BTM

[BTM @backtome321]

@Submersion13 @Chaki_phys Finsler geometry？但是和Kahler geometry不一样 它的结构太少 运算太复杂

[Taro Hayashi @rintaro11750504]

ストークスの定理はひとことで言えば「中で起きた変化は、境界に現れる」という定理。微積分の基本定理も、グリーンの定理も、発散定理も、実はこの一つの原理の仲間。

[Νευτρίνο(大変身1号) @Furietra]

Raychaudhuri方程式のおかげでEinsteinテンソルの物理的意味も想像が容易になった

[JFernandoPascualS @jfpas]

When Gravity acts in vacuum, two observers under free fall notice the tidal field ('electric' Weyl tensor) and if they are carrying gyroscopes, they notice the frame-drag field (or `magnetic' Weyl tensor).

This frame-drag field has no Newtonian analog.
https://t.co/bztMSduMv5

[BTM @backtome321]

@yifaer_chen 伤口去医院没有

[Ken W @kenw_2]

埃及导游用中文讲解木乃伊的历史，直截了当，没有废话。

[Maaneli (Max) Derakhshani @MaxDerakhshani]

Sabine: It is not true that either Ted Jacobson or the authors of this new paper (Dorau-Much) showed how gravity "emerges" from thermodynamics or how Einstein's classical field equations emerge that way. No such emergence has been shown in either case.

(1) Both Jacobson and Dorau-Much start by simply postulating a classical metric tensor field. It does not "emerge" from anything thermodynamical or otherwise.

(2) The semiclassical (not classical!) Einstein field equations (G_ab = < T_ab >) are simply postulated as well to govern the spacetime curvature associated with the postulated classical metric tensor field. They do not "emerge" from anything either. The motivation given (by Jacobson and accepted by Dorau-Much) for this postulate is ensuring that the equilibrium thermodynamic relation, dQ = T*dS, interpreted in terms of the energy flux (dQ) and Unruh temperature (T) of an accelerated observer just inside a local Rindler causal horizon of some area (dS), holds for all local Rindler causal horizons.

In other words, dQ = T*dS, as interpreted, does not hold unless G_ab = < T_ab > is postulated to govern the spacetime curvature associated with the postulated classical metric tensor to which an accelerated observer bathed in Unruh radiation is coupled.

At best, this is a mere consistency argument, not a derivation of the semiclassical Einstein equations. It can even be interpreted as saying that dQ = T*dS (for the situation described) does not hold unless the semiclassical Einstein equations are true.

(3) The Bekenstein-Hawking (BH) interpretation of dQ = T*dS, where dS is taken to be the area of a local Rindler horizon associated with an accelerated observer, is not thermodynamics to begin with.

The actual thermodynamic entropy a closed or open system in general relativity is not given by the BH relation that equates change in (scaled) horizon area to change in thermodynamic entropy.

Rather, the actual thermodynamic entropy is given by the Boltzmann entropy of a system (which can be defined in classical and semiclassical GR after suitable regularization of all physical degrees of freedom). The Boltzmann entropy is a function of the phase-space volume of the macrostate associated with the microstate of the system. It is never proportional to the area of a local Rindler horizon or the area of a black hole's event horizon, not under any approximations.

Ergo, the consistency argument actually has nothing to do with thermodynamic entropy or thermodynamics more generally (equilibrium or nonequilibrium).

(4) Finally, the semiclassical Einstein equations, G_ab = < T_ab >, are known to be inconsistent with Einstein's *classical* field equations, G_ab = T_ab, given the usual wavefunction collapse postulate and Born statistical interpretation of the wavefunction. The structure and empirical predictions of the semiclassical gravity theory do not reduce to the structure and empirical predictions of Einstein's classical theory under any approximations.

Consequently, any consistency argument involving the semiclassical Einstein equations (logically) do not and cannot entail a corresponding consistency argument involving Einstein's classical field equations.

[BTM @backtome321]

@yifaer_chen 去医院去医院去医院

[∇ₖPascal ∇ₚKwanten (∛) (Πασκάλ) @pascalkwanten]

💡From Quantum Relative Entropy to the Semiclassical Einstein Equations
https://t.co/nhUXFBlCw9

[BTM @backtome321]

@yifaer_chen 发姐，什么时候发线下见面会的官方视频 等不急了！我拍的太糊了，以后一定抢前排的。

[Chayanka_42 @42_gravity]

finally found something along these lines

learning objective here is how a spin 2 field fluctuation around minkowski + a bunch of consistency conditions give GR (eft if I am not wrong)

https://t.co/H0UoYORRxz

[corsaren @corsaren]

Local minima are extremely rare in high dimensional spaces, so if you ever feel stuck in a rut it’s probably just because you aren’t considering a wide enough set of orthogonal options

[Ramin Nasibov @RaminNasibov]

wake up!

[SciTech Era @SciTechera]

Physics is going to be as cooked as math. 🤯

A physicist just used Claude AI to explore an open problem in thermodynamics.

Gavin E. Crooks, a physicist known for his work in nonequilibrium statistical mechanics, tasked Claude with investigating what the Detailed Fluctuation Theorem can tell us about the statistics of entropy production.

- Claude explored the mathematical constraints, connected results from previous studies and helped investigate a broader framework for understanding how entropy-production fluctuations constrain thermodynamic processes.

- The work connects to the Thermodynamic Uncertainty Theorem, which studies fundamental limits on the fluctuations and precision of thermodynamic quantities such as heat, work and currents.

NOTE: The Thermodynamic Uncertainty Theorem itself is not a brand-new Claude discovery. The underlying theorem was published in 2023 by Kyle J. Ray, Alexander B. Boyd, Giacomo Guarnieri and James P. Crutchfield.

What's new and fascinating is the AI-driven research process. 👀

Claude wasn't simply asked to explain an existing physics concept.

It was used to explore a difficult theoretical problem, connect existing ideas and search for new mathematical structure.

That could become a much bigger story than one thermodynamics result:

AI is moving from solving problems we already know how to solve... to helping scientists explore problems we don't yet know how to solve.

Physics is entering its own AI acceleration era. 🫡♥️

[BTM @backtome321]

@gavincrooks oh my gosh！

[Gavin Crooks @gavincrooks]

https://t.co/VYYeAie4YZ

[如是我闻 @VicentYip]

19岁拉格朗日的神来之笔：一个方程，竟成了现代物理的基石 从A点到B点，最短路径是直线，但“最快”的路径也是直线吗？1696年的“最速降线”问题，引出了数学史上一段精彩故事。19岁的拉格朗日用一种全新的解析思路研究最优化问题，并推动了变分法的发展。从寻找一个函数的极值，到在无数条可能路径中寻找“最优路径”，最终导向著名的欧拉—拉格朗日方程。从一颗滑落的弹珠，到最小作用量原理，再到经典力学、电磁学与量子力学——变分法为什么如此重要？这期视频带你直观理解它背后的核心思想。#拉格朗日 #变分法 #欧拉拉格朗日方程 #最速降线 #最小作用量原理

[arXiv bot (hep-th) @krxiv_hep_th]

Celestial Holography, A Hitchhiker's Guide to the Celestial Sphere
https://t.co/Bkn861oAnO
Faïçal Barzi.
https://t.co/1sNXpCKEWP

[BTM @backtome321]

@Mumu__ovo 继续听