时空作为弹性介质的类比——我们能否从宇宙学常数Lambda推导出空间的热膨胀系数？
Analogy of space time as un elastic medium -- Can we establish a thermal expansion coefficient of space from the cosmological constant Lambda?
AI总结：
本文通过时空与弹性介质的类比，提出从宇宙学常数Lambda推导空间热膨胀系数的方法，进一步引入时间热膨胀系数构建含温度效应的狭义相对论间隔，提出暗能量可能是热时空曲率的新假说。
摘要：
本文通过拓展时空结构与弹性学之间的类比研究，推动了该领域的研究进展。由于此前尚无关于潜在时空热膨胀系数Lambda的研究，我们通过将宇宙学常数Lambda视为由宇宙网和冷真空产生的热梯度导致的空间框架附加曲率，探究了广义相对论（GR）与弹性理论的类比关系，并提出((Alpha×ΔT)/e)²=(1/R₀)²=Lambda，其中R₀为时空结构的曲率半径。\n从该类比以及由普朗克厚度Lp的薄片构成、被该热梯度ΔT弯曲的空间模型出发，我们推导出模拟空间的等效弹性介质的可能热膨胀系数Alpha_S=(Lp×Lambda^(1/2))/ΔT，其数量级与Alpha_S(QFT)=1.16×10^-6 K^-1相当。\n由于广义相对论中必须考虑时空而非仅空间，本文还提出了一种创新方法：在狭义相对论的间隔ds²中引入温度效应T（与时间流逝相关的熵变，基于始终会物理影响时钟的温度变化），该效应基于空间和时间的不同热膨胀系数，对于时间流t满足：c×t/c×n×τ=(k_B×t)/n×h×ΔT=Alpha_t×ΔT。当T=10^6 K、n=1时，对应的时间间隔为4.8×10^-17 s，Alpha_t=1.0×10^-6 K^-1。\n这些假设的结论是，暗能量可能成为一种热时空曲率((Alpha_f×T)/Lp)²，其中f根据温度取s或t，代表宇宙的热熵变、普朗克厚度和时间，自大爆炸以来持续增加，取决于时空热膨胀系数Alpha_s和Alpha_t，二者分别是Lambda、k_B/h×t的函数，这与广义相对论中描述的由质量/能量密度导致的时空曲率引力形成对比。
英文摘要：
This paper advances the state of the art by extending the study of the analogy between the spacetime fabric and elasticity.As no prior work exists about a potential spacetime thermal expansion coeff Lambda, we explore the analogy of GR with the elasticity theory by considering the cosmological constant Lambda as an additional space curvature of the space frame due to a thermal gradient coming from the cosmic web and the cold vacuum and we propose ((AlphaxDeltaT)/e)^2=(1/Ro)^2=Lambda with Ro being the curvature radius of the space fabric.It follows from this analogy and from the supposed space model consisting of thin sheets of Planck thickness Lp curved by this thermal gradient DeltaT a possible thermal expansion coefficient of the equivalent elastic medium modeling the space AlphaS=(LpxLambda^(1/2))/DeltaT of the order of Alphas(QFT)=1.16x10-6 K-1.As space-time and not only space must be considered in GR, this paper also proposes an innovative approach which consists in introducing into the interval ds^2 of special relativity a temp effect T,(entropy variations correlated with time laps, based on temperature variations affecting always physically the clocks) based on different thermal expansion coefficients for space and time with for the flow of time t:cxt/cxnxtau=(kBxt)/nxhxDeltaT=AlphatxDeltaT.With T=10^6 K, n=1, the associate time interval is 4.8x10^-17s and Alphat=1.0x10^-6K^-1.The consequence of these hypothesis is that dark energy potentially becomes a thermal space-time curvature ((AlphafxT)/Lp)^2 with f equal to s or t depending of the temperature, the thermal entropy variation of the universe, the Planck thickness and time, that increases since the Bigbang, depending on thermal expansion coefficients for space-time Alphas and Alphat as a function respectively of Lambda, kB/hxt, in opposition to space-time curvature gravity due to mass/energy density as described in GR.
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