Constants as Inter-Axis Scaling Factors

For more info on this framework, the git hub project is here. 

This view posits that physical constants like h, k_B, c, and G are not fundamental entities in themselves, but rather composite scaling factors that arise from our human-chosen system of units (like SI) when we try to relate different ways of measuring the same underlying physical "stuff" or phenomenon. Constants are the Jacobean coordinates that change the basis in unit space.

1. Underlying Unity: There's a single, underlying physical reality or "stuff." We perceive and measure different aspects of this "stuff" using distinct "axes of measurement" such as:

   • Time / Frequency (seconds, Hertz)

   • Length (meters)

   • Mass (kilograms)

   • Temperature (Kelvin)

   • (Energy (Joules) is often seen as a common quantity these all relate to)

2. Primary Scaling Ratios: The truly fundamental relationships are direct "unit scaling ratios" or "Jacobian coordinates" between these measurement axes. Examples include:

   • c: The intrinsic scaling between our unit of length and our unit of time.

   • Hz_kg (e.g., m/f): The intrinsic scaling between our unit of mass and our unit of frequency. Numerically in SI, this is h/c².

   • K_Hz (e.g., T/f or f/T): The intrinsic scaling between our unit of temperature and our unit of frequency. Numerically in SI, this involves h/k_B or k_B/h.

3. Constants as Composites: The familiar physical constants (h, k_B) are then derived combinations of these more primary scaling ratios, whose specific numerical values in SI are determined by how our base SI units (meter, kilogram, second, Ampere, Kelvin) are defined.

   • Example: h = Hz_kg * c². This means Planck's constant h is not "primitive" but is the result of combining the mass-frequency scaling with the length-time scaling (squared, to relate to energy).

   • The SI value of G is similarly a consequence of how these primary scalings combine with its dimensional structure when converting from a "natural" system where G_natural = 1.

4. Ubiquitous Scaling: These primary scaling ratios are implicitly "baked into" any SI quantity that uses the corresponding units. For instance, Hz_kg is present in any SI measurement involving kilograms.

5. Natural Units as Harmonization: "Natural units" (like Planck units) are systems where these primary scaling ratios between equivalent measurements of the same underlying stuff (and thus the composite constants like h, c, k_B, G but this is mostly not even important) are defined to be 1. This removes the arbitrary human scales and reveals the direct 1:1 relationships between the different measurement axes of the same underlying "stuff."

   • Planck units, in this view, use a fundamental timescale (t_Ph—derived from G, c, and Hz_kg) as the common basis, with other Planck quantities (length, mass, temperature) being direct scalings from this fundamental time/frequency.

In essence: The constants are artifacts of our "un-harmonized" SI measurement system. They are the necessary conversion factors that bridge the different scales (meter, kg, s, K) we've arbitrarily assigned to what are, at a deeper level, just different facets or "views" of the same fundamental physical quantities or states. Their numerical values tell us how our chosen unit sizes for mass, length, time, and temperature relate to each other through the intrinsic structure of physical law.