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spin network heuristic for pre-quantum picture
this is about Smolin's two most recent
http://arxiv.org/abs/hep-th/0605052
Generic predictions of quantum theories of gravity
Lee Smolin
For inclusion in "Approaches to Quantum Gravity - toward a new understanding of space, time, and matter", edited by D. Oriti, to be published by Cambridge University Press
"...generic consequences...of a class of background independent quantum theories of spacetime called causal spin network theories... Within the last few years three possible generic consequences have come to light. These are 1) Deformed special relativity as the symmetry of the ground state, 2) Elementary particles as coherent excitations of quantum geometry, 3) Locality is disordered. I discuss some possible experimental consequences of each."
in this paper (among others) is presented an idea of residual non-locality in emergent 3D space---as the spatial network evolves out of Planck conditions by a process of local moves: expansion moves and exchange moves performed on the network.
this picture of spatial evolution, by which expansion moves gradually almost but not quite eliminate all non-local relations and lead to a nearly perfect emergent 3D space, has apparently served as an HEURISTIC to give a promising idea of a deterministic process from which quantum mechanics emerges
http://arxiv.org/abs/quant-ph/0609109
Could quantum mechanics be an approximation to another theory?
Lee Smolin
10 pages
"We consider the hypothesis that quantum mechanics is an approximation to another, cosmological theory, accurate only for the description of subsystems of the universe. Quantum theory is then to be derived from the cosmological theory by averaging over variables which are not internal to the subsystem, which may be considered non-local hidden variables. We find conditions for arriving at quantum mechanics through such a procedure. The key lesson is that the effect of the coupling to the external degrees of freedom introduces noise into the evolution of the system degrees of freedom, while preserving a notion of averaged conserved energy and time reversal invariance.
These conditions imply that the effective description of the subsystem is Nelson's stochastic formulation of quantum theory. We show that Nelson's formulation is not, by itself, a classical stochastic theory as the conserved averaged energy is not a linear function of the probability density. We also investigate an argument of Wallstrom posed against the equivalence of Nelson's stochastic mechanics and quantum mechanics and show that, at least for a simple case, it is in error."
===my irresponsible comment ====
the heuristic idea is actually very simple.
if you start with a network of random connected nodes (undefined primitve idea) symbolizing very hot dense Planck regime where any node has a chance to be "adjacent" to any other, and then if you
EVOLVE that by expansion moves where a node can be replaced by several nodes in simplicial network, and by other local link-swapping moves
then eventually the expansion will WIPE OUT THE NONLOCALITY and some recognizable space will emerge where you can SAY who is close to whom and who is between which and it all makes sense
but there will still be ROGUE LINKS left over from Plancktime which didnt get ironed out in the regularization that happened thanks to expansion.
and these rogue link suckers could span across vast reaches. one in the chair you occupy could reach to the other side of the Big Whatever.
But you wouldn't know about it, because expansion has washed almost all the nonlocality out. We DON'T SEE THE SPORTS.
now comes the good part, where you want to DO COPENHAGEN ON IT and you place a plastic baggie around some part of the universe and you scrutinize inside the baggie (the System) and you deem that certain non-deterministic things are going on inside the baggie.
I better make a separate post about that.
this is about Smolin's two most recent
http://arxiv.org/abs/hep-th/0605052
Generic predictions of quantum theories of gravity
Lee Smolin
For inclusion in "Approaches to Quantum Gravity - toward a new understanding of space, time, and matter", edited by D. Oriti, to be published by Cambridge University Press
"...generic consequences...of a class of background independent quantum theories of spacetime called causal spin network theories... Within the last few years three possible generic consequences have come to light. These are 1) Deformed special relativity as the symmetry of the ground state, 2) Elementary particles as coherent excitations of quantum geometry, 3) Locality is disordered. I discuss some possible experimental consequences of each."
in this paper (among others) is presented an idea of residual non-locality in emergent 3D space---as the spatial network evolves out of Planck conditions by a process of local moves: expansion moves and exchange moves performed on the network.
this picture of spatial evolution, by which expansion moves gradually almost but not quite eliminate all non-local relations and lead to a nearly perfect emergent 3D space, has apparently served as an HEURISTIC to give a promising idea of a deterministic process from which quantum mechanics emerges
http://arxiv.org/abs/quant-ph/0609109
Could quantum mechanics be an approximation to another theory?
Lee Smolin
10 pages
"We consider the hypothesis that quantum mechanics is an approximation to another, cosmological theory, accurate only for the description of subsystems of the universe. Quantum theory is then to be derived from the cosmological theory by averaging over variables which are not internal to the subsystem, which may be considered non-local hidden variables. We find conditions for arriving at quantum mechanics through such a procedure. The key lesson is that the effect of the coupling to the external degrees of freedom introduces noise into the evolution of the system degrees of freedom, while preserving a notion of averaged conserved energy and time reversal invariance.
These conditions imply that the effective description of the subsystem is Nelson's stochastic formulation of quantum theory. We show that Nelson's formulation is not, by itself, a classical stochastic theory as the conserved averaged energy is not a linear function of the probability density. We also investigate an argument of Wallstrom posed against the equivalence of Nelson's stochastic mechanics and quantum mechanics and show that, at least for a simple case, it is in error."
===my irresponsible comment ====
the heuristic idea is actually very simple.
if you start with a network of random connected nodes (undefined primitve idea) symbolizing very hot dense Planck regime where any node has a chance to be "adjacent" to any other, and then if you
EVOLVE that by expansion moves where a node can be replaced by several nodes in simplicial network, and by other local link-swapping moves
then eventually the expansion will WIPE OUT THE NONLOCALITY and some recognizable space will emerge where you can SAY who is close to whom and who is between which and it all makes sense
but there will still be ROGUE LINKS left over from Plancktime which didnt get ironed out in the regularization that happened thanks to expansion.
and these rogue link suckers could span across vast reaches. one in the chair you occupy could reach to the other side of the Big Whatever.
But you wouldn't know about it, because expansion has washed almost all the nonlocality out. We DON'T SEE THE SPORTS.
now comes the good part, where you want to DO COPENHAGEN ON IT and you place a plastic baggie around some part of the universe and you scrutinize inside the baggie (the System) and you deem that certain non-deterministic things are going on inside the baggie.
I better make a separate post about that.
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