Gravity in the Context of the

1Second Invariant

Ian Beardsley — March 2026

Abstract. The discovery that a universal normal force

underlies the masses of the proton, neutron, and electron—and that the

same 1second invariant appears throughout the solar system, in ancient

metrology, and in monumental architecture—invites a fundamental

rethinking of gravity. In the standard relativistic picture, force emerges from

mass; here we explore the inverse: mass emerges from force, and gravity

may be a manifestation of the temporal dimension’s resistance to rotation.

Three possibilities are outlined, along with a mathematical sketch and

comparisons to general relativity.

1. The Inverted Paradigm

Einstein’s general relativity rests on the principle that mass-energy tells

spacetime how to curve, and curved spacetime dictates the motion of

masses. Force, in that view, is either fictitious (gravity) or emergent from

fundamental interactions. The work collected in From Quanta to the Solar

System suggests a reversal:

•

There exists a universal normal force with .

•

This force resists any rotation of a particle’s fourvelocity from the

temporal dimension into spatial dimensions.

•

The resistance to this rotation is experienced as inertia; the

quantitative measure of that resistance is what we call mass.

Here , and the cross-sectional area exposes the particle

to . Gravity, therefore, cannot be simply “attraction between masses” –

masses themselves are secondary. What, then, is gravity?

2. Reinterpreting Gravity: Three Possibilities

🔹 Possibility 1 – Gravity as a Gradient in

Although is a constant, its effect on spacetime may be mediated by . If

we treat as a measure of how couples to geometry, then the presence

of a mass creates a distortion in the “temporal resistance field”. This

distortion can be described by a tensor (temporal resistance tensor)

= h /(c ⋅ 1 s

)

c t

= 1 second

= κ

π r

, F

c (1 s)

= 1/(3α

)

= 1

π r

μν

whose gradient produces an effect indistinguishable from gravitational

acceleration.

In weak fields, the gradient of the component would play the role of the

Newtonian potential:

🔹 Possibility 2 – Gravity as the Residual of Temporal

Rotation

Every object at rest relative to a local frame has its four-velocity aligned with

the local time axis. Near a massive body, the orientation of the time axis is

rotated compared to distant regions. To remain at rest relative to the

massive body, an object must have its temporal direction forcibly aligned

with the local axis – i.e., its four-velocity must be rotated away from the

distant time direction. That rotation encounters the universal resistance .

What we feel as weight (the normal force from the ground) is precisely

this resistance. Free fall is the state where the four-velocity naturally aligns

with the local time axis without any forced rotation – there is no resistance,

hence no sensation of weight. In this picture, gravity itself is not a force; it is

the manifestation of the gradient in the orientation of time, and the

resistance to misalignment is .

🔹 Possibility 3 – Gravity as a Deficit in (Nonlinear

Overlap)

The mass of a composite body is built from the individual .

When two such bodies approach, their regions of “temporal influence”

overlap. Because the coupling involves in the denominator, the total

resistance is not simply additive; there is a nonlinearity that can be

interpreted as an effective attraction – a kind of Casimir-like effect for the

temporal resistance field. The system minimizes the total resistance by

bringing the masses closer, which we perceive as gravitational attraction.

3. Mathematical Sketch: Temporal Resistance

Tensor

To make these ideas more concrete, one can introduce a tensor field

that characterizes the local resistance to rotations into space. In empty, flat

spacetime, is proportional to the Minkowski metric with a scale set by :

≈ −

∂R

∂x

= κ

π r

μν

(x)

μν

(0)

μν

In the presence of matter, the tensor is perturbed: . A test

particle moves so as to minimize the total “rotation resistance” along its

worldline, leading to an equation of motion:

For a static, weak field and slow motion, this reduces to ,

exactly the form of Newtonian gravity if we identify (the gravitational

potential).

4. Comparison: General Relativity vs. The

TemporalResistance View

5. The Moon as Metric – Revisited

In the solar system analysis, the Moon emerged as the metric because its

mass appears cubed in the equations that yield the 1second invariant. If

gravity is a manifestation of the temporal resistance field, then the

EarthMoonSun system represents a three-body resonance in that field. The

Moon’s role in stabilizing Earth’s axial tilt also stabilizes the local orientation

of the temporal dimension relative to the Sun. The remarkable factor

(the eclipse ratio) and the appearance of seconds per day are

not coincidences – they reflect the nonlinear coupling of the temporal

resistance field, whose fundamental period is 1 second.

μν

= R

(0)

μν

+ δR

μν

(m)

dτ

(

μν

d x

dτ

)

∂R

αβ

∂x

d x

dτ

d x

dτ

≈ −

∂R

∂x

∝ ϕ

Aspect

General Relativity

TemporalResistance

Framework

Fundamental

entity

Source of field

Mass (as measure of resistance

to temporal rotation)

What curves /

varies

Spacetime geometry

Orientation and magnitude of

temporal resistance

Free fall

Geodesic of spacetime

Path of minimal temporal

rotation resistance

Weight

Resistance to geodesic

motion (normal force)

Coupling constant in

field equations

Direct manifestation of when

alignment is forced

Metric tensor

μν

Gravitational

constant

Mediator of how mass perturbs

μν

Stress-energy tensor

μν

Temporal resistance tensor

μν

≈ 400

× 400 = 86 400

6. The 1Second Everywhere

Because is built from invariants ( , , and the invariant

1 second), any phenomenon coupled to will exhibit that same timescale:

•

Quantum scale: proton radius/mass relation (with the

golden ratio conjugate) yields 1 second when inserted into the master

equation.

•

Human scale: a 2-cubit pendulum at the latitude of Egypt has a

halfperiod of 1.028 s; the megalithic yard gives 0.913 s; pyramid

diagonals give sound transit times ≈0.92 s.

•

Celestial scale: the ratio of the Moon’s kinetic energy to Earth’s,

multiplied by 24 h and , equals ≈1 s; the solar-system “Planck

constant” , leads to wave-equation solutions for

planetary orbits accurate to 99.5%.

All these systems are coupled to the same underlying temporal resistance

field. The 1 second is not an arbitrary human invention; it is the

characteristic period of spacetime’s resistance to rotation.

7. Conclusion: Gravity as the Manifestation of

Temporal Resistance

In the framework suggested by the 1second invariant, gravity is not a

fundamental force, nor merely spacetime curvature. It is the observable

effect of gradients in the temporal dimension’s resistance to rotation.

Mass is the measure of how strongly an object couples to that resistance.

The constancy of across all scales – from protons to planets – points to a

unified origin: the temporal dimension itself possesses a kind of “stiffness”,

and that stiffness has a natural period of one second.

These possibilities remain speculative, yet they emerge naturally from

equations that already show striking numerical agreement with experiment

(proton radius, planetary energies, archaeological metrology). If correct,

they invert the conventional relationship between force and mass, and they

place the Moon, the pyramids, and the proton on the same conceptual

footing – all as resonators coupled to the heartbeat of time.

References. Beardsley, I. (2026). A Proposal For A Universal Particle

Equation; Quantum Analog For The Solar System; The Second in the Cubit:

An Archaeological Inquiry; The Case For Nonhuman Intelligence; Chaos

Driven Order. All available at Zenodo and Academia.edu.

Presentation prepared March 2026. Correspondence:

eanbardsley@gmail.com

= h /(c ⋅ 1 s

)

= ϕ

cos(23.5

∘

)

ℏ

⊙

= (1 s)

K E

earth