Peter Woit wrote a nice blog posting about Perimeter Institute and the crisis in modern physics. He gave a link to a wellcome speech of Neil Turok for the new students. The tone of the speech was very warm and encouraging and raised optimism. Maybe theoretical physics is not dead discipline yet;-). What made me especially happy that Turok was not telling that superstring theory is the only possible theory as I have seen so many times being told in blogs.
Turok admitted that we have been building enormous number of models during last decades: GUTs, SUSYs, superstring models, loop quantum gravity models, and whatever. The common feature of these models is that they are extremely complicated whereas Nature according to LHC and cosmological data from Planck satellite seems to be very simple. Nowadays theoreticians everywhere in the world are totally confused: their expectations were totally wrong. Turok made some special points which deserve comments.
Does Higgs really have vacuum expectation value?
Turok made some very interesting comments related to the Higgs discovery at LHC. The problem is that the mass of Higgs believed to be dictated by its vacuum expectation value does not correspond to stable vacuum. Vacuum is only meta-stable and can decay to the stable vacuum by quantum tunnelling releasing enormous amount of energy. That Nature would have chosen metastability looks strange.
Turok did not continue with an additional question natural with my background. We have discovered Higgs particle but do we really know that Higgs has vacuum expectation in reality? We do not! Perhaps Higss field exists and has vacuum expectation only in quantum field theoretic approximation to particle physics? Are we perhaps trying to describe Higgs using a language, which has reached its limits of applicability. Is this the source of all this confusion and even despair manifesting as a belief that physics has reached its end?
What if their is no vacuum energy for Higgs? In TGD framework it is very natural to imagine that Higgs couples to fundamental fermions with a gradient coupling proportional to the mass of fermion. The dimensionless coupling of Higgs particle to fermions would be same for all fermions: this is very natural as any theoretician must admit! This would turn around the entire habit of thinking about Higgs. One would have naturality and one would get rid of the metastable vacuum since there would be neither vacuum expectation nor vacuum energy associated with Higgs.
This sounds nice but there is an objection. How can we understand the massivation of fermions and gauge bosons? This is quite a problem in quantum field theory context, and I am convinced that something more general is needed. If one is ready to take TGD seriously, situation changes. In TGD framework physics enjoys a property that I have christened number theoretical universality. As one particular consequence, p-adic number fields as physics of cognition become part of physics. The scope of physics extends to include also cognition and consciousness. It would be wonderful if LHC could force theoreticians to become consciousness theorists!
p-Adic thermodynamics assumes only conformal invariance and predicts with one per cent precision particle masses in terms of CP2 mass scale (about 10-4 times Planck mass) and single parameter - the p-adic prime p characterizing the particle. By p-adic length scale hypothesis - to be discussed below - p is near to power of two. Also gauge boson masses can be understood since in TGD framework gauge bosons are bound states of fermion and anti-fermion at opposite throats of wormhole contact.
Do we really understand all about scale and conformal invariance?
Turok talked about scale invariance and its generalization conformal symmetries as something very deep that has not been properly understood yet.
In TGD framework conformal symmetry generalizes to 4-D context since light-like 3-surfaces - the basic objects of TGD Universe - are metrically 2-D and possess extended conformal invariance. Perhaps the most important outcome is an explanation for why space-time dimension must be D=4: only in this dimension one can extend the ordinary 2-D conformal symmetries to even huger group of conformal symmetries.
The gigantic conformal symmetries give excellent hopes that the "world of classical worlds" (WCW) consisting of 4-surfaces has K\"ahler geometry: without these symmetries it fails to exist mathematically. Physics as classical physics for spinor fields in WCW is what TGD does for quantum field theory. More concretely, point like particle is replaced with 3-D surface and its "orbit" has interpretation as particle orbit or space-time depending on what the scale of the observer is.
Mathematically WCW would be union of symmetric K\"ahler manifolds parametrized by zero modes defining "classical" variables as opposed to quantum fluctuating degrees of freedom parametrized by coset spaces of symplectic group assignable to δ M4+× CP2.
Where do all those scales emerge in a physics without scales?
Scale invariant theories do not possess any scale. Physics is however characterized by preferred scales. Turok sees only Planck length, vacuum energy density, and Higgs scale as fundamental scales. I think that this view is not quite correct: to my opinion - actually conviction - also the mass scales of elementary particles varying in huge range as fundamental scales are "rather" fundamental.
In TGD Universe the really fundamental length scale is of course CP2 length scale defining a fundamental unit for length measurements: all other not quite so fundamental length scales are proportional to it. Where do the scales of the physics the pop up? Conformal field theories provide a mathematical description of conformal symmetry breaking but this is not enough. The mechanism of conformal symmetry breaking is the basic mystery: what is the the mechanism selecting some preferred scales from continuum? "p-Adic thermodynamics" is the TGD based answer to the question.
p-Adic thermodynamics brings in a completely new element: the condition of number theoretic existence for Boltzmann weights: exp(-E/T) is replaces with pE/T: and this exists only if one has E/T is positive integer. Both p-adic temperature 1/T and E are quantized to integer values! Energy E corresponds now to eigenvalue of conformal scaling generator L0 for which the spectrum is apart from vacuum contribution integer valued. Number theoretical existence requires conformal invariance!
p-Adic length scale hierarchy discretizes the continuous scale invariance so that only primes label the mass scales and renormalization group evolution also discretizes. p-Adic length scale hypothesis performs further selection - very much analogous to natural selection but generalized to the level of fundamental physics. It picks up primes near powers of two and Mersenne primes seem to be the best survivors since entire physics can be assigned to them - hadron physics, its lepto-hadronic counterparts, new hadron physics at TeV scale, and 4 Gaussian Mersennes in the length scale range from cell membrane thickness to the size of cell nucleus.
Holography and general coordinate invariance
Turok also mentioned holography as a key principle of future physics but not yet understood. I agree. In TGD framework holography reduces to general coordinate invariance and the strong form of this principle implies holography in strong sense. Quantum physics is almost 2-dimensional. Partonic 2-surface almost fix the physics but only almost: the 4-dimensional tangent space data of space-time surface at partonic 2-surfaces is what is needed. 4-D space-time is also needed to build quantum measurement theory: classical non-quantum fluctuating variables - zero modes in WCW geometry - are necessary since it is these which code for the outcomes of measurements.
WCW spinors and zero energy states as quantum superpositions of Boolean statements
Turok mentioned also the idea that the notion of quantum information might be fundamental and that it might be possible to build fermions and bosons from bits. This however requires identification of space-time as lattice and neither Turok or me can share this assumption. I believe however that there is deep connection between spinors and qubits and thus logic. Spinors basis for N-dimensional space defines Boolean algebra on N-bits. In the case of WCW this corresponds to infinite-D Boolean algebra. WCW spinors correspond to Fock states for second quantized fermions in space-time and Fock state basis correspond to statements of infinite-D Boolean algebra. WCW spinor fields correspond thus to logical statements in quantum Boolean algebra.
Spinor structure is square root of Riemannian metric so that logic, geometry, and quantum theory find each other. In zero energy ontology zero energy states correspond to quantum versions of statements of type A→ B that is quantum superpositions of their instances a→ b. Also 2-adic topology has a direct connection to Boolean algebras: 2-adic number can be regarded as a sequence of infinite number of bits such that the importance of higher bits decreases rapidly by the properties of p-adic topology. Hence binary cutoff becomes excellent approximation.
This connection makes sense also for p-adic topologies: in this case there are some "check bits" involved. For Mersenne prime 2k-1 the number of bits is k-1 and the remaining statements whose number is 2k-1-1 correspond to check bits. Mersenne primes allow maximum number of check bits and this could guarantee maximal stability for Boolean statements and thus maximum cognitive survival probability. Could this explain why Mersenne primes have been so successful in number theoretic survival of fittest?
Addition: For Lubos the turn of the tide forced by LHC is a painful event as becomes clear from his ranting: Lubos regresses to the level at which personal insults are meant to be scientific arguments.
Addition: Bee has a nice posting titled "Whatever happened to AdS/CFT and the Quark Gluon Plasma?" about not so successful attempts to apply AdS/CFT correspondence to QCD. The motivation comes from the findings from both RHIC for heavy nucleus collisions and from LHC for proton-heavy nucleus collisions. The findings demonstrate that perturative QCD (pQCD) fails and suggest strongly string like structures as cause of the effects. In this regime pQCD should work quite well in proton-heavy nucleus collisions. The application of AdS/CFT correspondence in turn is sensible in strong coupling regime so that it does not look at all well-motivated: no wonder if the results fail quantitatively and even qualitatively. To my opinion this issue is very important. If pQCD fails in an energy regime where it should work well, one can suspect that some new physics is involved: just this new physics LHC has been desperately trying to find. TGD proposal for this physics is M89 hadron physics, and I have discussed this topic many times in previous postings.
13 comments:
Matti,
this is a most excellent post and clears up where we differ from each other and the various complicated models in development and discovery.
I have asked you questions that you may not find necessary from your position, and this shows why. I for example began with some sort of lattice idea which (also as information, two bit at least, is more fundamental than our limiting quantum terminology and notation to which you remedy in the assumption of positive power dimension being the ground linear like level in its simplicity.
Essentially we point to the same directions where things meet. What is a quarter value of Planck's if not the minimum lattice that the forth power (set negative) is the general measure of (organic) metabolism?
From one view, we can dispense with the Higgs field itself as an assumption as well a different view may dispense with the dark phenomena assumption. You seem to see the GUT idea as also not fundamental from a scaleless view.
What then does that leave in this approach (fractal like) or absolute (binary and check bits (holograph like) but some still primary (nature privileging them via p-adics) but the elusive meaning or properties of uniqueness as prime numbers? My first thought is that among the symmetry ideas that we ask how they are broken this may be the question of the arithmetic and extended conformal way we factor composite numbers.
Binary cut offs may be dimensionless and open in influence, certainly dynamic, yet an absolute level of substance - not the evolution program as the most general state as approximation or any such statistical methods as the only available and logical way to access the nature of physics.
I added some illustrations that held what seemed disordered patterns that became more relevant simple numbers (fractions and the first few powers of primes and the all important even number exception, 2.
I know all this can be put into the standard number theory formuli but hands on counting and not reducting (or when it feels like generalizing) will not lose the context of information, nor hide it
from view - certainly in how we connect to the consciousness aspects of all this, the nuts and bolts of it.
As it stands to todays physics the minus one is at work here just as with Eddington his intelligible but finite system was derided as the old plus one when he said 137 and not 136 on that approximation of his vision of quantum relativity.
While pure TGD applies in its concepts in the new physics and does so outside other explanations in the physics is not necessarily the only model for such new systems - at least for now as the ideas may meet or be proven not able to do so.
With quasics also we need super-spinor concepts, but even then these as well as chirality may not be foundational or deep enough so as to relate all particles to the muon generation. If my universe is quasifinite and explicitly so then there is not problem with a view that in the non necessity logic it can be quasi-metastable.
I am in a sense derived from Fermat and you from Mersenne (things we rediscoved if not originated beyond them. They were correspondents and most likely part of the general wisdom of that age just as we have so many independent new theoreticians here.
In case you cannot access my http://www.pesla.blogspot.com I post from the last drawing this quotation of mine which is the state of my thoughts now...
"We can imagine the physical world to be wider in possibilities than numbers. By the same token some idea of number theory (such as integer philosophy), gives an idea reality of numbers physicality in a sense..." L. Edgar Otto
LOL Lubos is at it again his post just followed yours on this Turoks and from a negative evaluation of him. What is wrong with Canadian or English theoreticians especially if they are closer to the likes of Coxeter, Perose, Hoyle, Peter Rowlands... such models are not in confusion... just the level of intelligence and ability to abstract from them sanely.
To Otto:
Lubos belongs with his dogmatism to past. No need to be a psychologist to understand his bitterness. I am happy to see that this dark period in theoretical physics is coming to its end.
The responses to Lubos's posting demonstrate well that most his readers behave like blood thirsty fools. I am just wondering what went wrong with Lubos and his gang. Never a comment with real contents, only primitive expressions of rage from the level of reptilian brain.
Scale invariance makes me think of the Mellin transform
Dear Matti,
When point like particles of QM is replaced by 3-surfaces in TGD. position and momentum is replaced by what concepts?
This makes better to learning TGD, at least for me.
i have some guesses:
in QM, Kinetic term of Hamiltonian is proportional to square of momentum.
in TGD, Kinetic term of Lagrangian is proportional to square of induced kahler form.
therefore:
momentum are replaced by kahler form in transition from QM to TGD.
also another analogy: momentum is 1-form in cotangent bundle and kahler form is 2-form at cotangent bundle.
can one say position is replaced by metric?
Dear Hamed,
thank you for an interesting question. Answer depends on how literally one interprets momentum and position.
1. The concrete interpretation in terms of M^4 means assigning to partonic 2-surface center of mass coordinates and 4-momentum to these coordinates. This correspond to view about 3-surface as extended particle. For Super Virasoro representations this kind of interpretation is correct. What center of mass coordinates mean is not quite obvious and their choice is not unique: general coordinate invariance at the level of WCW however comes in rescue.
2. Your proposal would be more abstract. The following is analogous to your proposal but does not agree with it. I use *completely standard* procedure for fields by interpreting imbedding space coordinates as "fields".
a) The analogs of spatial coordinates must specify a point of WCW. Imbedding space coordinates as functions of coordinates of 3-surface do this and also define analogs of fields. Formally they indeed serve as WCW coordinates although they are not practical.
b) The analogs of momenta would be by generalizing Hamiltonian formalism for fields the canonical momentum densities defined by Kaehler action K by standard formulas.
Canonical momentum *currents* (vectors in both H and X^4) are given by
\Pi_k^{\alpha}= \partial K/\partial(partial_{\alpha} h^k))
(k refers to imbedding space coordinate and \alpha to space-time coordinate). Canonical momentum densities corresponds to its time component: \alpha=t: these would be the analogous of canonical momentum densities of field theories.
Note that field equations say that canonical momentum currents are covariantly divergenceless:
D_{\alpha}\Pi^{k,\alpha}=0.
[It might be a good idea deduce canonical momentum currents and densities for simple scalar field action in the case of ordinary QFT: you should get just gradient of the scalar field as canonical momentum currents].
Note that modified gamma matrices \Gamma^{\alpha}_m are contractions with ordinary gammas \Gamma^{\alpha}= \Pi_k^{\alpha}\gamma^k.
3. A more abstract coordinatization of WCW and non-local with respect to space-time surface would be in terms of flux integrals of Hamiltonians of delta M^4xCP_2 over partonic 2-surfaces. This represents only the degrees of freedom which are quantum fluctuating since they do not containing information about interior of 3-surface: this data corresponds to zero modes. Strong form of holography supports this identification for quantum fluctuating degrees of freedom.
Dear Hamed,
still a comment.
a) One cannot say that position is replaced with metric. In Wheeler's approach in which 3-metric is the dynamical variable this would make sense but now we have sub-manifold geometry and imbedding space coordinates replace the components of 3-metric as dynamical variables.
b) Nor does the momentum correspond to Kahler form. In electrodynamics were Kahler form would correspond to electromagnetic field and non-vanishing canonical momentum densities would correspond to components of electric field forming one half about the analog of Kahler form. This brings in mind your guess.
In any case, the interpretation is completely fixed by using just completely standard canonical formalism in the manner I described in previous posting. What is essential is that primary dynamical variables are neither metric nor Kahler form (as Maxwell field).
Thanks,
As i understand from your answer, although the Lagrangian of kahler field(as Maxwell filed) is a function of metric(g) and kahler form(j), but they are functions of imbedding space coordinates. therefore primary dynamical variables are imbedding space coordinates.
To Hamed:
Precisely, you can derive variational equations using chain rule for action as function g and J and g and J as function of h^k and their partial derivatives. The dependence of action is such that you can think of action as function of only partial derivatives of h^k and in the result replace outermost partial derivatives by covariant ones.
There are only 4 field like variables by general coordinate invariance -some subset of H coordinates depending on situation. This makes theory in some sense extremely simples as compared to a typical gauge theory. The shape and size of space-time surface in H however brings in compensating degrees of freedom (many-sheeted spacetime, topological field quantization etc...).
The basic objection is that linear superposition is lost. The linear superposition of effects to a particle topologicaly condensed to several space-time sheets simultaneously is not however lost and this is enough.
Matti,
Numbers are so strange deep down. Guess we need to clearly put things into deeper terms... a metaphysics of sorts. Loop Quantum Gravity and some Insights of String Theory seem to say similar things at some deep level where we see deeper than the languages we erect.
Did you see the article that said a gene was found relating to the embryonic development that determines if we are right or left handed... and we a rare or even only species that the outcome is 90% one way and not even? Right handed neutrinos? How many to the left and what analog to a deep gene code?
http://www.sciencedaily.com/releases/2013/09/130912203216.htm
Thing about intuition... one isolated soul can stop a circuit from working. On the other hand such a soul, can be in the way as well as from a distance color the whole... you know, a new theory like said of Non-Euclidean geometry sprouting up like violets.
We do not necessarily lose superposition in the vague intuitive super gauge ideas... a sequence string from unity sums into a cube of six on the side thru several quasic sheets (generations) of unified space... I mean we really should talk awhile on the number theory language under all these usual physics terms.
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