As a physicist funding my own research, I developed the Physics of Time framework, which explains how geometry-induced acceleration can create a transient negative effective coherent mass in open systems. This effect does not violate conservation laws — instead, it reveals how geometry can reshape pressure, momentum, and power exchange inside a machine.

In 2018–2025 I ran more than 100 combustion-cycle simulations using a floating secondary piston.
Every simulation showed the same phenomenon:

The moving boundary generated a transient negative effective inertial force contribution of ≈ –½ M_f during the expansion stroke, increasing useful work by 18–45% without violating global conservation.
 

Because each simulation required nearly a week, we used a power-ledger equation:

E(t)=12Mfg2t   to guide design decisions.
It never failed once in predicting the direction and magnitude of improvement.

Open systems enter a non-inertial frame where mass coherence, geometry, and acceleration interact to exchange power. This is the domain where the Physics of Time operates.

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We use:  E(t)=1/2Mf g2t   where:

To compare conventional and Relative Motion engines, we simulated the same fuel/air charge:

• Bore = 90 mm, stroke = 80 mm
• In Relative Motion, an internal      floating piston reduced effective bore to 65 mm

Simulation results (pressure-only comparison)   

Engine               MEP (bar)    W_output (J)   Power (kW)

Conventional   90 bar          3820 J                  298 kW (2-stroke) / 179 kW   (4-stroke)

Relative Motion 180 bar      4778 J                  224 kW

Relative Motion shows ≈25% improvement using standard thermodynamic analysis.

We use:  E(t)=1/2Mf g2t   where:

• Mf= effective coherent mass (from force*distance field) 
•  t=Vmean/4.905  
   

• Mf=90 Kg/cm^2
• t=21/4.9≈4.3  

E(t)=0.5×90×0.08x96x4.3≈1486 J/sE(t) 1486 J/s 

• Mf=180 kg/cm^2 iadjusted down to 157 kg/cm^2 ( effective surface).
• t=15/4.9≈3 sec 

E(t)=0.5×157×0.08x96×3=1808 J/s 

≈22% improvement — matching dyno results.

An engineer's response would be, we can practically operate at 140 bars, and calculation would be, down use the fuel by 25% and get the 1486 J/s 

Key point:
A conventional cylinder is easy to model; a variable-geometry cylinder is not.
E(t) bypasses multi-day CFD and predicts results in seconds.

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(Used on >100 simulations between 2018–2025)

P_geo=1/2Mf *g2 *t :

The reason it works:

• A moving boundary creates a cycle-average constraint acceleration
• This geometric acceleration interacts with A₁ to increase MEP
• Rigid-wall engines have zero geometric power
• Dynamic geometry increases M_f and reduces field time t, increasing work output.
   

               This equation predicts dyno brake-power to ±4%.

External accelerations superpose linearly:

akin=A1+A2a

Here A₂ is an external force (wind, second engine).
Follows Newton exactly: F=Mf(A1+A2) 

When the boundary moves, A₂ is a real geometry-induced acceleration:

• changes pressure 
• changes force pathway 
• changes coherent mass Mf 

Kinematics remain: akin=A1+A2 

But power uses the geometric product:

A_field =A1. A2 Units: m²/s⁴
This is the field-strength used in E(t).

• m/s² → motion (Newtonian)
• m²/s⁴ → power (field of time) based on the higher power of the unit s.
   

E(t) looks like power because:  P=Fv=(ma)(at)=ma^2t 

Field version: E(t) = 1/2 M_f g^2 t 

E(t) replaces:

• a with field acceleration g,
• m with coherence mass Mf 
• and evaluates at field-time (t=1 s  when average velocity → 4.9 m/s).

 Why our framework uses g² (gravitational field scale) as the “base acceleration,” instead of some arbitrary A²? 

 -  Because g is the only acceleration that is universal, constant, and frame-defining — it provides a shared origin and scale for all other accelerations, including A₂. 

1. g is the only universal, frame-invariant acceleration.
   All observers agree on it.
2. g defines the field second and the 4.9 m/s scale, giving a meaningful time base.
3. g provides the shared-origin-and-scale condition for comparing systems
4. A₂ is a shaping term, not the baseline field; it only has meaning relative to g.
5. Energy diagnostics must be tied to a universal field, not arbitrar local accelerations.

But only one acceleration defines a field scale in the real world: g.**

If we choose some arbitrary acceleration A, then:

• What sets its meaning?
• What defines its units beyond “m/s²”?
• How does another observer interpret it?
• What is the reference velocity that corresponds to “1 second in this field”?

g defines the “field second”

. This is the deep reason. E(t) equation uses the interval:

. t=1 second when v=4.9 m/s.

. Why 4.9 m/s? Because the average velocity over one second is based on : v=gt

. This is not arbitrary — it defines a physical clock.

. The “field-second” is the time it takes gravity to build a recognizable velocity.  

A2 is a modulator of the field, not the field scale

This is crucial.

• g sets the baseline scale.
• A₂ modifies how a system experiences or shapes that scale.

Conservation requires g², not A²

diagnostics must produce an energy/power quantity that:

• is comparable across experiments,
• obeys Newtonian conservation,
• is not dependent on arbitrary machine accelerations,
• can be measured without violating the shared-scale rule.

• Shared-Origin-and-Scale Condition
• A universal magnitude (9.8 m/s²),
• A universal average velocity after a motion span of 1 s (4.9 m/s).
   

           If we replaced it with some arbitrary A, you would immediately break:

• Frame invariance 
• Comparison between observers
• The ability to define coherence mass Mf

Most accelerations violate these rules when they change between frames.
But g does not (within small tolerances on Earth).

Key concepts :

• Time behaves as a mathematical field, a framework where relativity explicitly depends on time, redefining its role in physical systems.

• E(t) = ½ M_f g² t tracks open-system power 
• Mf​ is a coherence mass:  GR mass rests, Newtonian mass resists, M_f persists.
• Virtual Physical Distance (VPD) detects hidden geometric work. (catch an unrialesd geometric constraints of motion, as an increase or decrease of an expected work distance, where one Joule of energy moves a 1 kg object more or less than 1 meter due to field delivering a higher or lower pressure hen geometry changes)
• The Acceleration-Time Clock (t) defines field-distance. 
• A₂ is boundary-induced constraint acceleration.
• “Negative mass effect”  is a virtual geometric reaction force, not literal.
• Pascal’s Law extended in time captures power transfer under changing geometry.we will call it Paskal as a function of time when entegrating a 1000 interval readings of a simulated power stroke. (important to correctly read simulations when geometry is dynamically variable).

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note:

A moving-boundary engine has two acceleration channels:

• a real-force acceleration A1  acting over a characteristic time T1 
• a geometry-induced acceleration A2 ​ acting over its own time T2 

Each produces its own velocity scale, A1T1​ and A2T2
Their geometric product, (A1T1) (A2T2), is the local acceleration-energy of the system.

To make this quantity comparable across machines, we normalize it to the one universal acceleration g:

(A1T1) (A2T2)=gt1⋅gt2=g2(t1.t2) 

We combine the two time channels into a single field time t= (t1+t2 ) /2

which represents the cycle-averaged interaction of the two accelerations.

This produces the field-normalized power scale used in the open-system 

E(t) = 1/2 M_f ​*g^2 *t. 

 Final Integration: Field Time (t = V_{mean}/4.9)