QG five principles: superpos. locality diff-inv. cross-sym. Lorentz-inv.

Fra

Marcus, thanks for your further comments. I've again been away for a few days and just got back.

As for my own perspective, and it's association to LQG - I seek a NEW intrinsic measurement theory that is also built on an intrinsic information theory, where information is subjective and evolving transformations between observers, (rather than just relational with a structural realism view of the transformations as equivalence classes).

So key points to mer are

1. An INTRINSIC representation of information (ie. "memory" STORAGE)

2. Datacompression (different amounts of "information" can be stored in the same amount of memory, depending on the choice of compression - I suggest the compression algorithms are a result of evolution; the laws of physics "encode" compression algorithms of histories of intrinsic data).

3. The compression algorithms are also information. The coded data is meaningless if the coding systme is unknown.

4. Any given observer, has to evolve and test their own coding system. Only viable observers survive, and these have "fit" coding system. The only way to tell wether a coding system is "good" or "bad" is for the observer to interact with the environment and see wether it is fit enough to stay in business. So there is no objective measure of fitness.

Yes, that ambition fits my view of Rovelli's way of putting it too. I think he wrote somewhere that if we can just find ANY consistent theory that does the job, it would be a great step.

But I do not share that ambition. I think that acknowledging ALL issues with current models that we can distinguish, will make it easier, rather than harder to find the best next level of understanding.

It's in THIS respect that I do not quite find the abstract network interpretation motivated. The MOTIVATION seems to come from the various triangulations or embedded manifold view. Then afterwards it's true that one can capture the mathematics and forget about the manifold motivation, but then the obvious question is, is this the RIGHT framework we are looking for? I am not convinced. Maybe it's related to it, but I still think, if we acknowledge all the obvious points that there should be a first principle construction of the "abstract view" in terms of intrinsic measurements and notions.

When you say getting rid of the manifold, I see several possible meanings here

a) just get rid of the OBJECTIVE continuum manifold

a') get rid of the subjective continuum because it's unphysical, it's more like an interpolated mathematical continuum abstraction around the physical core.

b) get rid of the notion of objective event index (spacetime is really a kind of indexed set of events) (ie. wether discrete or continous). This is already done in GR - the hole argument etc. Ie. the lack of OBJECTIVE reality to points in the event index (if I allow myself to translade the hole argument to the case of a "discrete manifold")

b') get rid of the notion of subjective event index (since we want the theory of be observer invariant; and only talk about EQUIVALENCE CLASSES of observers)

I think we need to do a + a´+ b , but b´ is not possible since it is the very context in which any inference lives. I think Rovelli tries to do also b´and replace it with structural realism of the equivalence classes.

If you understand my argument and quest for an intrinsic inference, this is a sin and unphysical itself. I'm suggesting that the notion of observer invariant equivalence classes itlsef is "unphysical". (some of the arguements are those of smolin/unger)

But I also think that if we really reduce the discrete set of events to the pure information theoretic abstraction, we also remove the 3D structure. All we have is an index, and how order and dimensional meausres emergets must be described also from first principle selforganising.

So I expect the abstract reconstruction of "pure measurements" to start from a simple distinguishable index, combined with datastructures representing coded information, and communication between such structures (where the communication is what generates the index first as histories, then as recoded compressed structures) (*)

(*) I think this is what is missing. The abstract LQG view, is MOTIVATED from the normal manifold/GR analogy, and therefore it doesn't qualify as a first principle relation between pure measurements in the sense I think we need.

/Fredrik

Fra

Even when we do reduce the manifold to measurements, you still keep mentioning notions such as area and volume.

But from a first principle reconstruction - what do we really mean by "area" or "volume"?? I find it far from clear. I'd like to see the "geometric notions" (if they are even needed?) should be constructed more purely from information geometry than what is customer.

I think it needs to be rephrased into more abstract things such as capacity, amount of information, or channel bandwith etc. Then we also - automatically - can not distinguish matter and space of particular dimensions etc. This reconstruction seem to still be missing in LQG.

/Fredrik

atyy

I think GR itself provides some of this. GR is not geometrical. It only is geometrical if you measure spacetime with test partcles and ideal clocks ('observers'). However, neither of those exist in GR, since all you have is the coexistence of various fields (gravitational, electromagnetic etc.). There are no observers, except in certain parts of the universe where they emerge from fields, and are able to approximately isolate themselves and and say here is a test particle and an ideal clock which are not affected by the rest of the universe. What is unclear in classical GR is whether thesde observers can really emerge from the fields.

atyy

This paper the second in a pair of papers, the first http://arxiv.org/abs/0909.4221 is a conceptual summary, the second http://arxiv.org/abs/1001.5147 explains why certain steps like exchanging order of integration and summation are not cheating in particular cases.

I think the interesting comparison is between Ashtekar et al's Eq 3.10 of http://arxiv.org/abs/0909.4221 (same as Eq 3.20 of http://arxiv.org/abs/1001.5147) and Oriti's unnumbered final equation on p5 of http://arxiv.org/abs/gr-qc/0607032, which is the same as Freidel's Eq 11 in http://arxiv.org/abs/hep-th/0505016 .

There are some differences between the proposals, eg. Freidel proposes the physical scalar product to be his Eq 16, which differs from his Eq 11, whereas if you read Oriti's discussion, he is unsure whether it should be Freidel's Eq 11 or 16. It is also interesting to compare Ashtekar's and Oriti's discussions of GFT renormalization.

Edit: I fixed the typo above that marcus pointed out below.

marcus

Again thanks! I think there was a typo in the post. You may have meant:
And in that case you are of course right---same equation.
=================

My main focus needs to stay on Rovelli's April paper, but I will keep intermittently chewing on the two Ashtekar papers and trying to understand them better. Ashtekar has a different perspective and has been a formative and greatly influential QG figure over the long haul. I have to pay attention especially to his overview of the field. Differences in formal detail can work themselves out---I can probably get along with just Marseille notation. But I have to try to assimilate Ashtekar's vision. Both the papers you pointed to have introduction and conclusion overview sections that I'm finding helpful that way.

marcus

We may have a slight semantic difference here. When I think of a theory of geometry, I don't expect of it a "theory of everything" that would explain how life might evolve and how conscious beings able to make measurements and construct clocks might arise from the various matter fields.

All I ask from a classical theory of geometry is that it give me what GR gives----geometries.
A geometry is an equivalence class of metrics (with attendant matter) under diffeomorphism.

So for me GR is the paradigm theory of geometry---it more or less defines for me what geometry is. Granted the theory does not provide its own observers, but it is observer-ready in a kind of "plug-and-play" sense.

By itself a metric (with attendant matter distribution) gives the geometric relations among all material "events" (such as particle collisions). And it determines the world-lines of all "particles".

Admittedly the concept of a "particle" is either a bit ad hoc or a bit fuzzy---we must indulge the theory in small ways, allow it a few marbles. It does not explain or predict the existence of marbles. Or some people prefer clouds of dust---then the grains of dust are the marbles.

But that strikes me as a kind of comical quibbling. A theory of geometry does not have to explain how there could be a freely falling grain of dust. All it needs to be is ready for you to insert a marble or a cloud of dust into its picture of geometry---it will take charge from there on.

This may sound a pretty superficial and unphilosophical but that's how I think of classical geometry.

GR does what it needs to---explains what flat means and why geometry is usually nearly flat (because matter is sparse) and how distances to galaxies can expand and how you can get black holes and gravitational redshift and all that basic geometry stuff that we observe.
Anyway that is my simplistic attitude about geometry.

So your expressed reservation about GR seems like a non-reservation

atyy

It's not a reservation. I take the view that GR is not about geometry, except technically in the sense that all the fields of the standard model are geometrical because of the gauge symmetry. Thus in GR, observable geometry only emerges when one has matter. That, I believe, is the true lesson of GR. The plug and play view is not background independent, because you have test particles that move on a fixed background, without themselves affecting the background.

marcus

Atyy: "GR is not about geometry."
Marcus: "Geometry is precisely what GR is about. GR is the paradigm or model theory in that department."

No basis for discussion there---beyond sterile semantics. We had best get back to Rovelli's paper.

marcus

This will respond in part, as well, to Fra's concerns about the QG agenda.

Several of Fra's posts responded to my couching the agenda in negative terms--a manifoldless QG+M.

To put what I see as the main direction is more positive terms, I'll propose this alternative---a more fully relational QG+M.

This notion of a goal to work towards has been around for decades (I don't know how long). The idea is that GR---the paradigm classical theory---only tells us about the web of geometric relations among events.

There is no substantive objective continuum, because of diff-invariance. One can morph the situation around. Points have no definable identity except where marked by some physical event, like an intersection of worldlines---or some identifiable feature of the gravitational field itself which can mark an event.

So if space is anything, it is an insubstantial web of relationships. To pass to a quantum picture basically means to construct a hilbertspace of webs of relationships, and define operators on it. Or? Do you have some more accurate and concise way to put it?

(looking back at Fra's post #69 I think I may have just now said some things that were contained in what Fra said---except that he went quite a bit further in certain directions---the importance of the observer and information-theoretical considerations.)

================
BTW re Atyy's "not about geometry" comment: Actually GR has matter. You can have dust or marbles adrift on the righthand-side of the main GR equation. In that sense it as plenty of observers already (assuming you do not require observers to be conscious and wear conventional timepieces on their wrists and so forth). If a grain of sand can serve as an observer (and I would argue that it can) then you can put in as many observers as you want---the main equation is set up for it. The effect of those observers will be taken account of in the gravitational field. Logically there is no need for "test particles".

Fra

I don't mean to just provide "negative terms", I actually wanted to drive the discussion in the constructive sense, by providing noting some provocative points with the picture and focus on some foundational issues that exists conflicting between a measurement theory.

It's nothing new as it's related to the problem of what is an observable in GR and QG, but for some reason the points doesn't seem to get the attention I think it deserves.

As far as I understand LQG, this sounds like a good summary of one of it's constructing principles.

But I have an objection to exactly this, but the objection is as much a critique against QM.

My clear conviction is that this is an inappropriate application of QM formalism taking out of context. I suggest that the hilbert space of states of the webs of relations are non-physical as they are not inferrable by an real inside observer. They make sense in the mathematical sense only - and if you accept is as a strucutral realism.

I'm not describing LQG here but I would want put it like something like this (to compromise with your phrasing):

Space, is an insubstantial web of relationships (ie. it's not "material") BUT the information needed to specify this web of relationships is physically coded in matter. Each material system encodes the subjective perspective (up to some horizon).

I further suggest that this picture means that each material observer (matter system) "sees" it's own "hilbert space" (I use quotes as I think this implies a modification of QM as we know it today), and moreoever this hilbert space is not timeless, it evolves with time (where time is just a parameterization of an the entropic flow; which is different to each observer).

Since different observers see different state spaces, that inconsistency is what forms the negotiated consensus and defines the local equivalence classes. So each observers, sees "equivalence classes" of nearby "material observers" whose definition genereally evolve. but one can certainly imagine equilibrium conditions where stable quasi-global classes emerge.

So as I see it the "quantum picture" doesn't involve applying the quantum formalism as is, to the equivalence classes of diff-generated observers, the quantum picture is there from the beginning if we consider the proper discrete measurement theory. What STARTS OUT as a classical measurement theory (ie probability theory, but discrete) gets mixed up by the set of different encoding structures.

The difference as I see it between classical and quantum logic, is that classical logic just uses as simple probability space, where quantum logic uses sets of relates spaces that are related by lossy compressions (such as truncated fourier transforms). This is why logical operators are different.

I agree this is radical and speculative, and maybe it's optimistic to expect anyone bot buy into this long train of though, but the simple point I have is that:

Quantum theory are we know it, are verified only for what smolin calls subsystems. Which means the cases where the statistics and hilbert spaces can be effectively constructed and encoded in some lab environment before the entire environment has completey evolved into something different.

And some quite simple plausability arguments, and the quest for everything to be inferrable in the inductive rather than deductive sense suggest that the application of normal QM formalism to the equivalence class of GR observers in the suggested way may be the wrong way to approach the entire "QG" problem.

Note sure if that made sense? Because I have also deep concernts about QM foundations, it's not possible to comment on QG without getting into that as well.

/Fredrik

Fra

To try to make cleaner how we disagree.

"Since different observers see different state spaces, that inconsistency is what forms the negotiated consensus and defines the local equivalence classes."

LQG tries to make a "regular QM theory" to the STATES of the equivalence classes.

I think that we need to find the EVOLUTION of the SYSTEM of interacting observers.

So I guess what I say is that we need to make QM truly relational, like Einstein made SR into GR. Not, try to apply QM as we know it to the classical equivalence classeso GR. I think it's a mistake.

So I think we are seeking "Einsteins equation" for the relational QM. To apply non-relational QM formalism to Einsteins equation is not right.

So I'm suggesting that hte equivalence classes and their symmetries must be evovling, and that this pictures includes ALL interactions. Thus Strong, weak and EM as well. It's not something we can put "ontop" of the pure-gravity quantized. It makes no sense to me.

/Fredrik

atyy

So this would argue for unification, something like strings? In strings the graviton is sometimes a particle caused by an excitation of a string, but if you change your view it can become part of the background spacetime - and it can go the other way too, the background can become an excited string state about a different background.

Fra

Unification yes, and there are some ways for me to relate this construction to ST, but ST has many unsatisfactory traits. An certainly something is missing in the construction principles.

- ST makes use of the continuum, not only the manifolds, but maybe worse the string itself (which I view as a continuum index). This is highly unphysical and doesn't fit into the picture of a physical representation.

- ST have the same simple view of QM. So it does not solve the intrinsic measurement problem and coding of information problem of QM. ST is not the reconstruction of measurement and representation from the combinatorical perspective I think we need.

The second problem, is btw, what forces the higher background dimensions as it's the only way to "encode" all the variety ST wants to. But the problem is then that you do get this landscape that you don understand what it is. Is it real, is it an illusion? And why is there measure on the landscape?

From my point of view, some of the problems of ST might be gone if they replace the string with a more generic "set of sets" in the datacompression sense I mentioned before, that work from discrete indexes. But then, it just isn't string theory anymore.

Not to mention the action of the string, which is basically inherited from classical analogies.

In my view, all actions are generically related to probabilities or information divergences. The "action" is simply the generalized "entropy" in transition space, which is to be maximized. So all action forms should follow in this way (thus beeing inherently entropic).

There is a chance that "string like" structure, prove to be the simplest possible continuum structures in the large complexity limit, but that is still just a possible connection and the logic there is nothing like the logic of the string program.

Somehow, rovelli's reasoning as I've read it, although I object to it, is at least more clear and consistent that the string scheme which I find to be more of toyery.

/Fredrik

Fra

Generically this makes sense to me, and it would correspond to comparing two different observers. Just like any conditional assessment depends on perspective.

So such a general trait is I think sensible.

The Background should be part of the observer. The problem is that the way ST is constructed, the background complexity is not bounded. First of all because it's based on a continuum index, and it becomes highly ambigous IMHO at least how to COUNT and compare evidence in uncountable sets. The choice of limiting procedure becomes crucial. But no care is made about that in ST. The worst part is that the continuum itself is part of the baggage, and already there you have lost control before you've started as the counting procedure (from inference poitn of view) becomes more or less completely ambigous.

/Fredrik

atyy

Yes, I can never decide which I'd like better. On the one hand, it'd be nice if we only used integers in the formulation of the most basic theory. On the other hand, there are cases where discreteness emerges from the continuum - say eigenvalues in quantum mechanics - or non-relativistic quantum mechanics of atoms from relativistic quantum field theory.

Fra

I see what you mean. I think there is not really a conflict per see between continuum models and discrete ones, it's just that I think it's important to keep in mind from the point of view of inference and counting and rating evidence (inductive reasoning) what the physically distinguishable states are and what is "gauge".

By certain transformations (I'd like to call them datacompression) one can from limiting cases or continuum models compute key parameters that are independent from superficial embeddings or interpolated structures, that can be further used to "index" the continuum structures, maybe even in a countable way.

That's fine as long as we keep track of what the physically distinguishable states are, and what we should count. I prefer to start with the "backbone" and then picture this as indexing a continuum manifold if we need it for comparasion to old models, rather than start with a redundant description, get lost and try to figure out what's physical degrees of freedom and what's just continuum gauge.

For example when you start with a continuum structure, and try to apply inductive inference, construct various entropy or action measures, then it's crucial that we know how and what to count. In a continuum picture, by an ambigous choice of limiting procedure or measure one can pretty much get the results one wants.

This is even more important if one (like I want to) wants to construct also the expected action of this "observer complex", as they way I picture it, the prediction and computation of "probabilities" requires that the state spaces and transitions are countable. Actually finite, or if infinite, at minimum countable and have a well defined limiting procedure. Otherwise the physical measures are not computable.

/Fredrik

marcus

As we were talking about Rovelli's April paper in some other threads I was impressed by the level of misinformation/misunderstanding.

This is the paper that presents LQG in a manifoldless way giving it a "new look", as Rovelli's title indicates. Of course there is no distinction between canonical LQG and spinfoams here--those approaches were unified earlier. Network and foam are indeed inseparable but that is not what is new.

Someone in another thread stated with great confidence and authority that this version of Lqg had nothing to do with the Einstein-Hilbert action . (The Regge action is the relevant version of E-H, and is derived from the setup.)
Another person flatly stated his conclusion that the April paper merely presented a new spinfoam vertex. We need to get past a wall of ignorance/selective inattention. There is a kind of sea-change in progress---a general shift in the qg picture-- making it more important to be well informed.

In that other thread, Tom responded with a concise and helpful summary of what is happening in the April paper (1004.1780) the topic of this thread, so I'll copy here: