Radical new foundations for both quantum theory and space-time

[marcus]

This was just posted

http://arxiv.org/abs/1308.2206
Energetic Causal Sets
Marina Cortês, Lee Smolin
(Submitted on 9 Aug 2013)
We propose an approach to quantum theory based on the energetic causal sets, introduced in Cortês and Smolin (2013). Fundamental processes are causal sets whose events carry momentum and energy, which are transmitted along causal links and conserved at each event. Fundamentally there are amplitudes for such causal processes, but no space-time. An embedding of the causal processes in an emergent space-time arises only at the semiclassical level. Hence, fundamentally there are no commutation relations, no uncertainty principle and, indeed, no hbar. All that remains of quantum theory is the relationship between the absolute value squared of complex amplitudes and probabilities. Consequently, we find that neither locality, nor non locality, are primary concepts, only causality exists at the fundamental level.
9 pages. Article companion to http://arxiv.org/abs/1307.6167

 

[strangerep]

This was just posted

http://arxiv.org/abs/1308.2206
[...] Article companion to http://arxiv.org/abs/1307.6167

I'm puzzled why only energy and momentum are taken to be fundamental, with no mention of intrinsic spin, afaict. Their momenta seem to be 3-momenta, and there's nothing distinguishes each such momentum, hence one would expect a rotational symmetry and hence intrinsic spin.

Also, the Poincare mass$^2$ Casimir is assumed -- cf. eq(6) of 1308.2206, but no mention of 2nd Poincare Casimir.

Or did I miss something important?

 

[marcus]

...

http://arxiv.org/abs/1308.2206
[...] Article companion to http://arxiv.org/abs/1307.6167

...

Good reminder. Cortês and Smolin are apparently preparing for a series of four articles, two of which have appeared. Although Pauli matrices and twistor formulation occur in the first article, which is suggestive, I don't see anything that addresses your question. But we have two more of the series to look forward to. I'll list the titles, starting with 1307.6167 and 1308.2206:
The Universe as a Process of Unique Events
Energetic Causal Sets
Fundamental Irreversibility in Cosmology, to appear.
Partly emergent quantum mechanics, to appear.

 

[Quantumental]

Is this deterministic?

 

[xk_id]

Can anybody comment whether those are sensible ideas?

 

[marcus]

Can anybody comment whether those are sensible ideas?

I hope some other people respond to your question. I'll just give my personal reaction.

With something this radical we have to wait and see. At present there are only two people (Smolin and Cortês) in the whole theoretical physics, foundations, quantum gravity research community that are working on this. We have to see if some young researchers take up the idea whether it develops some momentum. We also have to see how the other two papers work out. S&C plan a series of 4, I listed their titles earlier. So far we've seen only the first two.

By contrast,take Loop gravity. It is very conservative in a sense. It retains the essential principles and much of the conceptual content of what has been successful in the past: GR, QFT. Lattice gauge theory. It is in reach (thru cosmology) of making testable predictions and has attracted phenomenologists like Aurelien Barrau.
So it does not make a radical leap.

S&C idea, Energetic Causal Sets, departs from all the established precedents and makes a highly risky radical leap. However if you want my opinion, I do indeed think it is SENSIBLE.
To me it looks highly logical, ingenious, economical conceptually, and at this stage remarkably fertile. It gets a lot out of a very limited set of concepts, really very little machinery.

If I were a 27 year old postdoc working in Loop gravity, would I jump into ECS? No. I would keep an eye on it and see how it develops over the next couple of years. I would not jump into the arms of every extremely radical idea that comes along and looks sensible, like it MIGHT succeed.
I would keep on working in the more conservative and populous line of QG research and just keep an eye on this very interesting ECS gamble,to see how it goes.

You said you wanted a comment. I hope somebody else volunteers something more insightful. This is the best I can do for now.

 

[Chronos]

Any notion of causality as fundamental, imo, implies some sense of determinism. This is not a revolutionary idea. It does, however, raise questions about the 'fundamentality' of statistical probability. I think this is a promising avenue to be explored.

 

[friend]

Thanks for the link, marcus. You know I'm a fan of foundational issues in QM.

A couple of things strike me with this paper. One is, how can you define momentum without first assuming a background spacetime in which something can move? Or for that matter, how can you have causality between topologically disconnected points without a medium (spacetime?) to transmit that causality?

Secondly, they take as postulates amplitudes and the sum and product rules of those amplitudes that allows them to define at least a discrete form of the path integral, which is the essense of QM. So they are not really explaining where quantum mechanics comes from. So I don't see how you can call this a radical new foundation. Or maybe I'm missing something.

 

[friend]

Any notion of causality as fundamental, imo, implies some sense of determinism. This is not a revolutionary idea. It does, however, raise questions about the 'fundamentality' of statistical probability. I think this is a promising avenue to be explored.

I would have to agree with you here, Chronos. It seems that if one can describe cause and effect with a probability distribution, then one can construct quantum mechanics from scratch.

 

[marcus]

Thanks for the link, marcus. You know I'm a fan of foundational issues in QM.

A couple of things strike me with this paper. One is, how can you define momentum without first assuming a background spacetime in which something can move? Or for that matter, how can you have causality between topologically disconnected points without a medium (spacetime?) to transmit that causality?

Secondly, they take as postulates amplitudes and the sum and product rules of those amplitudes that allows them to define at least a discrete form of the path integral, which is the essense of QM. So they are not really explaining where quantum mechanics comes from. So I don't see how you can call this a radical new foundation. Or maybe I'm missing something.

In any axiomatic system there are primitives whose meaning is determined by how they are used (rather than in terms of other concepts).

Causality IS the one-directional arrow connecting two points.
Points are not "topologically disconnected" because they are connected by arrows. How can they be "topologically disconnected" when there is, a priori, no space in which they live and no topology!
Momentum is a primitive concept of the axiomatic system. Its meaning is in how the axioms determine the concept shall be used. So in this situation they do not need space in order to define momentum.

So they are not really explaining where quantum mechanics comes from. So I don't see how you can call this a radical new foundation. Or maybe I'm missing something.
​

Euclid's axioms you learn as teenager do not explain where geometry "comes from" or why there should be lines and angles in the world of our experience. Same way with axiomatic set theory. The amazing thing is what can logically GROW out of a few postulates if you accept the postulates and start reasoning with them. That is what a foundation is, or so I think.

Axiomatic set theory has become the standard foundation of mathematics. calculus, functions, the complex numbers, vectors, Lie groups, etc etc are all founded on set theory. an ordered pair is a certain simple kind of set, a function is a set of ordered pairs, etc etc.

S&C are proposing a very simple logical board game with very simple chess-pieces and rules governing their use FROM WHICH SPACETIME MAY ARISE if they play the game right. and also from which (putting in as little as possible by hand) quantum theory might arise. So far the proofs are incomplete, it might or might not work. There are some tantalizing suggestions that it might work, but one cannot be certain at this stage.

If it happens to work, people will GET USED TO IT. I think it was the mathematician John von Neumann who said you basically never understand mathematics, you just get accustomed to it.

 

[friend]

... If it happens to work, people will GET USED TO IT.

That sounds like "shut up and calculate"... That seems contrary to the idea of finding the foundationas of QM.

 

[marcus]

Clearly two different viewpoints. To me it seems like the opposite of "shut up and calculate" which does not involve essential mental/conceptual growth. You just keep on with the familar concepts and routines that you have already assimilated and that people have ALREADY gotten used to.

Fundamental mental growth involves getting used to new ideas/ways of thinking for which there may NOT be any nice pat analogies with our experience as animals of a certain size and mass on a planet of a particular chemical composition talking a particular acoustic babble called English.

What people call "explanation"is often a bunch of metaphors/analogies that give them the feeling that some phenomenon relates to their experience as this kind of organism on that type of planet. But Nature is not obliged to run on rules that already make sense to our type of animal with our type of experience.

I really like what von Neumann (I think it was) said,and to me it is the very opposite of "shut up and calculate". But you do not understand it that way, you think he was saying "shut up and calculate".
OK, it is probably an unbridgeable difference of perspective that we just accept and let be. He was one of the most creative mathematicians that has ever lived. Here are a bunch of his sayings, including that one:
http://en.wikiquote.org/wiki/John_von_Neumann
The truth is often funny, I find

 

[Berlin]

Hi,
I think this is an exciting way to go, but I find two weak spots:
- first, why involve mass in your conservation laws, while mass is just a discrete level in energy space, which is acting 'strange' ( I mean different compared to letscsay photons) only in spacetime? It would conceptually be much stronger not to assume mass and only find those discrete mass levels as some solution! I am pretty sure that Smolin et al have to correct.
- second, the mentionings about h look like nonsense to me. H is still there, they only make it one like it is done in many textbooks before, nothing new here or am I missing the point?

Berlin

 

[marcus]

Hi,...
- second, the mentionings about h look like nonsense to me..., they only make it one like it is done in many textbooks before, nothing new here or am I missing the point?

I see your point, Berlin. What they say about ħ is not essential to their argument, more of a side comment. the way it works out they have this primitive quantity called "momentum" not defined in terms of anything else. They could call it "being" or "existence current" or anything. What it means is determined by the axioms governing the use of the concept.

Whatever units one chooses to quantify "momentum", when space emerges out of their causal web then the natural unit of length turns out to be reciprocal momentum. So then ħ is just a parameter that comes in if you use some other size unit of length. Otherwise it is, like you say, just equal to unity.

Actually in a way the fact that when length arises it turns out to be reciprocal momentum suggests to me that maybe they were right to call it "momentum" in the first place. But it is a primitive of the theory, so in principle there is no "correct"term for it.

This is just a trivial side comment but you probably will like to use LATEX for math symbols and equations. At the top of box where you write the message there is a menu of useful stuff starting with the B I U and ending with the the Ʃ . if you click on the Sigma you get a menu of greek letters and some math symbols, and over near the right end, beside some math arrows, the ħ.
You can write the h-bar either that way or with Latex as $\hbar$ .
Sometimes Latex expressions do not get processed until you click on browser reload.

I think that "momentum" was originally just some Latin word for "motion". http://en.wiktionary.org/wiki/movimentum back in history it was once a primitive vague undefined word for "amount of motion". Gradually we got used to it, and the idea crystallized in our language and our minds as having a definite meaning of the amount of matter (mass) multiplied by the speed it was moving----so it was "amount of motion". Who crystallized this initially vague idea for us? Galileo maybe, or Newton?

 

[marcus]

I think some of the issues that come up when you confront a new foundations proposal have to do with the tension between general principles and practice. Some people refer to general principles as "philosophy".
These folk-sayings, like "shut up and calculate", "not just stranger than we imagine but stranger than we CAN imagine", "what matters with a new mathematical idea is not its truth but its convenience", "you don't understand a new concept, you get used to it", reflect that tension between practical physics-as-usual and concern for deep fundamental or general principles.

Sometimes the appropriate thing to do is NOT worry about general principles---don't ask questions, just continue calculating along conventional lines. Other times it might be crucial to search for what is wrong with your theories at a deep almost philosophical level. To confront (and perhaps replace) the axioms. Doing that may involve learning new words which are not definable in terms of old words, or using mathematical terms in new ways (according to new axiomatics.) The test would then be how well it works---whether it is convenient---say, to provide a common foundation for QFT, QSM (quantum statistical mechanics), quantum theory itself, and 4D dynamical geometry.

Or how well, how conveniently, it works to cure known problems in several areas (GR has singularities, QFT is not general covariant and currently requires a fixed prior geometry like minkowski space) by discovering a single common axiomatic basis.

So sometimes the appropriate thing (even though prevailing theories may be excellent in their limited domains of effectiveness) IS to worry about general principles. And to try out new, possibly quite unintuitive, axiomatics.

I think that is what Cortês and Smolin are doing. And realistically one has to remember that it may fail. It's risky. On the other hand, from a bold attempt that makes some headway in a new direction one can learn ideas. I think it's going to prove a valuable initiative whatever the final outcome.

 

[Berlin]

Partcles with mass are not fundamental

Markus, first of all thanks for the explanation about the scientific symbols. Very difficult on an iphone...

I would like to elaborate on my remark about mass in the conservation laws in the last Cortes/ Smolin paper. My point is that I have the strong conviction that mass should not be part of the starting points of any fundamentel theory. It is understandable that people do it, but it is wrong. In fact, there are many -wrong- reasons why we keep using the concept of "free" particles with mass.

1. History. From Newton on: no asceleration, no force. So, constant movement implies a free particle. But even in Newtonian physics, constant movement is equivalent to no motion at all. You could call this confinement in space..., not free at all! NB, only photons escape this picture. They cannot be captured.
2. Beauty. Currently we are seduced by the beauty of the Dirac equation, including me. SR, particle/ anti-particle, fermion-spin, it's all there. Wow! Easy to switch on gauge forces after this.
3. SR. Maxwell, Lorentz invariance, this is the way to go. All photons stay free as a bird, but particles with mass have a heavy price to pay, so to say. To increase the speed you have to put in more and more energy to ascelerate. In 3-momentum space you will never escape. Sounds like a kind of confinement to me! Right in the center in the right frame...
4. GR. A geodesic only describes a test particle in the limit of small mass..! Free fall in GR is not the same as a free particle, it is a coupled system. And massless particles, like photons, do they escape this picture without contributing to the energy-momentum tensor? I bet they do, but this is only a guess.

In conclusion, particles with mass do behave 'strange'/ un-free in spacetime. Massless partlcles are much more natural as a starting point for fundamental physics. This would mean that using a Dirac like equation with mass (and adding forces after that) would already be an approximation, a symplification, where fundamental physics has been lost.

I did see that Cortes/Smolin started with massless particles in their first paper, but changed it in their last one. Probably they were -again- seduced by the joy of finding a "free" particle equation (with mass, of course) in the process, using approximations! You can speculate that not only spacetime is emerging but also the 3-momentum space inside the photon sphere, involving mass...

Berlin

NB, 't Hooft does use massless, c-speed physics in his cell automaton ideas...

 

[Berlin]

Edit:

Correction to my last post: when I said 3-momentum, I actually mean 3-velocity!

Berlin

 

[audioloop]

Any notion of causality as fundamental, imo, implies some sense of determinism. This is not a revolutionary idea. It does, however, raise questions about the 'fundamentality' of statistical probability. I think this is a promising avenue to be explored.

i think the inverse, full determinism, i.e. predeterminism or fatalism, obliterate causality, sweeps away it .
and the lack of determinism does not entail absence of causation.
determinism is not a thesis about causation.
.

 

[marcus]

http://arxiv.org/abs/1407.0032
Spin foam models as energetic causal sets
Marina Cortês, Lee Smolin
(Submitted on 30 Jun 2014)
Energetic causal sets are causal sets endowed by a flow of energy-momentum between causally related events. These incorporate a novel mechanism for the emergence of space-time from causal relations. Here we construct a spin foam model which is also an energetic causal set model. This model is closely related to the model introduced in parallel by Wolfgang Wieland in arXiv:1407.0025, and this construction makes use of results used there. What makes a spin foam model also an energetic causal set is Wieland's identification of new momenta, conserved at events (or four-simplices), whose norms are not mass, but the volume of tetrahedra. This realizes the torsion constraints, which are missing in previous spin foam models, and are needed to relate the connection dynamics to those of the metric, as in general relativity. This identification makes it possible to apply the new mechanism for the emergence of space-time to a spin foam model.
Comments:16 pages, 4 figures.

arXiv:1407.0025
New action for simplicial gravity in four dimensions
Wolfgang M. Wieland
(Submitted on 30 Jun 2014)
We develop a proposal for a theory of simplicial gravity with spinors as the fundamental configuration variables. The underlying action describes a mechanical system with finitely many degrees of freedom, the system has a Hamiltonian and local gauge symmetries. We will close with some comments on the resulting quantum theory, and explain the relation to loop quantum gravity and twisted geometries. The paper appears in parallel with an article by Cortês and Smolin, who study the relevance of the model for energetic causal sets and various other approaches to quantum gravity.
26 pages, 2 figures

http://relativity.phys.lsu.edu/ilqgs/
Tuesday, September 16th
Wolfgang Wieland, PennState
Title: Covariant loop quantum gravity: Its classical action, phase space and gauge symmetries
PDF of the talk (1Mb)
Audio [.wav 36MB]

The 16 September seminar talk presents the results of http://arxiv.org/abs/1407.0025. Download the PDF first, before you start the audio. The talk is well-organized and the slides are rather complete so that one can understand a lot just by reading the slides PDF.

Both regular Causal Sets (e.g. as developed by Rafael Sorkin, David Rideout, Fay Dowker and others) and regular Spin Foam QG (covariant LQG) are active lines of research with important results. This makes it especially interesting to see how the two recent tweaked versions of each can be closely related.

 

[Dryson]

which are transmitted along causal links and conserved at each event

Does this mean that energy traveling along the path of least resistance that arrives at the point of convergence is then conserved into a larger state of amassed properties such as planets and suns or a Big Bang?

 

[marcus]

which are transmitted along causal links and conserved at each event

Hi Dryson, I'm not sure what you meant about planets suns etc. But I recognized that you were quoting from the abstract of the August 2013 article that I mentioned in the first post. I think if I were starting this thread today I would not cite the August 2013 article but rather something more recent. It is a rapidly advancing line of research and the emphasis seems to have shifted some since a year ago. For reference here's the August 2013 paper.

...
http://arxiv.org/abs/1308.2206
Energetic Causal Sets
Marina Cortês, Lee Smolin
(Submitted on 9 Aug 2013)
We propose an approach to quantum theory based on the energetic causal sets, introduced in Cortês and Smolin (2013). Fundamental processes are causal sets whose events carry momentum and energy, which are transmitted along causal links and conserved at each event. Fundamentally there are amplitudes for such causal processes, but no space-time. An embedding of the causal processes in an emergent space-time arises only at the semiclassical level. Hence, fundamentally there are no commutation relations, no uncertainty principle and, indeed, no hbar. All that remains of quantum theory is the relationship between the absolute value squared of complex amplitudes and probabilities. Consequently, we find that neither locality, nor non locality, are primary concepts, only causality exists at the fundamental level.
9 pages. Article companion to http://arxiv.org/abs/1307.6167

The fundamental processes getting the most attention by this group of researchers are (not star and planet formation but) geometric processes. How space-time geometry arises, how this bit of curvature or volume affects that later bit of curvature or volume.
You sort of have to figure out geometry first because the other stuff, the matter, LIVES in geometry.

So the elements that make up the causal sets are very TINY and they represent geometric interactions above all.

The ideal would be to have a quantum model of how geometry evolves, how gravity works, how gravitational waves (ripples in geometry) are generated and how they spread.

So the theories people are working on involve small geometric elements called "simplices", for instance triangles, tetrahedra (four faced pyramids) and the 4d analog of tetrahedra. (think of them as space-time cells).

I'm afraid the current research is fairly technical. For a taste, look back at post #19 where I have a link to Cortes and Smolin's paper on causal spin foam models. Both that paper and the one by Wolfgang Wieland study a universe which arises from a swarm of tetrahedra which are constantly interacting with each other. the interactions form 4d space-time cells ("4-simplices") which accumulate and form the space-time past.

the theory needs to be developed further so that, for example, it can handle geometric expansion and contraction. Only then could the researchers tackle something line the "big bang" or "big bounce" of cosmology. You'll have to wait before there are satisfactory answers to those sorts of questions.
: ^)

 

[torsten]

http://arxiv.org/abs/1407.0032
arXiv:1407.0025
New action for simplicial gravity in four dimensions
Wolfgang M. Wieland
(Submitted on 30 Jun 2014)
We develop a proposal for a theory of simplicial gravity with spinors as the fundamental configuration variables. The underlying action describes a mechanical system with finitely many degrees of freedom, the system has a Hamiltonian and local gauge symmetries. We will close with some comments on the resulting quantum theory, and explain the relation to loop quantum gravity and twisted geometries. The paper appears in parallel with an article by Cortês and Smolin, who study the relevance of the model for energetic causal sets and various other approaches to quantum gravity.
26 pages, 2 figures

http://relativity.phys.lsu.edu/ilqgs/
Tuesday, September 16th
Wolfgang Wieland, PennState
Title: Covariant loop quantum gravity: Its classical action, phase space and gauge symmetries
PDF of the talk (1Mb)
Audio [.wav 36MB]

The 16 September seminar talk presents the results of http://arxiv.org/abs/1407.0025. Download the PDF first, before you start the audio. The talk is well-organized and the slides are rather complete so that one can understand a lot just by reading the slides PDF.

Both regular Causal Sets (e.g. as developed by Rafael Sorkin, David Rideout, Fay Dowker and others) and regular Spin Foam QG (covariant LQG) are active lines of research with important results. This makes it especially interesting to see how the two recent tweaked versions of each can be closely related.

Hi Marcus,
Really interesting approach by Wieland but it leaves me with questions:
1. Wieland states that one obtains the Graviton propagator from EPRL spin foam. But every calculation states to obtain a graviton propagator but with a different long-distance asymptotics. Is there any calculation (which I missed) to show the correct behaviour?
2. Here one speaks about simplices (which I know from topology). But simplices are used to triangulate a space and the space exists also between the vertices. In contrast for spin networks or spin foams, space does not exists between teh vertices. Or am I wrong?

 

[marcus]

Hi Torsten, nice to hear from you! I don't quite understand your question #1, so i will set it aside for now and look at #2.

...
Really interesting approach by Wieland but it leaves me with questions:
...
2. Here one speaks about simplices (which I know from topology). But simplices are used to triangulate a space and the space exists also between the vertices. In contrast for spin networks or spin foams, space does not exists between the vertices. ...

In my experience, many Spin Foam researchers restrict to spin foams which are dual to triangulations. So a SF vertex would have valence 5. It would correspond to a "pentachoron" with 5 tets for sides. The tets correspond to edges in the SF, so 5 edges would meet at the vertex.

This is a restriction on what the spin foam can be. It cannot be the general 2-skeleton of a general 2-complex.
Other LQG researchers do not assume this limitation. But you are a pro and more knowledgeable than me for sure! I'm not merely being modest!

BTW do you know about so-called "twisted" triangulations? The lengths of the sides do not have to be consistent. I have some things to do here, so must get back to this later. I'm glad you're interested in Wieland's "New Action" paper. I think it deserves serious attention.

 

[marcus]

Some new people may not be aware of your work on unusual differential structures (inequivalent types of smoothness that manifolds can have, and the possible effects on the physics). going back in the BtSM several years we have discussion of some of the early exotic smoothness papers, coauthored with Helge Rosé. I think newcomers who might be reading should have a link if they want to find out more, so here is a recent paper:
http://arxiv.org/abs/1401.4815
and list of some others by same author: http://arxiv.org/find/gr-qc/1/au:+Asselmeyer_Maluga_T/0/1/0/all/0/1

 

[torsten]

Hi Torsten, nice to hear from you! I don't quite understand your question #1, so i will set it aside for now and look at #2.

In my experience, many Spin Foam researchers restrict to spin foams which are dual to triangulations. So a SF vertex would have valence 5. It would correspond to a "pentachoron" with 5 tets for sides. The tets correspond to edges in the SF, so 5 edges would meet at the vertex.

This is a restriction on what the spin foam can be. It cannot be the general 2-skeleton of a general 2-complex.
Other LQG researchers do not assume this limitation. But you are a pro and more knowledgeable than me for sure! I'm not merely being modest!

BTW do you know about so-called "twisted" triangulations? The lengths of the sides do not have to be consistent. I have some things to do here, so must get back to this later. I'm glad you're interested in Wieland's "New Action" paper. I think it deserves serious attention.

Thanks marcus for the quick and helpful answer.
Right my first question was a little bit confusing. Here I try again:
In my knowledge, spin foam models had a problem to obtain a Graviton propagator with the correct long-range asymptotics. But Wieland mentioned this problem in his talk as solved. Where I can found the solution? Is Wieland wrong? I know only http://arxiv.org/abs/1103.1428 (and of course the Rovelli papers).
Thanks in advance

 

[torsten]

Some new people may not be aware of your work on unusual differential structures (inequivalent types of smoothness that manifolds can have, and the possible effects on the physics). going back in the BtSM several years we have discussion of some of the early exotic smoothness papers, coauthored with Helge Rosé. I think newcomers who might be reading should have a link if they want to find out more, so here is a recent paper:
http://arxiv.org/abs/1401.4815
and list of some others by same author: http://arxiv.org/find/gr-qc/1/au: Asselmeyer_Maluga_T/0/1/0/all/0/1

Thanks for mentioning our work. Exotic smoothness is a quite unusual topic. In particular, all these strcuture are ruled out by the choice of Σxℝ as spacetime. Currently our groups starts growing with PhD students in Poland and some interesting researchers in brasil.

 

[marcus]

...
In my knowledge, spin foam models had a problem to obtain a Graviton propagator with the correct long-range asymptotics. But Wieland mentioned this problem in his talk as solved. Where I can found the solution? Is Wieland wrong? I know only http://arxiv.org/abs/1103.1428 (and of course the Rovelli papers).
Thanks in advance

I would guess W.W. is probably not wrong. He is exceptionally careful and reliable. But I was unable to find a reply specifically rebutting the paper 1103.1428.
Aside from two self-citations it was only cited in the SF "living review" paper by Alejandro Perez.
http://arxiv.org/pdf/1205.2019.pdf
Take a look at page 77, where it says
"However, this seems to be a peculiarity of the Riemannian theory alone as the results of [58] for the Lorentzian models show. Non geometric configurations are exponentially suppressed. Finally, recently is has been shown that it is possible to restrict the state sum in order to obtain complex amplitudes [156] and [265, 266]."
References [265] [266] [267] are to that series of papers by Alexandar Mikovic et al.
Reference [267] is to the March 2011 paper you mention, but is not cited in the text. The one the Review CITES is [266] which came out in October. It is strange that there are no citations (aside from the kind of trivial "in passing" ones in Living Reviews).
It may be that Mikovic changed something in the October paper or for some other reason the March paper doesn't apply.
http://arxiv.org/abs/1110.6114
Effective action for EPRL/FK spin foam models
Aleksandar Mikovic, Marko Vojinovic
(Submitted on 27 Oct 2011)
We show that a natural modification of the EPRL/FK vertex amplitude gives a finite spin foam model whose effective action gives the Einstein-Hilbert action in the limit of large spins and arbitrarily fine spacetime triangulations. The first-order quantum corrections can be easily computed and we show how to calculate the higher-order corrections.
4 pages, proceedings of Loops 11 conference, Madrid; to appear in Journal of Physics: Conference Series

 

[marcus]

...BTW do you know about so-called "twisted" triangulations? The lengths of the sides do not have to be consistent. ...must get back to this later. ...

I mentioned twisted geometries but did not define, so I'll quote a concise description from page 24 of Wieland's New Action paper.
==quote http://arxiv.org/abs/1407.0032 ==
Next, we showed that the solutions of the equations of motion have a geometric interpretation in terms of twisted geometries.

Twisted geometries are piecewise flat geometries generalizing Regge geometries: In Regge calculus the edge lengths are the fundamental configuration variables, in twisted geometries there is no unique notion of length: Every tetrahedron has a unique volume, and every triangle has a unique area, but the length of a segment depends on whether we compute it from the flat metric in one simplex or the other. Finally we gave an argument why the model has curvature. Going around a triangle we pick up a deficit angle,...
==endquote==
As a reminder for anyone just dropping in on the discussion here's the paper we were talking about:
http://arxiv.org/abs/1407.0032
New action for simplicial gravity in four dimensions
Wolfgang M. Wieland
(Submitted on 30 Jun 2014)
We develop a proposal for a theory of simplicial gravity with spinors as the fundamental configuration variables. The underlying action describes a mechanical system with finitely many degrees of freedom, the system has a Hamiltonian and local gauge symmetries. We will close with some comments on the resulting quantum theory, and explain the relation to loop quantum gravity and twisted geometries. The paper appears in parallel with an article by Cortês and Smolin, who study the relevance of the model for energetic causal sets and various other approaches to quantum gravity.
26 pages, 2 figures

 

[Jimster41]

In the Cortes Smolin paper "The universe as a process of unique events" (arXiv: 1307.6167v2). Can anyone provide a little bit of lay-intuition regarding the physical meaning of constraint 3, "Energy momentum relations for massless photons"? (p.6)

 

[marcus]

Trying to get a foothold in first paper of this topic by Cortes and Smolin "The Universe as a process of unique events"

I probably will not be able to help you, Jimster. So people will be able to see what you are talking about, I will post the link to the paper you mention:
http://arxiv.org/abs/1307.6167

This is the C&S July 2013 paper. I'm not able to get into details with you about that just now. It's a bold leap into the ontological unknown and I find their later papers, C&S August 2013, and C&S July 2014 easier to relate to.

Just so your questions will not be overlooked I want to quote them. Maybe we can get back to them. Or someone else will tackle them.
==Jimster questions about C&S July 2013==
Constraint 1 on page 6 I can follow. Constraint 3 I think I get. I would be extremely grateful though If someone could explain a bit more about constraint 2. I thought the idea was that I was caused by K, so there would be no momenta going from I to K in the first place. Or is this all it is saying, that momenta from I to K is zero. [Never mind I see it says this] - So this is the causal constraint.
Is there an intuitive reason (in the framework being described at least) why that is that called "No redshifts"?

Regarding constraint 3. Is the implication of treating photons as having no momenta, that they are outside this model somehow, non events, time-less events, or momentum-less events but still in time. I other words if constraint 2 is defining causal direction, it still applies to photons right?
==endquote==
What is getting my attention, and I want to focus on is the remarkable coincidence that C&S July 2014 meets up with WW's July 2014 paper. I've given the links. they come from entirely different directions. Wolfgang Wieland is working in a comparatively bottom-up nuts and bolts way. He is concerned with making LQG-SF work better especially the spin foam (SF) approach. He has a really creative idea of how to do this which is to study the swarm of tetrahedra whose flight is the spin foam of changing geometry. The Tets interact whenever they come together and form Pents.

He is not making anything up, he is seeing something new in an approach that is over 10 years old, over 15 years old, that scores of people have worked on. The SF approach even bridges over to cosmology where there are observations, and to other types of quantum gravity. It is comparatively mature already, though still in a formative period.

It is extremely surprising that WW's paper, even though it is comparatively matter-of-fact nuts-and-bolts (making a 10 years old approach work better), should have an ontological consequence (space-time is made of the interactions where members of this swarm of Tets merge and give rise to other Tets, it is made of interactions, and there is a partial order of the interactions which is reminiscent of the C&S "causal sets" approach.)
The Energetic Causal Sets approach descended to us from the blue sky of philosophical considerations. That the two encounter each other and to some extent "engage" is nothing short of amazing.

So personally I'm tempted to just focus on the two July 2014 papers. I'm not a pro, or an expert--I have limited ability to understand, and even more limited ability to explain. So I have to concentrate. I'm hoping to see more papers by both C&S and by WW. I suppose they could even collaborate on research by all three of them (though that might be frustrating because of the different directions they come from philosophy versus nuts-bolts.)
Also i guess it would make sense for there to be numerical simulations---running computer models. So that might be in the offing too.

Fascinating stuff! I'm glad you are interested by it!

BTW take a look at part II of the "most important paper" poll for the recent quarter ( July-Sept)
https://www.physicsforums.com/threa...4-mip-most-important-qg-paper-part-ii.773590/
Both papers are on it. It's odd that one got so many more votes than the other. You can vote if you want. The MIP quarterly poll stays open.

 

[Jimster41]

Thanks Marcus, that is helpful. I have the later CS papers and Wieland also. I appreciate the guidance on piece-wise efforts at digestion. I had assumed I would be missing too too much without the first concepts from CS. I started with the (WW) paper but the geometry made me woozy, so I very much appreciate the outline you give at a very high level (with more context, I am looking forward to trying it again) and your impression that the coincidence of the two approaches is notable.

My understanding, such as it is of C&S 2013 paper (anyone who would correct me here please do):

• Axioms: 1)EnergyMomentum conservation, 2)Causal direction from event I to Event K (an event generator or clock), 3)A coherent gradient metric for EnergyMomentum (I think that's what 3 is)
• They derive a model by defining a virtual coordinate system, or "cost surface" for solving "action" given Axioms 1,2 and 3. It spits out a coordinate system like (Minkowski) space-time. (wow...)
• They chain (or network) some of these models together and show that they obey GR in-variance, you can accelerate one part of the network and the solution still works, because accounting gets done at each event boundary, clock stays local.
• They do the whole thing as a Twistor. here I am completely lost which is frustrating because they call this formulation ("... elegant"). Oof.
• They iterate a 2d model network in which the "event generator" favors events with similar pasts to define the next event, to show how momenta conservation under asymmetric time can show time symmetric or reversible behavior. The plots are spooky cool.
• They run the 2d model but evolving to favor maximally different pasts. A single past event dominates the future. Huh? I think this is super interesting. What if the selection rule used by the event generator had time structure itself, like maybe it traverses a range of history differences at a constant rate, as if the clock was counting something down or up - that affected event selection, or it was looping a selection gradient related to recycled or tapped past selections (partially non-local) anything that would cause events selected for interaction to reflect some time-coherent but "externally defined" (aka a-temporal) connection. Like Chronosynclasticinfudibulation... (Vonnegut me!)
• Wait, I think that's what they are doing in the last section (non-local interactions). Starting to investigate what happens when there are some hidden variables driving the event generator's selection rules... Spook-Like.

I got to say also, this whole thing (aside from being really cool) where the universe is like a big computer with a clock running registers based on rules reminds me of "Deep Thought" from Hitchhiker's Guide To the Galaxy.

Thanks again,

 

[RUTA]

"Fundamental processes are causal sets whose events carry momentum and energy, which are transmitted along causal links and conserved at each event. Fundamentally there are amplitudes for such causal processes, but no space-time."

Of course, you can't have concepts like momentum and energy without spatiotemporal measurements, i.e., you have assumed the existence of a spacetime metric. So, if your fundamental processes carry p and E, then fundamentally you have space-time.

 

[marcus]

"Fundamental processes are causal sets whose events carry momentum and energy, which are transmitted along causal links and conserved at each event. Fundamentally there are amplitudes for such causal processes, but no space-time."

Of course, you can't have concepts like momentum and energy without spatiotemporal measurements, i.e., you have assumed the existence of a spacetime metric. So, if your fundamental processes carry p and E, then fundamentally you have space-time.

I wouldn't say "of course" though : ^) There is at lease one small research literature in which energy and momentum play an important role without the existence of a globally defined space-time. In other words, in the context of that line of research by those researchers (e.g. Laurent Freidel, Giovanni Amelino, Jerzy Kowalski, Lee Smolin...), you have NOT "assumed the existence of a spacetime metric" when you talk about energy and momentum

I would have imagined that you knew about this, RUTA. Since you are sensitive to the different ontological approaches people take.
http://www.newscientist.com/article/mg21128241.700-beyond-spacetime-welcome-to-phase-space.html
http://en.wikipedia.org/wiki/Relative_locality
http://arxiv.org/abs/1101.0931
http://arxiv.org/abs/1106.0313

Mind you, I don't personally espouse or advocate that particular research initiative, and I wouldn't presume it is relevant to what we are talking about in this thread, namely ENERGETIC CAUSAL SETS as studied by Cortes and Smolin. This ECS is something new, not explicitly related to the 2011 papers on Relative Locality. But in this case, too, one is assuming that there is something which is conserved, which is prior to the definition of a spacetime. And which does NOT require one to assume that one already has a spacetime metric. : ^)

Maybe one of us should write to Cortes and Smolin and urge them not to use words like "energy" and "momentum" in a pre-geometry context. Advise them to make up different words to use, for the sake of semantic peace and harmony. Maybe they could be persuaded to use the word "Vigor" and call the mathematical structures they are investigating by the the name "vigorous causal sets" (VCS) instead of "energetic causal sets" : ^)

BTW Wolfgang Wieland has something similar to ECS he is studying (google "Wieland new action" to get his July 2014 paper) and he has a conserved quantity which he calls "volume". But this is also prior to the construction of a metric. So one cannot say that his having a conserved quantity called "volume" flowing through a bunch of interacting tetrahedra necessarily or "of course" presumes the prior existence of a spacetime.
Or so I think, anyway. If you have a look at the New Action paper you may conclude otherwise. Wieland's model has been called CAUSAL SPIN FOAMS.
I suppose that CSF and ECS could turn out to be closely related, or even the same theory.

 

[RUTA]

I'm just pointing out the obvious -- you can't talk about momentum or energy without a notion of spatiotemporal measure. A kg*m/s is meaningless if you don't know what a meter or a second is.

 

[marcus]

I understood what you were trying to say, RUTA. I can see that from your perspective you were just pointing out the "obvious" : ^)

However these researchers who work with pre-geometric concepts where you do not have an agreed-on spacetime or a spacetime metric as yet do, in fact, use terms like energy, momentum, volume.
Maybe they shouldn't! : ^D
But they do.
And I see them postulating that these prior-to-metric quantities are CONSERVED, even though there is no Noether theorem for miles around. There may in fact be no time, defined as yet, and yet these quantities are conserved. In the pre-geometric structure they are talking about.

It's basically a semantic issue. Do you want them to invent some term like "proto-ergon" so they wouldn't need to say "energy"? Maybe Cortes and Smolin should be calling what they study by some term like "Pre-ergetic Causal Sets".

So, when you say "of course" and "the obvious", I realize these things are obvious to you, but they might not be to those other researchers in their own context. It is fascinating stuff. I hope you google "cortes causal spin foam" and have a look at the July 2014 Cortes Smolin paper. Your comments could be very helpful, if you have some you want to share.

 

[RUTA]

It would be news if they could derive mass, space and time from something else more primitive, e.g., Vigor -- haha, love that. Otherwise, they're looking at something like Einstein's equations which tell you how the spacetime metric is to be "self-consistently" related to the stress-energy tensor.

 

[marcus]

It might help to get a more direct look at what we're talking about. I'll quote from Wolfgang Wieland's July paper. To get it without the link, google "wieland new action". As far as I can see there is no spacetime manifold here, and no spacetime metric. And yet analogs of several tools familiar with traditional GR analysis are present.
==quote http://arxiv.org/pdf/1407.0025v1.pdf abstract==
New action for simplicial gravity in four dimensions

We develop a proposal for a theory of simplicial gravity with spinors as the fundamental configuration variables. The underlying action describes a mechanical system with finitely many degrees of freedom, the system has a Hamiltonian and local gauge symmetries. We will close with some comments on the resulting quantum theory, and explain the relation to loop quantum gravity and twisted geometries. The paper appears in parallel with an article by Cortês and Smolin, who study the relevance of the model for energetic causal sets and various other approaches to quantum gravity.
==endquote==
I would suggest reading the paper before jumping to the conclusion that time here is some traditional GR observer's clock time, or that the Hamiltonian conforms to conventional preconceptions.
==quote http://arxiv.org/pdf/1407.0025v1.pdf page 24==
The relevance of the model
The action (50) describes a system of finitely many degrees of freedom propagating and interacting along the simplicial edges. The system has a phase space, local gauge symmetries and a Hamiltonian. What happens if we quantize this model? Do we get yet another proposal for a theory of quantum gravity? Recent results [23, 27, 36, 58] point into a more promising direction and suggest a convergence of ideas: The finite-dimensional phase space can be trivially quantized. The constraints of the theory glue the quantum states over the individual edges so as to form a Hilbert space over the entire boundary of the underlying simplical manifold. The boundary states represent projected spin-network functions [59, 60] in the kinematical Hilbert space of loop quantum gravity.
It is clear what should be done next: For any fixed boundary data we should define a path integral over the field configurations along the edges in the bulk. At this point, many details remain open, and we have only finished this construction for the corresponding model in three-dimensions [58], yet we do know, that whatever the mathematical details of the resulting amplitudes will be, they will define a version of spinfoam gravity [61].

Finally, there is the motion of the volume-weighted time normals, which endow the entire simplicial complex with a flow of conserved energy-momentum. As shown by Cortês and Smolin in a related paper [27], these momentum-variables introduce a causal structure, and allow us to view the simplicial complex as an energetic causal set [51, 52]—a generalization of causal sets carrying a local flow of energy-momentum between causally related events.

==endquote==

 

[RUTA]

If you're going to stick p and E on the links of a simplicial manifold, you can use that structure as a base to specify Regge-calculus-like least action equations to marry up p and E with a spacetime metric. But, still, without a spacetime metric, p and E don't make sense. Putting them on the links of a graph doesn't change that.