Entanglement Interpretation of Black Hole Entropy

"Entanglement entropy" is the latest article posted by Lubos Motl. From this ideas are brought back for consideration, with Nigel and myself in trying to explain. I am not to swift sometimes in my explanations, so the inudation of links here direct underscore the probabilistic valuation one might assign perspective in relation to the topic assigned by Lubos in titled Link.



Plato said:

I was going after consensus in terms of how temperature on Bekenstein bound was seen in context of 5th dimenison and 5d comparisons.

Bekenstein image is very useful here as was Lee Smolins discription.

If not in your surprize(?) I do not think Lubos Motl and Lee Smolin are too far apart? Here is a better picture of the Lava lamp. The Window on the Universes, has extended our understanding here as well.



Entanglement Interpretation of Black Hole Entropy in String Theory

This allows the comparison of the entanglement entropy with the entropy of the field theory dual, and thus, with the Bekenstein-Hawking entropy of the black hole. As an example, we discuss in detail the case of the five dimensional anti-de Sitter, black hole spacetime

Glast determination in "calorimeric views" would be consistent the deeper look of gluonic perception at such levels? It would be hard to know this starting point yet the environment is conducive, non?

Three quarks indicated by red, green and blue spheres (lower
left) are localized by the gluon field.

A quark-antiquark pair created from the gluon field is
illustrated by the green-antigreen (magenta) quark pair on the right. These quark pairs give rise to a meson cloud around the proton.

The masses of the quarks illustrated in this diagram account for only 3% of the proton mass. The gluon field is responsible for the remaining 97% of the proton's mass and is the origin of mass in most everything around us.

Experimentalists probe the structure of the proton by scattering electrons (white line) off quarks which interact by exchanging a quantum of light (wavy line) known as a photon.

Remember that the age is determined by the dark matter density. Mathematically, the length is roughly the geometric mean of the mean free path and the distance light can travel without obstruction (the horizon scale).

On the Hypothese at the foundations of Geometry

I am trying to make my case on the greatest physics paper over at Cosmic Variance. One notices the slight misinterpretation I assigned, "geometical propensity to physics" that the case is more then just physi,s but the limmerack added envisioned, over such a paper that leads into physics.:) I see no difference now. So I refer to it as the greatest physics paper!

The title of this thread is attributed to Bernhard Riemann and a paper he wrote that revolutionized our concept of space with geometry of distances(the metric). With Gauss's tuteluge on curvature that was being developed, Reimann moved to understand how such changes now would be considered, where space is no longer flat. He moved Pythagorean thereom from:

c²=a²+b² to c²=a²+b²-2ab cos Æ
where the right angle is no longer right but has magitude Æ then the above theorem has been generalized

The function that measures the instantaneous distance between two points was later used by Einstein where m and n vary over the intergers 1 and 2

ds²=g_mndx_mdx_n

On the Hypothese at the foundations of Geometry

By use of similar triangles and congruent parts of similar triangles on the Saccheri quadrilateral, ABDC with AC = BD and ‚A = ‚B = p/2, he establishes his first 32 theorems. Most are too complicated to be treated in a short paper, but here some examples are merely stated, some are illustrated and some are proven. For those proofs which are brief enough to show here, the main steps are indicated and the reader is invited to fill in the missing details of the argument. A century after Saccheri, the geometers, Lobachevsky, Bolyai and Gauss would realize that, by substituting the acute case or the obtuse case for Euclid's postulate Number V, they could create two consistent geometries. In doing so they built on the progress made by Saccheri who had already proven so many of the needed theorems. They were able to create what we recognize today as the "elliptical" and "hyperbolic" non-Euclidean geometries. Most of Saccheri's first 32 theorems can be found in today's non-Euclidean textbooks. Saccheri's theorems are prefaced by "Sac."

How far advanced our thinking has become, that we can move quickly here to other avenues of consideration? How much "inbetween" the leading thinking of Riemann that we can have gotten here in our "physics of geometries?" Is it a suttle generalization in words and limmerack that such a physics view could have seen nature at its finest, and explained in a mathematical way.

Gaussian Coordinates

We can sum this up as follows: Gauss invented a method for the mathematical treatment of continua in general, in which ?size-relations? (?distances? between neighbouring points) are defined. To every point of a continuum are assigned as many numbers (Gaussian co-ordinates) as the continuum has dimensions. This is done in such a way, that only one meaning can be attached to the assignment, and that numbers (Gaussian co-ordinates) which differ by an indefinitely small amount are assigned to adjacent points. The Gaussian co-ordinate system is a logical generalisation of the Cartesian co-ordinate system. It is also applicable to non-Euclidean continua, but only when, with respect to the defined ?size? or ? distance,? small parts of the continuum under consideration behave more nearly like a Euclidean system, the smaller the part of the continuum under our notice.

Yes so easy now that we can see this space in ways that the average person without the physics comprehension would have never found that the fancy brane worlds held to perspective on the developing sciences and recognition of such physics processes had been elevated.

Would the likes of a Peter Woit be stagnated on what he sees if such limitation to the math endowed creator of mind, would see that such limitations to spintronic value added, would only partake of the events held to this brane and that a wider audience would now see that such dynamicsi n this universe would be greatly enhanced by entering a whole new world of abstraction.

According to Einstein's general theory of relativity, the gravitational potential due to an isolated source is proportional to rho + 3P, where rho is the energy density and P is the pressure. For non-relativistic matter the pressure is negligibly small, whereas for radiation P = rho/3. Therefore, for the same value of the energy density, radiation produces a deeper and more attractive gravitational potential (left) than non-relativistic matter (centre). If rho + 3P is negative, as in the case of quintessence ­ in this example P = ­2rho/3 ­ the sign of the gravitational field is transformed from attractive to repulsive (right).

Win Some, Loose Some

Does it all now rest in the eye of the beholder? Pictorially we now have a synoptic view below, that ones askes, can such cosmic variance have arisen from such a thing? Above, the picturing is leading to that comprehensive view?

We use our new detailed picture to ask: "What happened earlier to make this picture happen?" We can now begin to probe the earliest moments of the universe: Inflation (the rapid expansion of the universe a fraction of a second after its birth.). We have ruled out a textbook example of a particular inflation model. But others will be supported with this new evidence.

The Cosmic Triangle

This link was added to paper by Steinhardt as ole picture was used for perspective had been updated, so I gave updated link to Steinhardt, as well as his paper.



The Cosmic Triangle and the State of the Universe

Moon Phases

I was looking for a moon phase site for a reason and I'll let you know why in a minute here. If you have ever felt the inadequacy of being able to answer such simple questions, I quickly realize how such simple points forced me to go back and understand exactly what the answer must be. This has a way of waking one up to the wonder of all that can be read. All that one might have gained from such research, to realize, how much more there will always be to learn.



My wife, my grandkid's Granmma and I, were making a memory last night before they leave this morning to go home. Now I should say, the night previous to this, our telescopes were set up, for my grandson, from earlier that day had told me what he wanted to spend his allowance on. So we made that trip to do his purchase.

That night we waited for the night sky to come. Being so young, he became tired quickly, and soon fell asleep. There in the north-north east the moon arose, and with it, it''s phase from the 23 of August. Waking our grandson as gently as we could, we asked if he wanted to see the moon. Sleep was stronger then his wonder, I'm afraid.

This is why last night, and with the help of my good wife, we again set up for the moon to arise. This is of course when all the questions about earth, the sun, the moon and so many bombarded Grandpa's intellect for such simple answers. "Why does the earth spin, Grandpa." The quick realization comes for responsible answers. Where shall I find these all these trusty answers?

So as the moon started to rise on the horizon, our kitchen being dark, here shone this computer screen set up for every question, as we punched up google for all these wonders of wonders. "Why do we see the moon, Grandpa?" "Why does the moon stay so close to the earth Grandpa?" It is aversion of, "are we there yet" that Granma quickly saids, "listen Grandpa to what they are saying."

As I sit this morning, it is not to strange that many will sit as grandparents for the generation much younger. Grandparents /Teachers, who will watch education move these younger minds to ask so many questions, and the better educated they become the more difficult these answers.

So I rushed quickly this morning to write about my grandchildren, for it was a wonderful sight to see each of them gaze upon the moons surface. Gain a little knowledge about how long it would take us to get there. How much the moon weights, and on and on.

I too also realized, that as a child of the wonder of it all, that I will also need a grandparent to answer such simple questions. So it would be with such patience and clarity, that such answers can be given in the hopes that as chldren, we will be quietly nudged from those ahead of us, in age and education, that such patience shall rule the day, as it must for the quiet and absorbed mind of a child that askes.

This I learnt last night, and how wonderful to see such participaton and questions. Such "tolerance" from those who blog. To set aside and be examples, for those in general, will reach out to try and touch that understanding they have.

View on the Expansion of the Universe

Georgi Dvali:The cosmic acceleration of the universe indicates that the laws of General Relativity get modified not only at very short but also at very large distances, Dvali says. It is this modification, and not dark energy, that is responsible for the accelerated expansion of the universe.

What Do Cosmologists want from String Theory?

More Views on the Landscape

How would such a "landscape" bring string theory into better comprehension? The
Most perfect fluid in face of strong coupling?

Yet at the other end, there is no deviation?

Eric Adelberger on Aug 12th, 2005 at 2:37 pm It is true that we are seeing an anomaly at shorter length scales but we have to show first that the anomaly is not some experimental artifact. Then, if it holds up, we have to check if the anomaly is due to new fundamental physics or to some subtle electromagnetic effect that penetrates our conducting shield. We are now checking

Lubos being on top of it, reveals new paper.

New Constraints on Yukawa-Type Deviations from Newtonian Gravity at 20 Microns

Recent theories of physics beyond the Standard Model have predicted deviations from Newtonian gravity at short distances. In order to test these theories, we have a built an apparatus that can measure attonewton-scale forces between gold masses separated by distances on the order of 25 microns. A micromachined silicon cantilever was used as the force sensor, and its displacement was measured with a fiber interferometer. We have used our measurements to set bounds on the magnitude alpha and length scale lambda of Yukawa-type deviations from Newtonian gravity; our results presented here yield the best experimental limit in the range of lambda=6--20 microns.

Don't cater to Intelligent Design debate Please?

I would say attitudes from respectable scientists had more to do it with then any intelligent design debate. Any repeated pattern of news, associated. This debate was fuelled.

While respected the stand taken against any position on "intelligent design" it would have been outright diagreement with the religious connotation for sure, then argue the basis of science assign to a differing group opinion. I stayed away from the source of this debate arising, as I watched Sean, Peter Woit and others villify and characterise(news jumped on this), a respective theoretical view, based on such association.

This hurt propsective views on recogniton of theoretical position.

The debate had to be rested in science, and any distinction of religion dropped from the conversation. Only the reason why such rejection, and such slogans pasted on other views contained. Lee Smolins attempt to draw other so science, and Lubos's attempted to clarify current scientific data. Argue then, Georgi Dvali's moon measure?

What Lies Beneath

The Bottom up approach?

R.B.Laughlin:

The paper by Senthil et al. [9] is an attempt to address this issue mathematically. It deals specifically with a suspicion many of us have had that quark confinement, one of the most cherished features of the standard model, may be a collective effect that emerges at a phase transition and thus not fundamental at all. The paper is complicated, an unfortunate side effect of the difficulty of the task, for it is not generally possible to deduce emergent phenomena from first principles. The best one can do is postulate them and then demonstrate plausibility by showing that small corrections get smaller as the measurement scale increases. Such convoluted arguments are ripe with opportunities for mistakes, regardless of how careful the authors have been, so the test of emergent universality that counts is always experimental. This, in turn, forces the theory to address not quark confinement itself but an allegory of it one might hope to test in a table-top experiment. The logic is maddeningly indirect, but unfortunately the only approach that is legitimately scientific.

Fig. 1. In quantum chromodynamics, a confining flux tube forms between distant static charges. This leads to quark confinement - the potential energy between (in this case) a quark and an antiquark increases linearly with the distance between them.



In the Q<->Q measure, the understanding of this distance in the metric was understandable?


Now this is March of 2000.


What Lies Beneath?



Still as a layman, such general talks need better clarification? If you set the stage from planck length, then how indeed does LQG arise here?

Here's another view.

Witten:One thing I can tell you, though, is that most string theorist's suspect that spacetime is a emergent Phenomena in the language of condensed matter physics.

http://online.kitp.ucsb.edu/online/kitp25/witten/oh/10.html

Robert Laughlin:The true origin of these rules is the tendancy of natural systems to organize themselves according to collective principles. Many phenomena in nature are like pointillist paintings. Observing the fine details yields nothing but meaningless fact. To cor rectly understand the painting one must step back and view it as a whole. In this situation a huge number of imperfect details can add up to larger entities of great perfection. We call this effect in the physical world emergence.

http://large.stanford.edu/rbl/lectures/index.htm

Observatories

What is Sun-Earth Day?

As I was reading Cliffords newest entry on Cosmic Variance site, his trip reminded me of the hike we took to see the Big Horn Medicine Wheel.

Now what is interesting about this is I am not one who has had much association with such places of observatories, but far up to the left of this wheel is one that seems very out of place.

Ironic in the sense that ole history about these "Medicine Wheels" could have brought such historical perspective to the science. Look at the universe, from a place where ancient artifacts gathered.

At the center of the wheel there is a raised central cairn, and several others on the periphery of the wheel. These have been alleged to have astronomical alignments. Astronomer John Eddy suggested that a line drawn between the central cairn and an outlying cairn at the Bighorn Medicine Wheel pointed to within 1/3 of a degree of the rising point of the sun at the summer solstice. The actual astronomical purpose of the design of these wheels remains controversial. The design may also have assisted in the performance of specific rituals and ceremonies that have been lost to us. The 28 spokes could indicate the lunar month, or the length of the female menstrual cycle.

But I am not going to join the speculative feature of this wonderment, but to bring forward the understanding that mountains that may look the same, may have other reasons like it does for Clifford and his views of home. That for him to look, and have something nagged his "observatory mind" would have been as simple as "cheez, it looks like home."

Well from a more suttle place, I bring forward the understanding that our perspective about cosmology, our understanding of the uniqueness of Omega? The implications of General Relativity, and how Alexanders Firedmann's eqaution is part and parcel of the understandng of a geometry. That helps lead the mind into the ability to see dynamicals of this universe. How would your obervation have changed with such paradigmal changes. In Toposense, is speak to that as well as relate that General Realtivity had it's saem consequence. Ask Sean about that one?

Now we engage the spacetime fabric. This dynamcial abiltiy would not be seen before without this geometrical prospensity. So having been taken over by paradigmal change, the visionistic approach is one based on geometrical design, where the uniqueness of such correlations in the views of where nature resides. Brings one closer to the very spots we call "home". This is a real place for clifford, and yet without inducing such mysticism, this is also a place I draw from.

Now you say this guy is nuts. But imagine the science that leads one to see such topolgical realizations would take cosmological priciples about this epxanding universe and find that in a Genus example of the spherical WMAP of creation, there are abilities of this universe to become, well, lets say like images of marbles on rubber sheets, and how did such isolated cases exist within the greater potential of this universe to unfold and one is lead to portions of objective collapses that help to bring a greater dynamcial view about this same cosmos.

What makes this different is I relate topo-sense as a real part of paradigmal change.

The theory of relativity predicts that, as it orbits the Sun, Mercury does not exactly retrace the same path each time, but rather swings around over time. We say therefore that the perihelion -- the point on its orbit when Mercury is closest to the Sun -- advances.

I encourage such changes when we learn( or are really a result of such learning). Who could not get this sense from, Mercuries Daisey, or Hulse and Taylor Binary star rotations that release "gravitation waves" that give us information about how close they are becoming. What's it's predictve date about coming together?

While I relate Mecuries orbital patterns, such sense is not limited to here. Other idealizations as well, that we might wonder indeed how vast this landcape idea, when you consider the >Lagrange points?:)

Space and Time: Einstein and Beyond

You know it's amazing sometimes when the question in mind being put out there is not really answered right away, yet, it is strange that you ask and sure enough the right paper seems to find you.

Plato said:Can this difference be as simple as, “a determination between “being discrete, and implying continuity“?



Being stuck on the differences between String/M-theory and Loop Quantum Gravity, it was nice to find this paper and help bring me up to speed.


Prof. Abhay Ashtekar

Quantum geometry is a precise,mathematical theory in which the primary objects-the fundamentals excitations of geometry-are one dimensional. Just as a piece of cloth appears to be smooth, two dimensional continuum although it obviously is woven by one dimensional threads, the Spacetime of General Relativity appears as a four-dimensional continuum although it is in fact, a coherent superposition of these one-dimensional excitations.

Length Scales

One does not forget the uncertainty at this point, or the relationship of crackpotiness for not mentioning where and how this uncertainty comes into the picture. One must remember I am learning, and the most elegant thing to me so far has been General Relativity and I lay no claims to a theory or a idea, but relationships that pop into mind, that might not always be right. I have certainly come to some conclusion with the way I see tihs dynamcial nature of a quantum world, that hosts all this uncertainty.

If string theory is a theory of quantum gravity, then this minimum length scale should be at least the size of the Planck length,

T-duality is something unique to string physics. It's something point particles cannot do, because they don't have winding modes. If string theory is a correct theory of Nature, then this implies that on some deep level, the separation between large vs. small distance scales in physics is not a fixed separation but a fluid one, dependent upon the type of probe we use to measure distance, and how we count the states of the probe.
This sounds like it goes against all traditional physics, but this is indeed a reasonable outcome for a quantum theory of gravity, because gravity comes from the metric tensor field that tells us the distances between events in spacetime.

Both positons needed to address the "length scale" so this was not to hard a subject to look into once it became apparent, the avenues of discreteness would come into play, as well as continuity. The article linked help with these clarifications.