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.