What is going on at NASA?

09/01/2015

ResearchBlogging.org

As a physicist I have been always interested about experiments that can corroborate theoretical findings. Most of these often become important applications for everyday life or change forever the course of the history of mankind. With this in view, I am currently following with great interest the efforts by the NASA group headed by Harold White.Harold "Sonny" White This work has arisen uproar in the web and in the media as it was come to envision the possibility to realize a warp drive, in the way Alcubierre devised it, and the stars were in the reach shortly. As it is well-known, Alcubierre drive implies exotic matter something that does not appear at hand neither in small nor in large quantity. On the other side, it was indirectly observed in the Casimir effect, a beautiful application of quantum field theory to real life. So, it is rather normal to link warp drive with exotic matter. It should be emphasized that nobody on Earth ever managed it in some way and it is not available at your nearest grocery store. The experiment carried out by Harold White and his group is realized with an interference device using lasers on an optical table. The idea is to observe a modification of space-time, a minuscule one, that would modify the paths of the laser beams. This would be comparable to the realization of the Chicago pile by Enrico Fermi that was the starting point for the Manhattan project. I would like to emphasize that such a laboratory small-scale manipulation of space-time would be a huge breakthrough in physics and would open up the way to a new kind of engineering, that of space-time. So, our hopes for a warp drive would be totally fulfilled.

There is an eager desire to obtain any possible information about the progress of White’s work but, of course, there are a couple of hurdles. The first one is that a scientist needs to be certain before to claim a result and we know very well why from some blatant examples in the last years. Extraordinary claims require extraordinary evidence. Last but not least, Harold White is employed at NASA and some restrictions could be required by the organization he is working with. So, it is really interesting a video appeared quite recently where White claims that the effect is there but further work is needed for confirmation. If you have a hour of your spare time, this video is worthwhile to be seen.

This video is interesting per se because Harold White is talking to his colleagues at NASA. But in the question time happens the interesting fact. A White’s colleague asks him “where is the exotic matter?”:

and here something interesting happens. White seems to avoid the question and admits that they talked before in the office. What is more interesting is what the White’s colleague is saying then unveiling some of the machinery behind the experiment. The colleague says that the experiment could be carried out in some strong coupling regime that makes the magic happen without any exotic matter. White denies and disagrees. We know that he is using strong electromagnetic fields in the interference zone. Indeed, the matter of the behaviour of the space-time in a strong perturbation was studied for cosmological aims by Belinski, Kalathnikov and Lifshitz, the BKL trio. David GarfinkleThis scenario was confirmed by numerical studies by David Garfinkle (see here). I was able to derive it by analysing the behaviour of the Einstein equations under a strong perturbation (see here) in analytical way. So, the chance to study such effects in a laboratory would be really striking and would mean an incredible breakthrough for people working in general relativity and related fields. What the exchange between White and his colleague implies is that this could be already at hand and without exotic matter. All the growing concerns about the work at NASA are then not applicable and a different kind of analysis would be needed. Particularly, Alcubierre drive should be devised in a different way. As a physicist, I am eager to learn more about this and to know the real answer, from the horse’s mouth, to the question “where is the exotic matter?”.

Miguel Alcubierre (2000). The warp drive: hyper-fast travel within general relativity Class.Quant.Grav.11:L73-L77,1994 arXiv: gr-qc/0009013v1

David Garfinkle (2003). Numerical simulations of generic singuarities Phys.Rev.Lett. 93 (2004) 161101 arXiv: gr-qc/0312117v4

Marco Frasca (2005). Strong coupling expansion for general relativity Int.J.Mod.Phys.D15:1373-1386,2006 arXiv: hep-th/0508246v3


Ashtekar and the BKL conjecture

18/02/2011

ResearchBlogging.org

Abhay Ashtekar is a well-known Indian physicist working at Pennsylvania State University. He has produced a fundamental paper in general relativity that has been the cornerstone of all the field of research of loop quantum gravity. Beyond the possible value that loop quantum gravity may have, we will see in the future, this result of Ashtekar will stand as a fundamental contribution to general relativity. Today on arxiv he, Adam Henderson and David Sloan posted a beautiful paper where the Ashtekar’s approach is used to reformulate the Belinski-Khalatnikov-Lifshitz (BKL) conjecture.

Let me explain why this conjecture is important in general relativity. The question to be answered is the behavior of gravitational fields near singularities. About this, there exist some fundamental theorems due to Roger Penrose and Stephen Hawking. These theorems just prove that singularities are an unavoidable consequence of the Einstein equations but are not able to state the exact form of the solutions near such singularities. Vladimir Belinski, Isaak Markovich Khalatnikov and Evgeny Lifshitz put forward a conjecture that gave them the possibility to get the exact analytical behavior of the solutions of the Einstein equations near a singularity: When a gravitational field is strong enough, as near a singularity, the spatial derivatives in the Einstein equations can be safely neglected and only derivatives with respect to time should be retained. With this hypothesis, these authors were able to reduce the Einstein equations to a set of ordinary differential equations, that are generally more treatable, and to draw important conclusions about the gravitational field in these situations. As you may note, they postulated a gradient expansion in a regime of a strong perturbation!

Initially, this conjecture met with skepticism. People simply have no reason to believe to it and, apparently, there was no reason why spatial variations in a solution of a non-linear equation with a strong non-linearity should have to be neglected. I had the luck to meet Vladimir Belinski at the University of Rome “La Sapienza”. I was there to follow some courses after my Laurea and Vladimir was teaching a general relativity course that I took. The course showed the BKL approach and gravitational solitons (another great contribution of Vladimir to general relativity). Vladimir is also known to have written some parts of the second volume of the books of Landau and Lifshitz on theoretical physics. After the lesson on the BKL approach I talked to him about the fact that I was able to get their results as their approach was just the leading order of a strong coupling expansion. It was on 1992 and I had just obtained the gradient expansion for the Schroedinger equation, also known in literature as the Wigner-Kirkwood expansion, through my approach to strong coupling expansion. The publication of my proof happened just on 2006 (see here), 14 years after our colloquium.

Back to Ashtekar, Henderson and Sloan’s paper, this contribution is relevant for a couple of reasons that go beyond application to quantum gravity. Firstly, they give a short but insightful excursus on the current situation about this conjecture and how computer simulations are showing that it is right (a gradient expansion is a strong coupling expansion!). Secondly, they provide a sound formulation using Ashtekar variables of the Einstein equations that is better suited for its study. In my proof too I use a Hamiltonian formulation but through ADM formalism. These authors have in mind quantum gravity instead and so ADM formalism could not be the best for this aim. In any case, such a different approach could also reveal useful for numerical simulations.

Finally, all this matter is a strong support to my view started with my paper on 1992 on Physical Review A. Since then, I have produced a lot of work with a multitude of applications in almost all areas of physics. I hope that the current trend of confirmations of the goodness of my ideas about perturbation theory will keep on. As a researcher, it is a privilege to be part of this adventure of humankind.

Ashtekar, A. (1986). New Variables for Classical and Quantum Gravity Physical Review Letters, 57 (18), 2244-2247 DOI: 10.1103/PhysRevLett.57.2244

Abhay Ashtekar, Adam Henderson, & David Sloan (2011). A Hamiltonian Formulation of the BKL Conjecture arxiv arXiv: 1102.3474v1

Marco Frasca (2005). Strong coupling expansion for general relativity Int.J.Mod.Phys. D15 (2006) 1373-1386 arXiv: hep-th/0508246v3

Frasca, M. (1992). Strong-field approximation for the Schrödinger equation Physical Review A, 45 (1), 43-46 DOI: 10.1103/PhysRevA.45.43


Physics laws and strong coupling

28/09/2008

It is a well acquired fact that all the laws of physics are expressed through differential equations and our ability as physicists is to unveil their solutions in a way or another. Indeed, almost all these equations are really difficult to solve in a straightforward way and are very far from the exercises at undergraduate courses. During the centuries people invented several techniques to manage such equations and the most generally known is surely perturbation theory. Perturbation theory applies when a small parameter enters into the equations and a series solution is so allowed. I remember I have seen this method the first time at the third year of my “laurea” course and was Giovanni Jona-Lasinio that showed it to me and other fellow students.

Presently, we see as small perturbation theory has become so pervasive that conclusions derived just at a perturbation level are sometime believed always true. An example of this is the Landau pole or, generally, what implies the renormalization program. It is not generally stated but it is quite common the prejudice that when a large parameter enters into a differential equation we are stuck and nothing can be done than using our physical intuition or numerical computation. This is true despite the fact that the inverse of such a large parameter is indeed a small parameter and most known functions have both a small parameter and a large parameter series as well.

As I said elsewhere this is just a prejudice and I have proved it wrong in a series of papers on Physical Review A (see here, here and here). I have given an overview in a recent paper. With such a great innovation to solve differential equations at hand is really tempting to try to apply it to all fields of physics. Indeed, I have worked for a lot of years in quantum optics testing the approach in a lot of successful ways and I have also found applications to condensed matter physics appeared on Physical Review B and Physica E.

The point is quite clear. How to apply all this to partial differential equations? What is the effect of a large perturbation on such equations? Indeed, I have had this understanding under my nose since the start but I have not been so able to catch it immediately. The reason is that the result is really counterintuitive. When a physical system is strongly perturbed all the terms that imply spatial variation can be neglected. So, a strong perturbation series is a gradient expansion and the converse is true as well. I have proved it numerically in a quite easy way using two or three lines of Maple. These results can be found in my very recent paper on quantum field theory (see here and here). Other results can be found by yourself with similar simple means and are very easy to verify.

As strange as may seem this conclusion, it has obtained a striking confirmation through numerical computations in general relativity. Indeed, I have applied this method also to general relativity (see here and here). Indeed this paper gives a sensible proof of the Belinski-Khalatnikov-Lifshitz or BKL conjecture on the behavior of space-time approaching a singularity. Indeed, BKL conjecture has been analyzed numerically by David Garfinkle with a very beatiful paper published on Physical Review Letters (see here and here). It is seen in a striking way how all the gradient contributions from Einstein equations become increasingly irrelevant as the singularity is approached. This is a clear proof of BKL conjecture and our approach of strong perturbations at work. Since then Prof. Garfinkle has done a lot of other very good work on general relativity (see here).

We hope to show in future posts how this machinery works for pdes. In case of odes we have already posted about (see here).


%d bloggers like this: