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May I quote from Yanniru's post:
"Quantum Theory from Quantum Gravity
Authors: Fotini Markopoulou, Lee Smolin
Comments: 17 pages, 2 eps figures
We provide a mechanism by which, from a background independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear.
Starting with an arbitrary abstract graph as the microscopic model of spacetime, our ansatz is that the microscopic dynamics can be chosen so that
1) the model has a low low energy limit which reproduces the non-relativistic classical dynamics of a system of N particles in flat spacetime,
2) there is a minimum length, and
3) some of the particles are in a thermal bath or otherwise evolve stochastically. We then construct simple functions of the degrees of freedom of the theory and show that their probability distributions evolve according to the Schroedinger equation.
The non-local hidden variables required to satisfy the conditions of Bell's theorem are the links in the fundamental graph that connect nodes adjacent in the graph but distant in the approximate metric of the low energy limit.
In the presence of these links, distant stochastic fluctuations are transferred into universal quantum fluctuations.
Full-text: PostScript, PDF, or Other formats
http://arxiv.org/abs/gr-qc/0311059"
I think I found a way of mapping LQG:
The basic model is this:
Consider two items: A and B.
They are like undefined categories say, that COULD overlap and partly define each other. Or like two points of view, that "spin" about each other say when seen from outside, prior to any "handshake" they make on agreeing to common ground.
A and B come together.
The togetherness of A and B can be called "C" say.
"C" is like a single combined viewpoint. It meets another perspective "D".
"C" and "D" COULD agree on common ground; a common space made from their respective spaces...
From outside "C" may seem to be spinning about "D"; and the original "A" and "B" may seem to be twisting about "D" through the "AB" ground "C".
(Gives rise to links to spinor and twistor theory say)(DNA structure appears to be forming too)
"C" and "D" come together: call this togetherness "E".
"E" meets a new pattern "F".
NOW:
When "E" met "F"; it could have been BEFORE "A" met "B": it could be "hidden" dimensions of "A" and "B" we are seeing.
So we have a LOOP in this model. The loop possibility occurs at the third: "separate items come together"; that had been thought of as a fourth but COULD have been detail before the first! (and what is 3? Pi/4 = 1 - 1/3 + 1/5 - 1/7 +1/9 - 1/11 ...)
Now this looks curious: four bases, three triplets, double helix....looks like DNA?
Gravity can be thought of as like centrifugal force (thanks to Dr. Stafford for suggesting a link); centrifugal force is where you were pulling the ball swinging around you on a string, a quarter-turn ago.
Gravity can be thought of say as "a coming together of patterns a quarter turn ago".
In this loop model: "a quarter turn ago" is caught up in the question of "what about a fourth coming together": LOOP QUANTUM GRAVITY!?
"Quantum" apears to mean "meeting".
"A" and "B" meet; come together in "C";
"C" and "D" meet; come together in "E" and so in "E" the "A" and "B" are gravitating together by "F" from a singular math count shell perspective.
That is: "A" and "B" do not have to come together (gravity is optional it seems); but by regarding each item in third model as a unit; well if "A" and "B" came togther in "C" and in "E" they must come together DIFFERENTLY in "E" so that would make them smaller in this singular counting, so to remain units they must overlap say in "E" on the second coming together it seems.
So they gravitate but only so far as they are COUNTED again and again (have "mass") in "E" via the postulated new coming together in "F".
But that postulated coming together in "F" COULD have been a new detail of the original "A" and "B" coming together. So have a LOOP where we don't say if "A" meets "B" is the same background as "E" meets "F".
This model gives an uncertainty in definition between LOOP; gravity; and quantum. It appears to mix PAST with FUTURE.
Quote:
"Starting with an arbitrary abstract graph as the microscopic model of spacetime, our ansatz is that the microscopic dynamics can be chosen so that"
this relates in the model I gave as:
The arbitrary abstract graph would be an arbitrary repeat of cycles "A" meets "B"; AB common ground "C" meets "D" as a 4-geometry graph...
Quote:
"1) the model has a low low energy limit which reproduces the non-relativistic classical dynamics of a system of N particles in flat spacetime,"
this relates in the model I gave as:
the 4-geometry is flat space-time; with a low low-alternatives limit I guess to magnify the two steps of coming together, to maximise the two-ness aspect? (Relativity maximises 4-ness?)
Quote:
"2) there is a minimum length"
becomes:
the three-ness of comparing two versions of two-ness and holding say either as constant to the other" is fixed as a certain unit to lock in a grid structure to space-time?
Quote:
"3) some of the particles are in a thermal bath or otherwise evolve stochastically. We then construct simple functions of the degrees of freedom of the theory and show that their probability distributions evolve according to the Schroedinger equation"
This becomes:
"particle" is "unit meets group" and "thermal bath" I guess is "jiggling about" so such particles are bigger than the minimum grid of space-time (so could involve blur-induced overlaps in grid-definition I guess). Some evolve "stochastically" means "evolve as if randomly generated". "Random" suggests "options open on their definition so this is like "keeping future options open" for defining those particles.
Such stochastically evolving particles would be where the LOOP is seen: the potential mixing of "A" meets "B" with "E" meets "F" definition space provides room for options say.
So the model has projected LOOP quantum gravity by drawing on the requirment for mixing stochastically evolving particles with thermal bath particls in a fixed graph flat space-time.
Quote:
"3) some of the particles are in a thermal bath or otherwise evolve stochastically. We then construct simple functions of the degrees of freedom of the theory and show that their probability distributions evolve according to the Schroedinger equation"
As I have shown: there would be degrees of freedom in the theory to get a mixing of "gravity" definition space with "loop" and "quantum" ("meeting") each loop gives you a quantum of gravity (a quarter-turn definition space-limit?) as the counting "again and again" of "meets F" gives "mass" to the singular "repeat" coming together of "AB: form C" in "CD may form E" due to "E" meet "F".
Need to check Shrodinger equation. May involve feedback in definition-space evolution?
Quote:
"quantum theory arises in the same limit in which spatial properties appear."
Sub-atomic particle patterns (see earlier post) and QED are involved in the simple "compare and match say two patterns; make a new comparison" idea. "Spatial properties" may be "countably "flat" (so potential conserved definition) properties of space; which are seen in model I've given as arising in the same definition limit as the accuracy projected by the LPG theory they give?
Quote:
"The non-local hidden variables required to satisfy the conditions of Bell's theorem are the links in the fundamental graph that connect nodes adjacent in the graph but distant in the approximate metric of the low energy limit.
In the presence of these links, distant stochastic fluctuations are transferred into universal quantum fluctuations. "
The non-local hidden variables appear to be projections of a grid-structure say on to the LOOP space in definition (loop involving question: AB or EF space?)(This space seems to reflect the singular-math system I noted where "gravity" only looks necessary where items are seen as units and one step necessitates assuming "Unit minus 1 step is smaller or maybe overlapped say)?
Thus they are indeed links in the graph which involves the very definition of "one step, next step" (which is a vital concept in Bose-Einstein condensation: topology considerations; see post).
Of course they sre distant in the approximate metric of the low energy limit? As that defines "two-ness" and by definition "one step, two step" will be distant in "two-space" approximate metric which tries to distinguish "one step" and "two step" (maybe at right angles so Dr. Stafford's Dirac delta function? need to check thinking).
The distant stochaistic fluctuations from the LOOP background scenario are transferred into a synchronised juggling with the uncertainty of "two" known as "quantum fluctuations" or something?
String theory:
the pattern underlying strings appears to be "number lines": "repeat counting in a particular definition space"?
Branes: these appear to be like "factorisation tables" (or "times-tables").
The thermal bath particles might see the minimum length as a string; the minimum length might see the bath particles as common factor sheets, branes?
The grid projected by say empasing "two-ness" might be seen from the LOOP perspective as "imaginary time" component to the system?
"Dark matter" and "dark energy" may be "ghosts" of the loop structures echoed in the interference between the graphical space-time model and the linear nature of traditional math-assuming-equal-sizes system of counting in numbers by self-reference definition of number and base or something?
Another interpretation:
"The Grand old Duke of York, he had ten thousand men; he marched them up to the top of the hill and he marched them down again. And when they were up they were up; and when they were down they were down; and when they were neither up nor down they were neither up nor down."
-just a bit rough in places
-dolphin
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