Enumerating the possibilities

[bascule]

Field theories (at least in within my limited ability to comprehend them) operate on space as if it were continuous. The standard model (I think) goes into this category.

 

A new group of theories models space as a discrete structure in the form of an evolving set of relationships. These structures take the form of spin networks or spin foam. Loop quantum gravity goes into this category.

 

BUT! As I understand it, a new class of theories has sprung up modeling space as something between these two extremes. I'm not really sure where to classify these approaches in my head, but they've been described as modeling space as something like a fractal.

 

If the above is correct, I don't know what theories fit into that category. I'm sure Martin has told me before. Can someone name some of them, or inform me I'm full of crap?

[ajb]

Field theories (at least in within my limited ability to comprehend them) operate on space as if it were continuous. The standard model (I think) goes into this category.

 

You mean the underlying space(-time) is continuous? (usually a manifold). Then yes.

 

A new group of theories models space as a discrete structure in the form of an evolving set of relationships. These structures take the form of spin networks or spin foam. Loop quantum gravity goes into this category.

 

Yes, ok.

 

Discrete as in a discrete set (a set with the discrete topology)? Things like causal set theory live in the category of sets. (Avoid calling collections of "theories" a category. A category has specific meanings and I am not sure if these collections are categories)

 

You can leave the category of sets completely and have "point-less geometry". Noncommutative differential geometry is of this kind.

 

I honestly don't know where LQG sits. There are people here who know more about it than I.

 

BUT! As I understand it, a new class of theories has sprung up modeling space as something between these two extremes. I'm not really sure where to classify these approaches in my head, but they've been described as modeling space as something like a fractal.

 

If the above is correct, I don't know what theories fit into that category. I'm sure Martin has told me before. Can someone name some of them, or inform me I'm full of crap?

 

Don't know. Martin will refresh our memories.

[Severian]

You can leave the category of sets completely and have "point-less geometry". Noncommutative differential geometry is of this kind.

 

I honestly don't know where LQG sits.

 

Come to think of it, LQG does seem a little bit pointless...

[fredrik]

Field theories (at least in within my limited ability to comprehend them) operate on space as if it were continuous. The standard model (I think) goes into this category.

 

A new group of theories models space as a discrete structure in the form of an evolving set of relationships. These structures take the form of spin networks or spin foam. Loop quantum gravity goes into this category.

 

BUT! As I understand it, a new class of theories has sprung up modeling space as something between these two extremes. I'm not really sure where to classify these approaches in my head, but they've been described as modeling space as something like a fractal.

 

I don't know of any papers from the top of my head but this seems to be in line with my own personal preference. I think that in a certain sense there does not need to be a contradiction between continous vs discrete structures. But I like to think of the "enumeration of possibilities" as something that ought to be described as a physical process - not a theoretical endeavour.

 

Since I prefer to think in terms of information and learning, to START with a continous index of possibilities just seems wrong, or at best like a speculative hidden structure. My guiding principle is to imagine how a real observer, doing real interactions can LEARN about this continuum. And I suspect that the observers bounded complexity is simply unable to relate to an arbitrarily complex environment. Instead the environment must be "mapped" and indexed from the inside so to speak. In this way of thinking starting out by assuming a massive manifold is a very non-trivial way of injecting information the backdoor. I don't like it.

 

I'm currently thinking about this myself, but is still looking.

 

I am leaning towards the idea that the laws of physics are dynamical and self-assembled in a manner similar to learning. I don't find it sensible to consider universal degrees of freedom, I only find sense in considering observable degrees of freedom, and in that sense it also means the the number of degrees of freedom are dynamical, and can possibly by built from a simple elementa of information by some self-organising logic.

 

Unlike the cellular automata idea, where there is some large microstructure wherein there is self-organisation, I think the microstrucutre itself is dynamical, and there is no global objective microstructure. Or rather, I see no reason to assume there is one. I do not ban it, but if it exists, it is will be emergent.

 

I started reading up on LQG, but took a break and is now reading penrose book. I am not sure I like it. I found that I may not completely agree on rovelli's reasoning so my motivation for further reading his stuff dropped temporarily.

 

As for fractal, I can relate to that if you associate the recursive definition with the self-organisation. But I doubt this rule is deterministic, I think it will be imperfect fractal. But possible perfect on average of something like that. Something like a fractal guided random walk.

 

 

/Fredrik

 

I think that in a certain sense there does not need to be a contradiction between continous vs discrete structures. But I like to think of the "enumeration of possibilities" as something that ought to be described as a physical process - not a theoretical endeavour.

 

Something that has become clear is that different people see the concept of a theory in different ways.

 

I think at least many who work with continuum models doesn't necessarily think there is a physical correspondence to the continuum. The continuum lives in the model, without mandatory physical correspondence. And that not everything in the model is observable.

 

Some choose not to be disturbed by this, but I am disturbed. I see it as a redundancy in the model. It is in this sense, that there might be a discrete model that gives the same predictions and thus really isn't in contradiction. But with some other possibly relative, benefits. What I personally want is to take the theory more seriously. Because ultimately the theory is living in the physical world, one way or the other. It's just that on human level, vs a particle accelerator it might be that we have been able to get away with this.

 

If you consider the "fitness" of a theory, as a viable entitry that is evolving, and possible competing with other theories, it should be suggestive that a theory with alot of redundancy or ghost degrees of freedom is possibly less fit, and is thus less likely to adapt, if you consider the adaption to be a physical process (think computation, which means there is a relation between computing time and complexity)

 

This is also similar to my own preference for such theories. However I think that since the degrees of freedom is dynamical, there may temporarily be a reason for "ghost degrees" of freedom, but with time these should dissipate as their support is lost. During that time I think I would not expect "conservation of probability".

 

/Fredrik

[Royston]

I think Bascule is referring to CDT Causal Dynamical Triangulation (though I could be wrong) it's fairly recent, but maybe there's some new approach that he's talking about. IIRC, CDT is fractal in nature around the planck scale.

 

Way beyond my scope, but hopefully Martin or somebody else can explain CDT in more depth.

[fredrik]

Here are a fairly readable CDT paper. If I am not mistaken(?) there was another thread around somewhere on this where Martin was involved?

 

The Emergence of Spacetime

or Quantum Gravity on Your Desktop

"Is there an approach to quantum gravity which is conceptually simple, relies on very few fundamental physical principles and ingredients, emphasizes geometric (as opposed to algebraic) properties, comes with a definite numerical approximation scheme, and produces robust results, which go beyond showing mere internal consistency of the formalism? The answer is a resounding yes: it is the attempt to construct a nonperturbative theory of quantum gravity, valid on all scales, with the technique of so-called Causal Dynamical Triangulations. Despite its conceptual simplicity, the results obtained up to now are far from trivial. Most remarkable at this stage is perhaps the fully dynamical emergence of a classical background (and solution to the Einstein equations) from a nonperturbative sum over geometries, without putting in any preferred geometric background at the outset. In addition, there is concrete evidence for the presence of a fractal spacetime foam on Planckian distance scales. The availability of a computational framework provides built-in reality checks of the approach, whose importance can hardly be overestimated."

-- http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.0273v2.pdf

 

I read that and I was not convinced that it was something for ME to spend more time on. I like some of the basic motivation, but they are referring to a kind of universality that I find somewhat ambigous and not satisfactory. But perhaps I just don't get it, so I'll recommend reading yourself. I also have issues with their choice of action. If you are to build something from nothing, you need some guide... and in a sense the action formulation is such a guide. But I sense that alot of information gets hardcoded as the action measure is chosen.

 

/Fredrik

 

From their conclusions section...

 

"Starting point (left of the dashed line) is the regularized form of the sum over geometries in terms of causal triangulations, which in itself is unphysical. By taking the continuum limit of this formulation (achieved by fine-tuning the bare cosmological constant to its critical value [20]), one arrives at a continuum theory of quantum gravity."

 

"By construction, if such a limit exists, the resulting continuum theory will not depend on many of the arbitrarily chosen regularization details, for example, the precise geometry of the building blocks and the details of the gluing rules. This implies a certain robustness of Planck-scale physics, as a consequence of the property of universality"

 

They seem to think that they are doing a fair sampling over the space of possible spacetimes.. in some sense... what I fail to understand however is how they knows it's fair. IMO, it looks like a guess, on the level similar to most equiprobability hypothesis that is often made. It's argued that given no observable difference equiprobability is the natural choice. It sounds very nice, but IMO it seems more to be something in line with that given that you don't know, any guess is as good as any. Which is true. But it's a guess nevertheless, which means it's also subject to revision.

 

But I suspect Martin can argue more in favour of the paper than I can.

/Fredrik

[bascule]

Here are a fairly readable CDT paper. If I am not mistaken(?) there was another thread around somewhere on this where Martin was involved?

 

Yep, Martin definitely linked me that same paper, and I tried to read it, and there were pictures!!!, but it's still beyond my understanding

 

Maybe I'll try again...

[fredrik]

Yep, Martin definitely linked me that same paper, and I tried to read it, and there were pictures!!!, but it's still beyond my understanding

 

Maybe I'll try again...

 

Some papers are harder to read than others, in various ways.

 

In some papers the start right a head trying to argue towards a particular goal, and implicitly assumes that the reader is already tuned in, and agree on the relevant questions that should be asked.

 

Other papers are technically difficult and work on an abstraction level that is sometimes also assumed to be known to the reader.

 

Many papers seems to belong to larger research programs, and they don't outline the research program in each paper. And for an amateur not knowing everything, it comes out as cryptic. The starting point and choice of reasoning seems to differ alot.

 

I'm not sure if you see it from the AI view but I am trying to merge information and physics more tighter, and try to connection physical interactions with information processing with focus on observability.

 

I see great AI couplings to fundamental physics, although I'm not a comp guy. The reason is that if you take QM seriously there are a layer of information processing that covers all of physics. Because whatever we learn about nature, and the laws of nature, this information is acquired. And the acquisition process certainly has to put constraints on things.

 

In a "true AI" the brain or computing device of the AI, must evolve too, and selected by fitness. My take on that is that all measures are relative, and that even measures can be assigned physical properties like information. And this may provide a way to unify evolution of matter and life as we normally call evolution, with a kind of evolution of the laws of physics. It could IMHO really be one coherent line of reasoning for all this.

 

The CDT does not attempt any of this as I can see. So if you want anything like the above, I'd keep looking. I have seen that Lee Smolin has expressed a sentiment towards what I inerpret as this direction in various papers. But nothing seems yet mature IMO.

 

/Fredrik

 

About readability I personally see this in two ways... you can read a paper and try to understand what the authors intentions and sentiments are, and acquire an understanding of that... the next step is to from that stance, try to understand the logic of the tentative suggestions outlined.

 

I am personally in a process of reading up on a few ideas, Rovelli's thinking, Penrose thinking and also some others. Often you can share questions, and see the general direction of the research and appreciate it, but still don't understand, or disagree with specific suggestions.

 

But I suspect that since these things are to a large extent open questions, I personally try to focus on the general ideas, and intentions, because this is more fundamental than specific ideas since the specific ideas are born out of these intensions, but in a slightly random process as is oftne the case with learning. But if one traces this down one level, it seems to get more clear.

 

Just reading how a particular person describes the problems, is often more enlightning than listening to speculative solutions without having the context. The solution is I think easier to guess from the formulation of the problem, than the other way around. And the formulation of the problem to me also determines my further motivation. If I don't agree on the questions, I would not be particularly interested in trying to answer those questions.

 

/Fredrik