Self-organizing quantum universe explained in July SciAm feature

[Fra]

I don't know half as much as Marcus on these things but I read some of their papers and here are some of my reflections...

What "microscopic components" do they mean? Not their simplices, I hope, which are just a calculationional tool, as I read you:

A general problem is that of counting geometries (or counting anything). Ie. one asks what is the set of possible geometries. The set of all possible geometries can be called a microstructure. And each geometry is a microstate.

If we also on that set can find a measure that assigns probability amplitudes between any two microstates, then one would expect that the result from "diffusion" or random walking from an arbitrary initial condition, should follow certain dynamics at the statistical level.

I think there is an ambigouity in their choice of this set of geometries and the action measures. If I were to dig into CDT these two points is what I'd try to improve.

They seem to want to give the impression that their way of counting geometries since it's based on random sampling over all possible geometries are universal and fair. But that's exactly the deceptive part. This problem exists also in classical stat mech.

What I am looking for is taking the process, that generates/constructs the sampling space seriously... and look for the physics in it. I think matter may come out of that, because matter may be the relational references that is missing to make this more conceptually consistent. Because in effect matter could as I like to think of it quality as "observers". And the logic of constructing and counting geometries may must IMO be attached to observers.

So while I like the statistical approach in CDT, the poins where I can't help disliking it's arguments are possibly also the points which should resolve once matter is incorporated.

If something like that will come out of CDT, I would be vary interested.

"...we are in the process of developing new and more refined methods to probe the geometry of the model further, and which eventuallyshould allow us to test aspects related to its local “transverse” degrees offreedom, the gravitons. We invite and challenge our readers to find such tests ina truly background-independent formalism of quantum gravity."

This seems to be from 2005 rather than 1995, from "Reconstructing the Universe"
J. Ambjorn, J. Jurkiewicz (U. Krakow), R. Loll (U. Utrecht)
http://arxiv.org/abs/hep-th/0505154

/Fredrik

 

[Fra]

To make a silly but illustrating analogy...

Because in effect matter could as I like to think of it quality as "observers". And the logic of constructing and counting geometries may must IMO be attached to observers.

How can a man finger only 10 fingers, count 20 apples? :)
And how does a man with no fingers understnad the concept of counting?

/Fredrik

 

[oldman]

I don't know half as much as Marcus on these things but I read some of their papers and here are some of my reflections...

And I don't know a hundredth as much as either of you --- but I find the discussions very interesting.

This seems to be from 2005 rather than 1995, from "Reconstructing the Universe"
J. Ambjorn, J. Jurkiewicz (U. Krakow), R. Loll (U. Utrecht)
http://arxiv.org/abs/hep-th/0505154

Thanks for this correction, Fredrick. Sorry for being ten years out of date!

 

[Fra]

How can a man finger only 10 fingers, count 20 apples? :)

If that didn't make sense, then I guess it's more challanging to ask him to count 1025 apples.

/Fredrik

 

[Coin]

If that didn't make sense, then I guess it's more challanging to ask him to count 1025 apples.

/Fredrik

Well, there are two joints, so you can do tristate if you want...

 

[marcus]

Like your questions!

. It turns out that the dimensionality can change with scale.

Is this the real importance of their approach?

To me as a retired mathematician it is one of the most intensely interesting things about it. It suggests that space is not modeled by a vintage-1850 smooth manifold.
In a manifold---still the standard continuum used in physics and most mathematics---the dimensionality is independent of scale. If it is 3 at large it is 3 all the way down no matter how small or how close you look.

Ambjorn Loll are promoting a totally new kind of continuum, which only looks like a smooth classical manifold at moderate to large scale.

Much of mathematics (including incidentally stringy math) is built on the classical manifold. Fields are defined on manifolds, strings vibrate in manifolds, branes are lower dimension manifolds. The classic 1850 continuum is the basic building material. If you introduce a new idea of the continuum into mathematics you get a revolution of historical proportions.

The fact that dimensionality is scale-dependent is the touchstone that shows it is a really new continuum, not to be modeled by anything previous. So that is quite an interesting result.

Ambjorn and Loll are introducing a fundamentally different sort of continuum which is the limit of a series of discrete buildingblock approximations.

the macroscopic space we experience emerges or arises as epiphenom from the fundamental atoms (as they point out)
and moreover there are no atoms because you can zoom in closer and get the same picture
namely again the macroscopic world emerges from the fundamental atoms (which are now smaller and more numerous)

If this is so it looks to me as if it let's a lot of steam out of their approach.

I don't see it that way at all! What they have is far BETTER than if it were made of a discrete finite set of atoms of a final fixed size.
At each scale-level, at each stage of magnification, it BEHAVES as if composed of building blocks---OK that is nice and that is what they are suggesting when they say atoms.

But if there were some minimal size and merely a discrete set of building blocks this would be very disappointing and there would be awful philosophical issues like what are the building blocks made of etc etc.

What they have, so far, is a prospect of a real continuum with no minimal size and no atoms but which behaves in a way that let's you calculate and do computer work as if there were atoms---this is far far better. It is way better than I expected when I first got deeply interested in quantum gravity. Then there seemed to be a naive choice between two unsatisfactory alternatives----a finite set of marbles or a classic smooth continuum----both of them essentially boring and studied to death.

If you want you can think of the Ambjorn Loll continuum as something which has its cake and eats it too. It has the benefit of discrete atoms, but that benefit extends consistently down to smaller and smaller scale without limit. the results they report coincide independent of how many simplexes are used----look at the charts---they superimpose the curves for each level of magnification and they approximately coincide. So it acts like atoms without there being any atoms. Cool?

 

[oldman]

To me as a retired mathematician ... think of the Ambjorn Loll continuum as something which has its cake and eats it too...it acts like atoms without there being any atoms. Cool?

Yes indeed. Your posts have illuminated for me, as a retired physicist, the mathematicians perspective. I find this more valuable that the rather formidable and dry technical expositions in such texts that I have available and struggle with, e.g. Schutz's Geometrical Methods of Mathematical Physics. I'm beginning to appreciate that an important difference between physics and mathematics stems from the different tools used by these disciplines.

From your posts I now appreciate that much of the mathematics used in physics is based ultimately on the continuum of real numbers, in that they underlie the notion of a differentiable manifold of the 1850's variety. The continuous character of real numbers and of manifolds appears to stem from the freedom that using one's imagination to stimulate ratiocination confers on mathematicians.

In physics, ultimately one has to measure-- but sadly, always with limited accuracy. Taking limits in a continuum context is a useful procedure but in practice, finite accuracy colours ones perspective, say as in defining SR's domain of applicability in curved spacetime. Such limitations engender prejudices: physicists tend always to look for finite 'marbles' that may underlie physical processes -- a little like looking for sea serpents over the edge of a world that you cannot always fully explore. Lucky mathematicians can prove theorems about sea serpents from their armchairs.

When I said that identifying simplices as building blocks in Ambjorn et al.'s work "let steam out of their approach", I was thinking of physics steam. But perhaps the new kind of continuum they are inventing may in the end usefully bridge the gap between different perspectives, in which case their program of incorporating mass will be successful. I hope sooner than later.

 

[Fra]

Marcus, would you mind commenting on these things? I am not sure if I asked you this before.

I don't see it that way at all! What they have is far BETTER than if it were made of a discrete finite set of atoms of a final fixed size.
At each scale-level, at each stage of magnification, it BEHAVES as if composed of building blocks---OK that is nice and that is what they are suggesting when they say atoms.

I want to say that I like sound of what you say here.

But, what is the physical meaning of this scale? Should this scaling and limiting procedure be considered theoretical tricks that has no physical meaning? I have a feeling that they don't consider it to have any physical meaning?

I can't help associating "the atoms" with distiniguishable states, which then directly gives this scale a physical meaning, that it is a relation between oberver and observed. Something may look like marbles, but wether it's due to the resolution of the communication channel, my memory, or that there really is marbles is IMO a question can't be answered.

It seems to me that there is a natural type of scaling that means scaling the information capacity and channel capacity. But then once the observer is chosen, the scale is set. To scale to infinite resolution to me, means inflating the observer to infinite mass. This doesn't make physical sense? or does it?

How do You avoid asking these questions when you see the CDT work? I don't mean to pick on it, I really aim to probe further on - what is the future of CDT? What is the next questions to be solved?

/Fredrik

 

[marcus]

Oldman and Fra, I'm going to transcribe the last couple of paragraphs because of this phrase that keeps gnawing on my mind: "a region of infinite boredom".
They haven't ruled out the possibility that people might find marbles, as they zoom into higher and higher magnification. But they are definitely contemplating the possibility that you find only fractal. Something that behaves like marbles at whatever scale you choose to look.
But which isn't really marbles, because you can always step up the magnification and look closer and it looks exactly the same.

I don't think they have ruled out the other, or that they are necessarily preferring the infinite zoom fractal continuum. But that is what their computer experiments so far found and so they are going with it---let your finding guide your imagination. I think any of us would too. If you find something unexpected, follow and see.

I think what Ambjorn Loll means by "a region of infinite boredom" is a range on the magnification scale knob. Up to a point, as you turn the knob and see spacetime at higher and higher magnification, you find interesting new structure. But then you reach a point where, if you turn the knob some more it keeps on looking the same----forever. That magnification range where spacetime is fractal or scale-independent or self-similar is what I think they mean by a region of infinite boredom. There is nothing new to learn by turning the knob.

Anyway the phrase gave me a mild shock--because I don't think of fractal as boring. I think its beautiful and I would love to live in a continuum which arises from fractal ground.
The phrase was unexpected, so it made an impression on me.

Here are those two paragraphs at the end of the article:
======quote======

On still shorter scales, quantum fluctuations of spacetime become so strong that classical, intuitive notions of geometry break down altogether. The number of dimensions drops from the classical four to a value of about two. Nevertheless, as far as we can tell, spacetime is still continuous and does not have any wormholes. It is not as wild as a burbling spacetime foam, as the late physicist John Wheeler and many others imagined. The geometry of spacetime obeys nonstandard and nonclasical rules, but the concept of distance still applies. We are now in the process of probing even finer scales. One possibility is that the universe become self-similar and looks the same on all scales below a certain threshhold. If so, spacetime does not consist of strings or atoms of spacetime, but a region of infinite boredom: the structure found just below the threshold will simply repeat itself on every smaller scale, ad infinitum.

It is difficult to imagine how physicists could get away with fewer ingredients and technical tools than we have used to creaae a quantum universe with realistic properties. We still need to perform many tests and experiments--for example, to understand how matter behaves in the universe and how matter in turn influences the universe's overall shape...
===endquote===

I didn't complete quote of the last paragraph because it is the obvious but necessary remark that validation requires empirical test of predictions derived from the model.

 

[marcus]

I want to say that I like sound of what you say here.

... To scale to infinite resolution to me, means inflating the observer to infinite mass. This doesn't make physical sense? or does it?
...

I'm pleased you like the tenor of the discussion, Fra. Thank you for saying so. A lot of the time, I think, your concerns are orthogonl to mine and all I can do is look at your concerns and then try to clearly state mine, for whatever it's worth.

Ambjorn Loll have discovered what may be a new mathematical continuum.
It looks like the usual model continuum until you examine closer and then its geometry gets a bit chaotic.

The question in my mind is whether or not the analog of LIE GROUPS will ever be defined for this model continuum. Back in the 19th, wonderful Riemann (a kind of mathy Mozart) tossed off the idea of a smooth manifold and then a Norwegian named Sophus Lie constructed a hybrid object which was at the same time algebraic and geometric---it was an algebraic group of symmetries and also a smooth manifold. Multiplication within the group was smooth. Sophus Lie's groups revolutionized physics.

So I am wondering if there is a CATEGORY of Ambjorn Loll continuums and if you can define morphisms---the analog of smooth maps---from one continuum to another. And if you can define a transformation group action.

And I am wondering this: you know John Baez occasional This Week's Finds (TWF) column. He has several hundred on line now. I am wondering if the Ambjorn Loll continuum will ever get to the point that Baez will write a TWF about it.

Right now Ambjorn Loll seem to me like a team of geologists who have found one end of a large bone sticking out of the ground and have begun digging. They want to see what is there and expose more of the bone.

It might turn out to be some quite useful mathematics, or it might not.
You would have to define the mappings, the morphisms, in a way that respects the underlying fractal microstructure. It might turn out to be elegant and natural to do this, or it might be discouragingly messy. Or the whole thing might suddenly be seen to be trivial and not worth bothering with.

At this point I think Ambjorn Loll are the only group that has what I would provisionally call a quantum continuum (if it works out). A continuum which has palpable quantum fluctuations in its geometry at microscopic scale. (And also where instead of a classical spacetime you have a path integral combining many possible histories.)

((But there recently have been some papers which align the spinfoam approach more closely with the Ambjorn Loll approach----Laurent Freidel posted one just a little while ago.))

So I don't think you can apply philosophical or information-theoretic criteria to the Ambjorn Loll approach just yet. You have to wait until they dig some more and expose more of the bone.

We could make a guessing game out it. Like, how soon will John Baez do a TWF on the category of Ambjorn Loll continua with Ambjorn Loll maps as the morphisms.
12 months, 18 months, 2 years, 3 years, never?

I expect a genuinely new continuum would revolutionize physics, but they might not have one

 

[marcus]

... But perhaps the new kind of continuum they are inventing may in the end usefully bridge the gap between different perspectives, in which case their program of incorporating mass will be successful. I hope sooner than later.

Exactly. I too.
Your questions and observations have been a considerable benefit to me, and a stimulus. Thanks. If I was younger I'd probably want to work on this, though it's clearly still a gamble.

BTW it seems that Gerard 't Hooft has an essay called The Fundamental Nature of Space and Time which he has contributed to this book
https://www.amazon.com/dp/0521860458/?tag=pfamazon01-20
supposed to come out March 2009 (I think the amazon page has the wrong date) Here is the publisher's catalog page
http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521860451
A student at Utrecht kindly tried to obtain a preprint or draft copy of 't Hooft's essay, but neither is being made available.
Since Loll and 't Hooft are at the same institute, one being aware of the other's work, I expect the essay, whenever it appears, might help get some perspective. And 't Hooft's own ideas on the subject should be extremely interesting.

I tell myself not to focus too much on this one approach but keep the others in periferal vision.

 

[Fra]

A lot of the time, I think, your concerns are orthogonl to mine and all I can do is look at your concerns and then try to clearly state mine, for whatever it's worth.

Thanks for your comments Marcus. I think you are right that I have chosen a slightly different perspective than you, but it is still interesting to follow the reasoning of others. After all I think we are probing for more or less the same things. Actually the most interesting thing is when two apparently different style of reasonings, seems to converge the same destination. To me this indicates that there is a deeper logic behind.

It might turn out to be some quite useful mathematics, or it might not.You would have to define the mappings, the morphisms, in a way that respects the underlying fractal microstructure. It might turn out to be elegant and natural to do this, or it might be discouragingly messy. Or the whole thing might suddenly be seen to be trivial and not worth bothering with.

Even though I do not have a matematicians perspective on this I am definitely with what I think you also seek - a new mathematical formalism, for the new physics. Or as I like to phrase it, new logic of reasoning in physics.

Discreteness vs continuum is also something I'm struggling with but from I think a different angle. I am try to see these things from an intrinsically observational information view. My personal expectations, and here I expect that 't Hooft will have something interesting to say, is that in the same way that old formalisms have considered intrinsic vs extrinstic geoemetry, there is intrinsic vs extrinsic information, and reasoning. What I mean with physical basis is exactly the vision for "intrinsic reasoning". Alot of the time there is extrinsic reasoning going on. It's easy to construct extrinsic questions, that simple are onposable from the intrinsic point of view. The comparasion here is vectors that point out of the tangent plane at a point of a manifold.

When I think of "manifolds" I think of information. I think two manifolds can measure each other, but I can't see that A relates to B like B relates to A. This is a different way (I think more fundamental way) to think of "background independence" that transcends spacetime.

If I do not fix the observer, I would also come the conclusion of running scales. Ie. you can zoom in indefinitely, however as far as I see this, there is no freedom to do this scaling. Also if I don't fix the observer, I am considering questions where I don't know who is asking. I'm afraid it will take us into the paradox of "The Hitchhiker's Guide to the Galaxy", where the problem becomes that of relation to the answer.

So I don't think you can apply philosophical or information-theoretic criteria to the Ambjorn Loll approach just yet. You have to wait until they dig some more and expose more of the bone.

This makes sense to me. It may well be that they are scratching the surface of something, but then I can't help speculating what they will find.

We could make a guessing game out it. Like, how soon will John Baez do a TWF on the category of Ambjorn Loll continua with Ambjorn Loll maps as the morphisms.
12 months, 18 months, 2 years, 3 years, never?

I expect a genuinely new continuum would revolutionize physics, but they might not have one

I love Baez columns, I don't read it regularly but he has made some excellent posts on a variety of topics.

I am not sure yet what this new continuum is. I think it should be ;) a relative continuum. In this way the continuum limit is no more real than the marble view. Ie. the answers you get depends on the questions you ask. The interesting parts like in the scaling of questions itself. But I would want to get hold of the physics of this scaling. As I read CDT so far at least, the physics is at the continuum limit only. And that the regularization they did is so far motivated merely as a way to make sure they get some non-divergent results.

If we see that as the first step that is awesome, and perhaps they still haven't realized what this could be? After all it seems to me some massive steps missing - for example to incorporate matter. That alone seems to suggest that if CDT is going to grow into some "toe" then the current progress is probably like a brick of the Dom where we still haven't understand the big picture?

/Fredrik

 

[marcus]

...
We could make a guessing game out it. Like, how soon will John Baez do a TWF on the category of Ambjorn Loll continua with Ambjorn Loll maps as the morphisms.
12 months, 18 months, 2 years, 3 years, never?
...

quick action. JB already on this one:
http://golem.ph.utexas.edu/category/2008/07/causality_in_discrete_models_o.html#more

not the full Monty yet, no category of Loll continua with Loll maps as morphisms
but still a nice long conversation at the N-CATEGORY CAFE

I halfseriously offered the question July 20
and the CAFE conversation kicked off one week later July 27.