A Unified View of Time, Mass, and Gravity: Planck Units as Dimensional Unscaling

 

Abstract

We propose a fundamental reinterpretation of mass, gravity, and black holes based on the dimensional analysis of Planck units. Rather than treating Planck units as fundamental scales, we demonstrate they function as unscaling operations that reveal the underlying dimensional unity of physical quantities. This leads to the insight that mass represents slowed time, gravity is the flow toward regions of time dilation, and black holes are regions where time flow approaches zero. This framework resolves several conceptual puzzles in general relativity and provides intuitive explanations for gravitational phenomena.

1. Introduction

The conventional interpretation of Planck units treats them as fundamental scales where quantum gravity effects become important. However, the Planck mass (~22 μg) being macroscopic rather than microscopic suggests these units may not represent physical limits but rather reveal something deeper about dimensional relationships in physics.

2. Dimensional Unity and the Hz_kg Ratio

2.1 The Fundamental Relationships

Setting c = 1 in natural units reveals that length and time are dimensionally equivalent: L = T. From Planck's relation ℏ = mc²/f, when c = 1, we obtain ℏ = m/f. Setting ℏ = 1 then requires m = f, revealing that mass and frequency are dimensionally equivalent.

This leads us to define the fundamental ratio:

Hz_kg = m/f = ℏ/c²

This ratio appears to be a fundamental property of the universe, defining the relationship between mass and frequency just as c defines the relationship between length and time.

2.2 Reinterpreting Physical Constants

With Hz_kg defined, we can express other fundamental constants:

• Boltzmann constant: k_B = K_Hz · Hz_kg · c² where K_Hz = k_B/ℏ
• Gravitational constant: G = t_P² · c³ / Hz_kg

3. Planck Units as Unscaling Operations

3.1 The True Nature of Planck Units

Rather than fundamental scales, Planck units function as conversion factors that strip away SI unit conventions:

m_P = √(ℏc/G) = Hz_kg/t_P
l_P = c · t_P  
T_P = Hz_kg/t_P

When we express a quantity in Planck units, we obtain:

Length_SI / l_P = Length_in_seconds / t_P
Mass_SI / m_P = (Mass_in_frequency_units) · t_P

3.2 The Dimensionless State Value S_u

For any physical system in state u, all Planck-scaled quantities yield the same dimensionless value S_u:

S_u = E/E_P = m/m_P = f · t_P = L/l_P = T/T_P

This suggests that S_u represents the true, invariant description of the system's state, while our conventional measurements (energy, mass, frequency) are merely different expressions of this single underlying quantity.

4. Mass as Slowed Time

4.1 The Geometric Interpretation

If we interpret distance as "delayed time" - the temporal delay required for causal influence to propagate - then massive objects represent regions where this delay is increased. Mass becomes a measure of how much time flow has been slowed in a given region.

4.2 Gravity as Time Flow

Gravitational attraction emerges naturally as the tendency for S_u patterns (particles) to flow toward regions of slower time flow, where the S_u oscillations have more "temporal space" to exist.

4.3 The Speed of Light as Causality Rate

The speed c represents the rate at which "now" propagates outward from any event, creating expanding spheres of causality. Nothing can exceed c because this would require negative temporal delay, which is meaningless.

5. Black Holes as Zero-Time Regions

5.1 The Event Horizon as Temporal Boundary

A black hole represents the ultimate expression of time dilation - a region where time flow approaches zero. The Schwarzschild radius is not a quantum gravity scale but simply the distance at which time dilation becomes total.

5.2 Why Gravity "Escapes" Black Holes

Gravity doesn't escape from black holes because gravity IS the time distortion that creates the black hole. The gravitational field is not produced by matter "inside" the black hole but is the geometric structure of spacetime itself - the pattern of time flow rates at different distances from the zero-time region.

5.3 Information Preservation

From an external observer's perspective, information never actually crosses the event horizon because there is no time flow available for this crossing to occur. Information becomes frozen at the boundary where time flow approaches zero, naturally resolving the information paradox.

6. Relativistic Effects as Causality Geometry

6.1 Doppler Effects and Time Dilation

When moving toward a source, an observer intersects the source's expanding causality spheres more frequently, experiencing the source's processes as accelerated. Conversely, the observer's own causality spheres are encountered less frequently by stationary observers, creating the reciprocal time dilation effect.

6.2 Equivalence Principle

The equivalence between gravitational and inertial effects becomes geometrically obvious: both represent different ways of intersecting the same causality sphere structure at different rates.

7. Implications and Predictions

7.1 Unified Field Theory

This framework suggests that all fundamental forces may be different manifestations of S_u oscillation patterns in the underlying causality structure. Gravity, electromagnetism, and nuclear forces could all be aspects of how S_u redistributes itself in spacetime.

7.2 Quantum Mechanics

Wave-particle duality becomes less mysterious when both are recognized as different expressions of the same S_u state value. The particle doesn't "switch" between wave and particle behavior; we simply choose to measure S_u in different ways.

7.3 Cosmological Implications

Dark matter and dark energy might be better understood as modifications to the S_u distribution or time flow patterns in the universe rather than exotic particles or fields.

8. Conclusion

By recognizing Planck units as dimensional unscaling operations rather than fundamental scales, we uncover a remarkably simple underlying structure to physics. Mass is slowed time, gravity is the flow toward time dilation, and black holes are regions of zero time flow. This perspective provides intuitive explanations for relativistic effects while suggesting new directions for theoretical development.

The universe appears to be fundamentally about S_u state values evolving in a causality structure defined by the propagation rate c, with all our conventional physical quantities being different expressions of this single underlying reality.