Does LQG Do Nothing Cool Even If It Is Right?

[Jimster41]

Nice find, thanks. His research is really cool. I need to spend some time with his slides etc. I'm definitely behind in my reading now (I am going to try to catch up though, so If I don't reply for awhile it's because I'm studying to learn how to say less goofy things)

Seems clear he's using Mathematica. Among other things he's trying to prove out, most of which I can't follow, is how Brownian Motion is emergent, which to my mind is sort of what Louiville's theorem says. Maybe somewhere in his presentation, which I just haven't seen yet, he describes using purely evolutionary approach to solution discovery, maybe for the fractal looking ones? To me that is what causal chain or network must be, pure stochastic iteration under rules.

I keep thinking there needs to be a problem setup consistent as pure stochastic evolution, which is why the manually controlled simulator has appeal, starting with just state n, a coherent description of the last event (surface) just before the photon hits the screen, and then see if there is anything anomalous, weird or cool, in what the rules would permit or require of state n+1. Or maybe working backwards from state n+1 requirement of interferene to see if any legal shape of an ECS space-time surface at state n is possible. I know that the ECS theory says "always causal" and "in one order", "momenta conserved" so - "everywhere local" but somehow that can't be the case for both those events (n, n+1). Unless I am missing some way of looking at the two slit experiment that makes it seem... more mundane.

Dubai. That is so cool. My wife is studying Sustainability Management at Harvard (she is the clever one of the family). She talks about Dubai often (she's into "Smart Cities") and I have heard enough and seen enough pictures that - having a beer in a lounge at the top of one of those skyscrapers, looking out over the 22nd century, is on my bucket list.

 

[marcus]

Jimster and Julcab (neat about Dubai!) I wanted to share this with you, a new paper NOT, first of all, to READ, but simply to KNOW EXISTS. It has to do with the emerging interest in (and possibly importance of) pachner moves in quantum geometry/gravity.

It seems to dovetail with the lines of research pursued by Bianca Dittrich and by both Wolfgang Wieland and Cortes Smolin. The idea of a geometric process based on Pachner moves.
http://arxiv.org/abs/1411.5672
Canonical linearized Regge Calculus: counting lattice gravitons with Pachner moves
Philipp A. Hoehn
(Submitted on 20 Nov 2014)
We afford a systematic and comprehensive account of the canonical dynamics of 4D Regge Calculus perturbatively expanded to linear order around a flat background. To this end, we consider the Pachner moves which generate the most basic and general simplicial evolution scheme. The linearized regime features a vertex displacement (`diffeomorphism') symmetry for which we derive an abelian constraint algebra. This permits to identify gauge invariant `lattice gravitons' as propagating curvature degrees of freedom. The Pachner moves admit a simple method to explicitly count the gauge and `graviton' degrees of freedom on an evolving triangulated hypersurface and we clarify the distinct role of each move in the dynamics. It is shown that the 1-4 move generates four `lapse and shift' variables and four conjugate vertex displacement generators; the 2-3 move generates a `graviton'; the 3-2 move removes one `graviton' and produces the only non-trivial equation of motion; and the 4-1 move removes four `lapse and shift' variables and trivializes the four conjugate symmetry generators. It is further shown that the Pachner moves preserve the vertex displacement generators. These results may provide new impetus for exploring `graviton dynamics' in discrete quantum gravity models.
26+12 pages, 2 appendices, many figures. This article is fairly self-contained

I think part of the mathematical appeal or convenience is that Pachner moves offer the possibility of a discrete finite vocabulary of geometric changes. So you can model geometric process in a discrete way. To me it seems great that Höhn has taken a LINEARIZED approach reminiscent of PERTURBATION theory, where you fix on a (usually flat) background geometry and study small "ripples" on that background. That's when the graviton concept really comes into its own, when instead of the whole dynamic geometry you can focus on small quanta of geometric disturbance on a fixed background. It seems great that he is able to represent that with the simple vocabulary of pachner moves.

It has some diagrams of the moves, and it has an idea of how the past is covered over with a layer of change (the present) which then becomes part of the past---and ready for a new layer. And this layer of change is made of pachner moves.

I'm not suggesting anybody read this particular article, just that it's one to know about---part, I think, of a trend on the QG front. And maybe one of the "cool things" that we take notice of in this thread : ^)

 

[Jimster41]

Thanks Marcus. I appreciate your synopsis for the layman. It enables me to read (re-read) and actually somewhat interpret the abstract at least! I know enough about the Perturbation approaches to have at least an image of the scheme.

Without looking at the article yet, I'm curious whether they are on the ECS train and just looking for clever ways to model stochastically evolving geometry, or whether they are still holding out for a fundamental continuum that propagates discretized waves of geometric information? I can imagine their scheme as you outline it being a useful tool with which to scale ECS up to semi-classical domains - where continuity and smoothness can be expected due to Gaussian expectations over lots of foamy quantum events (Brownian motion, Louiville's theorem?) I think I got something like that from the researcher Julcab referenced also - his analysis of distributions of space-time events in 2d over regions.

It hadn't occurred to me that any setup of the Two-slit experiment has to combine classical and quantum domains? Semi-classical? Sorry to keep coming back to the damn Two slit experiment. It just itches. (Later) after saying that I think that classical-quantum combination is consistent with a smooth-ish geometric surface with a rare hole or some kind of relatively extreme or non-Gaussian distortion (the tangled photons?)

 

[marcus]

Without looking at the article yet, I'm curious whether they are on the ECS train and just looking for clever ways to model stochastically evolving geometry, or whether they are still holding out for a fundamental continuum that propagates discretized waves of geometric information? ...

Hi Jimster, I think you are referring to Philipp Höhn's paper and to tell the truth I don't know what "ontology" or idea of reality he has in mind. Maybe no one in particular.
There are mathematical advances that provide technical grasp and utility that different people can use in different ways. Maybe in some sense they are the best kind, the more different uses the better! I see a potential for this to help the ECS program. But Philipp has collaborated a lot with Bianca Dittrich and I feel confident it could also be used in her approach to completing straight LQG/Spinfoams, and deriving their continuum limit. Her direction is more, to adapt your way of putting it, to model evolving quantum geometry in a clever way and show it behaves right in the appropriate limit.

I'm delighted when I see people with different goals trying to accomplish different things getting thrown together on convergent paths.

This convergence phenomenon was noted in a video seminar talk by Sylvain Carrozza that was just posted at PIRSA (perimeter institute recorded seminar archive). It was in an entirely different context! He was working on an approach to QG called "Group Field Theory" and, in particular, trying to see how renormalization could be done. And basically he commented "hey, this is looking more and more like LQG!" Don't let this distract you, its hard to stay focused with the variety of research paths being pursued. But just to make sure we know of Carrozza and that GFT exists here is his talk:
http://pirsa.org/14110129/
UV completion in Group Field Theories
Speaker(s): Sylvain Carrozza
Abstract: I will review recent work on tensorial group field theories (TGFTs). The renormalization methods being developed in this context provide more and more control over their field-theoretic structures, and for models which increasingly resemble loop quantum gravity. Perhaps surprisingly, some of these models are asymptotically free and can therefore be made sense of at arbitrary values of the (abstract) scale with respect to which they are organized. They define in this sense UV complete quantum field theories. I will focus on TGFTs with gauge invariance condition, which allow for such a behavior but also for more complicated scenarii involving non-trivial fixed points of the renormalization group flow. I will finally comment on the physical relevance of this notion of UV completion.
Date: 20/11/2014 - 2:30 pm
Series: Quantum Gravity

 

[Jimster41]

Thanks Marcus. Really appreciated your perspective, and all the work you do here keeping track of what is going on out there.

 

[marcus]

No problem, I feel tugged in two ways about this thread, one is your particular interest in ECS (especially the ontology or world picture latent in the Cortes Smolin work) and the other is the main topic of the thread which is the "cool things" coming out of current Loop gravity research. I'm always wobbling back and forth trying to do both, which is all right for me but may not work for you.

On the ECS side, we should note that Smolin's new book, with Roberto Unger, is scheduled to come out within a week---30 November. That the nominal date it goes on sale, that the Amazon web page gives:
https://www.amazon.com/dp/1107074061/?tag=pfamazon01-20
The web page let's you "Look inside". It allows some browsing.

It is always possible they won't make the published release date and the book will be delayed---that's happened before. But my sense is that it will be on the market very soon.

People will want to take issue with the book's assertion of the reality of time. I think that arose because the idea of the universe running on arbitrary fixed and eternal laws for which there is no explanation is philosophically unsatisfying. the idea is very appealing that the laws of physics evolved . But then one asks "evolved in what? don't you need a global time for them to evolve in?"

One of the foremost takeaway lessons of GR is that there is no global time. Change occurs at rates that vary all over the place depending very much on the observer's perspective. Moreover the original Causal Sets people like Sorkin Dowker Rideout and others took extreme care to avoid being forced into the trap of a global time. In stuff we've read in this thread we've seen this over and over. They manage to get a representation of the present moment and of happening without accepting a preferred global time.

How do they do this? By giving non-chronological causal structure priority over time. Metaphors we used were a family tree of events (where incest and inbreeding are possible) or the growth of a coral reef. in either case, birth order is not recorded. the growth does not occur in time, it occurs simply in the causal structure.

So the question naturally arises: "why do Smolin and Unger have to declare "the reality of time"? Why can't they just have physical laws evolve in the causal structure?

To me this seems more satisfactory, partly because I take the momentary signature change of the "silent bounce" seriously---that business proposed by Barrau Linsefors Mielczarek. It is an extremely bold proposal, but I have not seen it shot down yet. Essentially interaction between all microscopic degrees of freedom is SUPPRESSED at extreme density. A brief Euclidean phase, of total isolation and silence, at the bounce. In which the speed of light is effectively zero, light cones close and then, as density lessens, reopen.
The causal structure is momentarily trivial and I think time is impossible because no oscillator or cyclic process of any kind is possible, nor any counting of cycles. Operationally speaking, time cannot be defined or measured under such a clockless condition, so time is in some sense paralyzed, or it "crashes" and must be "rebooted" at the bounce. Degrees of freedom must be able to interact in order for there to be any sort of repetitive cycle. There is inevitably a kind of "round robin" in any oscillator. And I suspect that an even higher degree of interactive connectivity is needed to have a counter that is accumulating information about the causal past. So I can imagine a world in which causality functions (the coral reef grows) but interaction is as yet too primitive and limited for time to apply. Nothing there to "keep" it.

The "Silent Initial Conditions" paper is the fourth item on the fourth quarter MIP poll. Here's the poll link if you want to check out the abstracts of this and other interesting recent papers:
https://www.physicsforums.com/threads/first-part-of-fourth-quarter-2014-mip-poll.782086/

Probably one can get the Mielczarek et al paper just by googling "silent initial conditions". Yes! it is the first hit.
http://arxiv.org/abs/1411.0272
Silent initial conditions for cosmological perturbations with a change of space-time signature
Jakub Mielczarek, Linda Linsefors, Aurelien Barrau
(Submitted on 2 Nov 2014)

 

[Jimster41]

Marcus, thanks, I have been thinking about the important tension between mathematical "technology" as it were, and ontology. Clearly it's complicated but as you can probably guess I wish there was more out there for those who are not fluent in mathematics (compared to the practitioners) but who want to follow the way mathematical techniques are used in pursuit of ontology, because we understand that is "seeing the ontology for oneself" at some level, and somewhat irreducible. This Pachner moves tutorial, though way too time consuming (for you and Julcab) and too dialectic to be scale-able or sustainable is a great example of it - continued education for the non-practitioner, for which I am thankful.

To wish out loud for something more incrementally practical I wish someone would create an equation translator/annotator, even if all it did at first was list a glossary of all symbols used in whatever calculation was selected below the calc... or in call-out bubble (the live text model is appealing here because you can layer things in such away - to be accessed interactively). Mathematical software languages are an interesting hybrid, more instructive semantically, but I think not specific to the task, which is stay as close to canonical symbolism, but also explicate. I can read, and with my finger on the glossary I can often times track the technical description at the fine grain scale of ontology, often times. But it's logistically, a nightmare just to get them together.

Anyway, all that wishing aside

I do love when you get ontological...

To me this seems more satisfactory, partly because I take the momentary signature change of the "silent bounce" seriously---that business proposed by Barrau Linsefors Mielczarek. It is an extremely bold proposal, but I have not seen it shot down yet. Essentially interaction between all microscopic degrees of freedom is SUPPRESSED at extreme density. A brief Euclidean phase, of total isolation and silence, at the bounce. In which the speed of light is effectively zero, light cones close and then, as density lessens, reopen.
The causal structure is momentarily trivial and I think time is impossible because no oscillator or cyclic process of any kind is possible, nor any counting of cycles. Operationally speaking, time cannot be defined or measured under such a clockless condition, so time is in some sense "reset" or "rebooted" at the bounce. Degrees of freedom must be able to interact in order for there to be an kind of repetitive cycle. There is inevitably a kind of "round robin" in any oscillator. And I suspect that an even higher degree of interactive connectivity is needed to have a counter that is accumulating information about the causal past. So I can imagine a world in which causality functions (the coral reef grows) but interaction is as yet too primitive and limited for time to apply. Nothing there to "keep" it.

Clearly you understand this stuff at a level from which you can teach (is that what you do?)
I want to understand more about the bounce. I printed the paper you reference about the inflationary period implications of LQG but it was a bit referential and not enough context for me to get a lot from it. I got stuck on the ontology of the Friedman Equation - and the assumption of mass and energy defining the changing size of the universe, the shape of which seems to define them...? That paper though is a perfect example of one I think I could get better with an in-situ math glossary, because it is talking about physics or "specific ontology" - not just pure mathematics.

But my cartoon is that this is a new description of the "singularity" we found at the "going back down space-time" limit, the one that has been giving fits. With this one, instead of an infinity we get something that remains coherent, if zero is more coherent than infinity, which I think it is. I get why it could be consistent with a notion of cyclic time (I'm in the middle of Penrose "Cycles of Time"). I'm also curious about the "how would be know we were on the other side of the signularity?" question. In other words how do we know it's not a bounce as much as it is a passage - through the boundary-singularity, to the voluminous other-side...where things are different. I'd like to have a better picture of all this.

I am pretty enamored with this ECS notion to be sure, exactly because it is free of global time. To my mind this is an unavoidable requirement given the EPR paradox (or at least my cartoon of it). Clearly a simple table-top experiment with fairly common-place light and two slits, poses a staggering puzzle to ontology. How can there be such accessible domains that are... without time? How can temporally separated "events" interact as though happening at once? Eliminating Global-time seems the only option. I get that there are rules regarding that interaction, moving information through the time-less domain is a fail, mass energy velocity affect our visibility onto that domain, etc - so it's more subtle than sci-fi, but the mother of all puzzles is there. If anything the rules only make is even more tantalizing. I say it's more subtle than sci-fi but then I haven't seen "Interstellar" yet.

Causality itself is still a problem though IMHO when considering ECS vis-a-vis EPR, and I read a researcher dismissing ECS saying that it does no better than continuum approaches at the limit because of this implied background "ordinal" that separates events.

Maybe it doesn't describe the ultimate container-less set, But I don't agree it does no better, rather I take from it a picture composed of a universe of pure black unknown, except we know it can (and apparently must) contain no less than two "causal sets", each with different space-time, but intersecting - or more properly "inter-acting".

And I can't help but think of Entropy (the leaking in/out of total set configuration space) as the only veil we have, that outlines the collision. This is why Verlinde got my attention when he suggested that space-time is emergent from Entropy. I would be fascinated to see Entropy described in the SF causal set model - some uniform curvature convolved with the foam?

Anyway, I haven't forgotten about the Smolin et al. book. I am definitely getting it.
Thanks again..

 

[marcus]

ECS, and its connection with Causal Spin Foams via Wieland's work is definitely one of the cool things happening at present.
Something else just came up that should also be on our cool things list: Work involving curved-simplex simplicial complexes, incorporating the cosmological curvature constant Λ.
This has not appeared yet on arxiv. It is in progress, co-authored by Haggard, Han, Kaminski, and Riello.
Haggard and Riello just gave an hour talk on it at the ILQGS (international LQG seminar).

You know the so-called EPRL model is the standard spin foam model used in LQG and it is based on the idea of 4d simplicial complex, and its dual cell complex which carries certain information and constitutes the spin foam. Well, the 4d simplicial complex has always consisted of FLAT simplices, pents
, tets , triangles etc. But a nonzero Λ curvature constant says that there is a residual curvature that never goes away and is independent of the disposition of matter and energy. So why not incorporate curvature right at the basic simplex level, in the 3 simplices (tets ) and 4 simplices (pents ) themselves?
This they seem to be doing.

they call their new version of spin foam LQG by the name ΛEPRL ( "LambdaEPRL") this is work in progress that has clearly started to pick up momentum

 

[Jimster41]

Thanks Marcus. I look forward to hearing more. Just got a bit further through Penrose "Cycles Of Times" while traveling today - very helpful, and interesting.The research sound really intriguing. I am curious to know, If one applied a "distributable" curvature requirement to stochastic causal-set evolution (the spin foam), might we see emergent "massive particles". To me this is Verlinde. Mass doesn't curve space-time, probabilistically curved space-time causes massive Events?

 

[marcus]

... I am curious to know, If one applied a "distributable" curvature requirement to stochastic causal-set evolution (the spin foam), might we see emergent "massive particles"...

That is a really good general idea. in a general sense both GEOMETRY and MATTER must arise from the same thing, or be different aspects of the same thing, because they are so closely entwined with each other. geometry guides matter, which, in turn, curves geometry. they interact so constantly and profoundly that it seems intuitive they should be essentially the same being, at root. So you would like some theoretician to come up with a mathematical model of this their essential unity. I would too. Theorists have to work on problems that are ripe, problems that are ready for solution given the human concepts, the mathematics, the knowledge and language of the times. All of that is evolving, which means that problems are ripening and getting ready to be productively addressed. But its hard to know which are. I wonder if this problem (the common ground of geometry and matter) is actually ripe now, and i simply don't know that it is, and won't know, until some theorist springs a good idea on us.

Back in the mid Naughties, in 05 or 06, I think some theorist proposed that matter particles were the "topological defects" in geometry. Maybe it was Louis Crane (Kansas) or Laurent Freidel (Perimeter). Matter was perhaps imagined to be "conical singularities" The points of cones, where normal curvature would not be mathematically definable.
"Kinks" in the curvature, so to speak. I can't remember who it was who was briefly exploring this idea---several papers appeared, as I recall.

There is probably a lot more history I am not aware of. maybe the idea goes back to Einstein, or Lucretius, or Thales of Miletus. Or Adam :w
But to my limited and non expert knowledge the problem is not yet ripe.

Lee Smolin definitely WANTS matter to arise in some (perhaps still uninvented) type of energetic causal set, doesn't he? Making geometry arise in some sort of ecs is just the beginning, for him :)
Your idea could resemble something he tries along the way.

 

[inflector]

Lee Smolin definitely WANTS matter to arise in some (perhaps still uninvented) type of energetic causal set, doesn't he? Making geometry arise in some sort of ecs is just the beginning, for him :)
Your idea could resemble something he tries along the way.

Seems like in the Smolin world, matter could come from repeating causal loops where the energy of the causation is stored in the loop. By loop here, I mean loop in the algorithmic sense not in the geometric circle sense. More like the repeating oscillators in cellular automata like Conway's Game of Life.

The one problem I see in approaches so far, and I could easily be missing something obvious, is that the spacetime quanta approach, i.e. the building up from units of spacetime like the pentachorons still presents boundaries across which the very essence of matterness may be transferred in ways the simulations using quantized bits of spacetime (i.e. the pents) won't capture. It may be that there needs to be some torsional (curvature?) transfer between pents to represent matter. Another way of saying this is that perhaps simple causality is insufficient to represent matter. There may need to be some bending moment transfer across causal boundaries.

Curved spacetime units might be a step in this direction. However, since from GR we know that curvature differs locally from region to region depending on how curved adjacent spacetime is and how much matter is present; so it seems likely that an approach the allowed for varying degrees of curvature / torsion in the spacetime causality flow would be more likely to produce matter emergence than one that had uniform curvature and no allowance for much higher local curvature.

Perhaps that's all matter is, spacetime that's so locally curved as to maintain that curvature absent external inputs for at least a little time.

Anyway, I sure hope someone does take up your idea marcus.

 

[atyy]

Perhaps that's all matter is, spacetime that's so locally curved as to maintain that curvature absent external inputs for at least a little time.

The way Rovelli thinks about LQG, from its canonical roots to EPRL/FK is that it is a theory only of gravity, which can be coupled to matter as needed. However, there have been some ideas that the spin foam formalism secretly contains matter, eg.
http://arxiv.org/abs/hep-th/0512113
http://arxiv.org/abs/gr-qc/0702125
http://arxiv.org/abs/1001.2702

 

[Demystifier]

Atyy, do you perhaps think that you know more about physics than about biology? ;)
In any case, it seems to me that you know about physics more than many physicists.

 

[inflector]

The way Rovelli thinks about LQG, from its canonical roots to EPRL/FK is that it is a theory only of gravity, which can be coupled to matter as needed.

I've always interpreted Rovelli's hedging as him being fairly conservative in his claims, not that he didn't necessarily expect more over time.

What marcus said rings true:

In a general sense both GEOMETRY and MATTER must arise from the same thing, or be different aspects of the same thing, because they are so closely entwined with each other. geometry guides matter, which, in turn, curves geometry. they interact so constantly and profoundly that it seems intuitive they should be essentially the same being, at root.

So I'm encouraged by approaches that move in this direction.

 

[Jimster41]

Seems like in the Smolin world, matter could come from repeating causal loops where the energy of the causation is stored in the loop. By loop here, I mean loop in the algorithmic sense not in the geometric circle sense. More like the repeating oscillators in cellular automata like Conway's Game of Life.

Curved spacetime units might be a step in this direction. However, since from GR we know that curvature differs locally from region to region depending on how curved adjacent spacetime is and how much matter is present; so it seems likely that an approach the allowed for varying degrees of curvature / torsion in the spacetime causality flow would be more likely to produce matter emergence than one that had uniform curvature and no allowance for much higher local curvature.

Assuming for a second that some distributable (uneven) geometric curvature causes mass, one question I keep getting stuck on is what type of distribution evolution could explain such ubiquitous periodicity of mass (and energy). I can imagine a stochastic evolution that shows some kindof discrete scale invariance, a zoo of periodically similar stable curvature "attractors" but I also keep thinking that wave interference could be... In there

 

[atyy]

Atyy, do you perhaps think that you know more about physics than about biology? ;)
In any case, it seems to me that you know about physics more than many physicists.

Ah ha ha, thanks! I really am just an innocent bystander and could hardly calculate my way out of a paper bag. But maybe I am getting too much physics. Just the other day a colleague and I were discussing to what extent it is advantageous for the brain to represent the external world accurately. I thought it didn't have to be so accurate, just good enough to survive. Then he said that the counterargument was that there is a real world out there, and real photons coming out from objects. "Right?" he asked. I hesitated because I was trying to figure out whether photons are real. He sensed my uncertainty, and burst out laughing, "What, you don't believe in reality?" :D

 

[Paulibus]

Curved spacetime units might be a step in this direction...(and) I sure
hope someone does take up (this sort of?) idea

Assuming for a second that some distributable (uneven) geometric
curvature causes mass, one question I keep getting stuck on is what type of distribution evolution
could explain such ubiquitous periodicity of mass (and energy). I can imagine a stochastic
evolution that shows some kind of discrete scale invariance, a zoo of periodically similar stable
curvature "attractors" but I also keep thinking that wave interference could be... In there

It sounds to me as if some sort of wheel is waiting to be to be re-invented here, as the
attention of particle-physicists seems now to be turning towards patterns of distortion in
spacetime, with localised curvature, and variations in curvature, somehow endowing
mass/energy with a ‘gravitational’ interaction.

Are such folk aware that describing the behavior of patterns of the localised distortions that
disturb the translational symmetry in crystals is a well-developed cottage industry? Which might
serve as a template for understanding symmetry-disturbing ‘defects’ of the ‘vacuum’? For
crystal physicists linear ‘dislocations’, together with areal and point defects are quite ‘real’
interacting entities, although they are in essence just local symmetry-distorting patterns in an
underlying quite-symmetric substrate. Perhaps mass and energy masquerade similarly on the
symmetric stage we call the ‘vacuum’?

Squalid-state physics to the rescue?

 

[Paulibus]

The central thesis of LQG, namely that space is discrete rather than continuous, and the question:
how many angels can dance on the head of a pin? both seem to me to skate rather close to the
thin ice of sophistry. If space is intrinsically discrete, then I’d expect measurements of localised
‘position’ to yield discrete results, when a fine-enough probe was used. Reminiscent of
measurements of localised ‘energy’ in an atom revealing quantised energy levels, perhaps.

I then wonder what happens to a cornerstone of dynamics; namely the concept of conserved
momentum.

If a moving particle, say an electron or neutrino, has to be imagined as somehow jumping jerkily
from one ‘place’ to another; sans intervening ‘motion’, as it were: how is momentum then
conserved ‘during’ such a jump? Or is momentum conservation really just a convenient non-local
chimera that we use when describing the dynamics of macroscopic material objects, akin to a
macroscopic variable such as ‘position’ in discrete space? Are both concept of ‘place’ and
momentum only apparently continuous concepts?

What observable physics, if any, could be expected if this were so?

 

[marcus]

The central thesis of LQG, namely that space is discrete rather than continuous, ..
...
If a moving particle, say an electron or neutrino, has to be imagined as somehow jumping jerkily...

Hi Paulibus, this opens a rather deep question, when you say space, or geometry, or matter IS discrete it verges on ontology, and things like strict realism versus relational or interactive realism. I'm not well enough versed to do more than just tell you my own personal point of view. I'll try to do that, though.

I think the central stance of Lqg and indeed a lot of quantum thinking is that matter and geometry are discrete as you interact with them, their interactions are discrete, but they can be continuous all they want in private, on their own time.

Like an photon wave that undulates around all over the place but is only detected in a certain spot by a certain event in a certain detector.
Or an electron wave that does not have a continuous trajectory but does not "jump" either---it appears to have swum thru various slits on its way from emitter to detector so we know a DISCRETE sequence of locations corresponding to the event of passing thru one or more slits but we cannot say that a continuous trajectory even exists.

Such is the world. Information, interactions, measurements are finite and discrete, but what it IS we cannot say so definitely, it is rather more vague, like a vector in somebody's Hilbert space. Indeed we take the trouble to employ Hilbert spaces in part because they capture the right amount of vagueness, they and C* algebras. Or so I suspect.

I don't think of space as a thing or fabric or material. I think of geometry as a thing, that matter interacts with, that matter curves, and is guided by. And geometry is a thing you interact with by measuring the angles of triangles, and the relations between radiuses of round objects and their areas, or their volumes. So I think that measurements of areas, and angles, ought properly to be DISCRETE, like the measurement of the energy of an electron ought to be discrete. Because it is an interaction. Even though on its own time, in the privacy of its own parlor, the electron can have all different energies and spread out in a completely relaxed way. So likewise geometry should be allowed to be continuous as chocolate pudding or yoghurt, except when you measure something or when it is interacting with some matter in an in principle measurable way.

I admit that this attitude is subject to paradoxes and puzzles. It's hard to imagine how either matter or geometry could be like this! I also suspect that matter and geometry are fundamentally the same thing. This is why they can be so successfully enigmatic :D

 

[julcab12]

It's hard to imagine how either matter or geometry could be like this! I also suspect that matter and geometry are fundamentally the same thing. This is why they can be so successfully enigmatic

You are not alone Marcus! I used to think this picture of -- matter/energy instructing space how to curve and then space tells matter how to move. But 'what if' it's a masquerade of the same thing like what happened to the early fields.

 

[Paulibus]

Interesting remark:

But 'what if' it's a masquerade of the same thing like what happened to the early fields

My grip on physics history is shaky! Which early fields? Are you perhaps thinking of old vortex-theory days?

 

[marcus]

Michael Faraday? around 1820? I think he was the one who got the idea of "fields" (maybe like a field of grain or high grass, when the wind blows and the blades lay over in shifting patches pointing this way or that?). He had the idea of "field lines", looking for example like the lines of iron filings on a piece of paper with a magnet underneath.
He thought of fields with their field lines being the fundamental reality. (He did not accept the idea of "aether". The world was full of field lines, certain forces were in effect "made of" field lines.)

There were at least two kinds of fields. The electrostatic field lines that arise between pos and neg charges, and the magnetic field lines that arise from and connect the N and S poles of a magnet. These were different fields (for Faraday). They were produced differently, and affected different things, and behaved in different ways.

I think it was around 1870-1880 that Maxwell discovered that the E and the M fields of Faraday were actually different parts of the same field. There was really just one field, the EM field, and a change in one part produced changes in the other.

A change in the magnetic field seemed to produce electrostatic force in that it would push charge along a wire and make current flow. A conductive wire moving relative to a magnetic field, moving through a field, experienced change and a current would be induced in it. Also a current flowing in a wire would, itself, set up magnetic field lines. You could concentrate these magnetic field lines by winding the wire into a coil. The two types of force arise from the same thing, and so their influence on each other was eventually explained.

So maybe geometry and matter arise from the same thing and this could explain THEIR influence on each other

 

[Paulibus]

Thanks, Marcus. Yes, Faraday invented the field concept, which gains huge credibility when one looks at patterns of iron filings near a magnet and leads on later to Maxwell's quantitative description of interactions between charges in terms of dynamic E and B (or is it H?) fields. Fields are great mathematically tractable descriptive tools. But these fields are not the same thing as the charges (static or moving) that generate them. Similarly with the gravitational field; which is not the same thing as the mass/energy that is the field's source. And in linearly elastic media, where tensor fields describe both stresses and the strains that cause them, stresses are not the same animals as strains.So, being pernickety, I don't see that there's any masquerading in the description we give of gravitational interactions between lumps of mass/energy. In these cases cause and effect differ. I think?

 

[julcab12]

Interesting remark: My grip on physics history is shaky! Which early fields? ?

... It was Newton -- Newtonian spacetime. It is pictured as metrical structure. Then came Special relativity, loosing the strict distinction between "space" and the "time". The usual 3d space (Newton) became 4d manifold with a flat lorentzian metric. Dynamic objects moving over spacetime includes a field as well. Then, GR came with a tweak on the Newtonian spacetime into gravitational field which is represented by a field on spacetime. IN terms, the Newton's background spacetime is the same as gravitational field. We learned that GR's spacetime is a dynamical field, obeying dynamical equations. The gravitational wave is similar(almost) to an electromagnetic wave. Every dynamic object has a quantum property to it, which can be captured by formulation of dynamical theory within QM. Spacetime itself exhibit quantum properties -- metrical. We can consider that Spacetime / gravitational field, is a dynamic entity with Quantum properties.

-- I'm only saying this on a full relational view; nothing more but a construction of space(localization)/time and motion that is modeled fragmentary but deeply rooted like it is one of the same fundamentally. I'm just a reader and please do correct me if i went a bit far.

 

[Jimster41]

So maybe geometry and matter arise from the same thing and this could explain THEIR influence on each other

Whether or not space time itself is ultimately continuous or discrete or made of cheese-cats is unknowable (as Marcus says, "It's all just experience"). Schroedinger's amazing and spare "What is Life" is the best debunking of such philosophical conundrums I have ever read. As I recall it says basically the same thing. The question then is whether or not we are decomposing our (shared) experience of whatever it is as a set of continuum fields acting on particles, an approach that has hit some pretty major obstacles, or something else. What I like most about Energetic Causal Sets, or Causal Spin Foams, at least as I understand them, is that they free us from the notion of a continuum gravitational field (one major bugger obstacle). Instead they provide a way of thinking of space-time curvature and all it implies, gravity, mass, acceleration, as potentially being the emergent result of an evolutionary game called "space-time geometry". The stochastic math of Evolutionary Dynamics would say emergent structure is inevitable when states iterate under rules on a gradient, or "fitness landscape". And if all those key bugger tough pieces can be successfully imagined in this way then why not all the known particles and forces. At one level, this picture of fundamental physics as a smooth extension, or "root" of the more familiar kinds of evolution kind of seems disappointingly obvious. But if you do buy it for a second, the really intriguing question is, in what fitness landscape is all the hardware of our experience evolving? I think Verlinde might suggest it skulks around in the brilliant guise of "The Second Law of Thermodynamics". To me this is a profoundly coherent and complete picture... And it points to other puzzle pieces, the Hubble constant, "dark matter and energy", quantum non-locality, generally-ubiquitous-periodicity (or discrete scale invariance) and extreme space-time forms like Black Holes. These bother me a lot, because they almost seem to fit, in such a schema.

 

[Jimster41]

Dark Matter and Energy: If the driver of curvature is not Mass or Energy, but rather they are emergent types of curvature, then options for understanding other types of curvature seem to open up

The Hubble constant: The apparent acceleration of all objects away from each other, also a case of space-time curvature, does not need to be accounted for strictly from initial conditions. Rather it could be THE driving condition, manifest, the changing phase space of our space-time which drives the second law, causing all other space-time structure to emerge.

Quantum non-locality and Discrete Scale Invariance: tricky. Evolutionary dynamics allows for rich structure to emerge from simple rules under iteration, even periodic structure, especially periodic structure. However, if particles are emergent space time phenomenon, and the game of Space-time curvature evolution has non-local components, which by all accounts to date, it appears to - meaning the photon that went through the right slit at 2pm apparently interfered with the photon that was seen passing through the left slit, at 3pm, then there could (at one level there simply are) patterns of structure in our space time evolution that are caused by non-local, and/or a-temporal accounting. The implication, to me is that the causal wave that forms our space time is not wholly... All that is fundamental. This, points back to all of these other pieces - shedding new light on what they could mean.

Extreme space-time forms, black-holes, pulsars. These could be perceived as simple run-away emergence of space-time curvature structure, or even more outlandish, as structures of a-temporal resonance, feedback phenomenon, ringing in the true universe which must contain our parochial little space-time. Dark Matter and Energy could just be their extended limbs - or ripples or harmonics. The Big Bang could even be their lensed reflection on the surface of our space-time's container. Or the shape of the dent everything that will ever happen here, has made in that surface.

I'm working through Penrose' "Cycles of Time" I think his notion of conformal geometric symmetry (with inverted energy density) at the beginning and end of our space time plays very nicely with my fantasy of ECS. I do think he bangs his head looking for the continuum g field. Though it seems prescient that he speculates on a particle (even non interacting) having non constant rest mass.

Also I understand they are testing the last loophole in Bell's Inequality - the so called "free will loophole" I for one am perfectly happy to call it a day with 2 out of three, because if the hidden variables turn out to be "universal predetermination" I think it only makes the already crazy point the two slit seems to make anyway. Time is certainly a bizarre illusion we can't escape, and causality, well that's likely kind of the same deal.

 

[Jimster41]

It may seem off putting to imagine the "laws of physics" evolving. I don't think I'm speculating to that end, I'm suggesting (interpreting the Pros) that the fundamental objects of our experience all particle/energies, not just all the compound objects like plants and animals and stars could be (best) described in the language of Evolution, where some relatively simple system is iterating under a set of rules, and a fitness landscape and all other structure is emergent. For this to be, there has to be some at least relatively stable, though not necessarily fixed rule set, like the rules of ECS, and some similarly stable fitness landscape.

By proposing that space time curvature (aka gravitation force and the measure of Mass) is "an emergent result of entropy" Verlinde has bridged what seems to me to be an obvious gap, in hindsight. The evolution of space-time curvature is given it's fitness metric by changing (increasing) phase space which manifests as the second law and the "entropy tensor". From this evolutionary system, iteration emerges specific curvature forms. It seems of no small importance that this can provide a fundamental root cause for evolution as a whole, or rather is consistent with what we already know - that macroscopic natural evolutionary processes are driven by the 2nd Law. Life is an entropy minimization machine.

So how might the Hubble expansion of phase space (available states) induce curvature. I'm just trying to think about this... If I start with two coins, one bucket. Since there is only one bucket both coins have to be in that bucket. There is no freedom of configuration and no question about configuration equilibrium under repeated questions about configuration. If you add a bucket, you have introduced a "configuration tensor", an entropic gradient or curvature. Repeated random choices of configuration require even distribution to emerge from a state of uneven distribution, probability fills probability space evenly (Louiville's theorem).

So why doesn't the system go to equilibrium phase space distribution immediately? Why is the curvature so lumpy? Stochastic processes starting from nearly identical initial states, can have highly divergent end states. So you can imagine the small difference of the two coin two bucket case ending up in some intermediate-state with complex, lumpy, distribution structure after a whole bunch of buckets have been added, and the configuration question has been asked some number of times. However, I think I can imagine how the divergence to lumpiness might be driven by some additional effective cost term that resists the equilibrium distribution tendency. Maybe it's only the relationship between the rate at which re-configuration steps are taken, and the rate of buckets being added. My hunch is that something as simple as that ratio, given the surprising math of iteration and evolution, could explain locally stable curvature attractors, or "curvature sinks" - i.e. everything from massive particles to black holes.

So what about all the rest of the standard model, that is not gravity? Well to my thinking E=m*c^2 and all of that various mass and energy, since it exists in space-time, could be (should be) explainable as emergent structure of space-time curvature evolution. The zoo of fundamental particles would just be a case of discrete scale in-variance (repeated, and re-normalized patterns of emergence) in interacting or "co-emerging" structures, in other words they are just creature-like mixes of curvature attractors of different evolutionary histories.

Sorry about all this, I'm done.