MPP

MPP Unit System

The MPP system expresses all physical quantities in terms of fundamental constants, specifically Planck units. This document provides information about how traditional units (both SI and Imperial) are represented within this system.

Fundamental Constants

The system is built on these fundamental constants:

• π (Pi): The geometry constant
• P (Planck length): The smallest physical unit of length
• ħ (Reduced Planck constant): Fundamental quantum unit
• G (Gravitational constant): Determines strength of gravitation
• k (Boltzmann constant): Relates energy and temperature
• τ (Planck time): Time light takes to travel 1 Planck length
• c (Speed of light): Defined as P / τ
• α (Fine structure constant): Fundamental physical constant (~1/137)
• N_A (Avogadro constant): Foundational unit for amount of substance

SI Units in Planck Units

The core philosophy of MPP is to express all physical quantities in terms of fundamental constants, ultimately deriving them from Planck units. For example:

• Meter: Conceptually, ~6.18735 × 10^34 Planck lengths (P)
• Kilogram: Conceptually, ~4.59426 × 10^-8 Planck mass (M_P)
• Second: Conceptually, ~1.85487 × 10^43 Planck times (t_P)
• Kelvin: Conceptually, ~7.58329 × 10^-33 Planck temperature (T_P)
• Ampere: Derived from other units
• Mole: Based on Avogadro’s constant
• Candela: Based on luminous intensity

Imperial Units

Imperial units are defined in terms of SI units, which are themselves defined in Planck units:

• Inch: 0.0254 meters
• Foot: 0.3048 meters
• Pound: 0.45359237 kilograms
• Gallon (US): 3.78541 liters

Units as Symbolic Expressions

Ideally, all units within MPP are represented as symbolic expressions derived from fundamental constants like P, ħ, c, etc. This allows for algebraic manipulation and maintains the system’s symbolic closure. For instance, a meter would be a symbolic expression involving P and a rational scaling factor.

Practical Implementation and src/units.rs

While the ideal is pure symbolic representation, the src/units.rs module provides practical definitions for common SI and other units. These definitions often involve direct numerical values (e.g., f64 or BigInt) for interoperability and to bridge the gap with conventional unit systems.

For example, units.meter() might return a representation that, for practical purposes, uses a standard numerical value for the meter. However, the system’s underlying goal is to ensure that these practical units can be related back to their symbolic, Planck-unit-derived forms. Tests in tests/planck_units.rs focus on verifying these fundamental symbolic derivations.

The system aims to provide both:

1. A foundational layer where units are pure symbolic expressions in terms of fundamental constants.
2. A practical layer in src/units.rs that offers conventional unit values, while striving to maintain consistency with the symbolic foundation.

This dual approach allows MPP to be both theoretically rigorous and practically usable.

Foundational Units

Some units and constants are considered foundational to the MPP system:

• Avogadro’s Constant: Connects microscopic and macroscopic scales
• Fine Structure Constant: Fundamental dimensionless constant of nature

Dimensional Analysis

The MPP system tracks physical dimensions to ensure consistency. The dimension system includes:

• Length
• Mass
• Time
• Temperature
• Electric Charge
• Current
• Amount of Substance
• Luminous Intensity
• Information
• Angle

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