The discussion revolves around the concept of entropy in the context of Loop Quantum Gravity (LQG) and its relationship to spin network systems. Participants explore theoretical implications, interpretations, and potential applications of these ideas, referencing specific papers and models.
Participants express a range of views on the interpretation of spin networks and their implications for understanding entropy, with no clear consensus reached on the best approach or model. Disagreement exists regarding the physical interpretation of spin networks and the mechanisms proposed for their dimensionality.
Some limitations in the discussion include the lack of clarity on the mechanisms for thickening spin network edges, the dependence on specific interpretations of dimensionality, and the unresolved nature of how entropic bits interact with the concept of space.
Spin_Network said:Thanks marcus, it is refreshing to know that you don't let anything pass by!
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mccrone said:Swain - "What is being argued here is precisely that this may not be the case when one thinks about spin networks physically. In other words, instead of writing down a spin network in the usual way, thinking of the edges as 1-dimensional and the nodes as 0-dimensional, one should take the physical interpretation seriously and “thicken” the edges so that they have 2-dimensional cross-sections and the nodes so that they are small 3-dimensional balls. The actual sizes are unimportant as long as there is some minimum, which we already know from the quantization of area and volume
in loop quantum gravity."
Hey Spin, is this the bit that excites your interest?
You can also arrive at this same picture using a logic of self-organising, or semiotic, constraint.
Swain makes the correct point, but he has no real "mechanism" for thickening the lines. He can only appeal to a commonsense physicalism to correct the standard Euclidean mathematical imagery.
There are two ways to construct geometry - mechanical construction where you build up from 0D points, or organic/semiotic constraint where you constrain towards the desired dimensionality. So shrink a volume to an asymptote and you get a plane. Do the same to the plane to make a line, and then a line to a point.
A semiotic view of dimensionality would be much richer than this of course. But you can see how it turns Swain's problem on its head. We would start with the assumption that edges are multi-dimensional and have to be constrained - by a context, a "living" system of interpretance - towards a highly constrained 1D existence.
As a matter of (organic) logic, an actual 1D edge would be a mathematical fiction. The commonsense physical view would say that the approach to a 1D limit would be asymptotic. And the scale of the eventual "cut off" would be determined by the properties of the particular system exerting the constraint.
What is not clear to me as yet is whether cramming a volume with circuitry is that good a way of thinking about the situation. Well it is probably correct that stuffing a space full of crisp entropic bits will see a reduction in dimensionality.
Before anything is stuffed into it, the space will be a vagueness - a realm of potential - rather than just an empty space. So to fill it with crisp entropic bits, you are in effect stuffing it with both atoms and void. And if you then just measure the space by the number of entropic atoms you are able to create, then neglect the amount of void needed to frame the atoms. there will indeed seem a drop in the available dimensionality.
Cheers - John McCrone.
mccrone said:Swain - "What is being argued here is precisely that this may not be the case when one thinks about spin networks physically. In other words, instead of writing down a spin network in the usual way, thinking of the edges as 1-dimensional and the nodes as 0-dimensional, one should take the physical interpretation seriously and “thicken” the edges so that they have 2-dimensional cross-sections and the nodes so that they are small 3-dimensional balls. The actual sizes are unimportant as long as there is some minimum, which we already know from the quantization of area and volume
in loop quantum gravity."
Hey Spin, is this the bit that excites your interest?
You can also arrive at this same picture using a logic of self-organising, or semiotic, constraint.
Swain makes the correct point, but he has no real "mechanism" for thickening the lines. He can only appeal to a commonsense physicalism to correct the standard Euclidean mathematical imagery.
There are two ways to construct geometry - mechanical construction where you build up from 0D points, or organic/semiotic constraint where you constrain towards the desired dimensionality. So shrink a volume to an asymptote and you get a plane. Do the same to the plane to make a line, and then a line to a point.
A semiotic view of dimensionality would be much richer than this of course. But you can see how it turns Swain's problem on its head. We would start with the assumption that edges are multi-dimensional and have to be constrained - by a context, a "living" system of interpretance - towards a highly constrained 1D existence.
As a matter of (organic) logic, an actual 1D edge would be a mathematical fiction. The commonsense physical view would say that the approach to a 1D limit would be asymptotic. And the scale of the eventual "cut off" would be determined by the properties of the particular system exerting the constraint.
What is not clear to me as yet is whether cramming a volume with circuitry is that good a way of thinking about the situation. Well it is probably correct that stuffing a space full of crisp entropic bits will see a reduction in dimensionality.
Before anything is stuffed into it, the space will be a vagueness - a realm of potential - rather than just an empty space. So to fill it with crisp entropic bits, you are in effect stuffing it with both atoms and void. And if you then just measure the space by the number of entropic atoms you are able to create, then neglect the amount of void needed to frame the atoms. there will indeed seem a drop in the available dimensionality.
Cheers - John McCrone.