Causal Sets lectures have started (video online)

[marcus]

The first lecture of the series (18 October) is already online.
http://pirsa.org/C10020
The series is called Invitation to Causal Sets.

 

[Kevin_Axion]

Very interesting, thanks for the awesome links marcus! Might I add that the Perimeter Scholars is expanding their lectures each day for the 2010-2011 term. The link is http://pirsa.org/C10017, there has also been a large remodeling of the lectures to include more elaborate and interesting topics and to reduce the amount of similar subjects - I hope you don't mind me putting this here marcus, it just seemed appropriate. Many of the new subjects include:

PSI Mathematical Physics
This course will include the study of Perturbation Theory (Regular and Singular) Speeding Up Convergence and the Gibbs Phenomenon.
PSI Conformal Field Theory
An introduction to the key ideas and techniques of CFT. These theories play a central role in the study of phase transitions in statistical physics and condensed matter systems, as well as in string theory.
PSI Quantum Gravity
Linear gravity and gravitons. Gravitational path integral. Pertubative Lorentzian quantum gravity (QG) and the need for non-pertubative QG. Constrained Hamiltonian systems. Canonical formulation of GR. Non-pertubative canonical QG. The Wheeler-De Witt equation. Loop QG. Non-perturbative path-integral for gravity: lattice and discrete methods (Regge calculus) and causal dynamical triangulations (CDT). Surprises in non-perturbative approach.
PSI Gravitational Physics Review
Relativist's toolkit: the geometric framework of GR, Cartan formalism, Gauss-Codazzi equations and Kaluza Klein theories. Black Holes: 4D solutions, black hole theorems, Hawking radiation and thermodynamics. Extra dimensions: simple supergravity solutions in string theory (branes), the stability of these objects, then braneworlds and warped extra dimensions.
PSI Supersymmetry and Supergravity
The following topics will be discussed: The Lorentz Group: Properties and Representations; Manipulating Spinors; Supersymmetry Algebra and Representations; Superfields and Superspace; 4d Supersymmetric Lagrangians; Supersymmetry Breaking; Constructing the MSSM; Collider Phenomenology of Supersymmetric Theories; and Dark Matter

Quantum Gravity and Gravitational Physics aren't new but I believe the structure and content of the lectures has been redesigned.

 

[marcus]

I hope you don't mind ...

I don't mind a bit! I thought Dowker did a fine job BTW. I'm looking forward to tomorrow's lecture. The first part will be her finishing up what she started today, and then I think Sorkin will take over. They will be co-teaching, I believe, in alternation.

If anyone here is old enough to remember the Sixties TV series called the Avengers, with Diana Rigg and Patrick Macnee playing Emma Peel and John Steed, please let me know. Fay Dowker reminds me of Emma Peel. I may be the only person here who remembers the Avengers.

Dowker ended the 90 minute lecture talking about the Lorentz invariance of discrete points scattered out according to a poisson distribution. A random poisson sprinkling has no preferred frame.
If you want to understand lecture 2 (tomorrow) then you might have to go back and watch the last 15 minutes of lecture 1, where she starts talking about Lorentz invariance of a random sprinkling of discrete points, and shows a computer generated picture of a field with thousands of dots.

Do a boost (Lorentz) transformation and it will still look the same---indistinguishable in general appearance.
Stretching along one 45-degree null line and compressing along the other null line does not change the qualitative nature of poisson scattered points. Kind of neat.

Dowker and Sorkin are going to argue that there is a natural connection between discrete and Lorentz---that's something I never heard of. Very strange. They have at least an heuristic or suggestive case to make that the causality structure of spacetime is 90 percent of its geometry, and that spacetime is Lorentzian BECAUSE it is discrete.

I think they're cool and on the whole it's likely to be a good course.

 

[atyy]

"That's something you can ask of any theory of quantum gravity: at the end, are you going to take the continuum limit?"

 

[Fra]

Marcus, thanks for posting links to the selected talks. For some reason I never scan arxiv and these sites like you and others do.

I will try to check them out.

Dowker and Sorkin are going to argue that there is a natural connection between discrete and Lorentz---that's something I never heard of. Very strange. They have at least an heuristic or suggestive case to make that the causality structure of spacetime is 90 percent of its geometry, and that spacetime is Lorentzian BECAUSE it is discrete.

Sounds interesting: it sounds like of how I believe several different approches infer a maximum speed of information propagation which follows from assumptions of bounded processing and information capacity. The conceptual idea is that it's impossible to "compute=infer" arbitrary wild changes, without loosing confidence, because it takes a certain abount to "data" to establish confidence. Therefor, no observer, will even observe arbitrary speeds because it's not a computable conclusion. The limit would be related to the complexity bounds I think. Bit I'm not sure if it's related to what they do though. After all there is a possible distinction between discreteness and finiteness.

/Fredrik

 

[marcus]

"That's something you can ask of any theory of quantum gravity: at the end, are you going to take the continuum limit?"

I don't know if you are making a point, or a suggestion, or just repeating with approval. I share your approval in any case. I think Rovelli pointed out that same issue maybe in 1010.1939. And it's an interesting question.
In LQG/spinfoam the answer is NO. You don't let the "lattice spacing go to zero" because there is no distance corresponding to the lattice spacing---no background metric to make the graph have a metric significance.

So in LQG you let N --> infinity (number of nodes in graph) but you don't have some spacing a --> 0.

Now how about in Causal Sets? I think there too you do not take the continuum limit. I think I remember Dowker asking that same question and stressing the point that you don't. That you believe (in effect) in some kind of Lorentz-invariant discreteness.

 

[Fra]

I fell asleep at 50+ minutes in the lecture 1 last night, but the way I connect to this program is similar to how I connect to LQG.

The partial order, emerges naturally also in a computational sense since the input,output as defined by the computations or entropic processes define a natural order. So the computational perspective would explain also the origin of the causal order.

But then the question is, what about the total complexity of the causal set? If that -> infinitiy then they loose me, as it represents the limit of infinite computational power and memory.

As I associate the dynamics of these causal structurs should then be to understand the computational process, whereby the causal set is emerging and evolving?

/Fredrik

 

[Fra]

But then the question is, what about the total complexity of the causal set? If that -> infinitiy then they loose me, as it represents the limit of infinite computational power and memory.

As I see it, this boils down to a conceptual attitude towards the nature of the spacetime manifold (wether it's discrete or no) - do we think of objective equivalence classes of spacestimes, or do we think of particular observers "image" or knowledge of this from the point of view behind a horizon?

In the latter case, shouldn't the total complexity of the network, or set, manifold must be bounded, by a number relating to the observers compexity?

It's also a little bit like if you consider the horizon as a mirror, one one side you have the real by unknown thing, and on the other side you have a mirror image. Which side does the causal set aim to model? :)

/Fredrik

 

[Fra]

Dowker and Sorkin are going to argue that there is a natural connection between discrete and Lorentz---that's something I never heard of. Very strange. They have at least an heuristic or suggestive case to make that the causality structure of spacetime is 90 percent of its geometry, and that spacetime is Lorentzian BECAUSE it is discrete.

Since there are traits of this that do I like and their assumptions are simple and clean I decided to try an invest some time in this to learn more about how far they have come in this program.

I then stumbled upon this paper from math-ph

"A Derivation of Special Relativity from Causal Sets"
Kevin H. Knuth, Newshaw Bahrenyi, Sun, 29 Aug 2010

"We present a novel derivation of special relativity based on the information physics of events comprising a causal set. We postulate that events are fundamental, and that some events have the potential to receive information about other events, but not vice versa. This leads to the concept of a partially-ordered set of events, which is called a causal set. Quantification proceeds by selecting two chains of coordinated events, each of which represents an observer, and assigning a valuation to each chain. Events can be projected onto each chain by identifying the earliest event on the chain that can be informed about the event. In this way, each event can be quantified by a pair of numbers, referred to a pair, that derives from the valuations on the chains. Pairs can be decomposed into a sum of symmetric and antisymmetric pairs, which correspond to time-like and space-like coordinates. From this pair, we derive a scalar measure and show that this is the Minkowski metric. The Lorentz transformations follow, as well as the fact that speed is a relevant quantity relating two inertial frames, and that there exists a maximal speed, which is invariant in all inertial frames. All results follow directly from the Event Postulate and the adopted quantification scheme."
-- http://128.84.158.119/abs/1005.4172v2

I haven't read it yet but I will print it for reading later. It's just too bad I don't have time to read/listen to everything :( MAybe someone beats me to it an offers an analysis that's why I post the link. It is relevant to marcus comment.

/Fredrik

 

[Fra]

I am starting to like this guy Kevin Knuth has what seems to me a pretty good and attractive line of reasoning. I will definitely try to read some of the referencing papers. I particularly like the connection he makes to foundations of quantum theory.

The way he considers certain "chains" of events to define an observer, is good, but I think in order to include gravity one might need to see that there is an heierarchy where the two chains, an establishing lorentz symmetry, still must take place relativt to a third observer.

Knuth is it seems a professor in information physics at Albany, New York and is working (according to his website http://knuthlab.rit.albany.edu/) in a great direction mixing foundations of physical law, bayesian and mex ent methods. It just remains to see if he is subject to similar objections I've had on other writings, but there are things in that paper that makes me think he has some deep ambitions.

It seems to be that loosely speaking there are possible extensions where LQG and causal sets should meet, but it seems to me at least that the conceptual foundations and clarity of causal sets is superior to LQG. IF causal sets could also infer the QM logic from counting evidence from different chains, then it seems it should be good stuff.

/Fredrik

 

[marcus]

I am starting to like this guy Kevin Knuth has what seems to me a pretty good and attractive line of reasoning. I will definitely try to read some of the referencing papers. I particularly like the connection he makes to foundations of quantum theory...

I was impressed. Knuth has another paper here:
http://arxiv.org/abs/1009.5161
also impressive.

Some of us will have to start following his research. Thanks for the tip.

 

[Fra]

I was impressed. Knuth has another paper here:
http://arxiv.org/abs/1009.5161
also impressive.

Some of us will have to start following his research. Thanks for the tip.

Thanks for the further paper. Yes I will definitely skim through his furhter papers. Now I haven't read it all to form a final opinion yet, but IMO what he is doing is rightfully called the new frontier and it's exactly in the direction that I've been missing from the big programs. I'm excited to find that more on this.

/Fredrik

 

[Fra]

Another one of Knuth's papers I haven't (yet) read.

Origin of Complex Quantum Amplitudes and Feynman's Rules

"Complex numbers are an intrinsic part of the mathematical formalism of quantum theory, and
are perhaps its most characteristic feature. In this paper, we show that the complex nature of the quantum formalism can be derived directly from the assumption that a pair of real numbers is associated with each sequence of measurement outcomes, with the probability of this sequence being a real-valued function of this number pair. By making use of elementary symmetry conditions, and without assuming that these real number pairs have any other algebraic structure, we show that these pairs must be manipulated according to the rules of complex arithmetic. We demonstrate that these complex numbers combine according to Feynman's sum and product rules, with the modulus-squared yielding the probability of a sequence of outcomes."
-- http://arxiv.org/PS_cache/arxiv/pdf/0907/0907.0909v3.pdf

I have seen similar "derivations" of QM logic before, Ariel has one where the QM logic follows from consistency of complex amplitudes, but there the key assumption is the use of complex numbers! I'll check to see if Knuth has improve this. I suspect the latter part may be similar to what I've seen before. Assumption of pairs is possibly plausible if you relate to pairs referring to different sub-causets and thata QM emerges in systems which is composed of unions of such non-commutative causets.

/Fredrik

 

[Fra]

I was impressed. Knuth has another paper here:
http://arxiv.org/abs/1009.5161
also impressive.

Some of us will have to start following his research. Thanks for the tip.

I have a couple of handles on Knuths ideas that I will analyse in depth, and as is both clear, and also explicit in his papers, his work follows the tradition of Cox, Jaynes etc.

I have read (som of) Jaynes, and Ariels papers enough to understand they reasoning and I have to say that I find Knuth's writings more creative; in the right direction. The spirit if intent in his reasearch has just the right thinking.

I would encourage everyone that hasn't yet gotten the point with this "information theoretic" angle to read his papers. The one Marucs referred to above is an excellent starting point, and it's relatively short. (I don't like the book-type papers myself as they tend not to get read; the shorter the better).

Now to the possible points of debate: As I said, I find his approach to be far more creative than previous ones (Cox, Jaynes, Ariel), BUT the critial point that is the core assumption here is his assumption of what constitutes a "lattice". Like previous authors, he starts with a sequence of definitions and unojbectionable inferences, and suddently sometihng familiar and interesting just pops out! But one must keep in mind that since it's physics, the question is WHY certain axiomatic systems are USEFUL, and others are not? In particular why is the notion of a lattice interesting for partially ordered sets?

This is a non-trivial question. He also notes that in the general cases of course all posets we can imagine in reality doesn't qualify as lattices (having unique elements fitting with OR and AND operators of any two point, what he calles joing and meet). Then his idea is taht sometimes this can be extended, by defining a subset of the poset as a qualified lattice and then relate the residual elements from there. But even this I find nontrivial and requiring more thought - these are the things I personally will think more about, these are good questions, but not trivial to answer eithe way, but the scheme here certainly is one of the more promising ones I've seen published.

More later as I've given this more time. It takes me more than just skimming the paper to produce more meaningful comments.

So even if this is admittedly extremelt "simple" and non-complex, relative to other things, there is a conceptual depth in understanding behind these papers that makes me rate these papers high on my "worth reading" scale.

/Fredrik