Trying to understand Loop Quantum Gravity in layman's terms

[Galteeth]

Ok, I've been trying to follow what you guys have written about this.

Is it sort of like protein folding in biology, only instead of proteins you have space time, and you spin it around, and most of it is quantum foam vacuum stuff, but in some places it clumps in sort of oscillating ways that give that gives matter moving around but it's still kind of foamy at the very small level?

Or am i way off?

 

[marcus]

...
Or am i way off?

Other people might respond in a completely different way. I'll give you my personal take on what you're asking.

First understand the overall aim of (nonstring) quantum gravity in layman's terms.

All the various (nonstring) approaches have some mathematical representation of the 4D continuum, which is central. They have some way of representing the whole geometry of the universe (given enough triangle lego building blocks or enough tinkertoy balls and sticks, or whatever the particular approach uses) which can be simplified and scaled down and studied.

If you want a layman understanding of Loop or Foam then you should first get a general layman (nonmath, intuitive) understanding of the QG venture overall. And the best way to do that at present is to read a certain Scientific American article by a brilliant QG physicist named Renate Loll. It is a highly visual, pictorial, non-math article, that happens to be about one of the other QG approaches---not Loop or Foam. An approach called CDT that we can call simply "Triangulations QG". Loll and Ambjorn invented it in 1998, but it only hatched out, so to speak, in 2004, when they took on the full 4D case and began rapid progress.

Here is the SciAm article:
http://www.signallake.com/innovation/SelfOrganizingQuantumJul08.pdf

The title is "The Self-Organizing Quantum Universe" but what that really means is the self-organizing quantum geometry of a convenient-size universe that you can simulate and get to grow in a computer, so you can measure what's happening inside the little universe, experience what it would be like to wander around inside, study it. And build up statistics about the whole swarming quantum/random flock of little universes.

You get them to grow and get their geometry to evolve according to a quantum version of Einstein's 1915 rules (Gen. Rel. gives some comparatively simple rules for the evolution of geometry. Quantizing the rules provides for random fluctuation.)

In nonstring QG the focus is on the 3D or 4D geometry of the whole universe, how it evolves. How it responds to measurement. The uncertainty with which geometric measurements are correlated. How to get a handle on the whole geometry. How to produce simplified cases that you can study.

At a microscopic level the components (the building blocks or ball-and-stick set) may not correspond to familiar geometry notions. But they still represent the geometry in the sense that at large scale (when you zoom the camera out) it should blur together so you see a more usual geometry picture.

And at a certain level it doesn't seem to matter much what set of mathematical micro components you use.
All the main (nonstring) QG approaches are trying to do the same thing. They are all attracting young researchers now, so the number of researchers is growing. The main approaches have begun making more rapid progress than, say, before 2003 or 2004. And there are some signs of convergence of results. Loop and Foam turn out to agree on some things. Loop and Triangulations and the Renormalization Flow approach all show a curious agreement about reduced spacetime dimensionality at small scale. So there is growth and convergence.

That's why if you want a layman's grasp of modern QG you should, I think, give a careful reading to Loll's SciAm article. When you are clear about Triangulations QG (which is the easiest to grasp) then come back and ask how the spinfoams of LQG are trying to do the same thing but with different mathematical apparatus, different paraphernalia, different set of micro-components.

 

[Galteeth]

Other people might respond in a completely different way. I'll give you my personal take on what you're asking.

First understand the overall aim of (nonstring) quantum gravity in layman's terms.

All the various (nonstring) approaches have some mathematical representation of the 4D continuum, which is central. They have some way of representing the whole geometry of the universe (given enough triangle lego building blocks or enough tinkertoy balls and sticks, or whatever the particular approach uses) which can be simplified and scaled down and studied.

If you want a layman understanding of Loop or Foam then you should first get a general layman (nonmath, intuitive) understanding of the QG venture overall. And the best way to do that at present is to read a certain Scientific American article by a brilliant QG physicist named Renate Loll. It is a highly visual, pictorial, non-math article, that happens to be about one of the other QG approaches---not Loop or Foam. An approach called CDT that we can call simply "Triangulations QG". Loll and Ambjorn invented it in 1998, but it only hatched out, so to speak, in 2004, when they took on the full 4D case and began rapid progress.

Here is the SciAm article:
http://www.signallake.com/innovation/SelfOrganizingQuantumJul08.pdf

The title is "The Self-Organizing Quantum Universe" but what that really means is the self-organizing quantum geometry of a convenient-size universe that you can simulate and get to grow in a computer, so you can measure what's happening inside the little universe, experience what it would be like to wander around inside, study it. And build up statistics about the whole swarming quantum/random flock of little universes.

You get them to grow and get their geometry to evolve according to a quantum version of Einstein's 1915 rules (Gen. Rel. gives some comparatively simple rules for the evolution of geometry. Quantizing the rules provides for random fluctuation.)

In nonstring QG the focus is on the 3D or 4D geometry of the whole universe, how it evolves. How it responds to measurement. The uncertainty with which geometric measurements are correlated. How to get a handle on the whole geometry. How to produce simplified cases that you can study.

At a microscopic level the components (the building blocks or ball-and-stick set) may not correspond to familiar geometry notions. But they still represent the geometry in the sense that at large scale (when you zoom the camera out) it should blur together so you see a more usual geometry picture.

And at a certain level it doesn't seem to matter much what set of mathematical micro components you use.
All the main (nonstring) QG approaches are trying to do the same thing. They are all attracting young researchers now, so the number of researchers is growing. The main approaches have begun making more rapid progress than, say, before 2003 or 2004. And there are some signs of convergence of results. Loop and Foam turn out to agree on some things. Loop and Triangulations and the Renormalization Flow approach all show a curious agreement about reduced spacetime dimensionality at small scale. So there is growth and convergence.

That's why if you want a layman's grasp of modern QG you should, I think, give a careful reading to Loll's SciAm article. When you are clear about Triangulations QG (which is the easiest to grasp) then come back and ask how the spinfoams of LQG are trying to do the same thing but with different mathematical apparatus, different paraphernalia, different set of micro-components.

Ok, thanks! That's really usefull.

 

[Galteeth]

Ok, that article was interesting. I have many questions but I'll go with the order the article which seems logical to prevent conceptual misunderstandings.

I think I understand that the 4-simplices are not so much important in and of themselves but they give an approximate "building block" so as to help with quantization of curved space.

1: What does GR suggest that space would look like classically with no matter or energy? Is that the De-sitter spacetime?


2. Does adding an "arrow of time" in the context of the simulation mean that the movement of adjacent simplices must not look the same forwards and backward?

3. Can the 4-simplices be connected to each other in any manner imaginable, like different vertices or sides glued?

4. In terms of a simple grouping of connected 4-simplices, what would a relatively simple quantum fluctuation look like?

5. In the no causality simulation, how does one end up with a ball of infinite dimensions constructed out of 4-simplices even if they are in superpositions? It would seem intuitively that although the number of dimensions could get very very large, a finite number of objects made up of a finite number of dimensions with a finite number of possible combinations, even if they were arranged in every position imaginable simultaneously would still not lead to infinite dimensions (whichever definition of dimension you apply.)

 

[marcus]

...
1: What does GR suggest that space would look like classically with no matter or energy? Is that the De-sitter spacetime?

Yes! That's the solution to classic Einstein rules in the case where you have a positive cosmological constant, like it seems that our universe does.
Interesting point about that: I'm not sure but I think that the Loll approach requires a positive cosmo constant in order to make it work. A positive constant is always present in the equations that evolution is based on in their simulations.

2. Does adding an "arrow of time" in the context of the simulation mean that the movement of adjacent simplices must not look the same forwards and backward?​

There's a paper in arxiv that describes the details of their Monte Carlo---how they implement. It is analogous to shuffling a deck of cards. The rudimentary local "moves" look the same forwards and backwards. They simplices look the same, and how they fit together looks the same, forwards and backwards. I hope someone will correct me if I am mistaken about this!

3. Can the 4-simplices be connected to each other in any manner imaginable, like different vertices or sides glued?​

Basically the answer is yes, subject to the causal layering. There are some technicalities that this 2001 arxiv paper goes into. I have to go, will try to get back later and respond further. Maybe others will reply in the meantime.

4. In terms of a simple grouping of connected 4-simplices, what would a relatively simple quantum fluctuation look like?​

5. In the no causality simulation, how does one end up with a ball of infinite dimensions constructed out of 4-simplices even if they are in superpositions? It would seem intuitively that although the number of dimensions could get very very large, a finite number of objects made up of a finite number of dimensions with a finite number of possible combinations, even if they were arranged in every position imaginable simultaneously would still not lead to infinite dimensions (whichever definition of dimension you apply.)
​

 

[Galteeth]

​

Yes! That's the solution to classic Einstein rules in the case where you have a positive cosmological constant, like it seems that our universe does.
Interesting point about that: I'm not sure but I think that the Loll approach requires a positive cosmo constant in order to make it work. A positive constant is always present in the equations that evolution is based on in their simulations.

2. Does adding an "arrow of time" in the context of the simulation mean that the movement of adjacent simplices must not look the same forwards and backward?​

There's a paper in arxiv that describes the details of their Monte Carlo---how they implement. It is analogous to shuffling a deck of cards. The rudimentary local "moves" look the same forwards and backwards. They simplices look the same, and how they fit together looks the same, forwards and backwards. I hope someone will correct me if I am mistaken about this!

3. Can the 4-simplices be connected to each other in any manner imaginable, like different vertices or sides glued?​

Basically the answer is yes, subject to the causal layering. There are some technicalities that this 2001 arxiv paper goes into. I have to go, will try to get back later and respond further. Maybe others will reply in the meantime.

4. In terms of a simple grouping of connected 4-simplices, what would a relatively simple quantum fluctuation look like?​

5. In the no causality simulation, how does one end up with a ball of infinite dimensions constructed out of 4-simplices even if they are in superpositions? It would seem intuitively that although the number of dimensions could get very very large, a finite number of objects made up of a finite number of dimensions with a finite number of possible combinations, even if they were arranged in every position imaginable simultaneously would still not lead to infinite dimensions (whichever definition of dimension you apply.)
​

Thanks. I appreciate your responses.