A Brief Introduction to Loop Quantum Cosmology

A Brief Introduction to Loop Quantum Cosmology [arxiv:0907.5160]
Authors: Guillermo A. Mena Marugan

Abstract: In recent years, Loop Quantum Gravity has emerged as a solid candidate for a nonperturbative quantum theory of General Relativity. It is a background independent theory based on a description of the gravitational field in terms of holonomies and fluxes. In order to discuss its physical implications, a lot of attention has been paid to the application of the quantization techniques of Loop Quantum Gravity to symmetry reduced models with cosmological solutions, a line of research that has been called Loop Quantum Cosmology. We summarize its fundamentals and the main differences with respect to the more conventional quantization approaches employed in cosmology until now. In addition, we comment on the most important results that have been obtained in Loop Quantum Cosmology by analyzing simple homogeneous and isotropic models. These results include the resolution of the classical big-bang singularity, which is replaced by a quantum bounce.

Comments: 15 pages, published in AIP Conference Proceedings, Volume 1130, Geometry and Physics: XVII International Fall Workshop on Geometry and Physics

Einstein on axiomatization of physics

Here is the Einstein’s quote that I have previously promissed to post:

If, then, it is true that the axiomatic basis of theoretical physics cannot be extracted from experience but must be freely invented, can we ever hope to find the right way? Nay, more, has this right way any existence outside our illusions? Can we hope to be guided safely by experience at all when there exist theories (such as classical mechanics) which to a large extent do justice to experience, without getting to the root of the matter? I answer without hesitation that there is, in my opinion, a right way, and that we are capable of finding it. Our experience hitherto justifies us in believing that nature is the realization of the simplest conceivable mathematical ideas. I am convinced that we can discover by means of pure mathematical constructions the concepts and the laws connecting them with each other, which furnish the key to the understanding of natural phenomena. Experience may suggest the appropriate mathematical concepts, but they most certainly cannot be deduced from it. Experience remains, of course, the sole criterion of the physical utility of a mathematical construction. But the creative principle resides in mathematics. In a certain sense, therefore I hold it true that pure thought can grasp reality, as the ancients dreamed.

[my italics]

(Einstein, 1954, Ideas and Opinions, quoted from Schweber, “Einstein and Oppenheimer: the meaning of genius”)

I think the above quote by Einstein is remarkable is several ways, specially the privileged role of creativity and freedom of the human mind expressed in mathematical language, but at the same time the recognition of experience as the sole criterion of the physical utility of such mathematical constructions.

(The above quote, according to Schweber, was an observation by Einstein on Hilbert’s program of axiomatization of physics.)

How Far Are We from the Quantum Theory of Gravity?

How Far Are We from the Quantum Theory of Gravity? [arxiv:0907.4238]

R. P. Woodard (University of Florida)

Abstract: I give a pedagogical explanation of what it is about quantization that makes general relativity go from being a nearly perfect classical theory to a very problematic quantum one. I also explain why some quantization of gravity is unavoidable, why quantum field theories have divergences, why the divergences of quantum general relativity are worse than those of the other forces, what physicists think this means and what they might do with a consistent theory of quantum gravity if they had one. Finally, I discuss the quantum gravitational data that have recently become available from cosmology.

Comments: 106 page review article solicited by Reports on Progress in Physics

Nobel 2008 Lectures

Nobel Lectures from the 2008 winners have been recently published in Reviews of Modern Physics and are freely available:

Nobel Lecture: What does CP violation tell us?
Toshihide Maskawa

Nobel Lecture: CP violation and flavor mixing
Makoto Kobayashi

Nobel Lecture: Spontaneous symmetry breaking in particle physics: A case of cross fertilization
Yoichiro Nambu

Recent impact on Jupiter

Steinn Sigurðsson has an interesting post about this recent event over at his blog, Dynamics of Cats.

“New Look” and Twitter

I hope you like the “new look” of Theorema Egregium; notice also that I am “twittering” now– see the side bar. Just experimentally.

Open letter

I make here publically available my letter to Sabine (Backreaction) concerning ou recent exchange of comments over at her blog. I will not post her letter because it was personally addressed to me. However, since my letter was general enough, and perhaps elucidative enough, here it is.

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Dear Sabine,

Thanks for your email. I think that it is quite possible that I have not expressed myself the best possible way. My comments were an attempt at a criticism on the topics based on those that you have mentioned in your post, which I had assumed to be representative of the conference. All I want to say is that I do not care what people want to work on, but I am tired to see professional scientists working on non-scientific issues (viz., those which the scientific method is not applied) as scientific. I consider this very non-ehtical and a dis-service to the public.

Theory must provide a means to experimental verification (in principle, at least), if not, you have an unproven hypothesis. Some people at the frontier of physics are not taking care of this very important concept and elevate their unproven hypotheses to principles of truth, from which they base all their subsequent work. We cannot rely on our subjective judgements to consider some theory acceptable or not: this is why the scientific method exists as a pillar for science.

I think FQXi is perfect as a funding agency for non-mainstream, alternative approaches, which nevertheless are perfectly scientific. Also, philosophical themes (which is a completely different class of discipline, with its own epistemological rules). However, it appears that this question is not clear enough.

I am glad to learn that your work was well received. I hope that you have understood that my criticism was not aimed at your work on phenomenology, which is evidently scientific enough.

Best regards,
Christine
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EDIT: Sabine writes that “most of them [the projects] eventually won’t lead anywhere – that being the nature of the business”. The problem is not that some projects lead nowhere, but that any non-scientific project leads nowhere by construction. If one’s work is based on an unproven hypothesis which is elevated to a principle of truth, from which all subsequent work is based, then it is highly probable that it will indeed lead nowhere. Or the conclusions will be most probably false.

She also insists that I point to specific projects that I consider non-scientific. As I already emphasized, my comments were based on the themes that she highlighted on her post, not on the program, which was not made avaliable on the FQXi site at the time of the postings. In any case, I leave the excercise to the reader to apply the scientific method and find out the answer by him/herself.

—
Related posts:

Smolin Against the Timeless Multiverse

The Universe

Universes Everywhere

What is science for you? Up to 50 words

What is science – for me

Science is no longer scientific

Dear Traveller of the Future,

If for some reason this set of electronic ramblings reach you, I salute you.

But my salute is embeded in deep sorrow. I have just realized that I am a living testimony of the end of science — a human activity arduously conceived during centuries in order to objectively probe nature into her deepest substrate: a triumph of the human mind.

For some reason, many people engaged into such a dignified activity slowly gave up on the arduous road, and chose the easiest paths, which unfortunately often lead to the swampy terrain of incertitude and ignorance.

Although there are still many advancements, specially technical ones, there is Death waiting at the frontier.

Science is no longer scientific!

Best wishes to you, Traveller of the Future, to whom the idea of what was gained and what was lost may never be perceived, but I still hope that the starlight inspire your soul, somehow.

Christine

PS- This anecdote was inspired by a discussion developed here.

Favorite Prefaces V

Concepts in Solids

P. W. Anderson

I reread Concepts in Solids with both pride and embarrassment. Pride, both because it was this set of lectures which inspired Brian Josephson to invent his effect — not every book can point to the precise Nobel prize it inspired — and because l did, in a very brief space, manage to touch some of the key topics which are still not adequately covered in your average solid state theory book. For instance, it is shocking that the main texts used in this country still do not touch on the Mott transition or the “Magnetic State.” I was aiming at conceptual, not mechanical physics, and I hope I got there.

Embarrassment, because after all, there has been 30 years of physics since then. For instance, I note that I guessed absolutely wrong in dismissing tight-binding theory out of hand: it has not yet totally coine into its own but it is, in my present opinion, the right way to think about most bonding in solids. I am not ashamed of skipping localization – only Mott was interested in it, and neither of us yet knew where to go next. I was prescient about broken symmetry — as Josephson realized — but left out phase transitions, as I myself noted.

Nonetheless, I believe that the average student will still be harmed less by this book than by any number of other books I should not name, and I welcome the reissuance.

Your brain on the edge of chaos

No news to me. I’ve always suspected that. Now, seriously:

Though much of the time it [the brain] runs in an orderly and stable way, every now and again it suddenly and unpredictably lurches into a blizzard of noise.

Neuroscientists have long suspected as much. Only recently, however, have they come up with proof that brains work this way. Now they are trying to work out why. Some believe that near-chaotic states may be crucial to memory, and could explain why some people are smarter than others.

Read whole article by the New Scientist magazine:

Disorderly genius: How chaos drives the brain

A little bit of cosmographic sanity

Finally, an interesting paper on dark energy.

Cosmographic analysis of dark energy [http://arxiv.org/abs/0906.5407]

Authors: Matt Visser (Victoria University of Wellington), Celine Cattoen (Victoria University of Wellington)

Abstract: The Hubble relation between distance and redshift is a purely cosmographic relation that depends only on the symmetries of a FLRW spacetime, but does not intrinsically make any dynamical assumptions. This suggests that it should be possible to estimate the parameters defining the Hubble relation without making any dynamical assumptions. To test this idea, we perform a number of inter-related cosmographic fits to the legacy05 and gold06 supernova datasets, paying careful attention to the systematic uncertainties. Based on this supernova data, the “preponderance of evidence” certainly suggests an accelerating universe. However we would argue that (unless one uses additional dynamical and observational information, and makes additional theoretical assumptions) this conclusion is not currently supported “beyond reasonable doubt”. As part of the analysis we develop two particularly transparent graphical representations of the redshift-distance relation — representations in which acceleration versus deceleration reduces to the question of whether the relevant graph slopes up or down.