if we intend to continue the process of unification by including a new force, in this case, the gluonic strong force, now a simple one. Actually, strong force (s only) is already implicit "twice" in eletroweak force. Thus, the theoretical potentialities of superstrings would be subjected to evaluation only after changing the strategy of unification of forces.

  4. The unification of Quantum Mechanics with General Relativity will be impossible, not only because one is linear and the other non-linear, but also due to a deeper reason. That is to say, the former is subdetermined (probabilistic or logically paracomplete) and the latter overdetermined (geometries in 3+n dimension or logically paraconsistent) [15].

  5. It is very likely that he present quark model will be replaced by a new one, based on the now renamed strong force, which will account for both the interactions of extra and intraquarks [16]. Therefore, it will no longer be necessary to admit neither fractional charges or "inferred decimal" spins.

  6. There will be a proper cliname aº - as there are proper mass (rest mass) and proper angular moment (spin) -, working at distances smaller than dº (dº < or = 10-20m). Below dº, necessarily, F = = G.aº2 = constant. It is important to note that unlimited cliname would render impossible the existence of the Universe (hence, the idea of baby-universes and other oddities). Symmetrically, without a minimum spin (excluding zero by inner compensation) the world would become a chaos because to be would be infinitely close to not to be or to be something else.

  7. It is also very likely that the proton will never decay. This is because proton is a minimum-energy structure stemming from tau. Oddly enough, up to now, the proton has been considered a complex particle and tau, an elementary one!

  8. It is expected, by energetic considerations, that the particle of Higgs will be the next boson to be empirically discovered. However, using the constructive scheme shown in Figure 3, graviton or gluon will be certainly the next discoveries, remaining the particle of Higgs will take the last place.

  9. The concept of excitedvacuum will be found to be self-contradictory. Because of this, the present inflationary cosmological models and similar ones grounded in that concept will be ruled out.



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