Time's Central Role: What the Mathematics is Telling Us

 J. Rogers, SE Ohio, 03 Jun 2025, 2342

When we examine how physical constants and Planck units actually function mathematically, a puzzling pattern emerges. Rather than making claims about what this means, let's simply observe what the mathematics itself is showing us.

The Two-Step Process Hidden in Planck Units

Consider what happens when we construct Planck units:

For mass:

• Start with: mass_SI = frequency × Hz_kg (where Hz_kg = h/c²)
• Planck mass: m_P = Hz_kg / t_P
• Result: mass_planck = frequency × t_P

For length:

• Start with: length_SI = time × c
• Planck length: l_P = c × t_P
• Result: length_planck = length_SI / l_P = time × c / (c × t_P)

What's happening here? The mathematics appears to be performing two distinct operations:

1. Strip away SI units - convert everything to frequency/time relationships
2. Scale by Planck time - normalize to a fundamental time scale

The Universal Pattern

This pattern repeats across every physical property:

• Energy: E_planck ∝ frequency × Planck time
• Momentum: p_planck ∝ frequency × Planck time
• Temperature: T_planck ∝ frequency × Planck time
• All properties: Property_planck ∝ temporal_relationship × t_P

Why does every physical quantity, when stripped of human-imposed units, resolve into temporal relationships?

But every one of these properties for the same particle in the same state converts to the same dimensionless value at the Planck scale, a Universal state called S_u. 

The 4-Vector Connection

In relativity, the time component of the 4-momentum vector is E/c. But if we express this in terms of the universal state S_u:

Time component = S_u × (Planck momentum) = E/c

In Planck units, this time vector becomes simply S_u - dimensionless.

What does this suggest about the relationship between:

• Internal temporal intensity (S_u)
• Observable mass/energy
• Spacetime curvature
• Time dilation effects

Motion and Temporal Optimization

Objects follow geodesics - paths through spacetime that extremize proper time. Light follows Fermat's principle - paths that minimize travel time.

Is this coincidence, or is the mathematics pointing to a deeper principle? Are all physical trajectories expressions of temporal optimization?

If regions of higher mass density correspond to regions of slower time flow, and if objects naturally follow paths of least temporal "cost," then:

• Is gravity a consequence of temporal gradients?
• Are geodesics simply paths of minimum time expenditure?
• Is what we call "spacetime curvature" actually temporal topology?

The Constants as Conversion Factors

The fundamental constants (c, h, G, k_B) appear in our analysis as ratios between measurement axes:

• c: converts between spatial and temporal measurements
• h: converts between energy and frequency but inside it contains m/f and L/T ratios.
• G: encodes the scaling to non reduced natural (Planck) time units

Are these constants revealing something about the geometry of measurement itself rather than fundamental properties of reality?

The Puzzling Implication

The mathematics seems to be telling us that when we remove all human-imposed unit systems and scaling, everything reduces to temporal relationships scaled by a fundamental time unit.

Why would this be? What does it mean that:

• Every physical property becomes a function of time when properly scaled?
• The time component of 4-vectors connects directly to universal state?
• All motion appears to optimize temporal quantities?
• Physical constants function as temporal conversion factors?

The mathematics is consistent and the patterns are clear. But what is it trying to tell us about the nature of physical reality?

Questions This Raises

• If time relationships are mathematically fundamental, what does this say about the nature of space?
• Why do all measurement axes collapse to temporal expressions in natural units?
• Is temporal intensity the hidden variable behind all physical properties?
• Are we measuring different projections of the same temporal phenomenon?
• What would physics look like if we started from time as primary rather than space-time as equivalent?

The mathematics is pointing somewhere specific. The question is: are we ready to follow where it leads?