What does like a fractal mean, talking smallscale spacetime

[selfAdjoint]

These comments are well-said, Richard. I don't think the sandpile was intended to be taken literally, just a visual example of an emergent critical point. I have been trying to learn about anomalous dimension in Renormalization group theory, but it's very hard, and I believe over my head in terms of what I know and can do now. I'm reading the book http://www.pupress.princeton.edu/titles/5772.html by Giuseppe Benfatto and Giovanni Gallavotti, and they state in their introduction that the minumum level for reading the book with profit is ability to do simple first order calculations in QFT, and I'm not quite there yet. The problem is deducing the pattern of thought from the blizzard of integral and distributional developments.

 

[marcus]

Hi all

Hello Richard, pleased to see you back, glad you could make it.

M

 

[mccrone]

If we are going to try modeling spacetime as a sandpile, what part of the model replaces the force of gravity in the sandpile?

In Smolin, it would be the links in the spin network. They are spacetime paths and their curvature would be gravity.

In my meditations I have been trying to imagine an empty space of infinite dimension in which probability alone demands the emergence of form. Probability also demands that form emerges in more than one spacetime location, and that the simplest forms are the most common ones to emerge. Probability further demands that some forms have duration, and that some forms will emerge in common spaces where, having duration, there will be time for them to interact.

Invoking the process of natural selection of a space of possibility is definitely the way to go. But why start with nothingness? How could a something develop from a nothing? Why not instead consider a prior state of everythingness, a plenitude, and see the emergence of universes with only a very few dimensions as an act of self-organised constraint, a phase transition, of this everythingness?

You can chip away at a large block of stone to reveal the forms inside. But of course a block of stone is too substantial for our purposes. Instead the prior everythingness must be maximally vague.

Now imagine something more like the crackle of white noise on an untuned TV set. Are you watching nothing or everything - does potentially every TV show you've ever seen, or could see, exist in that crackle?

Why do you think string theorists talk about landscapes, Smolin about multiverses, Linde about eternal fractal inflation? Even CDT is based on Feynman averaging.

The only problem is that this is all probability theory based on discrete entities, crisp variety. Which IMHO is not the view of probability that you need for fundamental theories.

 

[selfAdjoint]

Jacques Distler has now done what I was unable to, critiqued Reuter's work on the asymptotic safeness of Quantum General Relativity. Distler's main point is that Reuter's exact theory is not exact in the usual sense of the word, and it is not non-perturbative. Furthermore the theory is unable to deal with the infinity of equations it generates and works with a finite truncated set. But as Distler says, the RG fixed point in the full QGR will surely be affected by non-perturbative and non-truncated contributions.Therefore Reuter's stated results on fixed points do not have any persuasive surety of carrying over to the full non-perturbative, untruncated case. This is a point I intuited and wanted to make but lacked the computational guns to do it. Distler has done the work and showed the result.

Reuter's work is interesting and valid as far as it goes, but it does not go far enough to be convincing about the asymptotic safety of QGR.

 

[rtharbaugh1]

Mccrone said:
"Invoking the process of natural selection of a space of possibility is definitely the way to go. But why start with nothingness? How could a something develop from a nothing? Why not instead consider a prior state of everythingness, a plenitude, and see the emergence of universes with only a very few dimensions as an act of self-organised constraint, a phase transition, of this everythingness?"

nothing is everything and everything is nothing. A blank sheet of paper is still blank no matter if the blank-ness is black or white or some other color. Barnsley takes a set theory approach to fractals. He says there are two sets that are simultaneously open and closed. One is the universal set, or as he calls it, the complete metric set, and the other is the set containing only one point.

I am reading about the metric that is natural to fractals. Barnsley denotes it by putting a fancy, squiggley capital H in front of the notation for a metric set...

H {X,d}

I suppose, although he has not said, that this is the Hausdorf metric set. He says that fractals have to live in such a metric. What does this mean in terms of background independence, I wonder?

SelfAdjoint, I have Zee's book on Quantum Field theory but have made little headway. I don't know the authors you mention. Barnesly is a difficult read for me. He likes to pose puzzles and leave you on your own for the answers. Still, I have been able to read some of it.


Hi again Marcus. The maples have turned red and are dropping their leaves, in embarrasment I suppose. It was a dry summer but recent rains have returned a hope for a colorful autumn. My winter nest isn't quite finished and I have a serious shortage of aged firewood at hand. Time passes, or we pass. Thanks for keeping a light in the library.

Richard

 

[marcus]

...
Hi again Marcus. The maples have turned red and are dropping their leaves, in embarrasment I suppose. It was a dry summer but recent rains have returned a hope for a colorful autumn. My winter nest isn't quite finished and I have a serious shortage of aged firewood at hand. Time passes, or we pass. Thanks for keeping a light in the library.
...

we do this for each other, Richard----keeping the library occupied so the chairs don't get dusty. Yeats mentioned that light. It was in an uncomplimentary poem about political leaders:

THE LEADERS OF THE CROWD

They must to keep their certainty accuse
All that are different of a base intent;
Pull down established honour; hawk for news
Whatever their loose fantasy invent
And murmur it with bated breath, as though
The abounding gutter had been Helicon
Or calumny a song. How can they know
Truth flourishes where the student's lamp has shone,
And there alone, that have no Solitude?...

 

[selfAdjoint]

Richard, don't worry about Zee, stick with your fractals book. I was just venting because I got the Benfatto & Gallavotti book to help me understand anomalous dimension and it's such a slog.

Yes the curly H means Hausdorf, and Hausdorf dimension is roughly the same as fractal dimension. It can come out non-integer. All the nice spaces are Hausdorf from the git-go; it means given any two distinct points you can find two non-intersecting neighborhoods in the space such that each point is in one of the neighborhoods (the neighborhoods are specified by the TOPOLOGY on the space, and the Hausdorf property is a property of that topology). The real interest here is in spaces that are Hausdorf but not any nicer than that. Fractal spaces for example.

The drive currently is to derive spacetime with its nice metric and curvature properties from something much simpler; "bare causality" maybe. Or tangles of colliding hyper-triangles. A constraint on all such efforts is that spacetime when you get to it has to be an interacting player in the physics, i.e. "background free".

 

[Spin_Network]

I see a great link you provided!..but forgive me for a while if I do not reply directly,(reletive to the numbers! ) that is, except to say if you could see a "spacetime vacuum field", then your image is pretty damn close! I need to collate a few things relevant to what I am doing, hopefully I am going to post soon, about 2 days before the loop conference, thanks again for a really interesting post, and great link.

John Baez is seeking some "handwaving" here:https://www.physicsforums.com/showthread.php?t=91813

one of his linked papers here:http://arxiv.org/abs/http://www.arxiv.org/abs/hep-th/9401137
gives an early Ambjorn interesting paper.

Having just read this paper today for the first time, I see the light!

Its just as I thought, the Loll et al Dynamical Triangulations, do not transform from 4-D to 2-D, there is a fundamental flaw "running" through the proposed model, along the lines of linearlity "dimensional renormalization".

Stringtheory, has world-lines that are not continueous from one dimension to another, example if one has a string source starting in 5-D , the only route to bring the string-path in a linear transformation from 5-D to 3-D,is to compact from a 5-D boundary, inversely. So 5-D volume space extends around a 3-D space, (5...(4...(3-+-3)...)4...)...5).

Extending dimensions exponentially form a compact lower volume source, starting from a zero-mode, stringtheory uses the interconnecting spaces at above ie (... as the linear world-line. If one starts at a low-energy source, and join the total volumes together, one gets a specific sheet of space forming a "background" .A 2-D area has only non-directional transforms, due to the fact that a 2-D world-sheet has no 3-D directional routes contained within, you only get rotational values.

http://groups.msn.com/RelativityandtheMind/shoebox.msnw?action=ShowPhoto&PhotoID=25

 

[selfAdjoint]

Stringtheory, has world-lines that are not continueous from one dimension to another, example if one has a string source starting in 5-D , the only route to bring the string-path in a linear transformation from 5-D to 3-D,is to compact from a 5-D boundary, inversely. So 5-D volume space extends around a 3-D space, (5...(4...(3-+-3)...)4...)...5).

Extending dimensions exponentially form a compact lower volume source, starting from a zero-mode, stringtheory uses the interconnecting spaces at above ie (... as the linear world-line. If one starts at a low-energy source, and join the total volumes together, one gets a specific sheet of space forming a "background" .A 2-D area has only non-directional transforms, due to the fact that a 2-D world-sheet has no 3-D directional routes contained within, you only get rotational values.

This evidently means something to you, but it sure doesn't convey anything to me. In string theory the compact 6D manifolds are orthogonal at every point of 4D spacetime, and a normal thing would be for the string to move smoothly through them. Of course they can get hung up on the non-trivial topology of the manifolds, wrapped around a handle, for example, but that is supposed to correspond to real and interesting physics. Your idea that there's some stupid error that nobody but you has spotted in either string theory or dynamic triangulations is just mistaken. You are not going to figure this stuff out with just the ininformed, untutored imagination.