Extending Energy Rest Frame for mass.

The frequency f in the rest frame is 1 Hz, so the relationships simplify there. However, in the observer’s frame, f scales the quantities due to worldline effects.

Here we set K = hc, and that makes h = K/c.  So we can replace h with K/c in the standard formulas for energy (E=hf), Momentum (p=hf/c), and Mass (m=hf/c^2). This K is just a unit scaling factor to convert 1/c into standard unit definitions.  It is entirely dependent on how we set unit definitions and s, kg, and m can all be redefined to make h = 1/c and hc  = 1 J m.  

Here's the revised explanation:

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1. The Energy Rest Frame

In the energy rest frame ($f = 1$ Hz), the intrinsic properties of the particle are expressed without the need for scaling by $f$:

Energy at Rest

$$E_{\text{rest}}=\frac{K}{c^{\mathrm{1}}}$$

Momentum at Rest

$$p_{\text{rest}}=\frac{K}{c^{\mathrm{2}}}$$

Mass at Rest

$$m_{\text{rest}}=\frac{K}{c^{\mathrm{3}}}$$

Here, $K$ is the fundamental scaling constant (K=hc, the ratio between h and c, it is neither h nor c), and these relationships represent the intrinsic (unscaled) properties of the particle or photon.  As you can see, energy is frequency/c, momentum is energy/c and finally Mass is momentum/c. The E, p, and m has to be converted to human units by multiplying by K.  The thing about relativity is that motion just scales an existing value, but that chain of scalings has to go back to an identical value that is the same energy rest frame in every particle. A ground truth if you will.

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2. The Observer Frame

When transitioning to the observer’s frame, where worldline effects introduce scaling based on the particle's frequency $f$, the relationships become:

Energy in the Observer Frame

$$E=\frac{Kf}{c^{\mathrm{1}}}$$

Momentum in the Observer Frame

$$p=\frac{Kf}{c^{\mathrm{2}}}$$

Mass in the Observer Frame

$$m=\frac{Kf}{c^{\mathrm{3}}}$$

The frequency $f$ scales these quantities based on the particle's motion through spacetime and the observer's reference frame.

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3. Geometric Scaling Progression

Rest Frame (Intrinsic Properties):

1. Energy: $$E_{\text{rest}}=\frac{K}{c^{\mathrm{1}}}$$
2. Momentum: $$p_{\text{rest}}=\frac{K}{c^{\mathrm{2}}}$$
3. Mass: $$m_{\text{rest}}=\frac{K}{c^{\mathrm{3}}}$$

Observer Frame (Worldline Scaling):

1. Energy: $$E=\frac{Kf}{c^{\mathrm{1}}}$$
2. Momentum: $$p=\frac{Kf}{c^{\mathrm{2}}}$$
3. Mass: $$m=\frac{Kf}{c^{\mathrm{3}}}$$

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4. Insights

1. Intrinsic Properties in the Rest Frame:
   The rest frame provides a "ground truth" for energy, momentum, and mass as defined by $K$, without the need for additional scaling factors like $f$. These intrinsic values represent the baseline of the particle's properties.

2. Worldline Scaling in the Observer Frame:
   The frequency $f$ reflects the scaling introduced by the motion of the particle through spacetime. It acts as a multiplier, modulating the intrinsic properties according to the worldline's interaction with the observer's frame.

3. Unified Relationships:
   The consistent dependence on $K/c^n$ across all quantities shows how frequency, energy, momentum, and mass are geometrically related through spacetime.  This is exactly what the current formulas all do for energy, momentum, and mas, they unify the worldline scaling and observers reference frame as a single combined scaling from the invariant rest energy frame.  It is just not clear eactly what