[论文解读] Black Hole Horizons as Patternless Binary Messages and Markers of Dimensionality

Szymon Łukaszyk|arXiv (Cornell University)|Oct 14, 2019

Cosmology and Gravitation Theories被引用 26

一句话总结

本文提出，黑洞事件视界作为具有最大香农熵的无模式二进制信息，充当全息屏幕以标记时空维度。通过引入变分势与惯性势，该研究以信息论重新诠释黑洞热力学，通过普朗克尺度简并与球形观测者上的非平衡热力学条件，解决信息悖论。

ABSTRACT

This study aims to reconcile quantum theory with the universality of the speed of light in vacuum and its implications on relativity through an information-theoretic approach. We introduce the concepts of a holographic sphere and variational potential. Entropy variation expressed in terms of the information capacity of this sphere results in the concept of binary potential in units of negative, squared speed of light in vacuum. Accordingly, the event horizon is a fundamental holographic sphere in thermodynamic equilibrium with only one exterior side: a noncompressible binary message that maximizes Shannon entropy. Therefore, the Jordan-Brouwer separation theorem and generalized Stokes theorem do not hold for black holes. We introduce the concept of inertial potential and demonstrate its equivalence to the variational potential, which ensures that any inertial acceleration represents a nonequilibrium thermodynamic condition. We introduce the concept of the complementary time period and relate it with the classical time period through integral powers of the imaginary unit to formulate the notions of unobservable velocity and acceleration, which are perpendicular and tangential to the holographic sphere, respectively, and bound with the observable velocity and acceleration based on Pythagorean relations. We further discuss certain dynamics scenarios between the two masses. The concept of black hole informationless emission is introduced as a complement to informationless Bekenstein absorption and extended to arbitrary wavelengths. Black hole quantum statistics with degeneracy interpreted as the number of Planck areas on the event horizon are discussed. The study concludes that holographic screens and equipotential surfaces are spherical equivalents, and every observer is a sphere in nonequilibrium thermodynamic condition. Lastly, we propose a solution to the black hole information paradox.

研究动机与目标

• 通过信息论原则，调和量子力学与光速不变性及相对论不变性。
• 确立黑洞视界作为热力学平衡下具有最大熵的根本全息球面。
• 通过将视界建模为无信息二进制信息，解决黑洞信息悖论。
• 定义惯性势与变分势等价，将加速度与非平衡热力学联系起来。
• 通过虚数单位的幂引入互补时间周期与不可观测速度，与可观测动力学相关联。

提出的方法

• 将全息球面定义为仅具有一个外侧的热力学边界，代表不可压缩的二进制信息。
• 以负的光速平方单位定义二进制势，源自信息容量中熵变的推导。
• 应用乔丹-布劳尔分离定理与广义斯托克斯定理，表明其在黑洞上不成立。
• 引入惯性势并证明其与变分势数学等价，将加速度与热力学非平衡状态联系起来。
• 利用虚数单位的积分幂，关联经典与互补时间周期，定义垂直于全息球面的不可观测速度与切向不可观测加速度。
• 应用勾股定理，连接全息球面上可观测与不可观测的速度与加速度分量。

实验结果

研究问题

• RQ1 黑洞视界如何被解释为具有最大香农熵的无模式二进制信息？
• RQ2 在此信息论框架下，乔丹-布劳尔定理与广义斯托克斯定理为何对黑洞不成立？
• RQ3 惯性势为何与变分势等价？这对非平衡热力学有何含义？
• RQ4 如何通过时间周期的虚数单位幂定义不可观测速度与加速度？它们与可观测动力学有何关系？
• RQ5 无信息辐射的概念如何解决黑洞信息悖论？

主要发现

• 事件视界作为热力学平衡下的全息球面，仅编码具有最大香农熵的不可压缩二进制信息。
• 二进制势以负的光速平方单位量化，源自信息容量中熵变的推导。
• 由于缺乏内侧且视界为单侧边界，乔丹-布劳尔定理与广义斯托克斯定理不适用于黑洞。
• 惯性势在数学上等价于变分势，证实任何惯性加速度均意味着非平衡热力学状态。
• 互补时间周期通过虚数单位的整数幂与经典周期相关联，分别定义垂直于全息球面的不可观测速度与切向不可观测加速度。
• 黑洞量子统计由事件视界上普朗克面积数的简并度导出，支持无信息辐射作为贝肯斯坦吸收的互补形式。