Smolin video LQG online course

[marcus]

http://streamer.perimeterinstitute.ca:81/mediasite/viewer/FrontEnd/Front.aspx?&shouldResize=False

scroll down the side menu to "Introduction to Quantum Gravity"

L.S. announced posting this course on Woit's blog

 

[marcus]

http://streamer.perimeterinstitute.ca:81/mediasite/viewer/FrontEnd/Front.aspx?&shouldResize=False

scroll down the side menu to "Introduction to Quantum Gravity"

L.S. announced posting this course on Woit's blog

four lectures are available so far.

I just watched #3 and liked it a lot.

does anyone want to comment?
[EDIT just a reminder about something unrelated that I need somewhere to jot down: gr-qc/0601121, Henson no time to put this in the proper thread]

 

[marcus]

Smolin says he will continue giving lectures in the course every Wednesay thru February, and then in March the day may change sometime to Thursday.

So far my favorites of what I have watched are Lectures #1 and #3.
I'm impressed with Smolin's ability as an explainer.

 

[duke_nemmerle]

This is an excellent find, I will check it out soon

 

[robousy]

nice find...but waaaay too much topology for me.
want/need to learn this someday but its completely new to me and I've been doing physics for years.

 

[marcus]

Now as of today SIX lectures are available.

when there were just 4 then my favorites were #1 and #3

(they are the morning halves, parts #2 and #4 were given in afternoon, maybe the morning audience is better, or Smolin is fresher, or maybe it just worked out that way)

Actually I was surprized at how basic and understandable the geometry/topology stuff is.
when you quantize gravity you are quantizing the SHAPE OF SPACETIME, so naturally you need geometric/topological tools because the geometry of spacetime is not a fixed framework but a dynamic uncertain thing. You need a handle on all possible geometries so that you can have quantum states of geometry which are blurred, uncertain, fuzzy shapes of spacetime----geometry governed by probability instead of certainty.

And that is what spacetime really is. It is not some clear fixed thing AFAIK.

So nobody should be surprised if you encounter a few new math concepts. The remarkable thing is that they aren't all that bad---they seem quite natural, as Smolin presents them IMHO.

I'm going to try #5 now.

 

[marcus]

Parts 7 and 8 of the Smolin lectures on Quantum Gravity are now available online

 

[marcus]

We should have a study group to go over these lectures one by one and figure out what the main ideas of each one are.

these are good lectures IMO.

I think it would repay the effort of watching them and discussing them here at PF

 

[selfAdjoint]

Has anyone had trouble watching them? I was watching the first one today and my IE browser crashed. I'll try again with Firefox.

But if I succeed, I'll be up for a study group. Perhaps we could start a subforum like they did in Philosophy for A Place for Consciousness?

Update: Same thing with Firefox. "Firefox has encountered a problem and needs to close". And at the same point in the video; just about 30 seconds - certainly less than a minute - into his discussion of the volume operator. He has chalked the words "operator on Hilbert space" on the board and begun to talk when it happens. Drat!

 

[marcus]

thanks for trying!
the only way we can assess what is possible and what isn't
is if people are willing to try it.

I have no trouble. But my wife and son forced me to get DSL last year. I would never have treated myself to it, unprodded, and now I see the point.
the whole thing is effortless and ordinarily runs without a hitch.
I have watched most of the 8 lectures so far---with some interruptions.

I would say that your being unable to participate more or less rules out having a study group here at PF----that is my guess, but we will see what happens.

 

[selfAdjoint]

I noticed something else, my virus checker got turned off. Now I ran a virus scan just yesterday and found nothing, but this is very supicious. I'll try a couple of things to see if I have some intrusive software that is screwing things up.

Also do you have the hep-th number for the Intro to GR as a Gauge Theory paper that he chalked on the board? I couldn't interpret his handwriting even though I have now seen it twice.

 

[marcus]

The paper he referred to for Intro to GR as a Gauge Theory
is http://arxiv.org/abs/hep-th/0209079

He said the relevant sections (for Lecture 1) were sections 2 and 3

I just looked at beginning of Lecture 1 video so I am sure about that.

At some point, according to Christine, he refers to one by Wipf
http://arxiv.org/abs/hep-th/9312078
but probably that is not in Lecture 1---some other in the series.

he says he will use Baez and Muniain. I don't have that book, regret to say.

 

[selfAdjoint]

The paper he referred to for Intro to GR as a Gauge Theory
is http://arxiv.org/abs/hep-th/0209079

He said the relevant sections (for Lecture 1) were sections 2 and 3

I just looked at beginning of Lecture 1 video so I am sure about that.

Thank you very much Marcus. I had written it down as "...029" insted of "...079", which is why I couldn't find it.

...
he says he will use Baez and Muniain. I don't have that book, regret to say.

I don't either. It's out of print.

AND it's a http://dogbert.abebooks.com/servlet/SearchResults?an=Baez+and+Muniain&y=9&x=37"

 

[George Jones]

AND it's a http://dogbert.abebooks.com/servlet/SearchResults?an=Baez+and+Muniain&y=9&x=37"

Wow!

Thinking that this result might be an anomaly, I also did a seach, with this http://www.bookfinder.com/search/?ac=sl&st=sl&qi=JlDfOJFh7JdFyFXvP.EEiMm0ZF0_9485734881_2:12:18".

I bought the book new shortly after it came out - I forget what I paid. Much of the book is a standard modern intro to differential geometry, so this material is easily found in other books. I'm (k)not sure what it does with knots though - I don't have it at hand.

Most university libraries probably have the book.

The idea for a study group is great, but, unfortunately, I won't be able to participate as much as I would like. I learn new things quite slowly, and I am swamped with work right now.

I will (at least) lurk, though.

Regards,
George

 

[Ratzinger]

I heard a second edition of that book is in preparation. I wish Baez would add the lecture notes on quantum gravity from his website to it. Then I could imagine it would nicely complement Penrose last book.

(And finally all the motivated but lesser-smart laymen like myself could make more sense of this cool stuff called mathematical physics.)

And please start a study group.

 

[marcus]

Lectures #9 and #10 are now available! I will start listening in a moment.

George Jones, glad to hear that you are interested and will watch----the important thing is to catch the lectures themselves whether or not you contribute comments here. But it would be nice if you did help out. It is actually a lot of work just to watch each lecture and say what it is about in one or two sentences! We need that kind of summary outline list for all 10 (so far) lectures.

... laymen like myself could make more sense of this cool stuff called mathematical physics.)

And please start a study group.

I expect we will have a study group if two things
A. selfAdjoint turns out to be able to get the lectures with his internet connection. If we do it, we should all be able to participate---or a fair chunk of us anyway, not just a small splinter.

B. someone starts posting a list of the topics of each lecture, little by little. I think that would clearly be helpful (I can't remember what the general outline is) and I think it is all it takes to get started.

BTW Christine Dantas has posted a list of the SYSTEM REQUIREMENTS for watching the Smolin Lectures.

 

[selfAdjoint]

My browser only gives me a few minutes of viewing time before crashing, but by stepping through the video from one crash point to the next I have now succeeded in viewing the whole first video. Needless to say this is tedious and I am not going to try the second one till tomorrow! Nevertheless I did take notes and am ready to discuss on the first.

 

[CD]

If you can disable the video plugin and manage to click through the slides on your own I can put up a passworded copy of videos. I don't really know what their usage rules are but since I use linux I started stripping and saving the videos.

Also, a study group would be great.

 

[selfAdjoint]

If you can disable the video plugin and manage to click through the slides on your own I can put up a passworded copy of videos. I don't really know what their usage rules are but since I use linux I started stripping and saving the videos.

Also, a study group would be great.

I don't quite know how to do this. I wouldn't want the slides apart from the videos. But let me see how session two goes and we'll talk. At this point I am up for a study session.


Did you see that Christine Dantas had some questions about the poset structure of the moves and how they related to Causal Sets and to GR causality? Of course causality in GR does force a poset structure on events. Two events have a causal relation if they are timelike related, in each other's light cones. But causality isn't even defined for spacelike related events; different coordinates will have them in different orders.

Smolin is saying that his moves satisfy the axioms for causal sets. I don't recall exactly what they are. Can anybody copy them to this thread?

 

[CD]

Well I have the first 5 available to download. Just pm me if anyone needs them and I'll send you an address and password. You'd just have to click through the slides manually instead of letting the javascript or whatever it is that is doing it automatically while watching the videos.

Causal set C

Transitivity
$$\forall{x,y,z}\epsilon{C}(x\prec{y}\prec{z}\Rightarrow{x}\prec{z} )$$
Irreflexivity
$$\forall{x}\epsilon{C}(x!\prec{x})$$
Locally Finite
$$\forall{x,z}\epsilon{C}(cardinality ( y \epsilon C | x \prec y \prec z ) < \infty)$$

 

[marcus]

Well I have the first 5 available to download. Just pm me if anyone needs them and I'll send you an address and password. You'd just have to click through the slides manually instead of letting the javascript or whatever it is that is doing it automatically while watching the videos.

Causal set C

Transitivity
$$\forall{x,y,z}\epsilon{C}(x\prec{y}\prec{z}\Rightarrow{x}\prec{z} )$$
Irreflexivity
$$\forall{x}\epsilon{C}(x!\prec{x})$$
Locally Finite
$$\forall{x,z}\epsilon{C}(cardinality ( y \epsilon C | x \prec y \prec z ) < \infty)$$

CD that is awesome
now maybe people that don't receive the PI streaming media version
can get copies of the Lectures from you

 

[Mike2]

My browser only gives me a few minutes of viewing time before crashing, but by stepping through the video from one crash point to the next I have now succeeded in viewing the whole first video. Needless to say this is tedious and I am not going to try the second one till tomorrow! Nevertheless I did take notes and am ready to discuss on the first.

I didn't quite get what he meant by "embedding" the "graphs" into his manifold. The manifold already has a number of dimensions, and then if you embed the graph, are you assiging the additional dimensionality of the graph to the already pre-existing dimensions of the manifold? Or are you defining the "graphs" with some subset of the manifold's points? Thanks.

 

[CD]

The way I took it was just that we keep the connectivity and relationships of the original graph upon an embedding. That it just establishes a relationship between points in the manifold where the graph embedding occurs.

 

[selfAdjoint]

Yes, initially he speciified the embedding to by "up to topology", so the embedding is just a one-to-one continious map from the graph into the manifold. Being continuous it preserves the vertex/edge relationships and he later remarks that the map is non-singlular too, so it doesn't run any edges into each other. If they should intersect that would be a different graph.

But the graph is just a subset of points in $$\Sigma$$, or better, an equivalence class under topological homeomorphism. Any twisting or warping that preseves the edge/vertex connectivity is OK.

 

[marcus]

I just watched Lecture 1 again and I think the only main homework or thing to check is the fact about a certain set of moves being ergodic (in this case meaning that you can get from any trivalent graph to any other by repeatedly applying just those moves)

should we try the homework?
did anyone already think about it?

do we have a workable venue for it? I think it requires sketching pictures on scratchpaper, or a blackboard, to see. And if we do that then we have to describe it in words to communicate. It is not worth a lot of bother---it's not a big deal. But it might be nice to have done at least one of Smolin homeworks.

 

[Mike2]

I'm hearing two things.

...so the embedding is just a one-to-one continious map from the graph into the manifold.

This sounds like a "graph" is an appendage to each point of the manifold, thus adding points/dimensionality/degrees of freedom to the already existing points of the manifold - like Calabi-Yau manifold appended to the 4D spacetime of GR.

But the graph is just a subset of points in $$\Sigma$$, or better, an equivalence class under topological homeomorphism. Any twisting or warping that preseves the edge/vertex connectivity is OK.

This sounds like some points of the manifold are used to for the graph, thus only the dimensionality of the original manifold are considered.

I could use some clarification. Thanks.

 

[selfAdjoint]

I'm hearing two things.


This sounds like a "graph" is an appendage to each point of the manifold, thus adding points/dimensionality/degrees of freedom to the already existing points of the manifold - like Calabi-Yau manifold appended to the 4D spacetime of GR.


This sounds like some points of the manifold are used to for the graph, thus only the dimensionality of the original manifold are considered.

I could use some clarification. Thanks.

Notice that $$\Sigma$$ is a three dimensional manifold, and a graph is just a one dimensional object, so we can just model what happens in our old familiar 3-space.

Imagine that you have a roll of magic string. The magic is this: when you want it to be limp and flexible, it is, but if you command it to stiffen up it will hold any shape you have got it into. It is also weightless so it doesn't sag on you while you're playing with it.

Now cut off a bunch of pieces of this string, which will be the edges of your graph, and knot them together at the ends, any way you want, to make the nodes. Now you have a graph, and it's "embedded in 3-space". Play with it, twist it, without changing the knots, and then command it to stiffen. Obiously you can get all sorts of configurations, and there are even more that you can't get this way (what you are doing are called "isotopies"). For example the graph that looks like reflection of your graph in a mirror is again topologically equivalent to it.

I emphasize that nothing more outre than this is going on. No extra dimensions are involved.

 

[marcus]

about the ergodicity the set of moves is {expand, contract, exchange}

expansion move just replaces a single trivalent vertex with a triangle of 3 trivalent vertices in the obvous way

a contraction is the opposite and it contracts 3 trivalent vertices down to one.

an exchange move deals with two adjacent trivalent vertices and reconnects them in the obvious way------he shows all this clearly on the blackboard and gives plenty of examples

TO PROVE THE HOMEWORK one would have to show that one can take an arbitary finite trivalent graph and shrink it down to a THETA.
the theta is the simplest trivalent graph. It looks like one lens of a somebody's bifocal spectacles------a round disk with a diameter.

So a theta is TWO VERTICES, each of which is trivalent.

FOR PRACTICE, convince yourself that the TETRAHEDRON GRAPH can be reduced to a theta in ONE MOVE, namely a contraction

the tetrahedron graph has 4 vertices and is completely connected and each of the 4 vertices is trivalent. doing a contraction move on it collapses 3 of the vertices to one------so there are now two vertices----and it is a theta.
===================

what we have to show, if we want to act like Smolin students, is that not just a tetrahedron but ANY trivalent graph can be reduced down to a theta.

===============

everybody, when they were a kid, had a glass prism as a toy. to make rainbows.

the edges of this glass prism are a trivalent graph

how do you reduce the prism graph down to a theta?

================

can anyone explain in words why ANY trivalent graph will collapse down to a theta?

 

[CD]

Hmm well any n-prism can be contracted n-1 times into a theta, correct?

 

[marcus]

Hmm well any n-prism can be contracted n-1 times into a theta, correct?

I am not the teacher, you may be smarter. please go slow. I don't know what an n-prism is. But basically, yeah, you are probably right.But CD, how do you show that ANY finite trivalent graph can be collapsed down?

==============
like take two circles side by side joined by a bar

like a pair of spectacles (ordinary glass, not bifocal :-) )

so it consists of two vertices side by side, joined by one edge, and each one joined to itself

O-O

there is a trivalent graph, so how does it collapse to a theta? or maybe the word is not collapse but simply change, how does it change to a theta?

(damn, CD probably sees immediately so this is not even fun for CD, does anyone else want to answer?)

 

[CD]

Anything I come up with is for closed graphs - no open ended vertices. In this case any finite trivalent graph will have an even number of nodes. Two representing a theta. In this case an even n node graph can be reduced to theta with (n-2)/2 contractions.

 

[Mike2]

Notice that $$\Sigma$$ is a three dimensional manifold, and a graph is just a one dimensional object, so we can just model what happens in our old familiar 3-space.

Imagine that you have a roll of magic string. The magic is this: when you want it to be limp and flexible, it is, but if you command it to stiffen up it will hold any shape you have got it into. It is also weightless so it doesn't sag on you while you're playing with it.

Now cut off a bunch of pieces of this string, which will be the edges of your graph, and knot them together at the ends, any way you want, to make the nodes. Now you have a graph, and it's "embedded in 3-space". Play with it, twist it, without changing the knots, and then command it to stiffen. Obiously you can get all sorts of configurations, and there are even more that you can't get this way (what you are doing are called "isotopies"). For example the graph that looks like reflection of your graph in a mirror is again topologically equivalent to it.

I emphasize that nothing more outre than this is going on. No extra dimensions are involved.

Thanks, that's starting to help. What you are describing seems to be the simplicial complexes of differential geometry, is it?

 

[selfAdjoint]

Thanks, that's starting to help. What you are describing seems to be the simplicial complexes of differential geometry, is it?

Yes, the graph could be used to define two-dimension simplices ("singular chains"), but I don't think Smolin is going to use them for that. I could be wrong though.

BTW I have now watched half of the second video, up to the point where he says he wants to build a real field theory, and notes that he needs fewer field equations, and after discussing counting of degrees of freedom asks the "class", "How can we get fewer field equations?" I'll watch the rest tomorrow. I think my crashing problem is a shaky cable service. Out here in the Wisconsin boonies the cables are not buried but strung on poles, and frequently there are small glitches, some big enough that even the service provider notices them, but others fleeting and no problem as long as I'm not using some streaming source. Last night was our big blizzard with howling winds, and I could hardly get 3 or 4 minutes at a pop. Tonight was much quieter and I got 20 minutes.

On the "spectacles problem" I tried enlarging each of the nodes to a triangle and then exchanging the bar to a vertical one, But to get further I think I need to show that any three connected nodes, not just a triangle, can be shrunk to one. Has anybody looked into that?

 

[marcus]

here is a trivalent graph with two vertices

O-O

it is not a theta graph
using our set of approved moves, how do you change it to a theta?

what is the magic word?
I want to know explicitly how to change it
CD, or anybody?

 

[marcus]

I just saw selfAdjoint response to this "spectacle" problem.

It is probably OK but not the quickest way.
You can do it in ONE MOVE

selfAdjoint, you say to start off by applying expansion moves to each vertex first which makes a bigger graph, now with 6 vertices, and then you have to collapse that down. so that might work but would take several more moves.

one exchange move changes spectacles to theta

=====================

but, like you say, we still have to prove that these moves will take down an arbitrary finite trivalent graph

how would you handle spectacles for a 3-eyed man?

O-O-O