The idea of emergence of gravitation is the newest fashion in the long sequence of fashions that has plagued theoretical physics during more than four decades. GUTs, supergravity, loop gravity, super string models, M-theory and its descendents, multiverse, AdS/CFT, reduction of physics to that of blackholes... Now it is fashionable to believe that Einstein was wrong: gravitation has a non-geometric origin: gravity as entropic force, emergence of gravition and 3-space and even space-time.
Verlinde argues that the origin is thermodynamical. That it cannot be became clear already for 6 years ago experimentally. I have written about this in more detail in previous blog posting. Gravitational potential appears in the Schrödinger equation of neutron: it should not if gravitational potential is a thermodynamical quantity: thermodynamical quantities should not appear in quantal equations since they are derived from the statistical predictions of quantum theory. This elementary fact was noticed by Kobakidzhe. For some funny reason, this simple observation has not got through and it is probably too late now: during next years entropic gravity will produce a lot of stuff in archives for the future sociologists of science. We are living post-truth period and theoretical physics has been the forerunner in this respect.
Bee mentions as an example about emergent gravity the model of Xiao-Gang Wen and collaborators. As usual, the model turned out to be a disappointment. Space-time emerges from space-time as it does also in other models in the best tradition of circular logic. One replaces space-time with a lattice keeping the 4-dimensionality: assigns finite-D Hilbert space at points of this 4-D lattice: essentially a discretization of quantum field theory is in question. One constructs Hamiltonian as sum of local Hamiltonians for a symmetric tensor field in such a manner that one obtains Einstein's equations in lowest order as continuum limit. Why I am not happy with this?
One of course should not have any lattice assumed to have structure of 4-D lattice. One should have no tensor fields. One should have only Hilbert space. One however starts from fields in continuous space-time, discretizes, it and makes continuous again! I have always wondered why these naive mathematically primitive tricks familiar already from loop gravity. Superstring theories were not physically correct simple because the dimension of fundamental objects was too small (1 instead of 3) and this actually led to the idea that space-time energes: either by compactication or as 3-brane or as it seems as both;-). String model was however based on refined mathematics. I can only imagine the pains suffered by Witten as he sees this intellectual degeneration of theoretical physics.
I have tried to explain that discretization occurs naturally due to the finite measurement resolution for both sensory experience and cognition. This however requires that consciousness and cognition are something which does not reduce to dynamics of particles. This leads to a notion of manifold involving naturally both discretization in terms of algebraic extensions of rationals and continuum aspects and also fusion of various number fields so that one can speak about adelic space-time - already Leibniz dreamed about this as he talked about monads. Most importanly, in this framework discretization does not lead to a loss of fundamental space-time symmetries: this is what killed loop gravity. Both the symmetries of special relativity and general coordinate invariance are exact and new infinite-dimensional symmetry algebras - in particular huge extension of conformal symmetries, are predicted.
I have also talked about emergence: very many things emerge in TGD. Elementary bosons and actually also elementary fermions emerge from induced spinor fields and topology of wormhole contact pairs. Standard model and general relativity emerge as approximation to many-sheeted space-time having most important application to biology, neuroscience, and consciousness. These are definitely not emergent for point like particles! Generalizations of the usual positive energy ontology to zero energy ontology and of quantum measurement theory are needed.
Classical gauge fields and gravitational fields at the level of single space-time sheet emerge from the dynamical geometry of space-time as a 4-D surface. The outcome is ridiculously simple: by general coordinate invariance there are only 4 fundamental field like degrees of freedom: for instance CP2 coordinates at macroscopic limit. Gravitational field of GRT and gauge fields of standrad model emerge as the sheets of the many-sheeted space-time are lumped together and the gauge potentials and deviation of metric from Minkowski metric sum up to gauge
potentials and gravitational field of GRT.
Space-time does not however emerge! Only the conscious experience about 3-space - proprioception - emerges through tensor nets formed by magnetic flux tubes meeting at nodes defined by 3-surfaces. How rapid the progress in physics would be if colleagues could finally accept that also the conscious observer must be understood physically.
For a summary of earlier postings see Latest progress in TGD.
2 comments:
Matti, once you have time take it to actually watch a lecture of Xiao-Gang Wen to see what he saying. The lattice description comes about half way in the story, he doesn't start with.
I think that I have seen his article. Do not remember for sure without checking. It is ironic that I must here take conservative attitude concerning space-time emergence and take continuous space-time as given although adelic physics forces to bring number theory (p-adic number fields, extensions of rationals) as basic element of physics of cognition and discretization emerges from finite cognitive resolution now.
The notion of emergence is far from obvious. What emerges and from what? In TGD gauge fields are not fundamental thet emerge from induced spinor fields. Einstein's general relativistic space-time emerges from description of physics in terms of space-time surfaces. A lot of things emerge but 3-space or space-time do not emerge from nothing.
One can of course ask whether space-time could emerge as moduli space. The problem here is that moduli spaces are typicallt highly unique and space-time as a notion is not and in quantum theory one cannot even speak about single space-time. In TGD imbedding space is (highly at least) unique and the world of classical worlds (WCW,typical moduli space) is unique from its geometric existence and in replaces space-time (point like particles are replaced with points).
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