To deeper waters

Higgs issue seems to divide theoreticians to two classes: the simple-minded pragmatists and real thinkers.

For pragmatists the existence of Higgs and Higgs mechanism is something absolute: Higgs exists of not and one can make a bet about it. Most bloggers and most phenomenologists applying numerical models belong to this group. In particular, bloggers have had heated discussions and have made bets pro and and co, mostly pro.

Thinkers see the situation in a wider perspective. The real issue is the status of quantum field theory as a description of fundamental forces. Is QFT something fundamental or is it only a low energy limit of a more fundamental microscopic theory? Could it even happen that QFT limit fails in some respects and could the description of particle massivation represent such an aspect?

Already string models taught (or at least should have taught) to see quantum field theory as an effective description of a microscopic theory working at low energy limit. Since string theorists have not been able cook up any convincing answer to the layman's innocent question "How would you describe atom using these tiny strings which are so awe inspiring?", QFT limits have become what string models actually are at the phenomenological level. AdS-CFT correspondence actually equates string theory with a conformal quantum field theory in Minkowski space so that hopes about genuine microscopic theory are lost. This is disappointing but not surprising since strings are still too simple: they are either open or closed, there is no interesting internal topology.

In TGD framework string world sheets are replaced with 4-D space-time surfaces. One ends up with a very concrete vision about matter based on the notion of many-sheeted space-time and the implications are highly non-trivial in all scales. For instance, blackhole interior is replaced with a space-time region with Euclidian signature of the induced metric characterizing any physical system be it elementary particle, condensed matter system, or astrophysical object. Therefore the key question becomes the following. Does TGD have QFT in M⁴ as low energy limit or rather - as a limit holding true in a given scale in the infinite length scale hierarchies predicted by theory (p-adic length scale hierarchy and hierarchy of effective Planck constants and hierarchy of causal diamonds)?

Deeper question: Does QFT limit of the fundamental theory exist?

Could the QFT limit defined as QFT in M⁴ fail to exist? After this question one cannot avoid questions about the character of Higgs and Higgs mechanism.

1. It is quite possible that in QFT framework Higgs mechanism is the only description of particle massivation. But this is just a mimicry, not a predictive description. QFT limit can only reproduce the spectrum of elementary particles masses or rather - mass ratios. The ratio of Planck mass (also an ad hoc concept) to proton mass remains a complete mystery.
   

   This failure has been convincingly demonstrated by a huge amount of work in particle phenomenology. First came the GUT theorists. They applied every imaginable gauge group with elementary particles put in all imaginable group representations to reproduce the known part of the particle spectrum. They have reproduced standard model gauge symmetries at low energy limit. They have also done the necessary fine-tuning to make proton long-lived enough, to give large enough masses for the exotics, and to make beta functions sensical.
   

   The same procedures have been repeated in SUSY framework and finally super string phenomenology has produced QFT limits with Higgs mechanism, and are now doing intense fine tuning to save poor SUSY from the aggressive attacks by LHC. During these 40 years of busy modeling practically nothing has been achieved but the work goes on since theoreticians have their methods and they must produce highly technical papers to preserve the illusion of hard science.
   
   

2. Higgs mechanism is also plagued by profound problems. The hierarchy problem means that the Higgs mechanism with mass of about 125 GeV is just at the border of stability. The problem is that the sign of mass squared term in Higgs potential can change by radiative corrections so that the vacuum with a vanishing Higgs expectation value becomes stable. SUSY was hoped to solve the hierarchy problem but LHC has made SUSY in standard sense implausible. Even if it exists cannot help in this issue. Another problem is that the coefficients of the fourth power in the Higgs potential can become negative so that vacuum becomes unstable: the bottom of a valley becomes top of a hill. The value of Higgs mass is such that also this seems to happen! (see the posting of Resonaances).
   

   Quite generally, fine tuning problems are the characteristic issues of the QFT limit. Proton must be long-lived enough, baryon and lepton number violating decay rates cannot be too high, the predicted exotic particles implied by the extension of the standard model gauge group must be massive enough, and so on... This requires a lot of fine tunng. Theory has transformed from a healer to a patient: the efforts of theoreticians reduce to attempts to resuscitate the patient. All this becomes understandable as one realizes that QFT is just a mimicry, not the fundamental theory.
   

   One could also see these two problems of the Higgs mechanism as the last attempt of the frustrated Nature to signal to the busy mainstream career builders something very profound about reality by using paradox as its last means. From TGD vantage point the intended message of Nature looks quite obvious and is actually taken for decades years ago!
   

Shut up and calculate

The basic problem in the recent theoretical physics is that thinking has not been allowed for more than half century. Thinking is seen as "philosophy" - something very very bad. The fathers of quantum theory were philosophers: they realized the deep problems of quantum measurement theory and considered possible conclusions for the world view. For instance, Bohr - whose view became orthodoxy - concluded that objective reality cannot exist at all and that quantum theory is just a collection of calculational recipes with Ψ having no real existence. Einstein had totally different view. He believed that quantum theory is somehow fundamentally wrong.

Neither of them was yet mature to see that the problem involves the conscious observer in a very intimate manner: in particular, how the subjective time and the geometric time of physicist - certainly not one and the same thing - relate to each other. Both were also unable to see that objective reality could be replaced by objective realities identified as "solutions of field equations" and that quantum jumps would take between them and give rise to conscious experience. This would resolve both the problem of time and the basic problem of quantum measurement theory.

Later theoreticians followed the advice which has been put to the mouth of Feynman, and decided to just shut up and calculate. This long silence has lasted more than half a century now. I belong to those few who refused to follow the advice with the consequence that the decision makers of Helsinki University gave me officially a label of a madman and besides intensive blackmailing did their best to prevent any support for my work (see previous posting motivated by a warning of young readers about the dangers of reading my blog - sent by presumably finnish physics authority calling himself Anonymous).

LHC has now demonstrated how catastrophic consequences can be when the profession of the theoretician reduces to mindless calculation. We have got lost generations of theoreticians who continue to fill hep-th and hep-ph with preprints with a minimal connection to physical reality and mostly trying to solve the problems created by the theory itself rather than those provided by physics. This is however what they are able to do: collective silence has lasted too long. Even string model gurus have lost their beliefs on The Only Possible Theory of Everything. Some of them have suffered a regression to surprisingly childish models of gravitation (entropic gravity). Some have begun to see everything as black-holes without realizing that blackholes as a mathematical failure of general relativity should have been the starting point rather than the end. Some are making bets and having learned debates about paradoxes related to blackholes (firewall paradox is the latest newcomer (see the blog posting).

Or could thinking be a rewarding activity after all?

There are also some theoreticians who have followed their own star and have not been able to resist the temptation to think and imagine. I have used to call my own star TGD. As described in previous posting, p-adic thermodynamics can be seen as a- or even the - microscopic mechanism of massivation in TGD framework. There are two options to consider. According to Option I p-adic thermodynamics alone explains only fermion masses and the microscopic counterpart of Higgs mechanism would give the dominant contribution to gauge boson masses. For Option II p-adic thermodynamics would produce both gauge boson and Higgs masses and Higgs mechanism could appear at QFT limit as a mere phenomenological description of the massivation.

Option II is the most conservative option and apparently conforms with the standard model view. It also treats all particles in the same position. Note that in standard model Higgs itself like eye which cannot see itself since its tachyonic bare mass is put in by hand. Option II is also aesthetically more satisfactory if one believes that QFT limit of TGD indeed exists. For Option I one should invent new QFT mechanism describing fermion massivation in QFT framework or give up the idea about QFT limit altogether. Option I or Option II? This question might find an answer within few days!

The existence of M⁴ QFT limit is not obvious in TGD framework (what this limit could be if it exists has been discussed in the previous posting). This is due to a dramatic simplification in the microscopic description of particles. The only fundamental fields are spinors of H=M⁴× CP₂ having just spin and electroweak quantum numbers and conserved carrying quark or lepton number depending on H-chirality. Color emerges and corresponds to color partial waves in H. Also bosons emerge meaning that gauge bosons, Higgs, and graviton have pairs of fermion and anti-fermion at the opposite throats of wormhole contacts as building bricks. Gauge fields, Higgs field, gravitational field and also Higgs mechanism can emerge in this approach only as a phenomenological description at M⁴ QFT limit assuming that it exists. Fermionic families emerge from topology and also bosons are expected the analog of family replication phenomen induced from the fermionic one.

Higgs like bosons exist as Euclidian pions or scalar particles and they might also develop coherent states characterized by the vacuum expectation value of Higgs but already this possibility must be taken critically since coherent states is a QFT based notion and it is not quite clear whether it generalizes to microscopic level (see this).

What is important that Higgs does not make fermions massive. For Option II this is true also for bosons. Rather, the couplings and vacuum expectation of Higgs are such that Higgs can pretend of achieving this feat. Higgs mechanism reproduces: p-adic thermodynamics predicts.

Standard model action is only an effective action providing tree diagrams so that the loop corrections leading to the hierarchy problem are not present unless the counterpart of fatal radiative corrections appear in the effective action which must depend on p-adic length scale (in TGD the discrete p-adic length scale evolution replaces the continuous renormalization group evolution of quantum field theories). Zero energy ontology however dramatically modifies the view about Feynman diagrammatics, and can save the situation since standard SUSY generalizes to super-conformal invariance.

There are of course lot of critical questions to be answered. I have written an entire book motivated by the challenge of understanding why p-adic thermodynamics should be needed in real number based physics. p-Adic physics for single prime is definitely not enough: one must fuse p-adic physics for various primes p and real physics to single coherent whole and this requires a lot of not yet existing mathematics such as generalization of number concept. The connections of p-adic physics to the description of cognition and intention in quantum consciousness theory are also obvious and p-adic space-time sheet would correspond to the "mind stuff" of Descartes. These few examples show how profound and totally unexpected new visions a more philosophical and imaginative attitude to physics generates.

Another book is devoted to the physical implications of p-adic physics and of the hierarchy of effective Planck constants, a notion implied by the very special properties of the basic variational principle dictating the space-time dynamics in TGD framework.

For a summary of the evolution of TGD inspired ideas about particle massivation see the chapter Higgs or something else?. See also the short article Is it really Higgs?.