Stringy Appeal
The most frustrasting element of the String Wars is the brick wall of the quark gluon plasma. As Mottle quite rightly points out: brainwashed clever string theorist to buy the idea that the physics of string theory is mostly wrong. In M Theory, we agree wholeheartedly that black hole physics dictates the behaviour of such plasmas. We disagree that classical geometry, classical symmetry principles and unobserved SUSY partners have much to do with it.
The black hole entropy is described by an entanglement measure which, using category theory, may be given meaning entirely outside the world of complex geometry. Even Hilbert spaces and spectral triples disappear. In this brave new world,naive stringy extra dimensions simply count operator sets. Lagrangians are emergent. So there is a place, on the other side of that brick wall, where people are standing and shouting back, finding it impossible to believe that they could (relatively speaking) be wrong. For string theorists, there is one question: do you seriously believe that your so called theory is crazy enough?
The minimum ratio of viscosity and the entropy density can be translated in another way: it is actually the maximum ratio of the entropy density to viscosity. For a fixed viscosity (and volume), which physical system has the highest entropy density (and therefore the net entropy)? Well, in the gravitational context we know the answer. Black holes maximize the entropy. They're the ultimate bound state of matter into which the matter collapses into, and by the second law of thermodynamics, they must maximize the entropy among all such bound systems.It is true that string theory correctly retrodicted this behaviour for plasmas. And it is also true that, under this observation, it must be well nigh impossible for a
The black hole entropy is described by an entanglement measure which, using category theory, may be given meaning entirely outside the world of complex geometry. Even Hilbert spaces and spectral triples disappear. In this brave new world,
posted by Kea | 8:33 PM
4 Comments:
Emergence is very interesting notion but I do not believe that physics can do without space-time geometry. Categories are a useful tool but I am convinced that physics is much richer than any axiomatic approach to mathematics.
In TGD framework the physical picture about emergence is rather clear: only fermions are fundamental and bosons are their bound states (fermion and antifermion at opposite throats of tiny wormhole contact). The challenge has been to translate this picture into quantitative formulas allowing to predict gauge couplings and their evolution.
At QFT limit this means that bosonic propagators should emerge from fermionic ones. During last weeks I have finally managed to formulate this notion precisely. The resulting QFT involves only Dirac action coupled to gauge potentials. There is no YM action at this level. The functional integral over fermions in presence of Grassman sources gives to the action bosonic kinetic term and all gauge boson propagators and gauge couplings are calculable from the simplest fermionic loops. Gauge invariance follows from the gauge invariance of Dirac action as can be seen by explicit calculation of Feynman diagrams involved.
I have just developed the first quantitatively precise view about how fine structure constant, which at electron's p-adic length scale equals to RG invariant Kaehler coupling strength, emerges from fermionic loop. This is of course not the final world and I believe that the picture will get more refined.
It is a pity that string theorists refuse to learn the lesson and consider the possibility that also string like structures could emerge from deeper theory. As they indeed do in TGD framework, where preferred extremals of Kaehler action allow dual slicing by stringy and partonic 2-surfaces.
Matti
Hi Matti. Although I'm sure your new results are very impressive, naturally I am also sure that you grossly underestimate the value of category theory in (a) clarifying the geometry of spacetimes, and (b) in providing new combinatorial tools to study beyond SM physics. Hopefully, by recovering your classical constructions, this will one day become clear.
I do not underestimate the value of category theory. I have considered several applications of category theory to TGD at the level of first principles.
My overall impression is that category theory is basically a theory about universal structures of mathematical theories: representing kind of reflective level of mathematics. It also catches the combinatorial aspects of quantum theory elegantly but becomes clumsy if one wants to describe everything using it. Category theory describes bones but also flesh is there.
To me the question is not about giving up Riemann geometry but generalizing it (its p-adic variants, generalization of imbedding space geometry allowing to describe the hierarchy of Planck constants, and infinite-D geometry for the "world of classical worlds"). Throwing away geometry would kill not only TGD but all successful theories of physics. Physics is very much about measurements of lengths and bringing in something new requires also building the bridge to old and well-established.
To sum up my position: there are many roads to Rome and theoretical physics is so difficult discipline that one must be ready to use any road available.
No successful physical formalism ever gets thrown out. But it gets replaced by something richer, in which the old geometry appears only under certain circumstances. Of course the big question is understanding measurements of lengths etc, a question that the likes of Grothendieck and Lawvere thought long and hard about. But imposing prejudices from classical geometry upon the concept of length just isn't the right way to think of observables in quantum gravity.
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