Kinematical Holographic Relation in Yang's Quantized Space-Time and Area-Entropy Relation in $D_0$ Brane Gas System
Sho Tanaka
备注：
25 pages, minor typos corrected, several sentences added and improved in sections 2.1, 2.2. 3.1 and the final section 5. arXiv admin note: substantial text overlap with arXiv:1006.2885
We investigate the possible inner relation between the familiar Bekenstein-Hawking area-entropy relation and ours presented in a simple $D_0$ brane gas system on the basis of the kinematical holographic relation [KHR] in the Yang's quantized space-time. We find out that the relation between them is well understood through the idea of {\it elementary} Schwarzschild black hole realized on a single $[site]$ of Planckian scale in our scheme. Related arguments explain the origin of a certain kind of universality as seen in $η=1/4$ in the Bekenstein-Hawking relation and lead us to notice the similarity between the effective mass of $D_0$ brane, $μ_S,$ inside black holes and the Hawking radiation temperature, $T_{H.R.} (= 1/(8πM_S))$, both inversely proportional to the black hole mass $M_S$ and having almost the same order of magnitude. Motivated by this fact, we attempt to examine further the physical implication of $η$ by introducing in our scheme an ansatz which enables us self-consistently to equate $μ_S$ to $T_{H.R.}$ and leads us to $η$ slightly shifted from $1/4.$
We try to find a possible origin of the holographic principle in the Lorentz-covariant Yang's quantized space-time algebra (YSTA). YSTA, which is intrinsically equipped with short- and long-scale parameters, $λ$ and $R$, gives a finite number of spatial degrees of freedom for any bounded spatial region, providing a basis for divergence-free quantum field theory. Furthermore, it gives a definite kinematical reduction of spatial degrees of freedom, compared with the ordinary lattice space. On account of the latter fact, we find a certain kind of kinematical holographic relation in YSTA, which ma…
In the preceding paper, we derived a kind of kinematical holographic relation (KHR) in the Lorentz-covariant Yang's quantized space-time algebra (YSTA). It essentially reflects the fundamental nature of the noncommutative geometry of YSTA and its representation, that is, a definite kinematical reduction of spatial degrees of freedom in comparison with the ordinary lattice space. On the basis of the relation and its extension to various spatial dimensions, we derive a new area-entropy relation in a simple $D_0$ brane gas system subject to YSTA, following the idea of M-theory. Furthermore, we ma…
In this paper we derive holographic wave equations for hadrons with arbitrary spin starting from an effective action in a higher-dimensional space asymptotic to anti-de Sitter (AdS) space. Our procedure takes advantage of the local tangent frame, and it applies to all spins, including half-integer spins. An essential element is the mapping of the higher-dimensional equations of motion to the light-front Hamiltonian, thus allowing a clear distinction between the kinematical and dynamical aspects of the holographic approach to hadron physics. Accordingly, the non-trivial geometry of pure AdS spa…
The present-day significance of Yang's quantized space-time algebra (YST) is pointed out from the holographic viewpoint. One finds that the D-dimensional YST and its modified version (MYST) have the background symmetry SO(D+1,1) and SO(D,2), which are well known to underlie the dS/CFT and AdS/CFT correspondences, respectively. This fact suggests a new possibility of dS/YST and AdS/MYST in parallel with dS/CFT and AdS/CFT, respectively. The spatial components of quantized space-time and momentum operators of YST have discrete eigenvalues and their respective minimums, $a$ and 1/R, without contr…
Recent attempts to calculate the black-hole entropy in loop quantum gravity are demonstrated to be erroneous. The correct solution of the problem is pointed out.
An equidistant spectrum of the horizon area of a quantized black hole does not follow from the correspondence principle or from general statistical arguments. Such a spectrum obtained earlier in loop quantum gravity (LQG) does not comply with the holographic bound. This bound fixes the Barbero-Immirzi parameter of LQG, and thus leads to the unique result for the spectrum of horizon area.
We investigate a possible inner relation between the familiar Bekenstein-Hawking area-entropy relation and ours presented in a simple $D_0$ brane gas model on the basis of the kinematical holographic relation [KHR] in the Yang's quantized space-time algebra (YSTA). We find out that the relation between them is well understood through the idea of an {\it elementary} Schwarzschild black hole realized on a single $[site]$ of Planckian scale in our scheme. Related arguments possibly explain the origin of a certain kind of universality as seen in $η=1/4$ in the Bekenstein-Hawking relation and lead …
An equidistant spectrum of the horizon area of a quantized black hole does not follow from the correspondence principle or from general statistical arguments. On the other hand, such a spectrum obtained in loop quantum gravity (LQG) either does not comply with the holographic bound, or demands a special choice of the Barbero-Immirzi parameter for the horizon surface, distinct from its value for other quantized surfaces. The problem of distinguishability of edges in LQG is discussed, with the following conclusion. Only under the assumption of partial distinguishability of the edges, the microca…
We emphasized the importance of underlying noncommutative geometry or Lorenz-covariant quantized space-time towards ultimate theory of quantum gravity and Planck scale physics. We focused there our attention on the statistical and substantial understanding of Bekenstein-Hawking's Area-Entropy Law of black holes in terms of Kinematical Holographic Relation (KHR). KHR manifestly holds in Yang's quantized space-time as the result of kinematical reduction of spatial degrees of freedom caused by its own nature of noncommutative geometry and plays an important role in our approach without any recour…
Splitting Dynamics of Multiply Quantized Vortices in Holographic Superfluid of Finite Temperature
Lingnan Normal University（岭南师范学院）；Hunan Normal University（湖南师范大学）；University of Chinese Academy of Sciences（中国科学院大学）；Zhejiang University（浙江大学）；Beijing Normal University（北京师范大学）
In confrontation with serious and fundamental problems towards ultimate theory of quantum gravity and physics of Planck scale, we emphasize the importance of underlying noncommutative space-time such as Snyder's or Yang's Lorentz-covariant quantized space-time. The background of Bekenstein-Hawking's Area-entropy law and Holographic principle is now substantially understood in terms of {\it Kinematical} Holographic Relation [KHR], which holds in Yang's quantized space-time as the result of the kinematical reduction of spatial degrees of freedom caused by its own nature of noncommutative geometr…
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