The logical meaning of the effective empirical proof of the existence of the particle of Higgs

Physics is the desire of Modernity; it has as its sole desideratum the One-in-trinity (²) – the world reduced to time, space and mass –, all put under measure and squared out in the obsessive rhetoric of the third excluded. Here is almost everything: from prologue to epilogue.

At last the first empirical signs obtained for the particle of Higgs have been announced(³). We can now easily foresee that in a short time  other similar news will be coming out, progressively with more and more assurance, until it will be confirmed by many and believed by as many that the particle really exists. After that, we hope, ‘Higgs’ (a sensible and just homage to the Scotsman who proposed its existence) will no longer be the name of a hypothetical mechanism but will designate what it truly is: a veritable force of Nature, sometimes diffused in a scalar field, sometimes condensed in the Higgs boson, whose physical attribute is nothing more than mass.

It is time for us to reaffirm our recognition to Weinberg and Salan and their commendable endeavor towards the unification of the electromagnetic and the weak forces. We know that in this theoretical process they were obliged to admit the intervenience of the “mechanism” of Higgs as a means to provide mass to the weak bosons W± e Z⁰ so that the weak bosons could, in cooling off, become different from the foton (breakdown of the electroweak symmetry and the inevitable fall in reality). For all that we can no longer disown the occurrence of an unexpected consequence: for the first time in the history of Physics, an human endeavor to unify something will have found an intrinsic physical resistance (is it possible that behind the scene, the ill-will of the logic of the One-in-trinity has been working against that?!). For, in the beginning we had two entities – the electromagnetic and the weak forces – which should have been unified in one, as it would have been politically and semantically correct. However, in the end we find ourselves with the same thing over again, that is, with two forces, the electroweak force and now the Higgs force.

So at this point we face a terrible number problem! How should we seriously count the Higgs force: as the fifth (⁴), or the fourth force of Nature? That is indeed a difficult question for which we have not so far found a satisfactory answer in the specialized literature. In our judgement  the reason for that may be because the question has not been formulated in the proper way. We must assume that there is no real reason to disqualify and hence to leave out as one of the forces of Nature the olden inter-nucleonics strong force suggested by Japanese scientist Yukawa in the 1930s, a force mediated by mésons p (pions), that really exist. Indeed the new strong gluonic force had come to explain the pionic interaction, not to abolish it, much as Mallarmé’s dices were not meant to abolish chance. In other words, the gluon (beyond other excelling virtues, such as aggregating quarks to produce protons and neutrons) is the force that structures internally the meson p. That is the fact as it is with no more or no less relevance!

Taking all this into account the correct question might be thus reformulated: Is the Higgs force the sixth or the fifth force of Nature? Well, considering that in the standard model there are 6 leptons and 6 quarks, who would bet that the forces  should not also be 6 instead of 5?! Moreover, taking that the 6 leptons and 6 quarks come in pairs, who would not also ask:  might not the Higgs force also be a member of one of the 3 pairs of the forces that total the supposed 6 forces of Nature?

Therefore, we propose that the Higgs force is neither the fifth nor the fourth but actually the sixth force of Nature. And as with the others, it comes with its best half.

With that reasoning we are not unduly proposing an increase in the number of forces in Nature, as some might hasten to conclude, but on the contrary we believe we are actually reducing their number. In essence and in accordance to the very essence of the desideratum of Physics, the forces are now only three, because three of them – the electromagnetic, the weak one, and Yukawa’s old strong one – can be considered composed forces, closely associated with the simple ones – respectively, the forces of Higgs, the gravitational, and the strong (gluonics) one, as shown in Figure 1. One may easily take notice that the composed forces all have well known mediators, which is not at all the case for the simple forces. No one can say that such things happen by mere chance!

In this regard, a moderate measure of intellectual honesty should suffice to conclude that the accepted reduction of Yukawa’s old strong force to the gluonic strong force could be taken as the first evidence of our generic proposition concerning forces that come in pairs. If such an idea once prospered and was later dismissed, who is to be blamed?

Figure 1 – The physical entities according to their fundamental attributes  (spin MT, cliname M/L and mass M)

It should not be difficult to apprehend that the proposed framework, constituted by eight essential physical entities – three simple or elementary forces, three derived or composed forces to which the vacuum and the (almost entire) class of fermions are joined  – is logically and perfectly structured upon the three fundamental attributes of materiality: spin, expressing the physical individuality (sameness); cliname, expressing in physical terms a relational disposition to other entities (being-with-others); and mass, which dialectically synthesizes the previous two attributes (⁵), as shown in Figure 2.

The vacuum (the material nothingness(⁶)), of course, has none of the three attributes; the simple forces have only one attribute each; the derived or composed forces have two attributes (where the missing attribute remains responsible for the internal structuring of the respective mediating boson, which constitutes the justification for its phenomenic absence); finally, we have the fermions, most of which are endowed with the three attributes, except for a unique and well justified item – the neutrino of the electron, which has no mass (⁷).  

Figure 2 – From the One-in-trinity to the triple materiality

Now we can focus all our attention on the ensemble of physical theories. Here we will ascertain that the great historical obstacle that has hampered the unification process (a possibility no more, because it is simply unthinkable that one day Physics should dilute its essential/originary One-in-trinity being) lies no less than within the Theory of General Relativity, precisely because it inherited a grave deficiency coming from the classic theory of gravitation. Newton is the genius who gave formal expression to the relational force pervading all material beings (the general law of gravitation), including the formulation of its characteristic constant (the gravitational constant, G). However, he did fail  in the question of whence its essence or fundament might come from, that is, how it (G) might constitute a bearer of a fundamental ontic commitment (not a simple identification) between mass (M) and space (L)(⁸). From a philosophical point of view, we can say that being constant is and will always be a secondary attribute that craves for a fundament. Apparently this serious shortcoming of the gravitational theory was not perceived by Einstein, neither on the moment of the formulation of the Special Relativity, nor later, during the formulation of the General Relativity. When Einstein took notice of the problem, better saying, when he felt its dramatic effects, namely the possibility of the collapse of a physical entity into a mathematical entity (later on, as is well known, the result of such a collapse was named a black hole), he thought that such inconsistency could be solved by itself in the context of General Relativity. Indeed he tried to  demonstrate(⁹) that the Schwarzschild radius had no more than an unstable limit value. A gravitational collapse on account of that radius was unimaginable for that great thinker – certainly Einstein thought at least at that time this would be nonsense (¹⁰).  The attempt to prove that point failed, but, ironically, in the same year of 1939 Oppenheimer and Snyder (¹¹) published an article showing that the occurrence of gravitational collapses (black holes) was admissible in the scope of the General Relativity. The Schwarzschild radius, as Einstein supposed, was in fact proven to be an unstable limit, however not as an infinitely steep wall but as the easiest way out from here to nowhere land! That may be why the much expected “proof” failed. On the other hand, after the discovery of quasars, whose intensity of energy was inexplicable by the theoretical resources of those times, there was no more room for speculation on the matter. To top it all, the search for sensationalism...

In order to find our way out of this entanglement it is necessary to define a good strategy, and Figure 3 may show us  a clear and safe map.  

The first step to take is to proceed to a deep revision of the Newtonian theory of gravitation, specifically concerning the essential meaning of the gravitational constant, G, which is interpreted here as a limitation to the intensity of the physical relational being. Just as it is unthinkable to conceive of the identity of a physical being as completely null (Planck’s h constant having zero value), it is impossible to conceive of a physical being having an absolute relationship with other one. Consequently we can easily conclude that the cliname, a (¹²), cannot assume an infinite value; therefore, it is necessary to introduce into the (Newtonian or classic) gravitational theory a postulate stating that any worldly cliname must have a value less than the cliname of Planck, that is to say,  a £ c²/2G (¹³). From now on that will justify the presence of the constant G.  

Figure 3 – Physical theories according to the compromise between the fundamental dimensions T, L and M

If we are right in thus correcting the Newtonian gravitational theory (from now on renamed gravitational theory* after the introduction of the new postulate of the cliname limitation), we can be assured that no inconsistencies in the scope of the Special Relativity (¹⁴) will appear due to the gravitational phenomenon. So, that makes us  free to articulate this latter theory with the gravitational theory in order to obtain a new, fully consistent General Relativity*.

Closer inspection of Figure 3 shows that, before we can think about a unified theory, we need to face the problem of quantum gravitation. It is a fact that nowadays the quantization of gravity is usually derived directly from General Relativity, which, as can be perceived in Figure 3, looks like a unhappy theoretical strategy. The need for a gravitational quantum theory must prevail directly only in microscopic scale, something that can only happen to conveniently reduced distances, from whence the gravitational field can collapse thus allowing it to compete with such other fields. We have concluded elsewhere (¹⁵) that at short distances (which we have precariously estimated at about 10^-19 m (¹⁶)), all lines of forces of the gravitational field abandon their radial configuration to converge onto the nearest object, thus making it a saturated force as intense as the other forces of Nature (10⁴³ times more intense than the common gravitational force that we are used to). In these circumstances, the intensity of the gravitational force will be expressed by the formula F = G.a₀², where                 a₀ @ 3,8 10¹⁰ kg/m is named own cliname, similarly to the well known own mass and own angular moment (spin).  

After all these considerations, it is unquestionable that the particle of Higgs does indeed exist. However, it might be prudent to ask: could all this assurance be compatible with the “discovery” thus announced? How could it happen that, without a clear and convincing justification, the factual discovery of a particle so essential as the Higgs boson would happen before the empirical certification of other, “less logically essential” ones as the gluon and the graviton? How could we fathom the discovery of the particle responsible for giving mass before the graviton linking mass? Keeping the proportions, it is as if the neutrino could have been discovered before the proton or the electron!

The “discovery” that is so sensationally announced implies that the particle in question does not have spin, which obviously excludes the possibility of it being a gluon. As it is not a gluon, then it will have to be necessarily a graviton, so long as it is proven (and we don’t doubt that it will soon) that it does not have rest mass. Not having spin nor rest mass, the only attribute left to it is cliname. In sum, it could not be but a graviton, which, however, to be fully demonstrated and acknowledged it will still have to wait, may be, for the LHC (¹⁷).

  In that case, however, how might that be made compatible with the much openly expected spin 2 (¹⁸) for the graviton?! Well, for all we can foresee that will no longer represent an important problem, for the General Relativity (without asterisk) which has been until now the upholder of that supposed value of spin, would have imploded for good (¹⁹)!  

Luiz Sergio Coelho de Sampaio

Rio de Janeiro, 29/12/2000

Notes

1. This paper is dedicated to Ricardo Kubrusly, with a light and friendly censure.  For a long time he has tried hard not to work towards entering  History and now he has got a lot more to work  to escape from it. If....

2. Physics is the desire of Modernity – it seeks the One-in-trinity, though submitted to measurement and calculus –, as Philosophy was the desire of the Greeks – who sought the being-one, though under the empire of the logos –, and as the Myth long ago was the desire of Neolithic culture – which sought the primordial father (the origin), though having killed him previously. In my studies on logic as that mode of reasoning that brings thinking and being together as one, physics is considered the epitome of the logic that bespeaks of, and submits the world to, measurement and calculus. That is the logic of modernity. Physics is controlled by classical Aristotelian logic, but as such it longs for the terms of the previous logic, the theological dialectic of the one-in-trinity. Therefore, its main constituents have been mass (M), space (L), and time (T). For further explanation see Sampaio, Lógica Ressuscitada, Rio de Janeiro, Eduerj, 2000.

3. ACCIARRI et al. Higgs Candidates in $e^+e^-$ Interations at $\sqrt{s}$=206.6 Gev. CERN-EP-2000-140. The value presently estimated by the physicists of CERN for the mass of the particle of Higgs is about 109 Gev. As this particle is being produced in association with the weak boson Z⁰, whose mass is 92 Gev, it would be necessary a minimum energy of 211 Gev to effectively produce the Higgs particle. This energy was being obtained by the LEP, though it is in the process of being dismounted so that the 27 km tunnel that holds it might be ready to receive in 2005 the more energetic  LHC (7 Tev).

4. Because of some anomalies found in the Newtonian gravitational force (still controversial) it is thought that they could come from a fifth force. However, that is a completely different story. WITKOWSKI, N., Dictionnaire de la Physique – atoms et particules, Paris, Albin Michel, 2000, pp. 87-89.

5. Physical entities whose dimensional formulas differ only with respect to one or other potency from the dimensional formula of speed (LT^-1)ⁿ are similar, that is, they are just modes of the same thing. Indeed, spin (MT), cliname (ML^-1), and mass (M), multiplied by the square of speed (LT^-1)² result in, respectively, angular moment (ML²T^-1)), force (MLT^-2), and energy (ML²T^-2). It is rather easy to perceive that the last three reproduce in a way the logical structure that has been made known to us: the being-in-itself (I), the being-with-the-other (D) and the dialectical synthesis of both (I/D).

6. The conception of the vacuum as a pure geometric bachground for physical entities is unfeasible. Any ontic knowledge of X has to elude its own ontological problematic: Why there is X and not just Nothing? That is quite evident in Mathematics: the zero is the signal that hides the Nothing (of numbers in general); the empty set hides the Nothing (of the set); the operation identity hides the Nothing (of operations), and so on. That is why they need to be defined in a paradoxical manner, as the number that does not count, the element that differs from itself, the operation that does not realize anything. Likewise, in Physics we need the Physical-zero or the vacuum in order to elude the Nothing (physical), and its definition will have to be a paradoxical negation of the physical essentiality, or materiality, or better yet, as we have done previously, it has to be defined as the “physical being” without spin, cliname, and mass. The idea of fluctuation of the vacuum needs to take that into account in order not to fall into the vicious circle of eluding the very elusion that is implicit in its origin.

7. As a matter of fact, that does not constitute a veritable exception insofar as it is logically necessary to compensate for the fact that the Higgs boson does not absolutely have spin. All other particles with spin zero have that sort of spin as an internal compensation, that is to say that they have internal, anti-parallel spins, a fact that can be verified in their eventual disintegration. For that reason it is quite exact to conclude that all particles, in the last instance, could be reduced to just these two – the neutrino and the Higgs boson, which deserve the just title of truly essential. In the distribution of the attributes of materiality between the essential fermion and the essential boson, a certain logical symmetry could only be preserved if spin (I) and cliname (D) should be left on one side, while mass (I/D) would be on the other side. And that was indeed “done”: on one side the neutrino of the electron has kept spin (1/2) and cliname a₀, while on the other side the Higgs particle has kept mass. Therefore, there should not be any particle of type X to mediate the passage of bosons to fermions and vice-versa, for this passage would be only of a logical nature. In short, the GUT, such as it stands today, appears to be like an illusion. For further details, see Sampaio, L. S. C. de, The octet of the physical beings – vacuum, the class of fermions and the six bosons mediating natural forces; as edited in Portuguese by www.editoraeletronica.net, 1999

 8. The speed of light in the vacuum (c) represents a compromise between time (T) and space (L); the Planck constant (h) (divided by c²), a compromise between mass (M) and time (1/frequency) (T). By the way, the physicist Gilles COHEN-TANNOUDJI in his book Les Consantes Universelles, Paris, Hachette, 1998, defends the idea that the constants represent compromises or limitations of an epistemological nature, not of an ontological (ontic, as we prefer) one. However, it is rather intriguing that he admits that he can’t find a good epistemological reason to explain one of the constants (and there are so few of them!) – precisely the gravitational constant G! He can’t find it, we believe, because the compromise was not acknowledged, as it should have been, by neither Newton himself (just recall the notion of material point!) nor later by Einstein. See SAMPAIO, L. S. C. de Lógica das constantes universais. Rio de Janeiro, UAB, 1997.

9. EINSTEIN, Albert. On a stationary system with spherical symmetry consisting of many gravitating masses published in the Annals of Mathematics 40 (4), October, 1939.

10. Besides the strong circumstantial evidence that he thought so, we now have the testimony presented by Freeman Dyson: But Einstein never acknowledged his brainchild. Einstein was not merely skeptical, he was actively hostile to the idea of black holes. He thought that black hole solution was a blemish to be removed from his theory by a better mathematical formulation, not a consequence to be tested by observation.  “The Scientist as rebel”, New York Review of Books, 25, 1995, p. 32. The first phrase of this quote does also indicate that Dyson kept apace with the events but had no idea of the deep reasons that lied underneath them.

11. OPPENHEIMER, J. R. and SNYDER, H. S. On continued gravitational contraction, Phys. Rev., 56, 455,1939. Dyson, cited in the previous note, asserts that Oppenheimer himself, in his maturity, seemed to be equally uninterested in his own great “discovery”. 12. The cliname determines almost directly the escape speed. In the case of a sphere with mass M and radius R, the superficial cliname is given by a = M/R  and the square of the escape speed on its surface by  v_e² = 2G.a.

13. From a theoretical point of view this postulate is almost a truism; from an empirical viewpoint, it functions as evidence for in all the Universe only neutron stars come close to this value (or equal it?!). Moreover, with this postulate Newton would not have gone through the chagrin to see, in shock phenomena, his “material points” glue themselves for all eternity!

One should not feel ill at ease with the expression Planck’s cliname, as much as other similar entities that had nothing to do with Planck were ascribed to be of a Planck nature. That should be taken as a just homage to a great physicist, not a generic significant to be used to designate insignificant entities.

14. Such inconsistency does in fact appear because it is possible to provoke an irreversible catastrophe by means of just a “moderate” change in referential (speed v being finitely smaller than c). That comes to strongly justify the introduction of the limiting postulate of the cliname already in Newtonian gravitation; otherwise, Special Relativity becomes itself inconsistent, and as such we miss one more justification to propose it as a component of a theory that would encompass it. See SAMPAIO, L. S. C. de, A Força gravitacional e os buracos negros, Rio de Janeiro, 1993/1998.

15. SAMPAIO, L. S. C. de, A força gravitacional e os buracos negros, op. cit.. 

16. ibid. This value corresponds to a particle with an equivalent mass of 1,4 Tev (1400 Gev), not merely 109 Gev, as that one that is being searched by the CERN (see note 3 above). In our estimate we take m_Z^o= 91,177 Gev and m_W = 80,42 Gev.

17. See once again note 3.

18. Every  Physics textbook ascribes spin 2 for the graviton, however oddly ignoring the logical and physico-theoretical studies that demonstrate that that leads up to inconsistencies, which, by the way, persist for spin of any value, including 0 and 1. But let us just think for a moment: if spin 2 is absolutely necessary to differentiate graviton from (spin 1) gluon, and as the existence of the cliname is not recognized by itself, it becomes desperately necessary to ascribe some spin to it in order to differentiate it from an unqualified specter!

19. This term does not seem overbearing to us if we take into account the discovery of the cosmic background radiation, which, by the way, places in great difficulty the consistency of the notion of a purely geometric universe, a problem that also confronts the notion of “absolute relativity”. Moreover, what could really be lost if, as Chandrasekahr has put it, “we have, as yet, no exact feature of general relativity that has been confirmed by observation; and none appears feasible in the foreseeable future”? For a further checking on this amazing conclusion, see CHANDRASEKAHR, S. Truth and Beauty – Aesthetics and Motivations in Science. Chicago, Un. of Chicago Pr., 1990, p. 149.