Does LQG Do Nothing Cool Even If It Is Right?

[Jimster41]

Trying to read some of these amazing papers - Do I understand correctly that these are ways of modeling how "space-time" atoms "proceed" or become events. But that they are not trying to address what they "contain".

For the Energetic-Causal Sets, Is the idea that the energy-momenta values are somehow non-zero to begin just a starting assumption.

Similarly for the Spin Foam model, what allows the the volumes of the tetrahedron (the mass?) to be non-zero to start with?

From what comes the pool of "un-ordered events"

Is the tacit assumption just ... Our universe got "non-zero" stuff from the big bang...we are interested here in understanding how the stuff we got works, not where it came from (mostly because we can't possibly speculate on that).

Or am I missing the way these models somehow really do obviate the need for that mysterious initial "content, potential, momentum". If this is the case, then I have to do a reset on my estimated level of confusion...

 

[marcus]

Jimster your questions and comments are a big encouragement to me to try to understand better. thanks! I think we are just at a preliminary stage of understanding nature's existence (as an ongoing process, never mind about beginnings : ^). Also I can only give my non-expert point of view, as someone who is fascinated by the stuff these professional researchers are working on.

There's a tentative merger between the two approaches (Causal Sets and Spinfoam) and as I see it both model ongoing process without attempting to say where it "came from" or why existence exists.

An important difference is that Loop cosmology has a BOUNCE at the start of expansion. When the Loop-Spinfoam people run their models back in time (essentially quantum versions of General Relativity and big bang cosmology) instead of breakdown at a "singularity" considered an unnatural glitch they find a rebound and a prior contracting phase of the universe.

This does not answer an ultimate question---it doesn't explain why existence exists, obviously. It just gets rid of the singularity where the classical un-quantized GR model broke down. In the quantized model, quantum effects come into play at extreme density and make gravity repel. Geometry (like other aspects of nature) has a kind of Heisenberg Uncertainty behavior and resists being "pinned down", so there's a rebound. Instead of contraction causing time-evolution to end, there's a bounce. Spinfoam QG is an outgrowth of LQG and presumably would share this feature if applied to cosmology.

But Causal Sets doesn't have that feature! And the new "Energetic" version of Causal Sets? I think it is very new and we can't say what it will look like a couple of years from now. I can't foresee. What I would LIKE to see is surely irrelevant, but i might as well tell you. I would like to see a successful merger which would see ECS acquire the bounce cosmology feature and become a new version of LQG perhaps called by the name which Cortes and Smolin offered, namely Causal Spin Foam.

"In exchange" so to speak, Loop/Spinfoam QG would get the growing universe ontology discussed a couple of posts back in post #35. IOW a physical representation of the present moment and the progress of time.

 

[Jimster41]

Thanks again for the assistance Marcus. I appreciate the catalog of threads you provide, it's really a useful guide. I saw the reference you made to the Bounce vs. the infinity problem at Planck scales. I do understand this has been the big thorn in the sides of QM and gravity(GR). I'm going after those papers now.

I'm a little bit confused that Cortes and Smolin start with a conserved Minkowski metric for momenta and then derive relativistic space-time as an emergent process by chaining events under that constraint? Is that a bit circular... Is it meant to be?

Regarding momenta having content, I keep imagining that Verlinde is saying that somehow momenta are non-zero because of entropy? I interpret him as saying you could start with the same rules as ECS, but zero values for momenta, add a bleed term ("our entropy") that has to be accounted for somehow, like a certain momentum change across all chains of n events (but no one event or specific event chain), and you would get "emergent" non-zero momenta - space-time atoms with mass and energy - per ECS. He's saying entropy is a force that affects/creates momenta?

I am looking forward to reading about about the bounce. I think it will help.

 

[marcus]

...I'm a little bit confused that Cortes and Smolin start with a conserved Minkowski metric for momenta and then derive relativistic space-time as an emergent process by chaining events under that constraint? Is that a bit circular... Is it meant to be?
...

That's an interesting point. It does seem a bit circular, albeit not entirely so. One starts with a feature of the "atoms", they then interact and a global reality is woven...and that global reality presents that same feature in the large. On the one hand it seems trivial, but it may not be as circular as it seems.

 

[marcus]

I think there are two ways of looking at this convergence of ECS and LQG (causal spin foams). One way, which is how I look at it, is that it represents a major new development in LQG (a "growing universe" version, the present/passage represented, Wieland's new action)
The other way is to see it from the perspective of Smolin Unger's new book: the idea that the laws of physics themselves evolve.

I will briefly sketch what I have seen of this new book, which has not come out on the market yet but is described in the Cambridge U.P. catalogue.
http://www.cambridge.org/us/academic/subjects/physics/history-philosophy-and-foundations-physics/singular-universe-and-reality-time-proposal-natural-philosophy

One could overschematize and say that the reason Smolin wants time and change to be represented in the theory as a real fundamental process is that he wants the very rules of the game to be continually evolving according to a deeper simpler rule.
He wants the regularities which we think of as the laws of physics to be explainable as having evolved (having become habituated by repetition, survival, and the accumulation of precedent somewhat as happens with human civil law). The laws of physics are to have evolved, then. Evolved over what? Evolved over TIME! Ahah, then time must be real and fundamental, not merely emergent or a phantom of our imagination.

 

[marcus]

I'll copy some catalogue description to have it handy for us:
==quote Cambridge UP catalogue "The Singular Universe" Smolin&Unger==
Description
Contents
About the Authors

• Cosmology is in crisis. The more we discover, the more puzzling the universe appears to be. How and why are the laws of nature what they are? A philosopher and a physicist, world-renowned for their radical ideas in their fields, argue for a revolution. To keep cosmology scientific, we must replace the old view in which the universe is governed by immutable laws by a new one in which laws evolve. Then we can hope to explain them. The revolution that Roberto Mangabeira Unger and Lee Smolin propose relies on three central ideas. There is only one universe at a time. Time is real: everything in the structure and regularities of nature changes sooner or later. Mathematics, which has trouble with time, is not the oracle of nature and the prophet of science; it is simply a tool with great power and immense limitations. The argument is readily accessible to non-scientists as well as to the physicists and cosmologists whom it challenges.
  ==endquote==

 

[marcus]

Quote from TOC
http://www.cambridge.org/us/academi...ity-time-proposal-natural-philosophy#contents
Introduction
Part I. Roberto Mangabeira Unger:------------------------- -1
1. The science of the one universe in time----------------- 5
2. The context and consequences of the argument------ 46
3. The singular existence of the universe----------------100
4. The inclusive reality of time----------------------------162
5. The mutability of the laws of nature-------------------259
6. The selective realism of mathematics-----------------302
Part II. Lee Smolin:---------------------------------------------------- 349
1. Cosmology in crisis------------------------------------------------- 353
2. Principles for a cosmological theory----------------------------- 367
3. The setting: the puzzles of contemporary cosmology---------- 393
4. Hypotheses for a new cosmology--------------------------------- 414
5. Mathematics--------------------------------------------------------- 422
6. Approaches to solving the metalaw dilemma------------------- 447
7. Implications of temporal naturalism for philosophy of mind-- 480
8. An agenda for science---------------------------------------------- 484
9. Concluding remarks------------------------------------------------- 500
A note concerning disagreements between our views.------------ 512

A more detailed TOC listing topics under these headings is available online as PDF here:
http://assets.cambridge.org/97811070/74064/toc/9781107074064_toc.pdf
If anyone wants to get an idea of how the book goes and the points they are making, I would suggest reading parts of this detailed TOC because the many subheadings (which I do not show here) are like the topic sentences of successive paragraphs and clarify the main themes of each section of the book.
An excerpt from the first part of Unger's section of the book is here:
http://assets.cambridge.org/97811070/74064/excerpt/9781107074064_excerpt.pdf
To get a preliminary idea of what Smolin, on the other hand, is saying one can find PIRSA videos of several of his seminar talks by googling "pirsa smolin"

 

[Jimster41]

Thanks Marcus, once again I greatly appreciate the introduction to sources. I'm going to read it as soon as it's out and I look forward to talking about it here.

I tried to get into the paper on the implications of LQG for Inflation and bounce http://arxiv.org/abs/1301.1264. Got caught out wondering if we did run a model into the "universe" before ours, would we have any idea we were there, If there's no singularity to define the edge? I know that's a bit goofy but it's distracting... Also, just can't get past the way the FLRW is already talking about mass. It just leaves me wondering where to go to find out where that mass came from.

I hope I didn't sound like I was trying to suggest the emergence of relativistic space time from the rules given by ECS (Cortes&Smolin) wasn't pretty shocking... My eyes popped out, even at the ideas they are proposing.

And I don't mean to try and diminish it when I sort of interpret it as a successful test of the ability of the ECS model to create emergent local reversibility, and relativistic dynamics, things they seemed heavily focused on in the first paper. I can imagine failing those tests with ECS and rules 1 and 3 would have provided a pretty solid "go back to the drawing board" - and that passing them provides a foothold from which to continue on.

And maybe I'm jumping the gun or misunderstanding but I can't shake the idea, which I keep getting from Verlinde somehow, and about which I think I am looking forward to reading in the coming book you reference, that Causal or Evolutionary Sets probably don't need the specific solution-like assumptions of rules 1 and 3 because some simpler set construction rule might provide emergence of those exact features. (As I thInk you also suggest in an earlier post).

One thing has been bugging me a lot though, about the "Causality" rule of ECS. What about quantum entanglement and "spook-like action at a distance", EPR Paradox and Bell's theorem? Hasn't it been shown unequivocally that there is non-locality, a-causality, when events are constructed a certain way at least?

Ooof. I have a headache now. Need beer.

 

[marcus]

Jimster, I wish there were a more knowledgeable and alert person than myself around at the moment to reply to you. I'm intrigued and stimulated by your questions but I'm not equipped to give confident/useful answers. I want to make it clear where I stand as regards the Smolin Unger book, and since we've turned a page I'll bring foreword my posts #37 and #40 to make the point. I think their book is something to know about but I personally do not follow their line of thought about evolving physical law.
They could be right! Laws of nature may have evolved. But as I see it we do not understand well enough how they are at present to productively consider the question of evolution. There is a right time to ask questions, one needs to focus on what is ready to be asked. So I want to know about this new book and share what I know of it, but I do not want to recommend it to you. My focus is on the development of quantum general relativity. The quantum theory of geometry and matter. I am "old school" in that I think of the laws of nature as (approximately) immutable and I do not try to explain why they are what they are and not something else. I trust that if they change it is so slowly that it is practical for us to try to discover them as if (for all practical purposes) they are static, eternal and inexplicable. They are the laws and they just are.

So what excites me about the seeming convergence (even collaboration) of Wieland's spin foam model and the ECS of Cortes Smolin does not have to do with evolving natural law. It has to do with something much simpler, but still very beautiful. The representation of "now" (and the passage of time) in Spin Foam QG. It has been called "causal spin foam". Wieland's action, with the swarm of interacting tetrahedra, appeals to me enormously. I want it to be verified that when this model is applied to cosmology one gets the bounce, as one gets with other versions of LQG.

I'll quote posts #37 and #40 to emphasize this "old school" attitude:

... I think we are just at a preliminary stage of understanding nature's existence (as an ongoing process, never mind about beginnings : ^). Also I can only give my non-expert point of view, as someone who is fascinated by the stuff these professional researchers are working on.

There's a tentative merger between the two approaches (Causal Sets and Spinfoam) and as I see it both model ongoing process without attempting to say where it "came from" or why existence exists.

An important difference is that Loop cosmology has a BOUNCE at the start of expansion. When the Loop-Spinfoam people run their models back in time (essentially quantum versions of General Relativity and big bang cosmology) instead of breakdown at a "singularity" considered an unnatural glitch they find a rebound and a prior contracting phase of the universe.

This does not answer an ultimate question---it doesn't explain why existence exists, obviously. It just gets rid of the singularity where the classical un-quantized GR model broke down. In the quantized model, quantum effects come into play at extreme density and make gravity repel. Geometry (like other aspects of nature) has a kind of Heisenberg Uncertainty behavior and resists being "pinned down", so there's a rebound. Instead of contraction causing time-evolution to end, there's a bounce. Spinfoam QG is an outgrowth of LQG and presumably would share this feature if applied to cosmology.

But Causal Sets doesn't have that feature! And the new "Energetic" version of Causal Sets? I think it is very new and we can't say what it will look like a couple of years from now. I can't foresee. What I would LIKE to see is surely irrelevant, but i might as well tell you. I would like to see a successful merger which would see ECS acquire the bounce cosmology feature and become a new version of LQG perhaps called by the name which Cortes and Smolin offered, namely Causal Spin Foam.

"In exchange" so to speak, Loop/Spinfoam QG would get the growing universe ontology discussed a couple of posts back in post #35. IOW a physical representation of the present moment and the progress of time.

I think there are two ways of looking at this convergence of ECS and LQG (causal spin foams). One way, which is how I look at it, is that it represents a major new development in LQG (a "growing universe" version, the present/passage represented, Wieland's new action)
The other way is to see it from the perspective of Smolin Unger's new book: the idea that the laws of physics themselves evolve.

I will briefly sketch what I have seen of this new book, which has not come out on the market yet but is described in the Cambridge U.P. catalogue.
http://www.cambridge.org/us/academic/subjects/physics/history-philosophy-and-foundations-physics/singular-universe-and-reality-time-proposal-natural-philosophy

One could overschematize and say that the reason Smolin wants time and change to be represented in the theory as a real fundamental process is that he wants the very rules of the game to be continually evolving according to a deeper simpler rule.
He wants the regularities which we think of as the laws of physics to be explainable as having evolved (having become habituated by repetition, survival, and the accumulation of precedent somewhat as happens with human civil law). The laws of physics are to have evolved, then. Evolved over what? Evolved over TIME! Ahah, then time must be real and fundamental, not merely emergent or a phantom of our imagination.

Let's see if the quote mechanism worked, and how this looks. It worked, I used the "+Quote" button at the lower right of each post to "add as quote", selecting the two posts, and then when writing this I clicked on "insert quotes" button that appears at the lower left of the space for writing when you have previously selected stuff to quote.

 

[Jimster41]

I apologize for not listening more carefully Marcus. By way of excuses, I have only that - as I started trying to Grok the Weiland paper I encountered immediate failure. There are just so many symbols and terms that refer to the vast canon of mathematics that I am immediately in a glossary swarm and my short term memory is insufficient to support any imago whatsoever of the model. This is just pathetic, because the stuff can be known. I just don't have the background. It's so daunting and I'm impatient. Thank god for Wikipedia.

Just to clarify (and agree I hope) I was thinking of the up-coming book more as an opportunity to connect to you and others here in a linguistic space around concepts related to the work going on in the canon of mathematical physics, so I might better understand the latter.
If there was one that might provide similar footing around CSF, or LQG I'd be totally interested.

Like you I am pretty uncomfortable with the notion of the laws of physics as we know them... changing. That doesn't seem that interesting, since they are static for all practical purposes for us... I'm more interested though in the way that they could be shown to be emergent, as we have them, from some background process that is more fundamental. This seems more about illuminating distant surroundings (and sources) than making reality some kind of unstable trip, which clearly it isn't. (Though I have to admit I've read enough sci-fi to wonder what might happen if we figured out that gravity is a function of information - somehow partially independent or a-priori at least, of mass and energy)

To do better at listening! I am taking your recommendations above...
And trying again (harder) on Wieland http://arxiv.org/abs/1407.0025v1 and also Cortes and Smolin http://arxiv.org/abs/1407.0032v2

I get the image of the CSF (Causal Spin Foam) better after a few runs at the first few pages of both (Cortes and Smolin is more accessible for me - and has allowed me to get further on the Weiland paper). In my imagination I see CSF connecting, how did you put it? "the sky high" notion of Causal Sets to a well developed model proven to describe (at least partly) fundamental particles and their interactions (Abelian Gauge Group?) if this is correct, I can see why that is a very useful reference against which to measure the former, and why the integration of the two would be profound and thrilling.

I also have harvested some additional papers from the references of the two mentioned here and also from your on-going thread on "Intuitive Loop Rovelli's... etc".

With Regards
Jimster

 

[marcus]

No apology called for! I didn't mean my post in any sense critically. Just wanted to make my personal "old school" view clear to anyone who happened to be reading. I also find the technical part of Wieland's paper tough going, and it helps me to do two things: spend more time mulling over the NON-technical parts where he says what he is doing and communicates more intuitively instead of with equations, and secondly to read Cortes Smolin along with it (even though I don't necessarily go along with the evolving laws part of their larger program).

I had an idea today that the two of us (plus whoever else wanted to join in) could start working on tutorial material about some basics like the PACHNER moves. Pachner moves are how, in Wieland's model, the swarming tetrahedra interact, giving rise to the next generation of Tets.
Pachner moves are important in a lot of geometry (differential, piecewise linear, anything involving triangulations which includes a lot) and its a beautiful simple idea you can do in any dimension. We could talk about Pachner moves in 2+1d and then move up to 3+1d by analogy.

I'll look up Pachner and see who he was.
==quote==
Pachner moves
From Wikipedia, the free encyclopedia
In topology, a branch of mathematics, Pachner moves, named after Udo Pachner, are ways of replacing a triangulation of a piecewise linear manifold by a different triangulation of a homoeomorphic manifold. Pachner moves are also called bistellar flips. Any two triangulations of a piecewise linear manifold are related by a finite sequence of Pachner moves.
Pachner, Udo (1991), P.L. homeomorphic manifolds are equivalent by elementary shellings, European Journal of Combinatorics 12 (2): 129–145
==endquote==
They are so simple that it amazes me they were not identified by mathematicians until the 1990s!

 

[marcus]

the challenge is to describe a simple pictorial idea without scratch paper or a black board, just using words.
In 2D the simplices are triangles and there are 3 Pachner moves.
2 --> 2 means for example two triangles joined along a NS edge are merged into a diamond shape and re-divided on a EW line. So you again have two triangles.
1 -->3 means one divides into 3, you put a point somewhere inside the first triangle and draw lines out to the corners, and cut into three.
3--> 1 is just the reverse, you take 3 triangles which all share a single vertex and they merge along the three sides radiating from that vertex, and then you remove that vertex which is no longer needed, and you have a single larger triangle.

The nice thing is that each of those moves corresponds to a Tet in 2+1d
1-->3 is like a Tet sitting on its flat bottom triangle, process time is upwards, process comes in the base triangle and branches out into the 3 upwards slanting sides
3-->1 is like a Tet balanced on a single vertex, the first picture turned upside down. process comes in the 3 bottom triangles and goes out the top
2-->2 is like a Tet balanced on an edge that runs NS. Two downwards facing triangles meet at that edge and two upwards facing triangles meet at a horizontal EW running edge. The process comes in the two lower and goes out the two upper.

The elementary interactions of triangles are mediated by tetrahedra. If the world were 2+1d then Wieland's action would involve a swarm of triangles interacting and constantly remaking themselves and by their interactions they would create the tetrahedra of 2+1d space-time.
=============
Dual: taking the dual of a "triangulation" (really a tetrahedralization) of 2+1d space-time means to replace each Tet by a point (a node) and replace each of the triangles which are sides to that Tet by line segments or links radiating from that point. So the dual is a kind of network where the nodes have "valence" equal to four. Unless they are at the boundary but let's imagine there is no boundary and not worry about such nodes.

I have to write Tet with a capital T because otherwise the spellchecker tries to change it to "get"
and if I write Tets without capitalizing it thinks I meant to write "test" and fixes it for me.
Hope its OK to capitalize

The official name for a 4d analog of a tetrahedron is a PENTACHORON. choron means a 3d space or room, just like heron means 2d side or wall.
We can say Pent for short. A Pent (or "4-simplex") has 5 sides each of which are Tets. 5 Tets surround a Pent. Just like 4 triangles form the boundary of a Tet.

Here are some basic interactions of tetrahedra:
1 --> 4 put a point inside the Tet and draw lines radiating out to each of the 4 vertices, you see how it divides into 4 Tets.
4 --> 1 take 4 Tets that share a vertex and merge them and reverse the 1 --> 4 process, to get one single Tet
2 --> 3 join 2 Tets along a horizontal triangle side...one points up and one points down. run an axis straight down from N pole to S pole, cut into 3 Tets. Like cutting an orange into 3 sectors, each 120 degrees of the full equatorial circumference.
3 --> 2 (have to go do something for wife, back later)

Back now. Anyway those four moves are all the Pachner moves for Tets. They are all the basic changes in a 3d triangulation. All the other triangulation changes, Pachner showed, can be gotten by repeating those four moves. The result of 2-->3 produces three Tets that are a bit funny looking. Each has one very long edge which was the N to S axis down the middle, and one relatively short edge which used to be out at the equator and is perpendicular to the axis. It runs EW.
You might want to sketch this 2-->3 move.

 

[Jimster41]

Very intersting Marcus, and helpful. You have supplied more than I had been able to glean from the C&S diagrams.

In the first two paragraphs where you translate the three move cases to tets,I think I must be missing a trick in the mind's eye cause I get the first two cases switched, when I read it, compared to what I see. I will give it another shot in the morning.

That said, to a first approximation at least I am now tracking the tets as moves or "events" in a three space, and I kindof believe those are the only ways to go from 3n triangles to more or less triangles with continuity. And I get this is a way of talking about action in state space.

I'm going to give his intro paragraphs another read tomorrow and try to collect some questions that I think are mostly due to lack of familiarity with terms. Like what does he mean by "first order gravity". I thought first order generally referred to the first derivative. I got confused right there before he even mentioned "lattice". At least I can picture a lattice.

 

[julcab12]

I made a quick animation 1-4 move during my free time(hope it's correct/ Evolution not included).



2-3 move. Ill try to animate a "Causal spin network evolution" soon. Any suggestion is welcome.^^

 

[Jimster41]

Those are really cool.

I think I could really use a remedial version, like one animation of Marcus 2d (triangle case) case. It's the introduction of process time to state evolution in that case that I need a key for. I can follow the process of your 1-4 evolutions just in terms of breaking and making triangles from/to triangles or tets from/to tets. But I'm having a hard time understanding how the sequence of process time is flowing through the state changes, and how the value constraints on the states play into it.

Do I understand correctly that the division into more states, or integration into fewer states, is tracing the possible paths of evolution of a set of states? It's combinatorial right?

But for instance in the 1-3 triangle case, if my 2d coordinates can only take 2 values (say 0 or 1) how do I divide 1 triangle defined by {01,00,10} into three triangles?

Sorry to be dense about it. That's my problem... I can understand things eventually, but in no way fast...

 

[marcus]

Those are really cool...

Yes! It's great to have the Julcab animated diagrams! It's an immediate "like", for me. I'm embarrassed to say I haven't even learned how to make still (non-animated) online diagrams. Jimster, what you say about getting a better understanding of the 2+1d case makes much sense. I looked back at Cortes Smolin July paper and realized they do a really good job of explaining Pachner moves, even just in words without their diagrams. They say it better than I did so I want to quote from their page 4, to have it in front of us.
==quote Cortes Smolin page 4==
2+1d Spin Networks

• Causally evolving spin networks are constructed from evolving states by one of a set of local evolution moves. In 2+1d a state is represented by a triangulation of a space-like surface. An evolution move is a discrete time step called Pachner move. Each Pachner move performed on the spatial slicing corresponds to an event.
• Each triangle in the spatial triangulation represents a locally flat piece of 2d space. The triangulation is dual to a three-valent spin network Γi embedded in a topologi- cal two manifold Σ. The center of each triangle is dual to a node in the spin network, and labeled by intertwiners. The sides of each triangle are dual to edges in the spin network and labeled by SU(2) spins.
• From this triangulation we evolve to the next state by adding tetrahedra on top of it. There are different kids of moves, each represented by a way to cover one, two or three adjacent triangles with the faces of the tetrahedra. For example, a so called 1 → 3 move is made by adding one more point to the future of a given triangle, which creates a tetrahedron. The initial triangle makes up the bottom (i.e. past) side of the tetrahedra. This triangle is now replaced by the three new triangles making up the top, or future, side of the tetrahedron. This tetrahedron represents the Pachner move and so generates the time step.
  
  The tetrahedron is formed by 4 glued triangles, part of these in the current spatial slice, the past, and part of these in the new spatial slice, the future. Splitting the 4 triangles in the tetrahedron between the past and future slices gives origin to different Pachner moves, and in 2+1d there are different 3 possibilities
• In 2+1d the available Pachner moves are 1 → 3 triangles, 2 → 2, and 3 → 1. If the tetrahedron is placed on top of one triangle in the current triangulation then that triangle is in the past slice and the three remaining triangles become part of the future triangulation, forming a 1 → 3 move, which we show in Figure 1 in the dual spin foam/ dynamical triangulation representation. If it’s placed on top of two adjacent triangles in the current triangulation, then the two complimentary triangles in the tetrahedron become part of the new representation, forming a 2 → 2 move, shown in Figure 2. Finally, if it’s placed on top of three adjacent triangles in the existing triangulation, the remaining triangle becomes part of the new triangulation forming a 3 → 1 move. This is just the reverse of the 1 → 3 of Figure 1.
  

The Pachner moves are repeated many times over, creating a causal spin foam SF. In the language of ECS introduced in Section 3 the Pachner moves represent events, VI . Each tetrahedron VI is an event. ...
...
=====endquote====
Understanding the Pachner moves by which the triangulation of a surface can evolve into a different triangulation won't solve all our problems!
: ^) Life isn't ever that simple. But it is a good first step. The idea of COVERING one two or three triangles with a Tet is good. Placing a Tet is the same as performing a move.
The moment you place even one Tet you have covered up one or more old triangles and you have now a new surface with one or more new triangles replacing the old.
We can imagine that the surface is curved in a discrete humpy bumpy way so there are grooves, pits and crevasses where one can place a Tet that covers two or three triangles. And we can imagine the Tets are made of some elastic material so we can squash them to cover two or three triangles even if the surface isn't all that crinkly and crumpled.

But even if you start with a flat surface triangulated with equilateral triangles all the same size, and your Tets are all the same shape, and you start placing Tets down, you can see how it would evolve into a highly irregular surface. Your first moves are all going to be 1-->3 because the surface is so flat that's the only way the Tets will go down, just covering a single triangle.
But as soon as you have placed two Tets side by side next to each other you have created a canyon where you can make a 2-->2 move by placing a Tet with its edge down in the canyon, covering two triangles. So the more you play this covering game the more complicated the surface gets and the more opportunities you have to make different moves.

So we can say that the geometry evolves. The 2d surface acquires geometric character and is no longer merely flat.

I think what these people (Cortes Smolin Wieland, maybe others) are saying first of all is "Let's look at this in two different ways."

Let's look at it as a story about a MILLING CROWD OF TRIANGLES that are constantly being destroyed and created as they interact, as they join and divide. Let's make the triangles the protagonists, and the Tets are merely a record of their INTERACTIONS. So 2d geometry evolves, wrinkling and unwrinkling every which way.

Or alternatively let's think of 3d SPACETIME AS MADE OF INTERACTIONS. Spacetime (this 3d toy version of our real 4d spacetime) exists and it is made of Tets, and it GROWS as the Tets pile up and get covered by other Tets as you play the game.

 

[marcus]

And then a kind of important idea by Rafael Sorkin comes in, that says "two such processes will be considered equivalent if they have the same family tree". This he argues is what is analogous (in this discrete game) to general covariance in the smooth GR case.

And it is what allows allows the theory to avoid getting stuck with a global time. The big concern here, always looming in the background, is the need to avoid stumbling into a commitment to a preferred time. Because we learned from SR and GR this is a no-no.

So what does it mean for two of these processes to have the same family tree. It means it does not matter in which order you put down the Tets as long as the same interactions eventually occur. the same two triangles eventually mate to produce the same two offspring. the same three eventually merge to make one, etc.

You know in your family's tree it does not matter whether you or your cousin was born first or which of your sister's kids was born first or married first, as long as the tree is unchanged. If all the interactions that are supposed to happen eventually do happen, the tree looks the same.

Sorkin in a 2007 paper Relativity theory does not imply that the future already exists: A Counterexample, a chapter in the book Relativity and the Dimensionality of the World edited by Petkov [ http://arxiv.org/abs/gr-qc/0703098 ] uses the image of an organism growing at many different locations so that the growth events are space-like separated and one cannot, in principle, say which occurred first.

What these people are driving for could be called a "growing universe ontology" where existence is able to grow and we can represent this in a model without accidentally committing us to a preferred global time.

There was that paper by Fay Dowker that you get by googling "Dowker passage" and another paper by Ruth Kastner that came out recently and I gave a link to earlier in this thread.
https://www.physicsforums.com/threa...ven-if-it-is-right.775104/page-2#post-4910170
I guess you could also get the Kastner by googling "kastner emergence causal" or "kastner spacetime causal" some such tag.

The Sorkin paper can be gotten by googling either "sorkin counterexample" or "future not exists sorkin". The abstract is very short so I might as well include it here:
http://arxiv.org/abs/gr-qc/0703098
Relativity theory does not imply that the future already exists: a counterexample
Rafael D. Sorkin (Perimeter Institute and Syracuse University)
(Submitted on 20 Mar 2007)
It is often said that the relativistic fusion of time with space rules out genuine change or ``becoming''. I offer the classical sequential growth models of causal set theory as counterexamples.
12 pages, no figures. To appear in Vesselin Petkov (editor), Relativity and the Dimensionality of the World (Springer 2007, in press).

 

[Jimster41]

Understanding the Pachner moves by which the triangulation of a surface can evolve into a different triangulation won't solve all our problems!
: ^) Life isn't ever that simple. But it is a good first step. The idea of COVERING one two or three triangles with a Tet is good. Placing a Tet is the same as performing a move.
The moment you place even one Tet you have covered up one or more old triangles and you have now a new surface with one or more new triangles replacing the old.
We can imagine that the surface is curved in a discrete humpy bumpy way so there are grooves, pits and crevasses where one can place a Tet that covers two or three triangles. And we can imagine the Tets are made of some elastic material so we can squash them to cover two or three triangles even if the surface isn't all that crinkly and crumpled.

But even if you start with a flat surface triangulated with equilateral triangles all the same size, and your Tets are all the same shape, and you start placing Tets down, you can see how it would evolve into a highly irregular surface. Your first moves are all going to be 1-->3 because the surface is so flat that's the only way the Tets will go down, just covering a single triangle.
But as soon as you have placed two Tets side by side next to each other you have created a canyon where you can make a 2-->2 move by placing a Tet with its edge down in the canyon, covering two triangles. So the more you play this covering game the more complicated the surface gets and the more opportunities you have to make different moves.

So we can say that the geometry evolves. The 2d surface acquires geometric character and is no longer merely flat.

I think what these people (Cortes Smolin Wieland, maybe others) are saying first of all is "Let's look at this in two different ways."

Let's look at it as a story about a MILLING CROWD OF TRIANGLES that are constantly being destroyed and created as they interact, as they join and divide. Let's make the triangles the protagonists, and the Tets are merely a record of their INTERACTIONS. So 2d geometry evolves, wrinkling and unwrinkling every which way.

Or alternatively let's think of 3d SPACETIME AS MADE OF INTERACTIONS. Spacetime (this 3d toy version of our real 4d spacetime) exists and it is made of Tets, and it

I have a pretty decent movie of the 2+1d case in my mind now guys, thank you.
And now it's pretty amazing to stare at the animations of the 3+1d version.

I wish now I had some cardboard tets and a poster with triangles printed on it. The movie is compelling, but it's hard to picture how triangles appear and disappear when you start attaching the tets, without consistently shaped objects or an animation like JulCab's

Now I just need to understand at some level the tricks he's doing to make the resulting surface smooth (Hamiltonian?) though frankly I don't see exactly why smoothness is a requirement, as long as there is no assumption of a smooth background that has to be reconciled against, and discrete operations (like tets) always resolve the dynamics?

Regarding the "merge to make one" and Sorkin, are they are saying in addition to accelerated frames under GR this kind of model can support EPR-Bell, and apparent a-causality? Or am I reading way too much into that?

If I'm not reading too much into that how does this square with C&S rule 2, or is your sense that the CSF model is more flexible and rich in this sense?

I'm trying to get my head around the "growing universe metaphor", though now I keep picturing a field of dark tets, somehow of a conspiratorial ilk, waiting for the bright wave of our 2d space-time events, to collect them. I got to work on picturing Pentachorons...

I liked both the Fay Dowker and Ruth Kastner papers. The Fay Dowker being of course really accessible. I'm going to revisit the Ruth Kastner paper. I have downloaded the Sorkin Paper you reference.

Thanks again.

 

[marcus]

I wish now I had some cardboard tets and a poster with triangles printed on it. The movie is compelling, but it's hard to picture how triangles appear and disappear when you start attaching the tets, without consistently shaped objects or an animation like JulCab's
...
If I'm not reading too much into that how does this square with C&S rule 2,
...
I'm trying to get my head around the "growing universe metaphor",
...
I liked both the Fay Dowker and Ruth Kastner papers. The Fay Dowker being of course really accessible...

I'm glad you liked the Dowker and Kastner papers! Indeed Dowker writes for wide audience really well and explains a lot clearly without equations. I like the dialogue she sets up between the 21st century "blockhead" and the skeptic.

The image of growing universe that comes to mind for me is that of a coral reef that keeps building up with new "cells" living on the surface. In a distributed process, uncoordinated in a uniform layer, everywhere local.

and even though the distances may only be a few kilometers between different parts of the reef, they are in principle "spacelike separated" so there is no actual simultaneity, synchronicity would depend on the observer (although we think of the growth running by a global time, clocks in different places measure a slightly different time). Anyway that's how I think of the "growing universe model" in contrast to the "block universe model".

Cardboard tetrahedra seems like a good idea. I remember making some of clay one time, equilateral triangle sides. I remember the first time I tipped one over onto an edge. the edge was like the keep of a boat running, say EW on the table. the curious thing you see is that now there is another horizontal edge, like the ridge of a house's roof, running NS. Of the four bounding triangles, two go down to join at the keel and two slope up to meet at the ridge-pole, like sides of a roof. Both are horizontal. For some reason I had not expected that. they lie in parallel planes but run in different directions. that orientation of Tet corresponds to the 2-->2 move

C&S talk a little about the DUAL of a triangulation, and show how to diagram Pachner moves in the dual. the dual turns out to be a network (like the spin networks used in LQG) Tets dual to points, their triangles dual to lines joining the points. I'm not sure that's important at this stage, for us, but they spend a couple of pages on it.

I was interested in your mentioning the RULES that C&S list. I wasn't sure which paper you were referencing. There is the one with prefix 1307 (July 2013) one with prefix 1308 (August) and one with prefix 1407 (July 2014).
I sometimes have trouble recalling stuff. It seems to me that there were four PRINCIPLES listed in the 1307 paper.
I keep having real world interruptions, with things I have to attend to right away. I'll try to track down the rules you mentioned as soon as I get back to the computer. Have to go for now.

 

[marcus]

OK I'm back now. You mentioned C&S rule #2. For some reason it slips my mind what that is! But here are the C&S papers:
1. arXiv:1407.0032
Spin foam models as energetic causal sets
Marina Cortês, Lee Smolin
Comments: 16 pages, 4 figures. v2 typo corrected, references added
Subjects: General Relativity and Quantum Cosmology (gr-qc)
2. arXiv:1308.2206
Energetic Causal Sets
Marina Cortês, Lee Smolin
Comments: 9 pages, no figures. Article companion to arXiv:1307.6167
Journal-ref: Phys. Rev. D 90, 044035 (2014)
Subjects: General Relativity and Quantum Cosmology (gr-qc); Quantum Physics (quant-ph)
3. arXiv:1307.6167
The Universe as a Process of Unique Events
Marina Cortês, Lee Smolin
Comments: 26 pages, 5 figures
Journal-ref: Phys. Rev. D 90, 084007 (2014)
Subjects: General Relativity and Quantum Cosmology (gr-qc)

When I go to http://arxiv.org/pdf/1308.2206v1.pdf I see these three points:
==quote==

1. It can be argued that the world cannot be purely defined by relationships. Relationships must relate something. If elements in a relational set don’t have labels, or an associated quantity, there will be no way of specifying which events are related. The events that make up the world must have an intrinsic quantity that allows them to be related to each other.
2. The formulation of relative locality [4, 5] teaches us that momentum and energy are the fundamental observables of dynamics. Space-time is a conventional construction, defined operationally, as Einstein taught us, by sending and receiving quanta that carry energy and momenta.
3. A major issue with the causal set program is getting space-time to emerge from a causal set. This problem is solved by the construction of energetic causal sets, as we show below.

Another issue that is addressed in this formulation is non-locality. Since space-time is emergent, at the fundamental level there is neither locality nor non-locality, just causality...
==endquote==
When I go to http://arxiv.org/pdf/1307.6167.pdf I see these four principles.
==quote==
Based on this view we propose four principles. Two concern the nature of time.

Principle A
Time is a fundamental quantity; the agency of time is the most elementary process in physics, by which new events are created out of present events. Causality results directly from irreversible agency of time.

Principle B
Time has a fundamental directionality. The future develops out of the present constantly; there are no causal loops and no regions or phenomena where time ”evolves backwards.” This implies that the fundamental laws that evolve the future from the past are irreversible in the sense that they have no inverse by which the past state can be reconstructed from the present state.

Principle C
We choose a relational point of view, according to which the space-time properties of an object or event arise from its relationship with other objects or events. All space-time properties have a dynamical origin.

Principle D
Energy is fundamental. Energy and momentum are not emergent from space-time, rather the opposite is the case, space-time is emergent from a more fundamental causal and dynamical regime in which energy and momentum are primitives.

The second two frame the way that the dynamics of the world may be expressed.

==endquote==

 

[marcus]

Jimster, I should have realized this from the start! Sometimes you have to spell things out for me very explicitly. this is the "Rule 2" you referred to:

"The formulation of relative locality [4, 5] teaches us that momentum and energy are the fundamental observables of dynamics. Space-time is a conventional construction, defined operationally, as Einstein taught us, by sending and receiving quanta that carry energy and momenta."​

I'm fairly sure of that now. I'll think about it, and try to say something tomorrow morning when I'm more awake. they are drawing on the relative locality papers---references 4 and 5. Relative locality is a fairly new idea and rather interesting. But for now I have to head off to bed.

 

[julcab12]

Hi Guys,

Sorry. Went for site visit yesterday. Well, I just finished some rough animation on Pachner evolution.



2d to 3d slicing, 1-3 move. While i was playing with it. I did a different version of the evolution. Instead of the usual 'gluing and move'. I tried the 'splitting'. --Starting from a point, splitting creates trajectories(line between 2 points), split again while keeping the trajectories intact creates another trajectory -- triangle(2D).Split succeeding end and create a tetra(3D) and so on.



Four- valent spin network embedded in a topological 3 manifold (just imagine each part tetra are glued instead of the splitting). Any corrections are appreciated.

O.T. Marcus! Your statement is as clear as a diagram. The program is just simple 3ds max(no scripts/ just basic animation) -- maybe i'll create a script later whenever i got the time. Cheers guys!

 

[Jimster41]

Principle A
Time is a fundamental quantity; the agency of time is the most elementary process in physics, by which new events are created out of present events. Causality results directly from irreversible agency of time.

Principle B
Time has a fundamental directionality. The future develops out of the present constantly; there are no causal loops and no regions or phenomena where time ”evolves backwards.” This implies that the fundamental laws that evolve the future from the past are irreversible in the sense that they have no inverse by which the past state can be reconstructed from the present state.

Principle C
We choose a relational point of view, according to which the space-time properties of an object or event arise from its relationship with other objects or events. All space-time properties have a dynamical origin.

Principle D
Energy is fundamental. Energy and momentum are not emergent from space-time, rather the opposite is the case, space-time is emergent from a more fundamental causal and dynamical regime in which energy and momentum are primitives.

Just catching up on the train. Lots to read and consider.

Nice image, the coral reef. Problem with all metaphors that try to describe this I guess, they imply some background, substrate, consumable -my sinister hovering tets, the coral's plankton and algae. Whether or not someone who can think mathematically is able shed that "instinct" of perception, I would love to know. I think the coral image does a better job of creating the illusion at least.

Yes the rule 2 I was thinking of for C&S was the "No redshifts" equation, or Principle B. Which by the way I felt was also in a bit of a collision (not just with EPR) but with the Kastner Paper http://arxiv.org/abs/1411.2072. The description of "symmetrically propagating offer and absorbtion waves" seems awfully close to breaking this rule and imagining said a-causal or pre-causal consumable.

JulCab, (I tried but wasn't able to quote your movies) the new videos are very helpful to me at least, and do I understand correctly you are drawing them to fit the math, an artists conception, as it were? Now I have to think - if Marcus 2d+1 visualization is correct w/respect to the causal set evolution model, and complete enough to use to study behavior, and the drawing stays geometrically consistent with that - is the result significantly different from an algorithm that would start from the math? I guess it might be hard to tell. Do I understand correctly that the stick diagrams inside the tets are the dual spin network representation?

I found this Mathematica demo that helped me break the visual perception of enclosed volume when thinking of a Pentachoron. It requires downloading a widget. I used to know a tiny bit of Mathematica (pretty amazing platform).. but it's changed a lot I think. I remember once sitting in my car in a parking lot (10 years ago) listening to Stephen Wolfram on a university radio station lecturing about how simulations will become the new paradigm of exploration, a more capable framework than symbolic analysis, or something to that effect. It was shocking stuff.

http://demonstrations.wolfram.com/StereogramOf4DPentachoronRotations/

To wit, has anyone tried to envision how the causal set model would play out in the sequence of a two-slit experiment? Staying in the 2d+1 case, I picture an unlikely "tendril of tets" climbing out of the foam, creating an arc above the mean surface, then blink a whole set of tets fills in beneath them, reconciling to the geometric socket they have formed... Or maybe, more likely, it's about creating a rare and fragile hole, or depression in the advancing foam by carefully isolating Kastner's un-transacted probabilistic quanta, which when released to evolve causally have some constrained future due to the same principle - the in-filling transactions have to fit the hole the advancing surface has formed around them? Is that breaking rule 2? Would that look like wave/particle interference?

I got to "make some donuts", a common phrase around here for doing boring old work.
Really enjoying this conversation. Just started reading the Sorkin paper.

 

[Jimster41]

Hi Guys,

Sorry. Went for site visit yesterday. Well, I just finished some rough animation on Pachner evolution.



2d to 3d slicing, 1-3 move. While i was playing with it. I did a different version of the evolution. Instead of the usual 'gluing and move'. I tried the 'splitting'. --Starting from a point, splitting creates trajectories(line between 2 points), split again while keeping the trajectories intact creates another trajectory -- triangle(2D).Split succeeding end and create a tetra(3D) and so on.



Four- valent spin network embedded in a topological 3 manifold (just imagine each part tetra are glued instead of the splitting). Any corrections are appreciated.

O.T. Marcus! Your statement is as clear as a diagram. The program is just simple 3ds max(no scripts/ just basic animation) -- maybe i'll create a script later whenever i got the time. Cheers guys!

Ah, now I can guote these. duh.
The second one is particularly helpful for me, because it looks like what I envision as Marcus 2d+1 movie, but in reverse.

 

[Jimster41]

Just found a really good one (for me) by Dowker. A little dated (2008) but tantalizingly accesssible http://arxiv.org/pdf/gr-qc/0508109.pdf

 

[julcab12]

do I understand correctly you are drawing them to fit the math, an artists conception, as it were? Now I have to thin

I tried lol. The original picture involves gluing and slicing in the Fotini's dual spin network diagram-- where the faces are labeled as spins while the tetra are intertwiners. http://inspirehep.net/record/922593/plots.

BTW. This fundamental thingy is still new to me. I've been working on fluid dynamics and fractals in the past but haven't skimmed on the basic for a while. I'll try to animate the standard picture soon 'gluing and slicing'.

Do I understand correctly that the stick diagrams inside the tets are the dual spin network representation

The joint -- where the lines meet (the animation is still a work in progress^^) are the spin network vertex – the so called building block of space. The animation(4) is shown in reversed. It is a 5-n move where the resulting triangulation is the new state and the initial triangulation is the past set. The 5-n are the future sets. If you notice, The splitting creates trajectories and rigid solid. The original picture involves slicing erasing those tetra and replaces with a complement tretra while keeping it intact.

Copy from Group Field Theory.

 

[julcab12]

Here is a remake of the animation(4). Spin network (I was unable to edit my old post... )

and the drawing stays geometrically consistent with that - is the result significantly different from an algorithm that would start from the math? I guess it might be hard to tell. Do I understand correctly that the stick diagrams inside the tets are the dual spin network representation?

...Quite a tall order. It would be cool if it does. The construction is quite neat to some extent. IMHO. I don't even know if it can be subject to testing. But, what's remarkable about it is that we have some fundamental actions that somehow relates to geometry.

. Do I understand correctly that the stick diagrams inside the tets are the dual spin network representation?

Yes. I'll create the slicing/gluing action later on. ^^

 

[Jimster41]

Fotini's dual spin network diagram-- where the faces are labeled as spins while the tetra are intertwiners. http://inspirehep.net/record/922593/plots.

This site is really helpful. Took me a minute to realize the figures are all duplicated! I thought I was really not getting it.

I'm still a bit confused about the slicing, which seems intuitive to you. So far I have been picturing a thing like Marcus' Coral Reef where Tets that were glued together to form the present 2d surface are still under there (back there?). When you say "sliced off" I interpret that to mean that the present always slices it's way forward via one transaction that conserves a tet and so must leave the past tet behind. I also get how, when viewed from the top, the addition of a new point (gluing a tet) "slices" the underlying state into three new states. Is that consistent with your view?

Why does that sound a lot like Entropy?

Your most recent animation is perfectly aligned with the movie I have been seeing since Marcus' tutorial, and I can now really see the relationship to the dual. I probably think those things are even cooler than you do! I'd love to be able to play with them and have a sense that what we see is something consistent with the Cortes, Smolin, Wieland SF-ECS model. But yeah that is a tall order and I'm not suggesting I wish you would do that. I appreciate your visualization helping me understand this stuff to the extent I do.

I'm now stuck on trying to picture the difference (in the 2d+1 case) between a transaction tet for a photon and one for a neutron. Or one for a neutron at rest vs. a neutron accelerated. I get that ECS theory tets preserve the "geometricity" between the two cases, making space-time invariant under Lorentz transformations(?). But a dynamically disrupted foam must not look like it's made of equilateral tets?

I want to picture the (run of the mill) photon tet as a big flat almost-triangle, compared to chuncky (run of the mill) neutron tet.

 

[julcab12]

I'm still a bit confused about the slicing, which seems intuitive to you. So far I have been picturing a thing like Marcus' Coral Reef where Tets that were glued together to form the present 2d surface are still under there (back there?). When you say "sliced off" I interpret that to mean that the present always slices it's way forward via one transaction that conserves a tet and so must leave the past tet behind. I also get how, when viewed from the top, the addition of a new point (gluing a tet) "slices" the underlying state into three new states. Is that consistent with your view?

Forgive me for my poor wording and hope i can demonstrate the diagram more.^^. Intuitive in sense that shapes has that property.

I haven't shown the 1-3 in a 2+1d pachner (trivalent) move yet. According to causal set spin foam models. 1 node becomes 3 nodes through move/slicing. Each node has trivalent spin network. The area or the face is the intertwiner and the edges of the triangle are spins. ( http://arxiv.org/pdf/gr-qc/9704013v1.pdf see figure 1:). We have triangle with a spin network content. In my animation. I added a dynamic of splitting. The 'Splitting' of 1 vertex (where 2 edges meet) can have the same geometry as dual triangulation in casual spin foam model --- 1 triangle becomes 3 triangles. The splitting produces a transition between trivalent SN to four-valent spin network shown in animation(5). Ops. Had to go. I'll be back later..

 

[Jimster41]

Thanks Julcab,

I just scanned the first couple of pages of the paper you reference. It looks like a good one (lots of pictures and words) and I'm looking forward to beating my head against it.

Currently, I have very little intuitive feel for how spin valences varying across the causal chain relate to the "shape of space time", whereas for momentum, mass, energy, I at least have an illusion of "feel".

 

[julcab12]

In continuation #64. Let's step back a bit and create a slide diagram of the animation(4). In the LCG diagram.

http://www.einstein-online.info/spotlights/spin_networks#section-0

"The arrows give each line a direction (in mathematics-speak, an orientation). Each line is labelled with a half-integral number. The mathematical background of this number is the same as that of spin numbers inparticle physics, a type of number used to describe a basic property of elementary particles. Consequently, this number is called a spin label. (In fact, there are also labels associated with each node, but their meaning is more complicated mathematically, and we will ignore them in this simplified account.) The result is what is called a spin network, and it is taken to represent the quantum state of space at a certain point in time.

The lines do not have an a priori length - after all, there is no background geometry from which to derive lengths. Instead, we are dealing with a quantum system: In order to to talk about geometric entities like lengths or areas one must give a prescription how to measure these entities. (In technical terms, one must construct suitable operators with respect to which the spin network states are eigenstates.) In order to visualize this, it is convenient to look at graphs like the one sketched above in a different way, in what mathematicians call a dual description."

---- Now we have the basic diagram. Let's incorporate a geometry(solidity) on the evolving spin network. In my animation(4). We have 2dual evolutionary representation of the solidity. (1) integration of shape evolution (splitting of points creating edges-triangle-tetra and so on ) and (2) evolving orientation of spin network. We have now the basic dynamic-structure of the foam.

"Here is an artist's conception of the dual of a spin network state, this problem is solved by expressing a face's spin label (and thus its area value) by a colour. Thus, somewhat counterintuitively, a face can have more or less area (determined by the label) than another face even if both faces appear to have the same extension and shape in the illustration. More specifically, red means a smaller area and violet means large area. Notice that what appears as an empty region in the picture is actually no space at all: Space is only existent wherever there are faces that are excited (coloured). If we would add matter to this model, it could only exist on coloured faces (equivalently: on the lines of the spin-network)."

http://www.nature.com/news/theoretical-physics-the-origins-of-space-and-time-1.13613#reality-- LQG section:Over time, lines of the spin network can disapppear or new lines can be created, and the value of the different spin labels can increase or decrease. One therefore could call the resulting theory Quantum Spin Dynamics (QSD) in analogy to the theory of the strong nuclear force, quantum chromodynamics. (Quantum chromodynamics defines a very similar dynamics of what is called the colour quantum numbers of elementary particles like quarks and gluons.) The details of quantum spin dynamics are such that new faces are always created or annihilated with lowest possible area (in the illustration: the red faces). The animation that can be downloaded from the following links shows an artist's impression of this. Notice that, in the animation, the colour on the faces of the whole complex changes discontinuously while we fly through the empty space of the complex... "

 

[julcab12]

Thanks Julcab,

I just scanned the first couple of pages of the paper you reference. It looks like a good one (lots of pictures and words) and I'm looking forward to beating my head against it.

Currently, I have very little intuitive feel for how spin valences varying across the causal chain relate to the "shape of space time", whereas for momentum, mass, energy, I at least have an illusion of "feel".

Your welcome men. TBH. I'm not even qualified to answer such questions lol. I hope i represented the idea well. I was hoping that someone would add or correct me. I've been working on shape dynamics my entire career but i never imagined this form of fascinating relational oddity. This development is intriguing to me and been following it ever since with a very little physics( I'm still working on that) in my arsenal. To me. The transition from geometry to particle physics is still a long shot(possibility?) but an exciting development nonetheless.

 

[Jimster41]

That was extremely helpful. And that movie is... well it woke me up before eve one sip of coffee
Mostly what I got from that was wonderful clarity.

But,

Notice how the artist in the animation is conflicted in that he is using the color as a proxy for structure "foam geometricity", but then he still feels the need to reduce color value (grayscale) to signify receding distance. At that point the movie seemed to me like an afterthought, meant to dazzle,not conceived as a practical tool.

but then I still may be missing something big

Why can't we practically depict an evolving 2d+1 causal spin foam in a 3d+1 media player or simulator without breaking the key feature of into color. The key feature to me is "the way 3d shape evolves from 3d geometricity accreted over steps.

I keep picturing the triangular surface Marcus portrayed, in lovely black lines against a white backdrop, but as if I'm hovering over it (the lie that is required to create a visualization). I have a menu of pre-defined tets at the top of my viewer ("photon at rest", "neutron at rest", "Plain Tet"). I click one and a Tet appears in view, it is given gray scale shading from a stage right light source, but just enough gray to expose it's shape and orientation in the volume of the view, but that is all. I pull it down to the surface and the triangles light up to show me where I can attach it. Once attached I can go to a menu and configure or edit it's momenta. Boom. Next one I do, say I attach it to the first one. Now the lines of the first one fade, to show deprecation w/ respect to the surface of the present. Also I can turn the dual on!

Okay, yeah that's a neat fantasy, implying about 900 man hours of work, even in a moderately sportive platform...

I had thought that to ask questions, like "What would an approximation of a Two-Slit problem look like" or "what would an EBR event horizon look like" you wouldn't need to account for all the permutations of momenta conservation that could solve the network, just someone who could stack tets in a way consistent with an approximation of the ECS rules, maybe constraining tet shape and connection to a subset sufficient for a human being to build a movie-like depiction of relationships of mass difference and boost. The addition of enforced assembly rules could be solved as part of the user's interaction with the assembly, "if you stick this Tet here it can only take on this shape or that one, due to momenta conservation, and causality. I realize I may be giving interest in particle types and interactions short shrift here compared to jest ions about puzzles of gravitation, mass and spacetime curvature here. I guess I could imagine breaking the problem down so you aren't necessarily trying to see both networks at once, but could work on how one, once built, might inform or constrain the other.

I'm a bit confused as to whether or not an ECS-SF simulator in 1d+1 is interesting? Clearly not as cool too look at, but the graph in the article you referenced does convey kinematic to some degree.

Yeah, I've had enough coffe...

Where are you from by the way? I get the feeling we are in different time zones.

 

[Jimster41]

Holy moly! That's what I'm talkin about. It looks fractal to me...

From the link you provided up top
http://www.nature.com/news/theoretical-physics-the-origins-of-space-and-time-1.13613#reality--

I'm not having any luck figuring exactly how this was made, what tool was used, who?

 

[julcab12]

Why can't we practically depict an evolving 2d+1 causal spin foam in a 3d+1 media player or simulator without breaking the key feature of into color. The key feature to me is "the way 3d shape evolves from 3d geometricity accreted over steps.

Actually they can or at least they are trying. http://www.nbi.dk/~budd/.

https://www.learner.org/courses/physics/visual/visual.html?shortname=causal_dynamical_triangulation

"Causal Dynamical Triangulation is an attempt to build four-dimensional spacetime from two-dimensional triangular regions that, when glued together, represent a possible configuration of quantum spacetime fluctuations. Each configuration of triangles, like the one shown above, obeys the postulates of special relativity. The sum of all possible configurations is a spacetime with the same four dimensions in which we live".

I had thought that to ask questions, like "What would an approximation of a Two-Slit problem look like" or "what would an EBR event horizon look like" you wouldn't need to account for all the permutations of momenta conservation that could solve the network, just someone who could stack tets in a way consistent with an approximation of the ECS rules, maybe constraining tet shape and connection to a subset sufficient for a human being to build a movie-like depiction of relationships of mass difference and boost

.

Hmm. That's a neat idea. I have a good picture now in my head. I'll try to break that idea into moves soon.

Where are you from by the way? I get the feeling we are in different time zones

Yep. Here in Dubai lol.

Holy moly! That's what I'm talkin about. It looks fractal to me...

Eerily familiar to julia sets in fractal.

Spatial topology change and tree bijections in 2d
"In causal dynamical triangulations the spatial topology of the universe is not allowed to change in time. However, at least in two dimensions, it is possible to incorporate sporadic topology changes while maintaining a sensible continuum limit, leading to so-called generalized CDT. We demonstrate how one can study this model by taking the continuum limit of random quadrangulations. The analysis relies heavily on bijections between quadrangulations and labeled trees."

OK.. now. They stretching this a bit..

http://www.nbi.dk/~budd/docs/slidesnijmegen.pdf

They already have the fundamental picture in 2d and 3d animation, Even the interactive part. Now it makes sense(well, geometrically speaking) especially when you look at "Geodesic distance in quantum Liouville gravity and Zooming in on 2D Quantum Gravity" . 0_0

http://www.nbi.dk/~budd/#slides1 --- scroll down on videos