The Universal State S_u : A Scalar Foundation for Particle Properties

J. Rogers, SE Ohio, 16 May 2025, 2341

In this framework, we propose that every particle possesses a conserved, dimensionless scalar quantity called the Universal State (or Stuff), denoted $S_u$. This scalar does not represent any one specific property such as energy, mass, or frequency; instead, it is the scaled essence of the particle — its worldline scalar, from which all measurable properties emerge through coordinate-dependent scaling.

1. The Core Insight: The Worldline Is $S_u$

Rather than treating energy, frequency, or momentum as fundamental, this view regards the particle's worldline in 4D spacetime as a geometric manifestation of $S_u$. The particle’s observable properties are projections of this underlying scalar along different axes of measurement — energy, frequency, mass, temperature, etc. Each axis is a scaled view of the same conserved quantity.

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2. $S_u$ as a 4D Scalar

• $S_u$ is dimensionless in natural (Planck) units.

• It is conserved across interactions: it can transfer between particles and spacetime, but is never created or destroyed within a closed local system.

• All measurable properties of a particle are rescalings of $S_u$ along specific coordinate axes using Planck unit ratios (e.g. $h$, $c$, $k$, etc.).

For instance:

$$\text{Energy} = S_u \cdot E_P,\quad \text{Mass} = S_u \cdot m_P,\quad \text{Frequency} = S_u \cdot f_P$$

This means $S_u$ can be recovered from any one property:

$$S_u = \frac{E}{E_P} = \frac{m}{m_P} = \frac{f}{f_P} = \cdots$$

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3. Three Phases of Scaling

We identify three distinct mechanisms by which $S_u$ becomes manifest in observable physics:

A. Emission (Initial State)

The particle is instantiated with a particular $S_u$ value. This sets the initial scaling along all measurable axes — e.g., a photon’s frequency at emission is the initial scaling of its $S_u$.

B. Propagation (Relativistic/Gravitational Scaling)

As a particle moves through curved spacetime or accelerates, its worldline experiences geometric distortions. These alter how the original $S_u$ is scaled — giving rise to relativistic effects like redshift, blueshift, and time dilation.

C. Observation (Frame-Dependent Projection)

The final measurement is a projection of the particle’s scaled $S_u$ along the observer’s own worldline. This results in perceived differences in energy, frequency, or mass — not because the particle’s essence changed, but because the relative scaling changed.

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4. Unified Interpretation of Physical Laws

This view suggests that constants like $h$, $c$, and $k$ are not fundamental substances, but unit scaling bridges that allow us to rotate $S_u$ between different axes of measurement. For example:

$$\frac{E_P}{t_P} = \frac{h}{t_P^2} \Rightarrow E_P \sim h \cdot f_P$$

Thus, Planck units define the geometry of measurement space, while $S_u$ defines the invariant “stuff” of a particle — its coordinate-free identity.

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5. Philosophical Implication

We do not directly measure $S_u$; we only experience its projections. Each new axis of measurement (mass, charge, spin, etc.) is just another view of the same conserved scalar — a different rotation in the measurement coordinate system.

The power of this approach lies in its reduction of all physical properties to a single conserved invariant, and in how it reflects the observer-dependent nature of spacetime without denying the reality of the thing being observed.

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Conclusion: Reframing Physics

This model reframes particle physics and relativity under a common structure: a conserved scalar worldline essence, $S_u$, from which all measurements emerge. This echoes Einstein's vision of physics based on coordinate-independent structures, grounding particle identity not in disparate properties, but in a unified, invariant scalar.

S_u in the 4 vector: 

In the standard 4-vector formalism, we write a particle’s energy-momentum vector as:

$$P^\mu = \left(\frac{E}{c}, \vec{p} \right)$$

But this assumes energy and momentum are the fundamental quantities. In your framework, this 4-vector should instead be interpreted as:

$$P^\mu = S_u \cdot \left( \frac{E_P}{c}, \vec{p}_P \right)$$

Here, $S_u$ is the scalar variant — the conserved essence of the particle — and $\left(\frac{E_P}{c}, \vec{p}_P\right)$ are the Planck unit directions (or scaling bases) for that measurement axis.

So rather than thinking of $\frac{E}{c}$ as a "component" of the worldline, we reinterpret it as:

$$\frac{E}{c} = S_u \cdot \frac{E_P}{c}$$

This makes it clear: momentum and energy are not ontologically primitive — they are projections of $S_u$ along measurement axes scaled by natural units.

Just as a vector can be rotated in space without changing its magnitude, the $S_u$ scalar is rotated between observable quantities by coordinate scaling — and the physical constants are the rotation factors. This unifies the apparent multiplicity of particle properties into a single geometrically-scaled entity.