Spin Foam Gravity at new stage of maturity/consistency

[marcus]

Spin Foam Gravity (SFG) has reached a stage of development where perhaps we could have a new abbreviation to distinguish it from previous Loop gravity formulations. I could be wrong about this, of course, but I want to see how things look from that angle. There seem to be some language/organization innovations in Wieland's thesis that preserve basic content but give the theory a different look. E.g. the use of spinors (which has become widespread in recent research), and see also the footnote on page 135.

==from page 6==
.. can show that spin foam gravity comes from the canonical quantisation of a classical theory. This is a version of first-order Regge calculus [64], with spinors as the fundamental configuration variables. I will present this result in chapters 3 and 4. It should be a convincing evidence that spinors provide a universal language to bring the two sides of the theory together.
==endquote==
http://tel.archives-ouvertes.fr/docs/00/95/24/98/PDF/diss.pdf
==from pages 134-135==
To canonically quantise gravity it is often thought that one first needs to start from a 3+1 split, study the ADM (Arnowitt–Deser–Miser) formulation in the “right” variables, identify the canonical structure and perform a Schrödinger quantisation. The results of this thesis question this idea.

The ADM formulation is very well adapted to a continuous spacetime, but in spinfoam gravity we are working with a discretisation of the manifold, hence lacking that assumption. Instead we have simplices glued together and should find a Hamiltonian formulation better adapted to the problem.

After the introductory chapters 1 and 2, we found such a Hamiltonian formalism for the discretised theory. The underlying Hamiltonian generates the time evolution along the edges of the spinfoam. The corresponding time variable parametrises the edges of the discretisation, it is nothing but a coordinate, and does not measure duration as given by a clock…
…
...
In summary, the classical part introduced a canonical formulation of spinfoam gravity adapted to a simplicial discretisation of spacetime. This framework should be of general interest, as it provides a solid foundation where different models could fruitfully be compared.

The last section was about quantum theory. With the Hamiltonian formulation of the spinfoam dynamics at hand, canonical quantisation was straight-forward. We used an auxiliary Hilbert space to define the operators. Physical states are in the kernel of the first-class constraints. The second-class constraints act as ladder operators. One of them (Fˆn) annihilates physical states, while the other one (Fˆn†) maps them to their orthogonal complement, i.e. into the spurious part of the auxiliary Hilbert space. This is exactly what happens in the Gupta–Bleuler formalism.

Dynamics is determined by the Schrödinger equation. We quantised the classical Hamiltonian and solved the Schrödinger equation that gives the evolution of the quantum states along the boundary of a spinfoam face. This boundary evolution matched the Schrödinger equation introduced by Bianchi in the thermodynamical analysis of spinfoam gravity [113]. Gluing the individual transition amplitudes together, we got the amplitude for a spinfoam face*, which was in exact agreement with the EPRL model.
…
..
__________________
*We can organise the EPRL amplitudes such that each spinfoam vertex contributes through its vertex amplitude to the total amplitude, while the contribution from the faces looks rather trivial. Here we do the opposite, and assign non-trivial amplitudes to the spinfoam faces. These are two different ways to write the same model. Reference [62] gives several equivalent definitions of the amplitudes, and explains the equivalence.
==endquote==

 

[marcus]

Spin Foam Gravity is apt to benefit from results obtained in kindred LQG and LQC research:

unproblematical black hole model, google "planck star" to get http://arxiv.org/abs/1401.6562
(no singularity, no information loss problem, unitarity preserved, no "firewall"-type paradoxes)

non-singular start of cosmological expansion
(no need to posit a "multiverse", or suppose a rare "fluctuation" event to start expansion)

with high probability, adequate inflation starts at the bounce, google "ashtekar probability inflation"
also google "barrau duration inflation" to get http://arxiv.org/abs/1301.1264

 

[marcus]

At the end of Wieland's thesis there is a section (pages 136, 137) on future research interests.
It's worth seeing how they are laid out. One very interesting section (which I'll skip) is on the "flatness problem." Another section is on INCLUSION OF MATTER which is interesting enough that I want to quote in full:

== http://tel.archives-ouvertes.fr/docs/00/95/24/98/PDF/diss.pdf pages 136-137==
Inclusion of matter
To aim at a phenomenology of loop quantum gravity [201–203], strong enough to turn it falsifiable, we need to better understand how matter (our “rulers” and “clocks”) couples to the theory. Unfortunately, after decades of research, we still cannot say much about this issue. To overcome this trouble, I can see four roads to attack the problem, three of which I would like to study by myself:

(i) At first, there is what has been always tried in loop quantum gravity when it comes to this problem. Take any standard matter described by some Lagrangian, put in on an irregular lattice corresponding to a spin network state and canonically quantise. Although this approach was tried for all kinds of matter it led to very little physical insight. I think it is time to try different strategies.

(ii) The first idea that comes to my mind originates from an old paper by t’ Hooft [204]. I think it is a logical possibility that loop quantum gravity already contains a certain form of matter. If we look at the curvature of our models we find it is concentrated on the two-dimensional surfaces of the spinfoam faces. This curvature has a non-vanishing Ricci part which we can use (employing Einstein’s equations) to assign an energy momentum tensor to the spinfoam face. Following this logic one may then be able to reformulate the dynamics of spinfoam gravity as a scattering process of these two-dimensional worldsheets (that now carry energy-momentum) in a locally flat ambient space.

(iii) Loop quantum gravity is a theory of quantised area-angle-variables. I think this suggests not to start from the standard model that couples matter to tetrad (i.e. length-angle) variables. Instead we should take the fundamental discreteness of loop quantum gravity seriously, and try to add matter fields to the natural geometrical structures appearing, e.g. the two-dimensional spinfoam faces. In fact, when looking at the kinetic term of the action (3.46) a candidate immediately appears. We could just replace the commuting (π, ω) spinors by anti-commuting Weyl (Majorana) spinors, yielding a simple coupling of uncharged spin 1/2 particles to a spinfoam.

(iv) The recent understanding of loop quantum gravity in terms of twistors is mirrored [205–209] by similar developments in the study of scattering amplitudes of e.g. N = 4 super Yang–Mills theory . It is tempting to say these results all point towards the same direction eventually yielding a twistorial framework for all interactions.
==endquote==

 

[David Horgan]

Hi Marcus thanks for highlighting this thesis, it's very interesting.

 

[marcus]

Well I was actually following your example, David. You have recently read and commented on several PhD theses of new LQG researchers at your blog "Quantum Tetrahedron"
Sample post:
http://quantumtetrahedron.wordpress.com/2014/03/25/a-curvature-operator-for-lqg-by-alesci-assanioussi-and-lewandowski/
Alesci's thesis in particular. It helps to have comment call attention to a valuable thesis.
Often a thesis can be more pedagogical and less condensed than a journal article. So can be more adapted to learn from.

No kidding I actually got the idea of studying theses from you. Also I have added this one of Wieland to the current MIP poll.

I'd appreciate knowing your assessment when you've had time to form an opinion on what he's doing, it would be good to have anther's perspective.

 

[marcus]

Fiona ("Fuzzyfelt") just called my attention to two conference talks Rovelli gave at Oxford last year which are good for getting an overview of goings-on with Quantum Foundations and Loop/Spinfoam Gravity in broader context.

Given that Wieland's thesis provides a remarkably clear understandable sketch of the current status and main-agenda problems specifically in Spin Foams, it's helpful have that complemented by these two more general talks (roughly 55 and 45 minutes in length).

These were given at the 10-12 June 2013 Conference on Cosmology and Quantum Foundations.



and

 

[marcus]

In the first lecture, especially starting just before minute 14, Rovelli gives a really cogent explanation of his type of REALISM. Quantum ontology is more LEAN AND SPARE than classical ontology. You have facts (that involve an interaction) and you do not fill in between facts with the mud of continuity. He illustrates by retelling Heisenberg's story of how he came to this perception.

He repeats DeFinetti's joke about probability and shows a slide "proving" the reality of the Caloric fluid.

Then he gives a concise account of the RELATIONAL way to make sense of Quantum Theory.


The first 14 minutes are devoted more to responding to earlier speakers like Max Tegmark and Simon Saunders, and explaining why we do not (as e.g. James Hartle may think) need a new kind of Quantum Theory to deal with mainstream cosmology because of the apparent lack of a separate observer. Cosmology deals with degrees of freedom, and modes, on a scale much larger than ourselves and our instruments, so we qualify as separate observers. The first 14 minutes of groundwork are interesting but somewhat special to the particular conference (philosophers and physicists at Oxford) and the immediate environment of speakers and ideas. So for me the main content came after that introduction.

Here's a link to the conference itself:
http://philcosmo.physics.ox.ac.uk/events
Here's the SCHEDULE:
http://philcosmo.physics.ox.ac.uk/sites/philcosmo.physics.ox.ac.uk/files/Schedule-CQF_0.pdf
Here's O'Raifeartaigh's blog about the final day:
http://coraifeartaigh.wordpress.com/2013/06/13/last-day-of-quantum-foundations-conference-at-oxford/

He says the last day's panel discussion between Rovelli, Saunders, David Wallace, and Antony Valentini was very good. I haven't watched that. Here's the link:


I see that on the schedule the title of Rovelli's first talk is listed as "Do not mix-up Problems: the Cosmos, the Observer, the Quanta"
The title of his second talk (the final one of the conference) was "Relational Quantum Mechanics. Spinfoam Cosmology"
To recall from previous post, the 41 minute "Spinfoam Cosmology" talk is:

and the 11 minute Q&A which followed (quite interesting!) is:

 

[marcus]

I neglected to mention it but there was also an 18 minute Q&A following the first talk. Anthony Valentini, Simon Saunders, and Max Tegmark asked questions as well as several others. Also at the end of the conference, after Rovelli's second talk, and the Q&A, there was a 4 person panel discussion involving Rovelli, Tegmark, Saunders and David Wallace (two Oxford philosophy of physics/quantum foundations people). The panel was moderated by philosopher of physics Jeremy Butterfield.



Just to have all five links gathered together I'll re-list them:
(58 min. cosmology and quantum theory: the relational view)
(18 min. Q&A abt cosmo+qt, relational view)
(41 minute talk, spinfoam quantum cosmology)
(11 minute Q&A about spinfoam QC)
(59 minute panel discussion)

 

[marcus]

Spelling correction to post#8: it's Antony V. (not Anthony). I got it right in previous post #7 but missed later.

 

[marcus]

At around minute 20 into the "relational view" talk there are a couple of core message slides:

Describe reality in terms of the facts appearing in interactions

*Realism (Max's ERH) Yes facts happen on Andromeda!
*No special role to humans (Max's NSSH) nor else (macro, records).
*Take physics and see what it implies for philosophy, not viceversa (Simon).
*Be real about facts like a, not about metaphysical waves in infinite dimensional configuration space.

[There is an illustration of Galileo measuring the spin of an electron and discovering that it is UP (this is the exemplary fact a.) The next slide, appearing shortly after minute 21, continues the theme of interactive fact realism.]

*Processes are what "happens". (Simon)
*The split of the world into individual processes is arbitrary (tensorial structure of QM).
*Interactions is what happens at the boundaries of processes (states).
*States code the way processes affect one another at the boundaries.

*(An object is a "monotonous process" (Nelson Goodman 1951).)

[No time was spent discussing objects in the talk, this fifth point seems merely an afterthought emphasizing that the focus here is on process rather than object. Algebraically, the division of the world into two interacting processes is identified with the tensor product A⊗B. I think this is what is meant by "tensorial structure" of QM formalism.]

These two slides are just an abbreviated outline, so are to be understood by listening to lecture surrounding them, particularly the few minutes on either side of minute 21, say minutes 19 to 23.

===========
Another key point comes around minute 31---the unreality of probabilities. Probabilities describe our lack of information and are useful as such, but our picture of the world shouldn't be built of probability functions (that is like attributing physical reality to heat as a fluid called the Caloric.) Bruno De Finetti's joke comes at minute 33.
Then at 34:30, "The realist who endows the 'quantum state' with ontological weight is barking at the wrong tree."
He says it's better to be a realist about the facts.
And (in classical physics) these facts are described by the position of the system in phase space,
while (in quantum physics) they are points in the spectra of elements of the observable algebra.

Around minute 37 is where he gives his argument against "multiverse" ontology. Basically "believe it if you want to, but it's not useful in doing physics". It's a 58 minute talk so there is more to summarize but this is enough for one post.

 

[MTd2]

So, objects can only be an ideal structure, since in QFT, a process is probabilistic. So, there is no being at it, so, no reason for ontology, or rather, it's ontology is a nothingness. Like Sartre says, it is a being-it-self. The experimenter, which has the capacity of imagination, can only be a being. But since this experimenter is aware that is composed by process, those ideals, it is full of nothingness inside it. So, this awareness of its nothingness causes a sensation of anguish, which causes the experimenter to always move forward, to fullfill its own anguish.

The only contact with the outside world is a measurement, which is by its own nature, composed of combination of pure states. But just lasts while it lasts, so this is how the being for itself, goes beyond itself, and capture this object. Since an object is an ideal and fuzzy, this is actually not an object, but a quasi-object. That is, the being captures a concept, which before existed as merely as expectation.

That's a bit of Sartre.

 

[MTd2]

Now, more seriously, does "*Realism (Max's ERH) Yes facts happen on Andromeda!" mean some kind of effect that enforces causality? For example, if wormholes exist their mouths will obey causality, regardless of what GR says about them? Or that faster than light particles will go through paths (3+1) that enforces causality?

 

[marcus]

?

I hope anyone who is interested will watch the talk

It's simple, straightforward, no exotic physics. Remarkably common-sensical and down-to-earth. So the most efficient way to understand is just to watch and listen.

 

[David Horgan]

Wieland's Spinfoam gravity thesis

Hi Marcus, hi forum, once again Marcus thanks for highlighting this thesis and Wieland's work in general. I've been studying this thesis in depth and the more I study it the more hopeful I feel about this approach. Of course the thesis is remarkably good and provides an extremely clear explanation of how it's results are derived.

I think you're right to regard this as a turning point. The thesis, it's associated articles and talks point in the direction of a very fruitful line of research. I'll review this work on my blog in a few weeks - I'll also be reviewing by own understanding of twistors and spinors at the same time of course :)