How Does Quantum Theory Suggest Spacetime Emerges from Simple Triangles?

[Naty1]

In the Cosmology forum a reference by Marcus references an article in Scientific American I think might be of interest to Quantum Physics readers:

(What are the (quantum) building blocks of space and time?)

http://www.signallake.com/innovation/SelfOrganizingQuantumJul08.pdf
(by Ambjorn, Jurkiewicz and Loll)

Here's a series of excerpts which provides an overview of the paper, a quantum gravity model:
(Italic scripts are my additions for clarity from other portions of the text )

(The) dynamical emergence of a four dimensional universe of essentially correct physical shape from first principles is the central achievement of our approach

If we think of empty spacetime as consisting of a very large number of minute structureless pieces (triangles which approximate curvature) and if we then let these interact with one another according to simple rules dictated by gravity and quantyum theory they will spontaneously arrange themselves into a whole that in many ways looks like the observed universe...(four dimensions with sufficient time) Similar mechanisms of self assembly and self organization occur across physics, biology and other fields of science...Casual Dynamic Triangulations approximates spacetime as a mosiac of triangles...Computer simulations dashed the (Stephen Hawking) hope that casuality would emerge as a large scale property from microscopic quantum fluctuations...Eucledean geometry indicates that space and time are treated equally...and does not build in a notion of causality...we must enforce causal gluing rules...an arrow of of time...for our model to work we needed to include from the outset a so-called cosmological constant (energy)...It is truly remarkable that by assembling microscopic building blocks (triangles) in an essentially random manner we end up with spacetime that on large scales has the highly symmetric shape of the de Sitter Universe...

The number of dimensions depends on the scale...spacetime appears to have a different number of dimensions (over time)...evidently a small object experiences spacetime in a profoundly different way than a large object does.

All of which sounds like some really interesting work.

Now my simple minded questions:

Inputs: simple triangles, gravity, quantum theory, causality, time, and a cosmological constant (vacuum energy);

Output: spacetime...

(1) Seems like a possible model for today, with expanding space...but how did it start? Were all those input quantities ALWAYS present?? Seems like an awful lot of "stuff" to have sponaneously emerged all at once! Seems too complicated..

(2) If you put in causal structure, do you automatically get out some kind of Lorentzian manifold of which de Sitter space is one? I think de Sitter space is slightly curved even in the absence of matter or energy. Is this a significant result??

 

[marcus]

In the Cosmology forum a reference by Marcus references an article in Scientific American I think might be of interest to Quantum Physics readers:

(What are the (quantum) building blocks of space and time?)

http://www.signallake.com/innovation/SelfOrganizingQuantumJul08.pdf
(by Ambjorn, Jurkiewicz and Loll)

Here's a series of excerpts which provides an overview of the paper, a quantum gravity model:
(Italic scripts are my additions for clarity from other portions of the text )

...
...
All of which sounds like some really interesting work.

Yes! That is such a great article! Thanks for posting these excerpts, Naty.
I hope you have or will try looking at one or more of their professional journal articles as well. They have a mixture of inaccessible stuff with moderately understandable more intuitive explanation. Here's some other Loll papers ranked by citation count (how often other research has cited them as reference)
http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=find+a+Loll+and+date+%3E+2003&FORMAT=WWW&SEQUENCE=citecount%28d%29

Now my... questions:

Inputs: simple triangles, gravity, quantum theory, causality, time, and a cosmological constant (vacuum energy);

Output: spacetime...

(1) Seems like a possible model for today, with expanding space...but how did it start? Were all those input quantities ALWAYS present?? Seems like an awful lot of "stuff" to have sponaneously emerged all at once! Seems too complicated..

(2) If you put in causal structure, do you automatically get out some kind of Lorentzian manifold of which de Sitter space is one? I think de Sitter space is slightly curved even in the absence of matter or energy. Is this a significant result??

You know how when you learn freshman college calculus, and learn integration, you approximate the integral with little rectangles and then let the size of the rectangles go to zero?

People can understand Loll team's approach in different ways. You can imagine what spacetime geometry is like microscopically in different ways.
The way I picture it, space and spacetime are not made of little triangles----it just happens to work to approximate their dynamic geometry using little triangles.
The way I think of it, you could use other shape building blocks and it would work just as well. Ultimately the theory has the size of the building blocks go to zero so it doesn't matter what original shape.
We can talk some more about this. I don't insist on my personal perspective. Back later.

 

[Naty1]

Good analogy...integration/differentiation...that's a part I can readily visualize...what I am having trouble getting my head around is so many input requirements necessary to generate space time. Seems something more fundamental is missing...sounds too complicated...

I CAN understand that from a model perspective...some "drivers" , something active/dynamic is required ...I can't quite imagine all those things being inherently present in "empty space"...the article mentions

On...shorter scales quantum fluctuations of spacetime become so strong thatclassical notions of geometry breakdown altogether...spacetime...is not as wild as a burbling spacetime foam as the late physicsts John Wheeler and many other imagined...

I wonder what constituents will ultimately be found present in "empty space" as a necessary and sufficient condition for the existence of quantum foam...causality? time? distance? gravity? cosmological constant (energy)? Or is simply a type of "chaos",quantum uncertainty, for example, enough to randomly begin the generation of space and time?

 

[Fra]

what I am having trouble getting my head around is so many input requirements necessary to generate space time. Seems something more fundamental is missing...sounds too complicated...

I CAN understand that from a model perspective...some "drivers" , something active/dynamic is required ...I can't quite imagine all those things being inherently present in "empty space"...the article mentions


I wonder what constituents will ultimately be found present in "empty space" as a necessary and sufficient condition for the existence of quantum foam...causality? time? distance? gravity? cosmological constant (energy)? Or is simply a type of "chaos",quantum uncertainty, for example, enough to randomly begin the generation of space and time?

I share a similar objection to this. I for a higher level of consistency of reasoning matter and observers has to emerge along with spacetime. There is something conceptually awkward with the "pure gravity", beucase it IMHO at least misses the physical basis of the image of spacetime.

Some others has expressed similar doubts, and think that matter and space must emerge hand in hand. To try to separate them, and first make a theory for empty spacetime because it's presumable less complex, and then somehow couple it to matter, will to me intuitively be more complicated because I think matters is needed to get the consistency.

I see the pure gravity, on the same levels are a measurement theory, that tries to make a model for measurement, but without incorporatin the observer. If some of the weirdness lies in the relation between observer and observer, like I think, then the separation will make it more complicated, not easier.

I think the story with matter and spacetime is similar, but it's just my current personal opinon.

/Fredrik

 

[friend]

Some others has expressed similar doubts, and think that matter and space must emerge hand in hand. To try to separate them, and first make a theory for empty spacetime because it's presumable less complex, and then somehow couple it to matter, will to me intuitively be more complicated because I think matters is needed to get the consistency.

I've seen attempts to describe QFT in curved spacetime where they replace the mass term in the flat space lagrangian of a free particle with a metric. They seem to justify this by noting that kinetic energy of a particle in flat space is formed from the inner product of its velocity vector in tangent space of configuration space with its dual momentum covector in the cotantent phase space. The mass there plays the role of a metric; they call it the "mass metric". When they generalize to curved spacetime, they replace the mass term with a metric, g_uv(x). So I have to wonder if General Relativity can be derived with this substitution. Such a substitution makes particles to be a local manifestation of gravity.

 

[Fra]

I've seen attempts to describe QFT in curved spacetime where they replace the mass term in the flat space lagrangian of a free particle with a metric. They seem to justify this by noting that kinetic energy of a particle in flat space is formed from the inner product of its velocity vector in tangent space of configuration space with its dual momentum covector in the cotantent phase space. The mass there plays the role of a metric; they call it the "mass metric". When they generalize to curved spacetime, they replace the mass term with a metric, g_uv(x). So I have to wonder if General Relativity can be derived with this substitution. Such a substitution makes particles to be a local manifestation of gravity.

I've also stumbled on some alternative way to argue towards alternative explanations of GR effects, that use calculations different that GR formalism, but it was fairly simple and not sure if it's what you refer to and I don't remember where I've seen it. Do you recall any references to any of that?

But in a sense, I think it's plausible that the information that is implied in the spacetime structure, has a basis. And I think the natural basis for this is matter, in the sense that a particles expectations about it's own environment (and space) is encoded in it's own behavioural properties, and the mass of the partle may somehow constrain the "mass" of the total information it has.

Even if you picture "empty space" with quantum fluctuations in say a lab, there importance of the boundaries as information reference can not be understimated. So that really isn't an intrinsic picture. It's rather the rest of the world, looking into a little bubble of "void". the picture would be quite different if you picture that the little bubble was the observer, looking out into the big unknown. His size/mass alone, should severaly constrain his possibilities.

So in a sense, there seems to be plasible that for each observer, there is a measure of the total "mass" of the amount of information it has about it's enviroment. But then also information about the environment is all we will ever have. The closest thing to the "real thing" is I think that a local group of observers seems to be in agreement about the information. But this still warrants nothing in a larger perspective.

But this also works the other way around, that realtive to a small observer, this limits the structure of the space it can relate to. And the behaviour of this small observer, might then be stronly coloured by this. Taken to it's extreme, the limiting case, the observer mass goes to zero, then the complexity of space also goes to zero from the INTRINSIC view. This doesn't mean the structure is simple relative to a massive observer, such as a gigantic accelerator, probing a tiny position.

Maybe the simplicity we seem to seek, exists in the inside view, and the the interaction between such "small observers" should be expected to be simpler and simpler as their information mass goes to zero.

/Fredrik

 

[Naty1]

I knew Loll's paper sounded familiar:

emergent quantum spacetime is discussed by Lee Smolin in THE TROUBLE WITH PHYSICS, 2007, Chapter 15, Physics after String Theory. For those who'd like another physicsts view of the paper this five or so page discussion is worthwhile.

One related discovery: By ...

assuming that a classical world emerges from causal set theory, Syracuse Physicst Raphael Sorkin and collaborators predicted that the cosmological constant would be about as small as has since been observed...(and Smolin says) As far I'm aware, this is so far the only clean solution to the cosmological constant problem...

And Smolin discusses yet another approach to quantum spacetime: Twistor theory

(from mathematical physicst Roger Penrose) which partly realizes the idea that spacetime may emerge from anjother structure