archived as
(also …Pitkanen_36.pdf) =>doc pdf URL-doc URL-pdf
more from Matti Pitkänen is on the /Pitkanen.htm page at doc pdf URL
note: because important websites are frequently "here today but gone tomorrow", the following was archived fromon January 19, 2010. This is NOT an attempt to divert readers from the aforementioned website. Indeed, the reader should only read this back-up copy if the updated original cannot be found at the original author's site.
24 Fundamental Questions for Elementary Physics
by Dr. Matti Pitkänen / January 28, 2010
Postal address:
Köydenpunojankatu 2 D 11
10940, Hanko, Finland
E-mail:
URL-address:
(former address:)
"Blog" forum:
Lubos Motl provided his own answers to Sean Carroll's 24 questions. Lubos answered these questions as a superstring fanatic. In the following, I will do the same as a TGD fanatic;-).
Lubos' answers appear in blocked text. My own answers follow his.
1. What breaks electroweak symmetry?
In contemporary physics, there are many questions that are too deep to be sensibly asked: we don't have the right tools and language to constructively think about them. There are many unanswered questions that are deep but that can already be asked. But there are also questions that have been answered, that are tautological, that are too shallow or too vague, that make some incorrect assumptions, or that have other reasons not to be interesting. Sean Carroll's "24 Questions" mostly belong to the latter category.
======
The electroweak symmetry is broken by the Higgs field's vacuum expectation value.
The unitarity of the WW scattering implies that a new term with a scalar exchange has to contribute below a TeV (a contribution from the exchange of a Higgs particle). This is no speculative physics. Steven Weinberg got most of his Nobel prize in 1979 for this insight.
The corresponding particle has to be relatively stable and its mass must be in an accessible interval to make it work. It will be seen at the LHC. Somewhat more speculatively, there may be several such Higgs fields (like in SUSY) or this Higgs field may be composite (like in technicolor). But these are technical additions that are not strictly necessary to answer the question above. The bulk of the question was answered by the first sentence.
Lubos gives the textbook answer -- i.e., the electroweak symmetry is broken by the Higgs field's vacuum expectation value. TGD allows the Higgs but reduces the description of the symmetry breaking to a much deeper level. CP2 geometry breaks the electroweak symmetry. For instance, color partial waves for different weak isospin states of imbedding space spinors have hugely different masses. The point is that the electroweak gauge group is the holonomy group of spinor connection and not a symmetry group unlike the color group, which acts as isometries.
For physical states are massless before p-adic thermal massivation due to the compensation of conformal weights of various operators. The most plausible option is that both the non-half integer part of vacuum conformal weight for particle and Higgs expectation are expressible in terms of the same parameter which corresponds to a generalized eigenvalue of the modified Dirac operator. Higgs expectation-massivation relation is transformed from causation to correlation.
2. What is the ultraviolet extrapolation of the Standard Model?
This question is amusing and the probable reason why it was asked was that the author didn't understand and doesn't understand the meaning of the word "extrapolation". The answer to the question in this form is, of course, "the Standard Model".
By a definition of "extrapolation", the formulae from the Standard Model are taken to be valid in all regimes regardless of the energy. In fact, the Standard Model may really be extrapolated up to the Planck scale as long as the Higgs mass belongs to a realistic range.
What Carroll probably wanted to ask is what is the ultraviolet "completion" of the Standard Model -- i.e. what theory replaces it when its extrapolation breaks down (just the opposite than what he asked). This is way too general a question because it essentially says "tell me everything about new physics". Supersymmetry, grand unified theory, Kaluza-Klein theory, etc. are all likely to be a part of the answer.
At any rate, this more ambitious question -- at this limited level of detail -- can also be answered and the most correct answer is string theory. However, it is even more certain that the question in the form that was asked is trivial and the answer is, once again, "the Standard Model".
Lubos violently explains that "UV extrapolation" in the above statement should be replaced with "UV completion". I would replace it with "the unified theory of fundamental interactions". Lubos, of course, answers as a proponent of string theory. The problem is that there is practically an infinite number of completions so that the predictivity is lost.
TGD geometrizes the symmetries of the Standard Model and reduces them to the symmetries of Classical number fields. Also octonionic infinite primes, one of the most exotic notions inspired by TGD, code standard model symmetries. The most general formulation of the World of Classical Worlds is as the space of hyper-quaternionic of co-hyper-quaternionic subalgebras of the local hyper-octonionic Clifford algebra of M8 or equivalent M4× CP2.
The answers by both Lubos and me involve also supersymmetry but in a different sense. In TGD framework, the oscillator operators of the induced spinor fields define the analog of the space-time SUSY so that the algebra of second quantization is replaced with N=∞ SUSY. This requires a modification of SUSY formalism. But N=1 SUSY associated with the right handed coveriantly constant neutrinos emerges as preferred sub-SUSY and counterpart of N=1 SUSY. The construction of infinite primes also involves supersymmetry.
3. Why is there a large hierarchy between the Planck scale, the weak scale, and the vacuum energy?
These are, of course, two most famous hierarchy problems of current physics.
The Planck-weak hierarchy is most likely stabilized by supersymmetry. The stabilization is necessary but not sufficient a condition for the hierarchy to occur. Supersymmetry probably plays some role in the smallness of the cosmological constant in the Planck units (the other problem included in this question).
However, the "truly tiny" observed value of the vacuum energy can't be derived at this moment. It is unclear whether a "canonical" dynamical explanation exists. It is plausible (but not guaranteed) that the anthropic explanation is everything one can obtain. It is surely true that if the cosmological constant were vastly different, Life similar to ours couldn't exist.
Individual vacua allow one to calculate all these values. Some of the vacua give answers that are vastly different from the observed hierarchies while some of them may give answers that are close or exactly equal to the observed figures.
These are the two most famous hierarchy problems of current physics as Lubos notices. In TGD framework, the Planck scale is replaced with CP2 length scale which is roughly by a factor 104 longer than the Planck length scale. Instead of the Planck length, it might be more appropriate to talk about gravitational constant which follows as a prediction in TGD framework.
p-Adic length scale hierarchy is needed to understand the hierarchy of mass scales. The inverse of the mass-squared scale comes as primes which are very near to octaves of a fundamental scale. Powers of 2 near Mersenne primes or Gaussian Mersennes are favored. This predicts a scaled-up copy of hadron physics which should become visible at the current LHC. Quite generally, unlimited number of scaled versions of Standard Model physics are possible in principle.
The vacuum energy density is the basic problem of superstring approach. How desperate the situation is becomes clear from the fact that rhetoric tricks such as the anthropic principle are considered seriously. Empirical findings (for some reason neglected by colleagues) suggests that cosmological constant depends on Time. In TGD framework, the cosmological constant is predicted to depend on the p-adic length scale of the space-time sheet and behaves roughly like 1/a2 where a is cosmic time identified as light-cone property time. Actually, the time parameter a is replaced by a corresponding p-adic length scale. The recent value is predicted correctly under natural assumptions.
What "dark energy" is becomes a second question. TGD suggests the identification as a matter at space-time sheets mediating gravitational interaction having gigantic values of Planck constant implying extremely long Compton lengths for elementary particles. This guarantees that the energy density is constant in excellent approximation. If gravitational space-time sheets correspond to dark magnetic flux tubes (i.e., expanded cosmic strings), the mysterious negative pressure can be identified Classically in terms of magnetic tension. If one takes seriously the correlation of the intelligence of conscious entities with the value of the Planck constant, these gravitational space-time sheets can be God-like entities.
4. How do strongly-interacting degrees of freedom resolve into weakly-interacting ones?
In Quantum Field Theory, the number of particles is not conserved. So particles of any kind can "transmute" into particles of other kinds as long as the strict Conservation Laws are obeyed.
The "character" of the final particles doesn't have to coincide with the "character" of the initial ones. For example, a strongly interacting pion may decay into 2 photons and/or various combinations of leptons that are only interacting by the electroweak interactions. There's nothing unusual to it. They decay via a virtual W boson or similar channels. This has been understood for more than 70 years (for example, recall Fermi's theory of beta-decay).
Lubos regards this question as strange and expresses this using colorful rhetoric. Maybe Carroll refers to QCD and hadronization. M8-M4× CP2 duality relates low energy and higher energy hadron physics to each other in TGD framework and corresponds group theoretically to SU(3)-SO(4) duality where SO(4) is the well-known strong isospin symmetry of low-energy hadron physics.
Or maybe Carroll talks about the technical problem of calculating the behavior of strongly interacting systems. Nature might have solved the latter problem by a phase transition increasing Planck constant so that perturbation theory based on larger value of Planck constant works. The particle spectrum however changes and system becomes anyonic in general.
5. Is there a pattern/explanation behind the family structure and parameters of the Standard Model?
Yes, of course.
Obviously, the multiplicity of leptons and quark families may only be derived from a "deeper" principle in the framework of string theory. Whoever is hoping that a non-stringy framework could ever shed light on any of these big questions is fighting a lost battle. It's simply not possible to avoid string theory in answering any of these questions.
The number of families may be calculated in various stringy constructions by well-understood mathematical algorithms. In the most Classical case of heterotic strings on Calabi-Yau manifolds (with the identified spin/gauge connections), the number of families equals one-half the Euler character of the Calabi-Yau.
Analogous-but-different formulae exist in other frameworks and more complicated vacua (e.g., braneworlds, vacua with fluxes, M-theory, F-theory). Also, Yukawa couplings, gauge couplings, masses, and other parameters may in principle be calculated although the calculation depends on the scenario. The right question that summarizes these unknown things is: Which limit of string theory (heterotic, IIA, M-theory, F-theory) is most useful (weakly coupled) to describe the reality?
I can only echo Lubos "of course there is". In superstring models, the large number of explanations tells that the real explanation is lacking. In TGD framework, fermion families correspond to various genera for partonic 2-surfaces (genus tells the number of handles attached to sphere to get the 2-dimensional topology). There is an infinite number of genera. But the 3 lowest genera are mathematically very special (hyper-ellipticity as a universal property) which makes them excellent candidates for light fermion families. The successful predictions for masses using p-adic thermodynamics and relying strongly on the genus dependent contribution from conformal moduli support the explanation.
Bosons correspond to wormhole contacts and are labeled by pairs of general implying a dynamical SU(3) symmetry with ordinary bosons identified as SU(3) singlets. SU(3) octet bosons (perhaps making themselves visible at today's LHC) are predicted and serve as a killer test.
The symmetries of the Standard Model reduce to the geometry of CP2 having a purely number theoretical interpretation in terms of the hyper-octonionic structure. Number theory fixes through associativity condition the dynamics of space-surfaces completely (hyper-quaternionicity or its co-property in appropriate sense).
6. What is the phenomenology of the "dark" sector?
Dark matter has the well-known gravitational effects on the galaxies etc. that forced the physicists to discover it a few decades ago. Besides that, various decays appear with some frequency.
And the dark matter particles (such as neutralinos) can participate in a limited number of additional types of interactions. Assuming the standard MSSM neutralino realizations (or other scenarios for that matter), these things are mostly understood. Dark matter accounts for a higher percentage of the mass of the Universe than the visible matter. But that doesn't mean that it has a more interesting phenomenology.
Even if the MSSM were wrong, it's pretty obvious that it is the other way around. Besides the basic gravitational impact and some decays and perhaps pairwise annihilation, dark matter probably doesn't exhibit too much interesting behavior. At least, that's the thing we should conclude -- in a preliminary way -- based on our knowledge and basic principles such as Occam's razor.
Lubos sees the "dark matter" as something relatively uninteresting. Just some exotic weakly-acting particles. How incredibly blind a theorist accepting 11-D space-time and landscape having absolutely no empirical support can be when it comes to actual experimental facts!
In TGD framework,"dark matter" means a revolution in the world view. Its description relies on the hierarchy of Planck constants requiring a generalization of the 8-D imbedding space M4 × CP2 to a book-like structure with pages partially characterized by the value of Planck constant. The most fascinating implications are in Biology. Also, the implications for our view about the nature of consciousness and our position in World Order are profound.
7. What symmetries appear in useful descriptions of nature?
One must be careful what types of symmetries we are talking about. Only global unbroken symmetries are "really objective" features of the reality. It's very likely that we have found the full list and it includes the CPT-symmetry, Poincaré symmetry (including Lorentz, translational, and rotational symmetries), and the U(1) from the conservation of the electric charge.
Additional symmetries may exist. But they are broken (i.e. non-linearly realized) SUSY and the electroweak symmetry. SU(3) is confined and there may exist additional confined groups. But the presence of gauge groups really depends on the description and it is never a sharply defined Physics question whether a symmetry in a description is "useful".
Asking whether something is "useful" doesn't belong to Physics, it's a "meta" question related to our strategy whose purpose is for us to be more capable to ask and answer other, more objective questions. Different dual descriptions of the same physics usually have different gauge symmetries and there's no contradiction here.
Also, perturbative string field theory may be usefully formulated with the help of an infinite-dimensional gauge symmetry principle (at each point). Such gauge symmetries may be pretty in formulations of physical theories. But they're not really necessary for Physics. They are not physical because physical states must be singlet under all gauge groups (so physical objects know nothing about the representation theory of these groups).
It's conceivable but far from guaranteed that a generalization of our knowledge about symmetries will lead to further progress in the understanding of the fundamental laws of Physics.
As Lubos says, one must be careful what types of symmetries we are talking about. Lubos says "Only global unbroken symmetries are 'really objective' features of the reality. It's very likely that we have found the full list and it includes the CPT-symmetry, Poincare symmetry (including Lorentz, translational, and rotational symmetries), and the U(1) from the conservation of the electric charge."
By adding color symmetry and separate baryuon and lepton conservation, one obtains the symmetries of Quantum-TGD. This prediction follows from number theoretical vision alone.