Afther this I am going to explain the reason of the topic. In physics, even in theoretical physics, there are many levels. One one side there are the "old fashioned" particle physicis. You can find some of them, teachers with academic positions in good universities, which hate even the yang mills theory as explained, for example, in the Cheng and Li book of particle physics, (or in any conventional QFT text book for what matters). They prefer the very heurisitc exposition of the subject presented in books such like the one of Halzen and Martin "quarks and leptons". This people usually like "solid physics" from colliders. In an intermediate, most reasonable, state are phenomenological people who accept and like QFT. This people can be working on hadron physiscs or even dealing with some posible phenomenology related to supersymmetrtry, mainly the MSSM (minimally supersimmetric standard model) and supersymmetric unification. Some even go beyond and are interested in string theory or (possible) alternatives to quantum gravity.

To read books for this people is a very good way to learn actually stablished physics and possible near future physics. I know two great books of this characteristics. The excelent one of Martin, squires and Collins "particle physics and cosmology", and the very recent one of Michel Dine "Supersymmetry and String theory". In some sense the last one is an (unintended) update of the previous. To be honest I find more understable and better writen the one Martin et all that the book of Dine. But still is a good book. The introduction to supersimmetry is very diferent, and the book of Amrtin et all includes also supergravity. On the other since the Dine´s books goes a lot deeper into string theory, withouth beeing a rigurous book on pure string theory (of course because that was not i´s purpose). I guess that everyone should read some book of this characteristics from time to time to keep contact with the details of phenomenology.

But detailled phenomenology is not everything in theoretical physics. You need to give good foundation to the enviroment in which the pheonomnological calculations are done. This requires at least to understand the proper foundations of quantum field theory and supersymmetry. A good modern exposition wuld be the three volumes book of Weinberg, but honestly, I see that book more like a reference book that anything else. A poit that string theorist signal is that one should be sure to study modern renormalization theory (It is not the same as the renormalization theory in classic QFT books such like the Itzikson-Zuber). I am doing this just now. I did a bad coice of review article that has delayed me for a time, but I guess that I am beguining to gain proper understanding of it. Beyond QFT there is supersymmetry. The books I mentioned previously are "all purpposed books" but there are textbooks specialized in supergravity. I have ocassionaly readed one (but unfortunately it is not in a very asscessible place now so I cant give you the exact reference). They concentrate in more theoretical aspects of supersymmetry and while string theory is a much more promising area of study they still have their point.

And of course we have string theory, and all the possible alternatives. That are pure theory. In fact still instring theory there are more "phenomenological" aspects, for example to find realistics compactifications or to solve the cosmological prblem, and more "theoretical aspects". Of this last I could signal to try to understand better what M-theory is, the superstring field theories, and the Maldacena conjecture, to say ones. Other topics, for example black hole theory, are somewhat in the middle.

And now the last topic, the "weird speculation". This is a broad subject. It can go from simple tings, like to get a proper understanding of the theories to more risked things. I´ll give a few examples of the first point. A very basic one is from nonrelativistic quantum mechanics, collision theory. When I was teached it I understood everything perfectly untill we arrived to resonances. Them the teacher explained you that the imaginary poles of the S-Matrix where resonances. Fine, it was a relatively easy thing to find that poles and to work with them. Inmediately later he toldd you that heuristically you would interprete that resonances as "metastable states". But he didn´t explain why. The book that he followed, and a fe other I readed, didn´t say more. Of course for me this was totally unsatisfactory. I could pass the exam withouth mayor problem even doing an exercise about resonances. But from my viewpoint I didn´t understand resonances at all. I asked the quesetion from time to time, but it was not untill that I casually readed the Landau chapter in the subject. There they explained why this math prescription came. You neded to think in outgoing waves with imaginary exponent and how this was related to the metastability (read the book for the details if you don´t know them, It is a total "you must").

In QFT I havent´t found (or at least I don´t remmeber them now) similar situations. But in strign theory I have found many. To beguin the very basic idea of string theory, such as I explained in the first entries of this blog. To read all the modern boooks on the subject didn´t convince me a bit that the idea of an string, such as presented, is a convincing one. Like string theoriest don´t care too much about it I try to do "weird speculation" about the subject. My initial idea of knotted strings is easy to state in a formal way. Afther reading the chapter 13 (if Idon´t remmember bad) of the Green -Schwartz-Witten bookd I have gained the knowledge that open strings can join their endpoints and to form a closed string. Well, aparently two open strings could get closed interlinking one to another. You would describe the collective state by a hilbert product state of the separate strings. If this configuration would be stable you would have states that would look like mixed states of conventinal particles. To elucidate aobut if this stability could exist I must go to another theory. Rañeda and Trueba made a topological formulation of electromagnetism. This consisted of expresing the vacuum Maxwell equations in terms of different fields. This allowed them to clasify the solutions with bounded energy (i.e. vanishing in the infinity) into topological sectors with different of a topological quantity which could be identified with the heilicity of the electromagnetic field. The configurations with non trivial topology (identificalbe, among another possible ways, as a kind of knoting) presented extra stability, and it was conjetures that they could be related to the atsosferic pehnomenon know as "ray balls" (the actual article is published in nature, so be totally sure it is not "crackpot phuysic"). The idea could possibly be extended to Yang Mills theories. ANd here is where I think that it could be connected somehow to this "knotted strings" . If the string which get knotted are in a vibrational state corresponding to yang mill fields it could be that they could be somehow resemble some knotted configuration of Yang Mill fields and become stable. Of course this is very wild speculation, and withouth confronting more detaills and consistency checks is not something to be considered seriously.

The key point of knotted strigs is that if one takes serioulsy the idea of string theory they I.M.H.O. would be considered (soon I´ll explain another possible argument). But I still am dissapointed with the idea of strings. I am triying to search for a natural way inwhich strigns make sense (and don´t disgregate intoit´s constituent points). I knowt thaat one should addopt the coherence of the string as a postulate. But I still try to go beyond that. From the accepted string theoretical viewpoit there are a few possible aproachs to it that I try to consider. S-duality relate the strong coupling limit of an string theory to the weak coupling limt of another. Under this duality fundamental strings of a theory canbe identified with D1-branes of the other. But D1-Branes suposedly can be charasterized as some kind of topological deffects. Topological deffects are stable things, so that could justify a posteriory the stability of fundamental strings. The problem is that to arrive to the D-brane idea one must beguin with perturbative strings. There is the viewpoint of "D-brane democracy". This means that dpednidn on energy,or maybe better said, inthe history of the universsee, of thepossible equivalent ways to describe string theoyr (all the five strig theorys, M-theory and F-theory) the universe is in an state in chich "fundamental" strings are agood description of observable physic, but still the reason of their stability must be explained in the D1-Brane ansatz.

A more drastic departure to try to assign a "naturality" to the idea of string (here is where the profesional string theorisst will definitively lose it´s patience if he has resisted untill this pint) could come from the following scenary. In some aspects thje idea of string separates the universe intotow scales. The scale greater than the string and the scale smaller (In fact d-branes canprobe distances smaller than the size of an string, but let´s accept the premise for a while). Well, let´s try to get the same idea in a diferent viewpoint. We must have an "inner theory" for distances smaller than the planck scale that in the limits reproduce ordinary quantum field theory. Under the planck size the usuall notions of QFT and relativity (in particular the Lorentz invariance) would dissapear, or more properly said, they could not experimentally stablished. That would mean that if we try to be sure that if a particular state is an electron, a photon or whatever in distances shorter than the panck one we cant so we must deal with states that are a superpostion of all the possibilities. String are good for it. Of course this is not more than cheap philosophy in this state. Another way totry to sse this I gues that it can be related to M-theory. While reading about horava-witten theory I have got more involved withthe bizarre aspects of M-theory. FOr example there are arguments that it´s proper description cant be given in termos of a lagrangian. This means that it doesnt go under the prescription of a variational principle. There are not classical configurations that minimize and action and quantum corrections. But this means that we are in a democracy where every trajectory is equally good, and there is not quantum physic. On the other hand M-Theory is the strong coupling constant of string theory. I am not totally sure but i think than that means that it studies the behaviour of the shortes vibrational modes of the string. This modes somehow would explore a region where evrything is beyond the planck scale. AS the planck constant has magnitudes of action whe are exploringn zones wher the notion of action does´nt apply. This could explain why there is no lagrangian (i.e. action based) description of M-theory. Once agian, this is weird, and weak, and cheap speculation. Dont confuse it with anything accepted by the mainstream os string theorists.

Another thing in string theory which I want to understand properly is why D-branes are suposed to be infinitely extended. If a D1-brane is the dual oof a fundamental string, a very shor object, why the hel it must be infinitellly extended .Somone pointed me that infact a priory it wouldn´t be necesary, but that stabiilty reasons force one to have infinitely extendend D-branes. Well, I don´t know where that calculations are done, may be inthe K-theory program, in the analisys ob non BPS branes, it could be related to th tachyonic condnesation, or maybe it is explained in some arkane text about the M-branes. At least now I have the certainty that it is not a trivial thing and that the a priory idea that D-branes would be of a finite size was a reasonable question. B.T.W., I had said that tere were another possible way to explain ths stability of "knotted stirngs" if that configuartios would form. Of course that would be seen to come from a D1-Brane perspective. If infinite sized branes cross among them it looks like that would be very stable topologicaly.

This was weird speculation within string theory. Now I am going to say an example of speculation outside it. Pitkannen proposes in it´s topological geometrodynamic that oneshould worry about the possibiilty that because of some reasonone would care about p-adic metrics. In a p-adic metric ponts very far away inthe conventional metric are very nearby. I think that he try to present an scenary where the nature of the real world is p-adic (at least in some cases). That would explain, inhis viewpoint the colapse of the wavefunction. He subscribes a viewpoint where concsciece is related to that, and it implies that humans brians have the capability to ifluence long distances. Well, maybe he would like becuase of this some weird paper (commented inLubos blog) that hte observation of the cosmological constant has modifeid the stae of the universe, or maybe not, you can ask him in his own blog. What I wondered yesterday was nothing of this. I had said that if one tries togive a ynnamical topology change, explianing the formation of a wormhole, it appear natural to expect that it connects nearby distnces. Infact quantum fluctuation (basically here the usual Heisenberg uncertainty betwen postion and momenta)could justify an small posibity that it would connect far points. But,

Well, I hope that if I am very clear staitng when I speak about accepted physics and when i am divagating (and triying to pose a quote to the degree of divagation) the reader can actually have a realistic perspective of physics, and maybe somes even fun (interesting would be a too exigent word) fan the weird speculations. Anyway, I´ll try to post mainly about divulgation of conventionally accepted physics.

## 1 comment:

Dear Javier,

thank you for mentioning also TGD in this respected company;-). I have some hopefully clarifying comments about p-adic physics and its relation to state function reduction.

First of all, I want to emphasize the fact that I do not try to reduce state function reduction to p-adicity. These are quite independent things.

State function reduction (part of quantum jump besides state preparation and unitary process) is an important part of TGD and TGD inspired theory of consciousness and leads to a new view about ontology. In certain approximation one can say that quantum jump occurs between entire deterministic time evolutions of Schrodinger equation completely outside the realm of space-time and state space. This resolves the basic paradox of quantum measurement theory (the conflict between the determinism of Schrodinger equation and state function reduction).

This implies a new view about the relation between experienced time and geometric time very essential in the recent construction of M-matrix, which can be seen as "square root" of density matrix identifiable almost uniquely in terms of Connes tensor product characterizing finite measurement resolution in terms of inclusion of hyperfinite factors of type II_1. M-matrix is the product of real square root of density matrix and unitary S-matrix - thus kind of matrix valued Schrodinger amplitude. The non-uniqueness relates to the freedom of having different density matrices. Zero energy ontology is second important element of the construction and relates to the new view about time.

Concerning p-adic numbers the basic idea is to generalize the notions of number by fusing reals and p-adic number fields plus their extensions along numbers which are common to them (including rationals). Imbedding space H=M^4xCP_2 is generalized in same manner and becomes a book like structure having H:s corresponding to various number fields as pages.

p-Adic physics brings in space-time correlates of intentionality and cognition and these space-time aspects of existence are literally cosmic since p-adic infinitesimal rational is infinite as a real number. p-Adic space-time sheets have infinite duration and size in real sense. Only sensory consciousness has contents localized to some corner of cosmos.

p-Adic physics makes predictions about real physics. The first argument is that if real and p-adic space-time surface have a lot of intersection points then also real surface obeys *effective* p-adic topology in some length scale range. Theory actually assigns to given partonic 2-surface a p-adic prime characterizing the cognitive aspects assignable to it.

Secondly, algebraic universality allows to consider the possibility that p-adic thermodynamics and real thermodynamics used to calculate elementary particle mass squared are equivalent. Number theoretical existence of p-adic Boltzmann weights and of partition function give extremely powerful conditions on the real sector otherwise absent.

With p-adic length scale hypothesis stating that p-adic primes near powers of 2 are selected in cosmic evolution (hypothesis has now justification at the level of M-matrix construction) one ends up with successful predictions of elementary particle and hadron masses.

p-Adic mass scale becomes an additional concept and in this framework it is absolutely idiotic to try to force top quark and neutrinos to same multiplet of symmetry group (mass ratio is about 10^(12)!). One prediction is that elementary particles, say neutrinos, can appear also with mass scale differing from standard one, and there is evidence for this. The latest evidence comes from the convergence of Higg mass to values differing by a factor about 13: TGD prediction for the ratio is 2^4=16 is consistent with experiment.

To sum up, to my opinion the long-stagnation in theoretical physics -lasted already for more than 30 years - is due to the fact that we are using an ontology which is completely out of date. Even the most advanced mathematical methods are useless without a radical revision of ontology.

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