How a field request capacity of a channel?
Not sure what your question means. As far as I know, in the LQG spin network context there are no channels and no flow of information along the links. I told you what my intuition was, at a heuristic level, but please don't misinterpret or misunderstand what I am saying as something about LQG physics! What I am talking about is how I personally assimilate these things.
You can see if my intuition is helpful, use it or don't use it as you wish. Maybe it will work for you, maybe not.
Here is something to try, if you want: Start by picturing a LQG black hole--the area of the BH horizon is given by the network links which pass through it.
Each link has a label that tells two things:
1. the area that the link contributes to the total horizon area
2. the dimension of a finite dimensional Hilbert associated with the link.
These two things are the SAME thing---my intuition is that at some deep level area and information are identical because they are told by a single spin network label. A finite dimensional Hilbert space is a way of representing information---a range of choice. How much information is represented by picking one state vector out of the whole range of possibilities. (Read about Shannon information theory, codes, channels--it is just something to give intuition about the physics, it is not the physics itself )
This is how I personally understand that in the LQG discussion of black hole entropy, the entropy turns out to be related to dimension of a Hilbert space associated with the BH horizon. And of course that Hilbert space is also connected to the area.
BTW I don't know what you meant by "fields control". In my comment in the other thread I did not say anything about "fields" or about "controlling" capacity. Channel capacity is a Shannon info theory concept which I was borrowing from a distant cousin of quantum theory just to be a help to intuition.
Let me take the point of view that gravity is entropic, holographic and there are no gravitons. Gravity will be caused by an entropic area relation, which involves only labels of the links. The labels of the link carry the size of the Hilbert space that sends information between nodes. How a field is able to allocate bandwidth?
In the viewpoint you are adopting, there is no field. Gravity is "emergent" from more basic stuff.
The illusion or mirage of a field of force is something that appears to us largescale animals who observe the overall statistical collective effect of more basic micro business.
And that's what I am adressing. Certainly there is something that makes distance decrease, even if with neutral charges. More labels shrinks the paths.
Now, using this point of view, it doesn't make sense in "coupling" matter with "gravity", but how bigger the representations the greater the paths are shrunk.
If you mean something more general (as in GR) by the field, then the field is the geometry itself.
That is represented either by the class of the GR metric, or at a quantum level by the spin network itself.
Field = geometry = spin network.
There is no question of needing some other exotic entity called "MTd2 field" to control anything about the spin network. The network is it. It is the dynamically evolving control, if you think of geometry in those terms. (Assuming, as I said, that you mean something more general than some kind of force or particle field.)
No, I didn't mean that.
How a field, like the strong field, weak field, request capacity of a channel?
Does spacetime exist without matter fields?
Does gravity exist without matter fields?
I see. You are wondering how a spin network responds to MATTER fields.
That will be, I suppose, a whole new chapter in the dynamics.
Both the spin network and the spinfoam model will have to be expanded to include matter labels.
Spin networks consist of nodes and links, and the links could carry, for example, lines of flux. Some type of flux lines passing through the area represented by the link. Including matter by further labeling of the links and nodes was already discussed in Rovelli's talk at the Strings 2008 conference.
That goes beyond where I can speculate. I suppose it would mean defining a new, more complicated, spinfoam vertex. A new more complicated Hamiltonian constraint for canonical Lqg.
Not really. I am wondering if a spin network should exist at all without matter, with this interpretation, because all the links should be only due matter fields, forget about adding further structure like flux to accommodate matter fields.
On second thought, marcus, it is very reasonable to think that all labels are due matter fields, if you keep in mind Erik`s prescription that there is no gravity. If there were any label not due a matter field, entropy would have a contribution from pure gravity, which is pure geometry in the point of view of spin networks, even if there wasn`t a graviton in the theory.
So, gravity is about the entropy of the matter fields, but such entropy happen as if they were caused by pure gravity, without matter fields.
It fits your sugestion:
"Spin networks consist of nodes and links, and the links could carry, for example, lines of flux. Some type of flux lines passing through the area represented by the link." Lines of flux whose hilbert space has the size of the link.
It also has the weird sugestion that it doesn`t make sense to talk about emergence of gravity or even as gravity as a force. It seems that gravity is a property suficient and necessary for interaction, and that`s why it appears in spin network scattering calculations, even without matter fields assumed. I speculate that natter field is assumed somehow, if Erik is right.
Mtd2, can you elaborate what your suggestion is? I don't think I understand what you mean except it's something about the relation between matter and gravity and how it emerges.
Here is a question, let me know if it connects to yours?
If the spin-network represents the the quantum state of the gravitational field, then the question is - from the point of view of which observer?
And if we are looking at an observer invariant notion of information state, then what does that even mean?
Two simple questions, less easy to answer, but that appear to be avoided.
IMO - I associate the observer to matter; just like it should be clear, that it makes no sense to talke about measurement theory that is observer independent, it then by association makes no sense to talk about quantum states without matter, just like there is no sense in talking about an information state without a context that serves as a storage device.
Does this relate to that observers as assumed? Sometimes it's like rovelli talkes about sets of observers, and that the states in his model rather represent states of collective of observers. But that would only make sense if the set of observers is static or in equilibrium. When the set of observers (set of physically relevant "reference frames" as opposed to the infinite set of mathematically possible) are evolving, this idea just doesn't make sense to me in the sense that I don't understand how to conenct it to a real information processing agent.
If this had nothign to do with your question then just ignore it.
This point can even be used to re-analyse Einstiens hole argument. The original conclusion (reformulated in more abstract information theoretic form):
1) Either the laws of physics are not observer invariant
2) it makes no sense to talk about physically distinguishable events
There is a problem here becauase if we reject (2) then we also reject in deept sense a prerequisite for measurement hteorhy. This was not a problem for Einstein since he was working with deterministic views. If we reanalyse this argument today... there are more subtle things here that no longer makes sense to me at least.
I think the correct conclusion is that
1) there are no inferrable _objective_ eternal fixed laws
2) there are no _objective_ notion of events; rather each observer has their own "real" but subjective events. And that the only way for two observers to level anything is by means of interaction.
So, IMO, in the light of today I would reject the notion of objective manifold, BUT I would also reject the notion of objectivce timeless laws of physics because no real observer, can be processing information from real measurement reach a 100% confident deduction about that state of hte eternal laws of the entire universe, as the inference processes are taking place in time. And I think this is more than a practical curiosity. It must havec implicuiations also for how we understand the laws of physics.
1.: All observers from the space like slice you have chosen. But that is what is expected, so not really the novelty here.
2.:I don't understand.
3.:Yes, that's what I mean. An observer is the measurement of a node at its links and the node in an instant of time.
4.:Yes. And they are static. I am only talking here about a state of system, a snapshot. Given that an observer is the measurement of a node at its links and the node in an instant of time, it will only exist while the states measured by a node and the node itself are not decoherenced.
1.Yes, sure. This is a concept that is fundamental in experimental physics. There is always the possibility that even newton's laws are wrong at its traditional limits. But the probability is vanishingly small. But what we are talking here is something that is not even speculative, it is best a conceptual discussion. So, I don't think it is useful for 1. But, even if it were a model, you couldn't arrive at such conclusion because this would be just a model.
2.Yes, I agree about this.
I'm not sure I fully understnad your suggest but thanks for your coments.
Wait. I thought we were (or at least I were) probing for a deeper information abstracted view of the spin network. Now you raise the word "slice of space"? I guess what I ask for, is, how does the notion of space, and slice of space, emerge from the inside view?
The question is: How can a given observer, make an inference - given information from it's own interaction history only - that is independent of it's own context? It just doesn't make sense.
Then you picture some approximation right? where we still seek to understnad th non-equilibrium case?
The idea I have is that this makes a measurable difference. The idea is combined with the idea that each finite observer acts rationally on it's available information, in order to maximize it's chances of survival and persistience.
This means also that it's RATIONAL to argue like you do. Ie. the possibility is vanishingly small, therefore we ignore it. This is in line with rational action. I just suggest that this should be formalized and taken seriously.
The conclusion is that the laws of physics have to evolve, as seen by any observer. Locally effectively static laws are simply a local equilibrium, due to local negotiation. The best analogy is with emergence of social laws.
Edit: Humans often act AS IF, "rare events" NEVER happens. This is rational, because the information processing agent has limited resources, and it's simply not rational(from a gambling point of view) to occupy resources for such rare events, as you can use the resources more intelligently.
The action of a given observer, could follow from a rational aciton principle, (in an entropic sense) from it's subjective view of the laws of physics. These evolving laws are possible also a key to unification. So I do not think the points I raised are just conceptual only. I think there are constructive points that could be used to find a better framework.
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