How SI units contain instructions to become natural units.

 Here's a combined compact summary with the text explanation and equivalences across SI, natural, and Planck units:

Physical constants aren't mysterious; they're unit-scaling bridges. Our familiar SI units (kg, meter) are human constructs. They act as conversion instructions, translating the universe's fundamental, natural-scale quantities (often expressible as frequencies or times) into our everyday measurements. Constants like c, h (via Hz_kg), and G (via t_Ph) facilitate this translation. Planck units take this further, normalizing these natural quantities into truly universal, dimensionless ratios by incorporating the inherent Planck scale.

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Summary

When we express physical quantities like mass and length, the units (kg, meter, etc.) are not intrinsic properties but conversion factors that map natural, dimensionless physical values into familiar human-scale measurements.

• The natural units represent these quantities in fundamental, often frequency- or time-based forms (e.g., mass as Hz, length as seconds).

• The SI units scale these natural values by universal constants such as $Hz_{kg}$, the speed of light $c$, and Planck time $t_{Ph}$.

• The Planck units normalize these natural values further into dimensionless quantities by incorporating Planck-scale constants, providing a universal, unit-independent representation.

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Equivalences Across Unit Systems

Quantity	SI Units	Natural Units	Planck Units
Mass	$M_{\rm SI}$[kg]	$m_n$ [Hz]	$m_P$ [dimensionless]
	$M_{\rm SI} = m_n \times Hz_{kg}$	$m_n = m_P / t_{Ph}$	$m_P=m_n\times t_{P\mathrm{h}}$
	$= m_P \times \frac{Hz_{kg}}{t_{Ph}}$
Length	$r_{\rm SI}$ [m]	$r_n$ [s]	$r_P$ [dimensionless]
	$r_{\rm SI} = r_n \times c$	$r_n=r_P\times t_{P\mathrm{h}}$	$r_P = r_n / t_{Ph}$
	$= r_P \times c \times t_{Ph}$

Interpretation

• SI units instruct us how to convert from everyday measurable values to natural physical quantities.

• Natural units encode the fundamental physical essence using frequencies and times.

• Planck units strip away arbitrary human conventions, revealing dimensionless ratios that are universal and fundamental.

This framework demystifies physical constants by showing they serve as scaling bridges between human-scale measurements and natural, fundamental quantities.