Can loop quantum gravity tell us something about the recent phenomena of the neutrinos?
I would say Not. Modern LQG has a manifestly Lorentz invariant formulation.
There is mounting evidence that it reproduces GR. (Recent papers derive GR in various cases or under various assumptions--as more restrictions are removed one may expect a general proof.)
I would say modern LQG, the prevailing version since 2007 or 2008, tells us NOT to expect the neutrino finding by OPERA to hold up. If the superlumy nus were sustained this would, I think, cause a major shakeup in LQG. This is just my opinion as a sideline observer.
Lorentz covariance of loop quantum gravity
Carlo Rovelli, Simone Speziale
(Submitted on 8 Dec 2010)
The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where Lorentz covariance is manifest. K can be described in terms of a certain subset of the "projected" spin networks studied by Livine, Alexandrov and Dupuis. It is formed by SL(2,C) functions completely determined by their restriction on SU(2). These are square-integrable in the SU(2) scalar product, but not in the SL(2,C) one. Thus, SU(2)-spin-network states can be represented by Lorentz-covariant SL(2,C) functions, as two-component photons can be described in the Lorentz-covariant Gupta-Bleuler formalism. As shown by Wolfgang Wieland in a related paper, this manifestly Lorentz-covariant formulation can also be directly obtained from canonical quantization. We show that the spinfoam dynamics of loop quantum gravity is locally SL(2,C)-invariant in the bulk, and yields states that are preciseley in K on the boundary. This clarifies how the SL(2,C) spinfoam formalism yields an SU(2) theory on the boundary. These structures define a tidy Lorentz-covariant formalism for loop gravity.
6 pages, 1 figure.
Carlo Rovelli's comment on the alleged finding by OPERA was "In Italy everybody disregards the speed limit, OK? Let's wait for confirmation before we take this seriously."
Or words to that effect. It is not yet time for Loopsters to get excited about this, they have plenty to work on already and it will be a while before OPERA is confirmed or disconfirmed.
Also, LQG is not a theory of everything, unlike string theory. In particular, it is not a theory of Italy.
So, string theory is a theory of Italy too? It is good to know that it contains Italy, as it seems that it doesn't contain other things.
It certainly contains Italy, Greece, Germany and other European countries b/c thanks to all these extradimensions it's the first theory that helps us to understand where all the money goes ...
In addition I think Rovelli's reasoning that "in Italy everybody disregards the speed limit" is not correct; that would perhaps apply to Italian neutrinos, not to Swiss neutrinos.
LQG does not say anything special regarding different particles. If there would be some violation of Lorentz covariance in LQG (which is not case as marcus expalined above) there would be no reason why it should apply to neutrinos but not to other particles.
Isn't it something embarrassing that a theory of everything can't give us a testable experiment??
This is to my knowledge.
You might like to review the ways phenomenologists have proposed to test Loop cosmology by observation.
There is a considerable literature dating from 2008 onwards.
The "energy dependent speed of light" business was a vintage 2005 (or earlier) idea that did not pan out, at least as a test of LQG.
So the currently proposed observational tests do not have to do with stuff going faster than c.
In direct answer to your question, Casco, YES it is embarrassing when theorists spend time elaborating theories which cannot, even in principle, be empirically tested. One gets the feeling that it should be against the rules, maybe it is. A betrayal of the trust we place in them. A departure from the centuries-old scientific tradition. Which if allowed to continue could endanger something more precious than their own careers.
If you want a link to some test-related papers let me know and I will fetch one.
Just to clarify, I'm not against string theory, I think that even if some day someone can prove that it's or isn't a theory wrong, it will leave something productive for the humanity, I think that it is not a waste of time.
For me this is very similar to aether of 100 years ago.
And the references about what you're talking about, I'm interested if you can give them to me it would be great.
Fine. This is not a perfect list. It probably gets some wrong ones and misses some good ones.
It gets 40-some papers from 2009 onwards that are all or largely about ways to test LQG by observing features of the microwave background. That is by looking for effects on the early universe resulting from Loop cosmology bounce.
This is a typical result of LQG. When GR gravity is quantized LQG-style one sees that at very high density gravity is repellent instead of attractive. So a collapsing classical region rebounds and re-expands into another classical region.
There is even a natural period of inflation that occur automatically without making any extra assumption involving an exotic "inflation" field. The bounce itself causes a brief jolt of faster-than-exponential expansion. It is technically called "superinflation" because with inflation you just have exponential expansion. Whereas here the scalefactor goes as eHt with increasing H, and one can say something about the behavior of H. The particular way the bounce happens in LQG (even compared with other bounce cosmologies) should leave a footprint on the early universe.
So people, including outsiders, have beein comparing what LQG leads them to expect about the early universe with actual data from the WMAP mission and more importantly, I guess, preparing to confront the theory with data from the Planck mission.
It is pretty interesting. Professional testing people---phenomenologists---have gotten into it. They have no committment one way or another to any particular theory. Their professional committment is to testing, win or lose. So they score points either way if they develop a way to confront anybody's theory with data.
Several of these papers envisage a follow-on CMB mission beyond WMAP and the current Planck. Something that can map the *polarization* of the CMB, not just the temperature.
And do it more precisely than Planck spacecraft.
However I cannot promise that the main part of these 40-some papers will be understandable. They are all recent (as I said, 2009 and later), quite technical, and make no effort at popularization or pedagogy. You get it warts-and-all, but is the only way I know to manage a glimpse of what is going on in the area of Loop cosmology testing.
Sometimes the first and last pages of an otherwise incomprehensible paper will be in plain English. You may know this from other research you have done. Look for the introduction paragraph and the conclusions section at the end.
nice discussion and answers to my physics.se question
Maybe it is better to ask here in this forum about LQG than at SE ...
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