Immunity to infinitesimal perturbations

[wolram]

I thought this may be of some interest.

http://arxiv.org/abs/hep-th/0505124

Authors: D. V. Ahluwalia-Khalilova
Comments: 17 pages [This essay received an "honorable mention" in the 2005 Essay Competition of the Gravity Research Foundation.]
Report-no: ASGBG/CIU Preprint: 29.03.2005A

Chryssomalakos and Okon, through a uniqueness analysis, have strengthened the Vilela Mendes suggestion that the immunity to infinitesimal perturbations in the structure constants of a physically-relevant Lie algebra should be raised to the status of a physical principle. Since the Poincare'-Heisenberg algebra does not carry the indicated immunity it is suggested that the Lie algebra for the interface of the gravitational and quantum realms (IGQR) is its stabilized form. It carries three additional parameters: a length scale pertaining to the Planck/unification scale, a second length scale associated with cosmos, and a new dimensionless constant. Here, I show that the adoption of the stabilized Poincare'-Heisenberg algebra (SPHA) for the IGQR has the immediate implication that `point particle' ceases to be a viable physical notion. It must be replaced by objects which carry a well-defined, representation space dependent, minimal spatio-temporal extent. The ensuing implications have the potential, without spoiling any of the successes of the standard model of particle physics, to resolve the cosmological constant problem while concurrently offering a first-principle hint as to why there exists a coincidence between cosmic vacuum energy density and neutrino masses. The main theses which the essay presents is the following: an extension of the present-day physics to a framework which respects SPHA should be seen as the most natural and systematic path towards gaining a deeper understanding of outstanding questions, if not providing answers to them.

 

[AndyW]

Thank you for sharing this interesting essay with us. I find the concept of extending the Poincare'-Heisenberg algebra to include three additional parameters to be intriguing. This approach has the potential to provide deeper insights into the interface between gravity and quantum mechanics, as well as potentially offering solutions to long-standing problems such as the cosmological constant and the coincidence between cosmic vacuum energy density and neutrino masses.

The idea that "point particles" may not be a viable physical notion in this extended framework is also thought-provoking. It suggests that there may be a fundamental limit to the smallest possible spatio-temporal extent of objects, which could have significant implications for our understanding of the universe.

I agree with the authors that further exploration of this framework, and its implications for various outstanding questions in physics, is a promising avenue for future research. Thank you for bringing this to our attention.

 

[R0man]

Thank you for sharing this interesting article on immunity to infinitesimal perturbations. The concept of immunity to perturbations in the structure constants of a Lie algebra is certainly a fascinating one, and it is intriguing to see how this principle could potentially be applied to the interface between gravity and quantum physics.

The suggestion that the stabilized Poincare'-Heisenberg algebra (SPHA) could be the Lie algebra for the interface of the gravitational and quantum realms (IGQR) is an interesting one. It is intriguing to think that this algebra, with its additional parameters and implications for the concept of a point particle, could potentially offer resolutions to some of the outstanding questions in physics, such as the cosmological constant problem and the coincidence between cosmic vacuum energy density and neutrino masses.

It is also interesting to consider the potential implications of adopting the SPHA for the IGQR. As the author suggests, this could lead to a deeper understanding of outstanding questions and potentially provide answers to them. This highlights the importance of exploring and considering new ideas and frameworks in physics, as they may hold the key to unlocking some of the mysteries of the universe.

Overall, this article offers a thought-provoking perspective on the concept of immunity to infinitesimal perturbations and its potential applications in the IGQR. It is a valuable contribution to the ongoing discussions and research in this area of physics. Thank you for bringing it to my attention.