Research | Jinming Hu

信息带宽：相对论与量子力学的逻辑必然性

Thu, 19 Feb 2026 00:00:00 +0000

最近重写了之前那篇关于信息有限性的论文。新版的核心变化是引入了一个新的基本常数 i（Information Maximum Transfer Speed，信息最大传输速度），并给出了一个可实验检验的预测。以下是论文的主要内容。

基础公理：信息有限性

论文的起点不变：宇宙中任何物理系统所包含的信息量，必须是有限的。任何允许信息量趋于无穷大的物理理论，在逻辑上都是不自洽的。

信息最大传输速度 i

新版论文最大的变化，是提出了一个比光速 c 更根本的常数 i。

核心假设是：i > c。

在这个框架下，光速 c 不是宇宙的终极限速，而是光子（规范玻色子）在宇宙信息基底中传播时所能达到的最大速度。两者之间的差值 Δ = i − c 代表真空的"计算阻力"——类似于网络中理论带宽和实际吞吐量之间的差距。

将 i 代入洛伦兹变换后，c 不再是一个需要被假设的常数，而成为信息基底特性的一个衍生结果。整个相对论的数学框架因此变得更加自然。

为什么必须有相对论

如果 i = ∞（信息传递无速度上限），宇宙中任意两点之间都存在可以产生瞬时交互的可能性，每个局部坐标点都必须同时包含全宇宙所有状态的信息。通过香农信息论，我们可以计算得出，此时局部信息密度趋于无穷大，直接违反有限信息公理。

因此，i 必须是有限值。一旦 i 有限，宇宙就必须被划分为因果隔离的区域（光锥），各区域之间只能以有限速率交换信息。相对论所描述的因果结构和时空特性，本质上是维持信息有限性的必要机制。

为什么必须有量子力学

如果空间是完美连续的，描述一个粒子的精确位置需要无穷多比特的信息。根据贝肯斯坦上限，有限空间内的信息容量是有限的，连续空间会导致信息量超出物理系统的承载能力。

为了避免这种"分辨率溢出"，空间和能量必须是离散化的（普朗克长度 $\ell_P$、普朗克常数 $h$）。量子力学的存在，是宇宙在微观尺度上维持信息有限性的手段。

万有理论为什么不可能

任何"描述一切"的理论 $\mathcal{T}$ 本身也是宇宙中的信息，必须编码在宇宙之内。如果 $\mathcal{T}$ 要描述整个宇宙，就必须包含对自身计算开销的描述，由此产生无限递归：

$$\mathcal{T}_{n+1} = \mathcal{T}_n + \text{Info}(\text{computation of } \mathcal{T}_n)$$

随着迭代次数增加，理论的信息量会超过宇宙的总容量。因此，科学研究注定是一个渐近过程——知识可以无限逼近，但永远不会闭合。

实验预测：计算红移

这是新版论文最重要的新增内容。如果 i > c 成立，那么我们观测到的天体红移中应包含一个额外的微小分量，来自信息基底的传输延迟，我们将其称为"计算红移"（Computational Redshift, CRI）。

论文给出了一个修正的多普勒公式：

$$\tanh(\ln(1+z)) = \frac{v}{i}$$

通过精确测量遥远类星体的红移 z 和退行速度 v，可以反推 i 的值。如果 i 被测出是一个有限的、略大于 c 的常数，就意味着光速确实是被信息基底"限速"的结果，宇宙本质上是一个有限带宽的计算系统。

总结

相对论和量子力学不只是经验科学的发现，它们更像是信息有限性这一底层约束的逻辑推论。相对论防止宏观传递的信息溢出，量子力学防止微观分辨率的信息溢出。新版论文的关键进展在于：引入了 i 作为比 c 更根本的常数，将光速从"公理"降格为"推论"；同时给出了计算红移这一可检验的实验预测，使得整个框架具备了可证伪性。

原始论文： The Informational Foundation of Physical Reality: Proving the Necessity of Relativity and Quantics via Information Bandwidth — Jinming Hu, Sea-Land AI Research, 2026

The Computational Event Horizon: The Universal Quantifier Trap

Sun, 21 Dec 2025 00:00:00 +0000

Why have we solved the Poincaré Conjecture but not Navier-Stokes? Why does the Riemann Hypothesis feel "true" while $P$ vs $NP$ feels "impossible"?

We posit that mathematical problems exist on a spectrum of Simulational Capacity.

Class I (Structural): Systems governed by rigid symmetries or smoothing operators. The evolution of the system destroys distinct information states, collapsing the phase space into a predictable manifold.
Class II (Simulational): Systems capable of encoding arbitrary Boolean logic and unbounded memory. These are effectively "fluid computers" where the system’s evolution is computationally irreducible.

Our central thesis is logic-theoretic: One cannot prove a Universal Statement ($\forall x, P(x)$) if the domain $x$ contains an embedded Turing Complete subspace.

Class I: The Domain of Structure

Class I problems inhabit structures where information is either conserved (symmetry) or destroyed (smoothing).

The Poincaré Conjecture (Solved)

Perelman’s proof utilizing Ricci Flow ($\partial_t g_{ij} = -2 R_{ij}$) is the archetype of Class I. Physically, this is a heat equation. Diffusion increases entropy and erases "memory."

Principle (Information Destruction): A diffusive flow smoothes out arbitrary topological complexity. It destroys the distinct, stable states required for bit transitions. Because the flow "forgets" the microscopic details of the initial metric, the final state is topologically simple ($S^3$). The proof succeeds because the system naturally compresses itself.

The Riemann Hypothesis (RH)

While unsolved, RH is likely Class I. By the Hilbert-Pólya conjecture, the zeros of $\zeta(s)$ correspond to eigenvalues of a self-adjoint operator in a chaotic quantum system.

Unlike a general computer which can halt at arbitrary times, the spectrum of physical operators exhibits "rigidity" (GUE statistics). The system lacks the degrees of freedom to encode a logical paradox (like the Halting Problem) into the distribution of primes.

Class II: The Domain of Simulation

We define Class II problems as those defined on substrates rich enough to support Universal Computation.

The Universality Hypothesis: If a dynamical system $\Psi$ is Turing-complete, then determining its global asymptotic stability entails solving the Halting Problem for all possible programs.

Navier-Stokes (NS)

The non-linearity of the inertial term $(u \cdot \nabla)u$ allows for constructive interference of vortices. Tao has suggested that Euler and NS equations might be capable of simulating a von Neumann machine.

If a fluid can "compute," then the initial velocity field $u_0(x)$ acts as the "software" (input tape). To prove Global Regularity, one must prove that no software causes the machine to crash (blow up).

$P$ vs $NP$

This is the archetype of Class II. Disproving $P \neq NP$ would require finding a polynomial algorithm that compresses the search space of all boolean circuits.

The Natural Proofs barrier implies that current methods fail because they cannot distinguish "hard" pseudo-random functions from truly random ones. In our framework: the "hardness" of $NP$ problems comes from their incompressibility.

The Universal Quantifier Trap

Here we formalize why Class II problems are likely independent of $ZFC$. The obstruction is not that all inputs are hard, but that some inputs act as undecidable logic gates.

The Logical Structure of the Problems

The Millennium Problems are framed as Universal Statements: $$ \forall x \in \mathcal{S}, \quad \Phi(x) \text{ holds.} $$ Where $\mathcal{S}$ is the set of all initial conditions (fluids) or all languages (complexity).

Embedding Turing Machines

The Embeddability Lemma: Let $\mathcal{S}$ be the domain of a Class II system. Because the system is Turing Complete, there exists an injective mapping $\Gamma: \mathbb{N} \to \mathcal{S}$ such that for any Turing Machine $M_n$, there exists a corresponding initial state $x_n = \Gamma(n) \in \mathcal{S}$ that simulates $M_n$.

For Navier-Stokes, $x_n$ would be a highly complex, geometrically precise arrangement of vortices designed to execute logic operations.

The Undecidability Mechanism

Let the property $\Phi(x)$ be "The solution remains regular/bounded for all time." In the context of the embedded simulation, a "singularity" (blow-up) corresponds to the machine reaching a specific "Halt" state.

Thus: $$ \Phi(x_n) \text{ is False} \iff M_n \text{ Halts.} $$

The Quantifier Obstruction Theorem: The statement "$\forall x \in \mathcal{S}, \Phi(x)$" implies "$\forall n, M_n \text{ does not Halt}$" (assuming we are testing for non-blowup). However, the set of indices $n$ for which $M_n$ halts is recursively enumerable but not recursive. There exist indices $k$ such that the statement "$M_k$ does not Halt" is undecidable in $ZFC$ (Gödel/Turing).

Therefore, the truth value of $\Phi(x_k)$ is undecidable. Since the Universal Statement requires $\Phi(x)$ to be true for all $x$, and we cannot determine the truth for $x_k$, the Universal Statement cannot be proven.

Remark: It does not matter if the "rogue" inputs $x_k$ are rare (measure zero). In a logical proof, a single counter-example falsifies the theorem. If the existence of that counter-example is undecidable, the theorem is independent.

Conclusion

The Millennium Prize problems are not merely difficult; they are categorized by their logical compressibility.

Problem	Mechanism	Status
Poincaré	Info. Destruction	Class I (Provable)
Riemann Hyp.	Spectral Rigidity	Class I (Provable)
Navier-Stokes	Universal Sim.	Class II (Indep.)
$P$ vs $NP$	Circuit Univ.	Class II (Indep.)

For Class II problems, we are not hitting a lack of technique; we are hitting the Computational Event Horizon. The domain of inputs contains embedded logical paradoxes. To prove the theorem, one would have to resolve the Halting Problem. Thus, the answers lie beyond the reach of finite axiomatic systems.

This post is based on my recent paper: The Computational Event Horizon