Wednesday, December 28, 2005

Laval Nozzle and the Blackhole

Often times model changes help perspective, where previously idealization will be contained. Moving beyond the experimental grasp for new ways in which to interpret, require a mode and offensive into producing new variations of ole thngs held in context? Ths is why such models like string that began in one mode in terms of quark confinement have now bloossomed into modes cocnerned with quantum gravity.



Discovering new dimensions at LHC

More dramatically still, the LHC could produce fundamental string relations of our familiar particles, such as higher-spin relatives of electrons or photons. There is also a possibility that, owing to the now much stronger gravitational interactions, microscopically tiny black holes could be produced with striking signals.


Once idealization and understanding developed in quark Confinement, it is understood the shift to the metric and the idealization of that measure became a property I found in the way we now deal with the perceptions containing dimensional significance? Strng Theory, that had graduade from the model apprehensions early on, here to a more fundamental pursuate of how we see in those extra dimensions, compact as they may be?

Acoustic Metric (29 Dec 2005 Wiki)

In mathematical physics, a metric (mathematics) describes the arrangement of relative distances within a surface or volume, usually measured by signals passing through the region – essentially describing the intrinsic geometry of the region. An acoustic metric will describe the signal-carrying properties characteristic of a given particulate medium in acoustics, or in fluid dynamics. Other descriptive names such as sonic metric are also sometimes used, interchangeably.

Since "acoustic" behaviour is intuitively familiar from everyday experience, many complex "acoustic" effects can be confidently described without recourse to advanced mathematics. The rest of this article contrasts the "everyday" properties of an acoustic metric with the more intensely studied and better-documented "gravitational" behaviour of general relativity


On the Universality of the Hawking Effectby William G. Unruh and Ralf Schutzhold

Addressing the question of whether the Hawking effect depends on degrees of freedom at ultra-high (e.g., Planckian) energies/momenta, we propose three rather general conditions on these degrees of freedom under which the Hawking effect is reproduced to lowest order. As a generalization of Corley’s results, we present a rather general model based on non-linear dispersion relations satisfying these conditions together with a derivation of the Hawking effect for that model. However, we also demonstrate counter-examples, which do not appear to be unphysical or artificial, displaying strong deviations from Hawking’s result. Therefore, whether real black holes emit Hawking radiation remains an open question and could give non-trivial information about Planckian physics.


It is important that when thinking about this universality that the derivations of such thinking is understood by me so I ahve to lay it out in a sequence that suports the end part of this post so that it is brought togher in a nice way. I bold mark thos epoints that help greatly in my understanding.

Acoustic_theory(28 Dec 2005 Wiki)

Acoustic theory is the field relating to mathematical description of sound waves. It is derived from fluid dynamics. See acoustics for the engineering approach.

The propagation of sound waves in air can be modeled by an equation of motion (conservation of momentum) and an equation of continuity (conservation of mass). With some simplifications, in particular constant density, they can be given as follows:


where is the acoustic pressure and is the acoustic fluid velocity vector, is the vector of spatial coordinates x,y,z, t is the time, ρ0 is the static density of air and c is the speed of sound in air.



Fluid Dynamics (28 Dec 2005 Wiki)

Fluid dynamics offers a mathematical structure, which underlies these practical discipines, that embraces empirical and semi-empirical laws, derived from flow measurement, used to solve practical problems. The solution of a fluid dynamics problem typically involves calculating for various properties of the fluid, such as velocity, pressure, density, and temperature, as functions of space and time


So these ideas in terms of analogies help to push forarwd understanding where we might have been limited in our views before. I know, they certainly help me.

"Analogue Gravity"
by Carlos Barceló and Stefano Liberati and Matt Visser

Abstract

Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing) and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity).


and here......


Parentani showed that the effects of the fluctuations of the metric (due to the in-going flux of energy at the horizon) on the out-going radiation led to a description of Hawking radiation similar to that obtained with analogue models. It would be interesting to develop the equivalent formalism for quantum analogue models and to investigate the different emerging approximate regimes.


I am always interested in how science might take these analogies in concert with how we understand blackhole horizon abilites. To exemplify the understanding of where "this place of virtual reality might issue from such a ground state" might be, in terms of what might flow one way, and what will flow in another, as photon pairs do from around the blackhole.

How far can this be taken as we look to understand Hawking radiation? How would such constrictions pave the way for sound emitted and held in context of Hawking Radiation, flowing through a pipe? We've had our lessons from Cosmic Variance on this, but would it have ever been taken this far?

Well, I still like to think about the gravitational comparisons here, so I would be very happy to have found some geometrical propensities towards how the horizon would have given us a good picture of what "first principle" might be as we look at the nature of hawking radiation, and how the standard model is featured from that horizon. So of course I am thinking deeply about all the things I have been learning.

I hope one day a comprehensive picture forms so that I can finally understand what is going on?

Further "Analogy" sought by me to help my perspective.

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