MPP

The Postulate of Informational Mass

Overview

The foundational postulate of the Mħπ project is the redefinition of mass [M] as a derived dimension. It is proposed that mass is not a fundamental property of matter, but rather an emergent quality representing a rate of information flow over time.

• Core Postulate: Mass is the rate of information flow.
• Dimensional Formula: [M] = [Ω][T]⁻¹

Here, [T] represents the dimension of Time, and [Ω] represents the new fundamental dimension of Information. This document explores the theoretical basis and potential interpretations of [Ω].

The Nature of [Ω]

The introduction of [Ω] as a fundamental dimension is the most significant departure of this theory from standard physics. While the Mħπ engine treats it as an axiomatic unit for the purpose of ensuring mathematical self-consistency, a complete physical theory must postulate its nature. What, precisely, is this information?

Several interpretations are being explored:

1. Thermodynamic / Statistical Interpretation (Shannon Entropy)

In this view, [Ω] is related to the entropy of a system, measured in “nats” or bits. A particle’s mass would be proportional to the rate at which the informational complexity of its quantum state changes.

• Analogy: Imagine a particle as a message being constantly re-written. A more massive particle is a longer, more complex message being re-written more frequently. Its inertia (resistance to change) is a consequence of the vast amount of information that must be updated to reflect a new state of motion.
• Connection: This aligns with the Bekenstein-Hawking entropy of a black hole, where the entropy (information content) is proportional to the area of the event horizon, and its mass is a fundamental property.

2. Quantum Interpretation (Von Neumann Entropy)

This interpretation connects [Ω] to the quantum entanglement and purity of a state, as described by Von Neumann entropy.

• Analogy: A particle’s mass could be a measure of its degree of entanglement with the rest of the universe. A higher mass implies a more complex web of quantum connections. To move or accelerate the particle requires updating this entire entanglement structure, which manifests as inertia.
• Connection: This provides a natural link to quantum field theory, where particles are excitations of underlying fields that are interconnected at every point in spacetime.

3. Geometric Interpretation

A more speculative view is that [Ω] relates to the topological complexity or curvature of a localized region of spacetime at the Planck scale. Mass would emerge from the richness of the geometry itself.

Current Status in Mħπ

Currently, the Mħπ engine treats [Ω] as a primitive, abstract dimension. The primary goal of the tests/informational_mass.rs and tests/theory_validation.rs suites is to prove that, regardless of its ultimate definition, defining it as a fundamental unit and deriving all other physical dimensions from it ([M] = [Ω T⁻¹], [E] = [Ω L² T⁻³], etc.) results in a system that is mathematically self-consistent and fully compatible with the invariant laws of General Relativity, Quantum Mechanics, and Electromagnetism.

The success of these tests validates the mathematical framework. The next stage of the theory will be to propose experiments or cosmological observations that could distinguish between these potential definitions of [Ω].

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