Control emissions at the cylinder level, with Zero CO, Zero HC and near zero NO
Time is a Form of Energy
Dr. Ibrahim Mounir Hanna
Physics of Time & Boundary-Induced Acceleration
As a physicist funding my own research, I developed the Physics of Time (PoT) framework to diagnose how geometry-induced acceleration in open systems redistributes pressure, momentum, and power without violating conservation laws.
Within non-inertial systems containing moving boundaries, geometric constraint acceleration can introduce a transient negative effective inertial reaction term. This effect is conservative, time-limited, and strictly geometry-driven.
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Empirical Basis (2018–2025)
Between 2018 and 2025, more than 100 combustion-cycle CFD simulations were conducted using a floating secondary piston architecture.
Each simulation required approximately one week of computation.
Every case exhibited the same phenomenon:
Boundary motion generated a cycle-averaged geometric constraint acceleration
This produced a transient negative effective inertial contribution of approximately –½ M_f during the expansion stroke
Net useful work increased by 18–45%, with no violation of global conservation
To guide design decisions efficiently, we employed the time-primary power ledger:
E(t)=1/2 M_f g^2 t
This diagnostic never failed in predicting the direction and magnitude of improvement across the full simulation set.
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Engineering Comparison (Same Fuel / Same Charge)
Geometry:
Bore = 80 mm
Stroke = 80 mm
Relative-Motion configuration uses an internal floating piston, reducing effective bore to 65 mm
Pressure-Only Results:
Engine Type MEP (bar) Work Output (J) Power (kW)
Conventional 90 3820 298 (2-stroke) / 179 (4-stroke)
Relative-Motion 180 4778 224
Standard thermodynamic analysis shows a ≈25% improvement.
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PoT Evaluation Using E(t)
We evaluate per square centimeter of piston surface:
E(t)=1/2 M_f g^2 t
Where:
M_f= effective coherent mass (from force × field-distance)
t=V_"mean" /4.905(field-normalized exposure time)
Conventional Cylinder
M_f=90 kg/cm^2
t≈4.3 s
E(t)≈1486 J/s
Relative-Motion Cylinder
M_f=157 kg/cm^2(surface-adjusted)
t≈3.0 s
E(t)≈1808 J/s
Result: ≈22% improvement — matching dyno data.
For Physicists
Closed vs Open Systems and the Role of Boundary-Induced Acceleration
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1. Closed Systems (Inertial Frames)
In closed systems, all accelerations arise from external real forces and therefore superpose linearly.
a_kin =A_1+A_2
Here, A_2represents an external force–derived acceleration (e.g., wind load, secondary engine thrust).
Newton’s second law applies directly and completely:
F=M_f (A_1+A_2)
No additional structure is required.
All quantities are evaluated in a shared inertial frame, and conservation is enforced locally and globally.
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2. Open Systems (Non-Inertial Frames)
In open systems, the boundary itself moves.
The resulting acceleration A_2is not an externally applied force, but a real geometry-induced acceleration arising from boundary motion or constraint evolution.
This acceleration:
reshapes pressure fields, ( specifically increasng the pressure/volume ratio.
alters force pathways,
modifies the effective coherent mass M_f. ( calculated as a positive trap mass in simulation software, without actually adding any air or fuel during the power stroke)
The kinematics remain unchanged:
However, power accounting does not.
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Power Accounting in Open Systems
In non-inertial systems, power is governed by the geometric interaction between motion-driven acceleration and constraint-driven acceleration.
The relevant field strength is:
A_field =A_1⋅A_2
with units:
[A_field" ]=m^2/s^4
This is the acceleration product that enters the time-primary power ledger:
E(t)=1/2 M_f g^2 t ,
Based on this equation, a time-unit of field seperation, VPD_sec , secures the conservation ledger in open systems and non-inertial frames, the same way "meter" serve as the unit inveriant of conservation ledgers in closed systems.
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For Mathematicians
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Why the Power Ledger Takes the Form E(t)=1/2 M_f g^2 t
1. Why E(t)Has the Dimensions of Power
Start from classical mechanics:
P=Fv
With constant acceleration,
F=ma,v=at
So,
P=(ma)(at)=ma^2 t
This shows that power is naturally proportional to an acceleration squared times time.
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2. Field-Normalized Form
The Physics of Time framework uses the field-normalized version:
E(t)=1/2 M_f g^2 t
Relative to the classical expression:
m→M_f(effective/coherent mass)
a→g(field acceleration)
evaluation is performed at field-time, defined below
This is not a reinterpretation of power, but a choice of invariant normalization.
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3. Why the Baseline Must Be g^2, Not an Arbitrary A^2
Mathematically, any acceleration could be squared.
Physically, only one acceleration defines a universal field scale, where:
Gravity_g is:
universal (present for all material systems),
constant to high precision over laboratory scales,
shared by all observers,
frame-defining rather than system-dependent.
Because of this, g provides a shared origin and scale for all other accelerations, including geometry-induced A_2.
An arbitrary acceleration A, does not.
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4. The Field Second
Gravity defines a physical time scale, not a coordinate convention.
From constant acceleration:
v=gt
At t=1" s,
v=gt⇒v=9.81" m/s
The average velocity over that interval is:
v ˉ=1/2 gt=4.905" m/s
This defines the field second:
the time required for gravity to build a recognizable velocity scale.
This is not arbitrary.
It is a physically grounded clock defined by a universal field.
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5. Role of A_2
A_2is not a baseline field acceleration.
gdefines the scale.
A_2modulates how a system experiences that scale.
In open systems, A_2reshapes:
pressure distributions,
force pathways,
effective coherence mass M_f.
But it has no absolute meaning unless referenced to g.
Thus:
A_2 " is a shaping term,not a field scale"
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6. Conservation and Comparability
Using g^2ensures that diagnostics:
are comparable across experiments,
obey Newtonian conservation,
do not depend on machine-specific accelerations,
satisfy the shared-origin-and-scale condition.
This is why conservation in open systems requires field normalization, not arbitrary acceleration normalization.
Key Concepts of the Framework
• Time as a Field (Diagnostic Sense)
Time functions as a field-normalized diagnostic framework in which relativistic and mechanical behavior depends explicitly on acceleration exposure over duration. This does not introduce a new force or substance; it redefines how time participates in power realization in open systems.
• Time-Primary Power Ledger
E(t)=1/2 M_f g^2 t
This expression tracks power availability in open systems, where geometry and boundary motion redistribute pressure and work without violating conservation.
• Coherence Mass M_f
M_fis an effective coherence mass:
Newtonian mass resists acceleration,
relativistic mass rests as energy content,
coherence mass persists as the portion of matter effectively coupled to pressure, geometry, and acceleration pathways over time.
• Virtual Physical Distance (VPD)
VPD detects hidden geometric work by comparing realized motion against a field-normalized reference.
It captures unrealized or redistributed geometric constraints, appearing as an increase or decrease in effective work distance—where one joule of energy moves a 1 kg object more or less than 1 meter due to geometry-induced changes in pressure and force pathways.
• Acceleration–Time Clock
The variable tfunctions as an acceleration-time clock, defining field distance rather than coordinate time. It measures exposure to acceleration under a shared field scale.
• Boundary-Induced Constraint Acceleration (A_2)
A_2represents real, geometry-induced acceleration arising from moving boundaries or evolving constraints. It reshapes pressure fields and force pathways without acting as an external force.
• Negative Mass Effect (Virtual)
The so-called “negative mass effect” is a virtual geometric reaction associated with boundary-induced acceleration in non-inertial frames. It is not a literal negative mass and does not violate conservation laws.
• Pascal’s Law Extended in Time
Pascal’s law is extended to time-resolved, dynamically varying geometry, capturing power transfer through pressure under boundary motion.
In practice, this is evaluated as Pascal’s law as a function of time, typically by integrating thousands of instantaneous pressure and force readings over a simulated power stroke—an essential step for correctly interpreting simulations of variable-geometry systems.
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note:
How Two Local Accelerations Collapse into the Field Term g2t
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)
Understand the field
Geometry itself can do work — when the walls move
Understanding the Field
Geometry by itself does not supply power.
However, when boundaries evolve with motion,driven by a netforce acceleration (A1) , geometry becomes an active pathway through which power is redistributed, pressure to volume ratio changes and a second effective acceleration (A2) can be tracked under power conservation rules and work output results.
This distinction is central to open-system physics.
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Understanding the Field
(For Physicists)
In classical mechanics, engineers routinely introduce apparent or inertial forces (D’Alembert forces) to describe motion in non-inertial frames. These forces may appear “negative,” but they do not represent new sources of power; they account for how mass resists acceleration when the reference frame itself accelerates.
The Physics of Time framework extends this treatment by identifying when a negative effective force corresponds to a physically real power interaction, as a result of non-static geometry changing pressure to volume ratio of the motion path, the coherent mass participation in motion or field traversing efficiency.
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When Negative Effective Force Becomes Physically Real
The key condition is geometric acceleration, we call (A2).
When a combustion chamber geometry changes volume capacity during a power stroke, a moving boundary alters the pressure field, specifically the pressure-to-volume ratio.
This change produces a real, measurable reaction force on both the working fluid and the piston, resulting in a measurable redistribution of instantaneous power.
This force is not fictitious.
It arises from:
moving-boundary altering pressure gradients.
fluid _motion coupling, (Mf) through altered pressure and effective work time.
added-fluid displacemenr capacity when a second floating piston compete with fluid for volume.
In this regime, the effective geometric force can be written schematically as:
F_ geom = - M_f ∘ A_2
where:
A_1 is real-force acceleration,
A_2 is geometry-induced acceleration,
the product indicates power-relevant coupling, not vector addition.
The negative sign reflects a reaction force opposing inertial response, while remaining fully conservative in the power ledger.
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Geometry as a Power Pathway
Geometry alone does not generate power.
But when boundaries move under power-delivering acceleration A_1, they reshape the pressure distribution.
The geometry-induced acceleration A_2 determines how power is transmitted through the fluid by modifying the instantaneous pressure field via the boundary-motion rate:
dV/dt
Thus:
A_1— delivers power
(pressure, combustion, thrust, gravity)
A_2— shapes power delivery
(moving boundaries, changing volume, kinematic constraints)
All power still originates from the same source associated with A_1.
A_2does not violate conservation; it redistributes when and where power appears as useful work.
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Reynolds Transport Theorem (RTT)
The Classical Root of Open-System Power Accounting
The Reynolds Transport Theorem generalizes Newton’s laws to systems in which:
mass enters and exits,
boundaries move,
geometry evolves in time.
RTT provides the mathematical foundation for understanding:
how the effective coherence mass M_f evolves,
how geometry produces A_2,
how open systems redistribute power,
why the time-primary power ledger E(t) remains conservative.
In this framework, RTT generalizes:
F=ma
to open systems where:
the participating mass is the effective mass M_f,
acceleration contains both A_1 (real-force acceleration) and A_2 (geometry-induced shaping),
time is field-normalized for power comparison across systems with different boundary motion.
This leads to the substitutions:
m→ M_f,t_ clock → t_field"
Open-system power dynamics requires this shift.
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Definitions
Effective Mass M_f
Field-coherent mass–force (kg, specified per unit active area)
M_frepresents the portion of matter whose inertia is actively coupled to the local field geometry — meaning the mass that participates in pressure-based power exchange at a given instant.
It is not simply the inertial mass of the piston or gas.
Instead, M_fdepends on:
moving boundaries and changing geometry,
pressure-field coherence, defined by the pressure/volume ratio and work time.
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A_1— Net-Force Acceleration
Acceleration due to real forces:
pressure,
combustion,
thrust,
gravity.
Units: m/s²
This is the power-delivering component.
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A_2— Geometry-Induced (Constraint) Acceleration
Acceleration arising from changing geometry:
moving boundaries,
dynamically changing chambers,
orbital curvature,
piston kinematics.
A_2:
reshapes motion,
modifies pressure pathways,
affects coherence M_f,
adjusts instantaneous working force and instantaneous power via dV/dt.
External forces such as wind always belong to A_1, not A_2.
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Coordinates in the Time Field
We define a diagnostic Cartesian space:
x=t"(field time)"
y=A_1 "(real-force acceleration)"
z=A_2 "(geometry-induced acceleration)"
The origin corresponds to the instantaneous value of M_f, the mass effectively coupled to the field. Mf defines the the cartesian origin, which does not represent a physical position.
It is a power-diagnostic field space expressing how time, real forces, and geometry interact in an open system.
Within this representation:
M_f A_1 *t , ties the momentum / realized-power channel,
M_f A_2 *t , ties the coherence / power-shaping field velocity channel.
We also call A2_t, the field velocity, to express how momentum changes relative to the field.
This Cartesian structure makes explicit how geometry reshapes power pathways in open systems while remaining fully conservative.