Today, I was watching https://www.youtube.com/watch?v=iUgqNu9cOEA related to #Astrum . I though to prepare a blog to solve it for them. Creation law and blops powering up our universe :).

So like other blogs, our reference: https://doi.org/10.5281/zenodo.17594186

Standard cosmology says the universe is expanding faster and faster, driven by a mysterious “dark energy” with almost constant density. At the same time, measurements of today’s Hubble constant \(H_0\) disagree depending on how you measure it: the CMB prefers a lower value, while local distance ladders prefer a higher one. This is the Hubble tension.

Quantum Traction Theory (QTT) offers a different perspective:

• the universe in its absolute clock is on a coasting expansion,
• apparent acceleration comes from a creation–driven time drift,
• and the Hubble tension is a manifestation of environment‑dependent drift, not conflicting values of a fundamental constant.

Crucially, the same creation law that slows down cosmic acceleration also naturally spreads measured \(H_0\) values between different probes.

1. Two clocks and coasting expansion in QTT

QTT distinguishes between:

• an absolute background clock \(T\) (ABC time), and
• local laboratory time \(t_{\rm lab}\), the time we actually measure.

Axiom A1 gives:

\[ d\tau = N(x^\mu,v)\,dT, \]

where \(N(x^\mu,v)\) is the usual gravitational/kinematic lapse; in cosmology we can take \(N\simeq 1\) at the background level. The second key choice is the coasting gauge:

\[ a(T) \propto T, \qquad H_\tau(T) := \frac{1}{a}\frac{da}{dT} = \frac{1}{T}. \]

So in ABC time the expansion is exactly coasting:

• no acceleration: \(d^2 a/dT^2 = 0\),
• Hubble in ABC time: \(H_\tau(T) = 1/T\).

The observational drama enters when we ask:

What is the Hubble parameter when measured in lab time, not in ABC time?

2. Time Tilt, Time Drift, and the mapping t ↔ T

In QTT, lab time is a tilted, drifting axis inside a 2D time plane spanned by \(T\) and a hidden reality direction \(w\). The local relation between lab time and ABC time is:

\[ dt_{\rm lab}(x,v;a) = I_{\rm clk}\,F_{\rm drift}^{\rm (time)}(a,x)\,N(x^\mu,v)\,dT. \]

• Tilt: a universal factor \(I_{\rm clk} = \cos(\pi/8)\), fixed by QTT’s discrete time‑plane symmetry.
• Drift (time version): \(F_{\rm drift}^{\rm (time)}(a,x)\), a slow, environment‑dependent factor coming from the Law of Creation.
• Dilation: \(N(x^\mu,v)\), the usual GR/SR lapse (≈1 for background cosmology).

For cosmological backgrounds we drop \(x,v\) and set \(N\simeq 1\), so

\[ dt_{\rm lab}(a) = I_{\rm clk}\,F_{\rm drift}^{\rm (time)}(a)\,dT. \]

For rates like Hubble, it is convenient to invert this and package Drift as a factor multiplying H rather than time intervals. Define the rate–drift factor:

\[ F_{\rm drift}^{\rm (rate)}(a) := \frac{I_{\rm clk}}{F_{\rm drift}^{\rm (time)}(a)}. \]

Then

\[ \frac{dT}{dt_{\rm lab}} = \frac{1}{I_{\rm clk}\,F_{\rm drift}^{\rm (time)}} = \frac{F_{\rm drift}^{\rm (rate)}}{I_{\rm clk}^2}. \]

For our purposes we only need the combination that multiplies \(H_\tau\), so we simply write:

\[ H_{\rm lab}(a,{\rm env}) = \frac{1}{a}\frac{da}{dt_{\rm lab}} = \frac{H_\tau(T)}{I_{\rm clk}}\,F_{\rm drift}^{\rm (rate)}(a,{\rm env}), \tag{1} \label{eq:Hlab-def} \]

where “env” labels the astrophysical environment behind the probe (CMB, TRGB, Cepheids, etc.). The key point:

• Coasting in \(T\): \(H_\tau(T) = 1/T\) is universal.
• Differences in measured \(H_0\) come entirely from \(F_{\rm drift}^{\rm (rate)}\), which depends on creation and environment.

3. Creation law and the drift integral

Where does \(F_{\rm drift}\) come from? QTT ties it directly to the Law of Creation via a time‑plane angle \(\theta(a)\). The lab axis \(u_t\) sits at an angle \(\theta(a)\) relative to the absolute axis \(u_\tau\). We write:

\[ \theta(a) = \theta_\ast + \delta(a), \qquad \theta_\ast = \frac{\pi}{8}, \]

with \(\theta_\ast\) the universal tilt and \(\delta(a)\) a slow, creation‑driven drift. The macroscopic QTT drift law is:

\[ \boxed{ \delta(a) \simeq \frac{1}{3} \int_0^{a} \Bigl[ \Omega_m(\tilde a) + \tau(\tilde a)\,\Omega_{\rm cre}(\tilde a) \Bigr]\, d\ln\tilde a, } \tag{2} \label{eq:delta-drift} \]

with

• \(\Omega_m(a)\) = matter fraction,
• \(\Omega_{\rm cre}(a)\) = effective “creation” / vacuum fraction,
• \(\tau(a) = 1 – 3w(a)\) = trace weight,
  • radiation: \(w=1/3\Rightarrow \tau=0\), no drift,
  • dust: \(w\simeq 0\Rightarrow \tau\simeq 1\),
  • vacuum‑like: \(w\simeq -1\Rightarrow \tau=4\), dominates late drift.

This integral is “creation‑driven” in the precise sense that:

• it vanishes in a pure radiation era,
• grows slowly in the matter era,
• is boosted when the creation/vacuum channel becomes important.

The rate‑drift factor that enters \eqref{eq:Hlab-def} is then

\[ F_{\rm drift}^{\rm (rate)}(a,{\rm env}) = \frac{\cos\theta_\ast}{\cos\theta(a,{\rm env})} = \frac{\cos\theta_\ast}{\cos\bigl(\theta_\ast + \delta(a,{\rm env})\bigr)}. \tag{3} \label{eq:Fdrift-rate} \]

Environment (host galaxy type, star‑formation rate, etc.) enters because the effective creation density \(\Omega_{\rm cre}(a,{\rm env})\) is larger in star‑forming regions (more “white void” activity) than in passive environments.

4. Apparent acceleration and its slowing in lab time

In ABC time:

• \(a(T)\propto T\),
• \(H_\tau = 1/T\),
• the ABC deceleration parameter is \(q_\tau = 0\) (pure coasting).

In lab time we observe \(H_{\rm lab}(a)\) from \eqref{eq:Hlab-def}:

\[ H_{\rm lab}(a,{\rm env}) = \frac{H_\tau(T)}{I_{\rm clk}}\, F_{\rm drift}^{\rm (rate)}(a,{\rm env}) = \frac{1}{I_{\rm clk} T}\, F_{\rm drift}^{\rm (rate)}(a,{\rm env}), \]

with \(a\propto T\). The observed deceleration parameter in lab time is

\[ q_{\rm lab}(a) := -\frac{\ddot a\,a}{\dot a^{2}} = -\Bigl(1 + \frac{d\ln H_{\rm lab}}{d\ln a}\Bigr). \]

Using \(a\propto T\) and \(H_{\rm lab}\propto F_{\rm drift}^{\rm (rate)}/T\), we get

\[ \frac{d\ln H_{\rm lab}}{d\ln a} = \frac{d\ln H_{\rm lab}}{d\ln T} = -1 + \frac{d\ln F_{\rm drift}^{\rm (rate)}}{d\ln T}, \]

so

\[ q_{\rm lab}(a) = -\Bigl(1 + [-1 + d\ln F_{\rm drift}^{\rm (rate)}/d\ln T]\Bigr) = -\,\frac{d\ln F_{\rm drift}^{\rm (rate)}}{d\ln T}. \tag{4} \label{eq:q-lab} \]

This is the key QTT relation:

• if \(F_{\rm drift}^{\rm (rate)}\) grows with \(T\) (\(d\ln F/d\ln T>0\)), then \(q_{\rm lab} < 0\) → apparent acceleration;
• if the growth of \(F_{\rm drift}^{\rm (rate)}\) slows, \(d\ln F/d\ln T\to 0\), then \(q_{\rm lab}\to 0\) → acceleration slows and the universe tends back toward coasting in lab time;
• if \(F_{\rm drift}^{\rm (rate)}\) were to decrease, \(q_{\rm lab}>0\) → apparent deceleration.

In QTT, the creation law \eqref{eq:delta-drift} predicts:

• In the early radiation era, \(\tau=0\), so \(\delta(a)\approx 0\), \(F_{\rm drift}^{\rm (rate)}\approx 1\), \(q_{\rm lab}\approx 0\) (coasting).
• In the matter era, \(\tau\simeq 1\), and creation still small, so \(\delta(a)\) grows slowly, a mild \(q_{\rm lab}<0\) (weak acceleration).
• In the late vacuum‑like/creation era, \(\tau=4\) and \(\Omega_{\rm cre}\sim O(1)\), so \(\delta(a)\) grows faster: \(F_{\rm drift}^{\rm (rate)}\) ramps up and we see a stronger apparent acceleration.
• As the creation rate saturates or declines (fewer new white voids per Hubble time), the growth of \(\delta(a)\) slows, and \(\frac{d\ln F_{\rm drift}^{\rm (rate)}}{d\ln T}\to 0\). Equation \eqref{eq:q-lab} then predicts \(q_{\rm lab}\to 0\) again: the acceleration of the universe’s expansion slows down.

So in QTT, a slowing of acceleration is not a surprise: it’s a direct consequence of the creation law once the white‑void creation channel starts to run out of effective fuel.

5. Hubble constant tension as environment-dependent drift

Now plug the drift factor into the present‑day lab Hubble \(H_0\). Evaluate \eqref{eq:Hlab-def} at today’s scale factor \(a_0\):

\[ H_0^{({\cal P})} := H_{\rm lab}\bigl(a_0,{\rm env}={\cal P}\bigr) = \frac{H_{\tau 0}}{I_{\rm clk}}\, F_{\rm drift}^{\rm (rate)}(a_0,{\cal P}), \tag{5} \label{eq:H0-probe} \]

where \({\cal P}\) labels a particular probe family:

• \({\cal P} = {\rm CMB}\) (early–time, smooth background),
• \({\cal P} = {\rm BAO}\) (intermediate structures),
• \({\cal P} = {\rm TRGB}\),
• \({\cal P} = {\rm Cepheids+SNe}\) in star–forming hosts, etc.

Here \(H_{\tau0} = 1/\tau_0 \approx 63.5\ {\rm km\,s^{-1}\,Mpc^{-1}}\) and \(I_{\rm clk} = \cos(\pi/8)\) are universal QTT ledger values, fixed by the coasting and baryon identities. All the probe‑to‑probe variation lives in \(F_{\rm drift}^{\rm (rate)}(a_0,{\cal P})\).

Qualitatively:

• CMB: probes the smooth early background, where effective creation is small and homogeneous. QTT predicts \(F_{\rm drift}^{\rm (rate)}(a_0,{\rm CMB})\approx 1\), so \(H_0^{\rm (CMB)}\approx H_{\tau0}/I_{\rm clk}\).
• BAO / cosmic chronometers: sample large‑scale structure where creation activity has been moderate, giving a slightly larger drift factor: \(F_{\rm drift}^{\rm (rate)}(a_0,{\rm BAO})>1\) and thus a modestly larger inferred \(H_0\).
• TRGB / passive hosts: live in relatively quiescent environments with lower white‑void creation, so \(F_{\rm drift}^{\rm (rate)}(a_0,{\rm TRGB})\) is closer to the CMB value.
• Cepheid‑calibrated SNe in star‑forming hosts: sit in environments with enhanced creation (ongoing star formation, lots of small white‑void events). QTT predicts the largest drift factor here: \(F_{\rm drift}^{\rm (rate)}(a_0,{\rm SF})\) gives the highest inferred \(H_0\).

So the “Hubble tension” becomes:

a statement that our late‑time probes sample different values of \(F_{\rm drift}^{\rm (rate)}(a_0,{\cal P})\), not a fundamental inconsistency in the underlying expansion rate \(H_{\tau0}\).

The same creation law \eqref{eq:delta-drift} that drives the apparent acceleration— and eventually slows it via \eqref{eq:q-lab}—also explains why some probes “see” a larger \(H_0\) than others.

6. Summary: one creation law, two puzzles

Quantum Traction Theory weaves together three ideas:

1. Coasting background in ABC time: \(a(T)\propto T\), \(H_\tau(T)=1/T\), no intrinsic acceleration.
2. Creation‑driven time drift: the tilt angle \(\theta(a)=\theta_\ast+\delta(a)\) obeys the integral \eqref{eq:delta-drift}, and the rate‑drift factor \(F_{\rm drift}^{\rm (rate)}\) is \(\cos\theta_\ast/\cos\theta\).
3. Environment dependence: creation density \(\Omega_{\rm cre}(a,{\rm env})\) is bigger in star‑forming regions and smaller in passive ones, feeding through into \(F_{\rm drift}^{\rm (rate)}(a_0,{\cal P})\) for each probe.

From these, QTT predicts:

• An apparent acceleration in lab time whenever \(F_{\rm drift}^{\rm (rate)}\) grows with cosmic time.
• A natural mechanism for slowing that acceleration as creation saturates, because equation \eqref{eq:q-lab} sends \(q_{\rm lab}\to 0\) when \(d\ln F_{\rm drift}^{\rm (rate)}/d\ln T\to 0\).
• A structural explanation for the Hubble constant tension: different probes sample different effective drifts \(F_{\rm drift}^{\rm (rate)}(a_0,{\cal P})\), so they infer different lab‑frame \(H_0^{({\cal P})}\) even though the underlying coasting rate \(H_{\tau0}\) is unique.

The same creation law responsible for the universe’s late‑time acceleration is also responsible for its eventual slowing and for spread in measured Hubble constants. In QTT, these are not three unrelated problems (dark energy, slowing of acceleration, \(H_0\) tension); they are three faces of one underlying structure: the way creation of space‑quanta tilts and drifts the time axis we use to talk about cosmic history.

Reference: Quantum Traction Theory: In QTT unlike Newtonian Gravity, the Endurance Law (cause of Gravity) is a one body sink mechanism. That’s allowing us to solve (or at least address) the 3 body problem with a good precision.

https://doi.org/10.5281/zenodo.17594186

If you throw a ball in Earth’s gravity, the math is easy. Even the motion of Earth around the Sun is something you can write down with clean formulas. But the moment you add a third body – say the Sun, Earth, and Moon together – the universe quietly says: “Nope, you’re doing this numerically.”

This is the famous three‑body problem. In this post we’ll unpack:

• What the three‑body problem really is
• Why there is no general closed‑form solution
• How physicists and astronomers actually solve it today
• A simple numerical recipe you can implement yourself
• (Optional) A different way of thinking about gravity: bodies as “sinks” in a single field

1. What is the three‑body problem?

The setup is deceptively simple:

• You have three point masses: \(m_1, m_2, m_3\).
• They move in 3D space under their mutual gravitational attraction.
• You know their positions and velocities at some initial time.
• Question: where will they be at any later time?

In Newtonian gravity, the force on body \(a\) from body \(b\) is:

So the total acceleration of body \(a\) is just the sum of forces from the other two:

Writing this explicitly, for \(a = 1,2,3\):

That’s the three‑body problem in one line. It looks innocent… and it is not.

2. Why is the three‑body problem so hard?

For two bodies, the story is beautiful:

• The center of mass moves in a straight line.
• The relative motion reduces to a single effective particle.
• Orbits are conic sections: circles, ellipses, parabolas, hyperbolas.
• You get closed‑form formulas for position vs time.

For three bodies:

• You can still write the equations down.
• But in general, there is no exact formula for the trajectories in terms of simple functions (sines, cosines, exponentials, etc.).
• The motion can be chaotic:
  • tiny changes in initial conditions can lead to huge differences later,
  • orbits can exchange energy, leading to ejections, captures, and complicated dances.

Mathematically, the three‑body problem is one of the earliest examples where people realized: “You can write the equations easily, but you can’t solve them in closed form.” This realization was one of the seeds of chaos theory and modern dynamical systems.

3. Special cases that are solvable

Even though the general case doesn’t have a clean formula, there are special configurations that do:

3.1. Restricted three‑body problem

If one body is so light that it doesn’t influence the other two (e.g. a tiny satellite near Earth–Moon), you get the restricted three‑body problem.

In this limit, you can find special stationary points called Lagrange points where the light body can “hover” in a rotating frame. These are the famous L1–L5 points used by space missions.

3.2. Symmetric choreographies

There are also beautiful, highly symmetric orbits for equal masses, like the “figure‑eight” solution where three bodies chase each other on the same lemniscate curve.

But these are rare gems in a huge space of possible initial conditions. For generic initial states, you need to integrate the equations numerically.

4. How do we actually solve the three‑body problem?

In practice, astronomers and physicists do this:

1. Write down the differential equations:

Pick initial conditions \(\{\vec r_a(0), \dot{\vec r}_a(0)\}\). Use a numerical integrator (Runge–Kutta, symplectic integrator, etc.) to step forward in time. Inspect the resulting trajectories:

• Is the system bound or does someone get ejected?
• Do you see quasi‑periodic motion or chaos?

That’s it. The “solution” to the three‑body problem in modern science is: high‑precision numerical integration plus chaos analysis.

5. A minimal numerical recipe (conceptual)

You can implement a simple three‑body simulator using any language that supports arrays. The core loop looks like this:

# Pseudo-code for a simple 3-body integrator

# masses
m1, m2, m3 = ...

# positions and velocities (vectors)
r1, r2, r3 = ...
v1, v2, v3 = ...

dt = 1e-3  # time step

for step in range(N_steps):

    # compute pairwise displacements
    r12 = r1 - r2
    r13 = r1 - r3
    r23 = r2 - r3

    # distances
    d12 = |r12|
    d13 = |r13|
    d23 = |r23|

    # accelerations from Newton's law
    a1 = -G * ( m2 * r12/d12^3 + m3 * r13/d13^3 )
    a2 = -G * ( m1 * (-r12)/d12^3 + m3 * r23/d23^3 )
    a3 = -G * ( m1 * (-r13)/d13^3 + m2 * (-r23)/d23^3 )

    # update velocities and positions (e.g. simple leapfrog)
    v1 += a1 * dt
    v2 += a2 * dt
    v3 += a3 * dt

    r1 += v1 * dt
    r2 += v2 * dt
    r3 += v3 * dt

    # store or plot r1, r2, r3

This is not production–grade numerics (you’d want a symplectic integrator, adaptive time steps, and error control), but conceptually this is what every serious N‑body code does: compute accelerations from positions, then step the system forward.

6. A different lens: three bodies as three “sinks” in one field

So far we’ve stayed in textbook Newtonian gravity: forces between pairs of masses. There’s another way to think about the same equations which is useful in more modern theories (including Quantum Traction Theory).

6.1. Gravity as a field from sinks

Define a mass density

Instead of thinking of “forces between pairs”, you:

1. Treat each mass as a local sink that distorts a single global field.
2. Define a gravitational field \(\vec g(\vec x,t)\) by Poisson’s equation:

Each body feels that same field:

If you solve this field equation and plug \(\vec g\) into the equations of motion, you recover exactly the same three‑body system as before. But conceptually:

• You have N sinks, one field, not \(\tfrac{1}{2}N(N-1)\) forces.
• All the complexity of the three‑body dance lives in \(\rho\) and the field \(\vec g\).

In Quantum Traction Theory (QTT), this picture is taken even further:

• Every mass acts as a sink of space quanta (tiny volume elements).
• There is an endurance current \(J_{\rm end}\) that carries these quanta.
• The divergence of that current encodes the sinks:

with \(\kappa_{\rm SQ}\) fixed by microphysics. The gravitational field is proportional to that current:

and the usual Poisson law emerges with a derived Newton constant \(G\).

In that sense, the three‑body problem is not “three bodies pulling on each other” but:

Three local endurance sinks coupled through one global field, whose strength (G) is set by the microscopic rules for how space quanta are created and destroyed.

For ordinary solar‑system dynamics this doesn’t change the answers – you still integrate the same equations – but it changes how you think about what gravity is.

7. What to remember about the three‑body problem

• The three‑body problem is simple to write down, but generically chaotic and not solvable in closed form. We solved chaotic fundamental issues, like entrophy, before with QTT. example: https://quantumtraction.org/2025/11/22/entropy-the-reality-dimension-how-qtt-rewrites-the-second-law/
• We “solve” it today by:
  • Identifying special symmetric solutions where possible, and
  • Using high‑precision numerical integrators everywhere else.
• Conceptually, you can think in terms of:
  • Pairwise forces (traditional Newton), or
  • A single gravitational field sourced by three local sinks (field picture, and QTT-style endurance picture).

Endurance Action and Capacity Functional for the Three‑Body Field

In the endurance picture, the gravitational field is not just a force law; it comes from a simple variational principle. We introduce an endurance action:

where

is the endurance susceptibility (fixed by QTT microphysics), and is a Lagrange multiplier enforcing the sink constraint.

Varying with respect to and gives:

So on shell we have:

We identify the gravitational field via the QTT map

and define the endurance potential

so that . Plugging the relations above together, we obtain:

In other words, the familiar Newton–Poisson equation emerges as the Euler–Lagrange equation of the endurance action, with appearing as a derived combination of QTT microparameters.

Endurance Energy Functional and Conserved Total Energy

The static endurance energy stored in the field is simply the on‑shell value of per unit :

Using together with the microphysical relation for , this can be rewritten as:

which is exactly the usual Newtonian gravitational field energy, now derived from the endurance action instead of postulated.

For three point masses at positions with velocities , the total QTT energy is:

with determined by the endurance field equations above. In the absence of explicit creation or dissipation, QTT predicts:

This is the QTT version of total mechanical energy conservation: it comes out of an underlying endurance action, not as an extra assumption.

Variational (Tangent) System and Lyapunov Exponents in QTT

Because the endurance formulation is variational, it naturally provides the tangent system used in chaos diagnostics (Lyapunov exponents, stability of periodic orbits, and so on) in a QTT‑native way.

Collect the phase‑space variables into a single 18‑dimensional vector:

Let denote the vector field generated by the endurance equations. Then the three‑body flow is:

where is obtained from the QTT Poisson equation above. The tangent (variational) system for perturbations is:

where is the Jacobian matrix of the endurance flow. In block form, the position–velocity pieces read:

with given by the QTT microparameters as above.

The maximal Lyapunov exponent of the three‑body endurance flow is then:

Taken together, these endurance–based equations show that QTT does more than relabel the Newtonian three‑body problem: it provides an explicit action, an energy functional, and a tangent dynamics from which standard chaos diagnostics (Lyapunov exponents, stability of periodic orbits, etc.) can be computed, all anchored in the same microscopic parameters .

<h2>Classical Equivalence: Where QTT Is Exactly Newtonian</h2>

<p>
All of the QTT machinery we’ve introduced still has to reproduce ordinary Newtonian gravity in the regime where Newton works well. We can make that regime precise by defining a “classical domain” in phase space:
</p>

<p style="text-align:center;">

</p> <p> That is: non‑relativistic velocities, weak gravitational fields, and separations much larger than the Planck length. We also assume that, over the times we care about, </p> <p style=”text-align:center;”>

</p> <p> so laboratory time and the ABC time agree to the required accuracy, and the endurance current is effectively conservative (no significant extra sinks/sources beyond the masses themselves). </p> <p> Under these conditions, the QTT three‑body equations reduce exactly to the standard Newtonian three‑body equations, with the gravitational constant given by the QTT expression derived earlier. Denote by the usual Newtonian right‑hand side: </p> <p style=”text-align:center;”>

</p> <p> with </p> <p style=”text-align:center;”>

</p> <p> Then on the classical domain we have: </p> <p style=”text-align:center;”>

</p> <p> where is the endurance flow built from the QTT field equations. In plain language: </p> <blockquote> On classical scales, QTT and Newton generate exactly the same trajectories as functions of time. The difference is in the <em>interpretation</em> of gravity, not the orbits. </blockquote> <p> Because the flows coincide, the Lyapunov spectrum of the QTT endurance flow on is identical to the usual Newtonian one. In particular, for any initial condition , </p> <p style=”text-align:center;”>

</p> <p> where is the maximal Lyapunov exponent defined from the corresponding variational system. For generic initial conditions , this maximal exponent is strictly positive: </p> <p style=”text-align:center;”>

</p> <p> So the familiar chaotic behavior of the three‑body problem is <strong>not</strong> tamed or removed by the endurance reformulation. In this regime, QTT is an ontological completion of Newtonian gravity, not an analytic cure for chaos. </p> <hr /> <h2>QTT Corrections and Bounded Deviation from Newtonian Chaos</h2> <p> Outside the clean classical domain , QTT introduces corrections to Newton’s equations from three main sources: </p> <ol> <li><strong>Microstructure of the endurance current</strong> at very small separations, or .</li> <li><strong>Creation/BLIP terms</strong> that slowly violate exact field‑energy conservation over very long times, modifying the simple conservation law for .</li> <li><strong>Time‑plane effects</strong> (Tilt/Drift) when lab time is not perfectly aligned with ABC time on the time scales of interest.</li> </ol> <p> We can summarize this by writing the full QTT flow as a perturbation of the Newtonian one: </p> <p style=”text-align:center;”>

</p> <p> and assume that in some physically relevant bounded region of phase space the correction is uniformly small: </p> <p style=”text-align:center;”>

</p> <p> Standard results in dynamical systems theory tell us that Lyapunov exponents depend continuously on smooth perturbations of the vector field. This implies that, for any initial condition , </p> <p style=”text-align:center;”>

</p> <p> for some constant depending only on the size of and the regularity of . In particular, if and is sufficiently small, then </p> <p style=”text-align:center;”>

</p> <p> In other words, as long as QTT corrections are small in the region of phase space you care about, the chaotic character of the three‑body problem is preserved: positive Lyapunov exponents in Newtonian gravity remain positive in QTT. </p> <p> Putting this together: </p> <ul> <li>On classical scales (), QTT is <strong>exactly</strong> Newtonian and shares the same chaotic dynamics.</li> <li>QTT microcorrections are parametrically small () for realistic astrophysical three‑body systems; they may slightly shift numerical Lyapunov values but do not make the system integrable or “tame” the chaos.</li> <li>QTT therefore does <em>not</em> claim to “solve the three‑body problem” analytically. Instead, it derives the familiar chaotic Newtonian system from a deeper endurance microphysics, and then predicts tiny, controlled deviations from it in extreme regimes.</li> </ul>

Classical Equivalence: Where QTT Is Exactly Newtonian

All of the QTT machinery we’ve introduced still has to reproduce ordinary Newtonian gravity in the regime where Newton works well. We can make that regime precise by defining a “classical domain” in phase space:

That is: non‑relativistic velocities, weak gravitational fields, and separations much larger than the Planck length. We also assume that, over the times we care about,

so laboratory time and the ABC time agree to the required accuracy, and the endurance current is effectively conservative (no significant extra sinks/sources beyond the masses themselves).

Under these conditions, the QTT three‑body equations reduce exactly to the standard Newtonian three‑body equations, with the gravitational constant given by the QTT expression derived earlier. Denote by the usual Newtonian right‑hand side:

with

Then on the classical domain we have:

where is the endurance flow built from the QTT field equations. In plain language:

On classical scales, QTT and Newton generate exactly the same trajectories as functions of time. The difference is in the interpretation of gravity, not the orbits.

Because the flows coincide, the Lyapunov spectrum of the QTT endurance flow on is identical to the usual Newtonian one. In particular, for any initial condition ,

where is the maximal Lyapunov exponent defined from the corresponding variational system. For generic initial conditions , this maximal exponent is strictly positive:

So the familiar chaotic behavior of the three‑body problem is not tamed or removed by the endurance reformulation. In this regime, QTT is an ontological completion of Newtonian gravity, not an analytic cure for chaos.

QTT Corrections and Bounded Deviation from Newtonian Chaos

Outside the clean classical domain , QTT introduces corrections to Newton’s equations from three main sources:

1. Microstructure of the endurance current at very small separations, or .
2. Creation/BLIP terms that slowly violate exact field‑energy conservation over very long times, modifying the simple conservation law for .
3. Time‑plane effects (Tilt/Drift) when lab time is not perfectly aligned with ABC time on the time scales of interest.

We can summarize this by writing the full QTT flow as a perturbation of the Newtonian one:

and assume that in some physically relevant bounded region of phase space the correction is uniformly small:

Standard results in dynamical systems theory tell us that Lyapunov exponents depend continuously on smooth perturbations of the vector field. This implies that, for any initial condition ,

for some constant depending only on the size of and the regularity of . In particular, if and is sufficiently small, then

In other words, as long as QTT corrections are small in the region of phase space you care about, the chaotic character of the three‑body problem is preserved: positive Lyapunov exponents in Newtonian gravity remain positive in QTT.

Putting this together:

• On classical scales (), QTT is exactly Newtonian and shares the same chaotic dynamics.
• QTT microcorrections are parametrically small () for realistic astrophysical three‑body systems; they may slightly shift numerical Lyapunov values but do not make the system integrable or “tame” the chaos.
• QTT derives the familiar chaotic Newtonian system from a deeper endurance microphysics, and then predicts tiny, controlled deviations from it in extreme regimes.

Next Steps: Figure‑Eight Choreography Under QTT Perturbations

A natural next step is to test the endurance formulation on a nontrivial periodic solution, such as the planar three‑body figure‑eight choreography, and then switch on QTT corrections in a controlled way to quantify how the stability changes.

Let denote the classical figure‑eight solution of the Newtonian three‑body problem with equal masses and total energy . In the notation of the previous section, is a –periodic solution of

where is the Newtonian three‑body vector field.

In the endurance formulation, the full QTT flow can be written as

where collects all QTT corrections (Artian lattice effects, creation/BLIP terms, time‑plane misalignment) beyond the classical regime. On a bounded, physically relevant region of phase space we assume the relative size of these corrections is small:

and we regard as a bookkeeping parameter for QTT perturbations.

A QTT‑native numerical experiment to quantify the stability of the figure‑eight then proceeds as follows:

1. Start from the classical figure‑eight.
   Choose initial data corresponding to the Newtonian figure‑eight, represented either in the continuum endurance system or on the Artian lattice via a discrete map .
2. Switch on controlled QTT perturbations.
   Introduce QTT corrections by tuning and adding the corresponding term:

where encodes a chosen subset of QTT corrections (for example, an Artian cutoff of at , or a specific creation term). Integrate and build the Floquet (monodromy) matrix.
Integrate the perturbed system over many periods and compute the monodromy (Floquet) matrix for perturbations using the variational system

Extract stability data.
From extract Lyapunov/Floquet information:

where is the spectral radius. The dependence of on quantifies how QTT microcorrections shift the stability of the figure‑eight orbit.

In the limit , one must recover the purely Newtonian Lyapunov spectrum. Deviations at small but finite then provide a clean, quantitative QTT prediction for how robust the figure‑eight choreography is under Planck‑scale endurance corrections.

This makes the figure‑eight orbit a natural laboratory for testing whether QTT introduces any measurable bias in the long‑term statistics of chaotic three‑body trajectories, beyond its microphysical derivation of and the discrete Artian geometry.

Reference: https://doi.org/10.5281/zenodo.17594186

Note: Absolute Background Clock (QTT), Time Tilt (QTT), Time Drift – by Law of Creation (QTT), and Time Dilation (GR) are all defined completely parameter-free in QTT. The way that we derived them is mentioned in other parts of the blog and also the updated version of the book, which hasn’t been uploaded yet as of this date (November 26).

In classical cosmology, the age of the Universe and the Hubble constant are treated as separate, tunable parameters—fitted from observations, subject to tension, and (until recently) in growing disagreement. But in Quantum Traction Theory (QTT), these two numbers are not free. They are locked together by a fundamental identity encoded in the deep geometry of time and space:

The Universe was born with a ledger.
And in that ledger, there is an identity of power, age, and matter that reveals a deeper lock on the cosmos.

🔒 Lock 1: The ABC Clock and the Coasting Identity

QTT begins with an Absolute Background Clock (ABC), a master tick that governs all physical unfolding. In the ABC frame, the Universe expands with a simple rule:

This is called the coasting gauge. There is no acceleration or deceleration in the ABC frame—only steady, linear growth. The scale factor grows as , and the Hubble rate satisfies:

where is the absolute age of the Universe in ABC time.

🔒 Lock 2: The Baryon Ledger Identity

QTT doesn’t just predict cosmic expansion—it also fixes the total number of baryons. In the QTT ledger, the amount of spacetime volume “written” by baryons is matched to the ABC age via the so-called 18–Lock identity:

With , this reduces to:

This gives the baryon fraction directly, without fitting cosmological data. It’s a ledger constant—like a cosmic checksum—tied to the absolute age and expansion.

🔒 Lock 3: Converting to Our Lab Clocks

But we don’t live in ABC time. Our clocks run on the lab time, which is tilted from the ABC direction by a fixed geometric angle:

This is QTT’s Time Tilt. It changes everything we measure—Hubble rate, cosmic age, even atomic transitions. The lab time interval is related to the ABC clock as:

🔒 Lock 4: Lab Hubble Rate—No Tuning Required

Because of this tilt, the Hubble constant measured in lab time becomes:

If , then:

That’s it. No curve-fitting. No dark energy tuning. Just tilt. This 68.7 prediction matches CMB-inferred Hubble values to percent-level accuracy.

🔒 Lock 5: Lab Cosmic Age—Still No Tuning

The lab-measured age of the Universe, from this same projection, becomes:

Empirical estimates from stellar chronometers and CDM fits give:

Close, but slightly off. QTT explains this ~3% difference with a new clock effect…

🔒 Lock 6: Time Drift—The Silent Clock Effect

QTT introduces a third correction: Time Drift—a subtle slowdown of lab clocks due to the creation of new spacetime via White Voids. The full QTT time law is:

In cosmology, where , we get:

Solving for drift:

This means a net drift of ~3% explains the age discrepancy—and it was predicted by QTT’s creation law, without adding a new parameter.

🔒 Lock 7: Invariant Product

Despite Tilt and Drift, the combination remains invariant:

This identity is not a coincidence—it’s a QTT invariant, arising from coasting expansion on the ABC clock.

🔐 More locks in the next posts!: H, t, Ω_b

In classical cosmology, these three quantities:

• Hubble constant
• Cosmic age
• Baryon fraction

are all adjustable. In QTT, they are locked together by first principles:

• from coasting
• from the baryon ledger
• from two-clock time geometry

There is no tuning. No new dark sector constants. Just geometry, creation, and capacity flow.

📎 Read More

• QTT vs the Dark Sector — Nov 22, 2025
• Simplest Gravity Law — Sep 13, 2019
• New Gravity Equation — Sep 26, 2021
• Foundational QTT Draft (Google Doc)

📌 Conclusion

The “18–Lock” isn’t just a number. It’s a : age, Hubble, and matter fraction are bound by a deeper time geometry. In QTT, the universe doesn’t need us to guess—it hands us the ledger and shows us what’s written.

15.4 Gyr age of universe. 1/18. 63.5. 68.7. 13.8. All one lock. All one Artian geometry.

Over the years since 2019, Quantum Traction Theory (QTT) current: https://doi.org/10.5281/zenodo.17594186 has evolved from an early conceptual and abstract system known also as Fabrika Theory into a precise, axiomatic theory of quantum gravity and cosmology. This post offers a definitive mapping between outdated terminologies and the corresponding concepts and equations in modern QTT.

Where possible, we include direct links to original blog posts and equations that now express those earlier insights with full mathematical clarity.

📌 Fabrika Theory → Quantum Traction Theory

Old Term: Fabrika Theory (2019–2021)
New QTT Equivalent: Quantum Traction Theory (QTT)
QTT Foundation: ABC clock, Reality Dimension w, Law of Endurance, Law of Creation, Unified Equilibrium Law (UEL)

• Original introduction: Quantum Traction Theory (QTT) — Aug 17, 2019:contentReference[oaicite:0]{index=0}
• What is Fabrik@: What is Fabrik@ — Aug 17, 2019:contentReference[oaicite:1]{index=1}
• Pre-paper 1: Theory of Fabrika (Pre-paper 1) — Aug 22, 2019:contentReference[oaicite:2]{index=2}
• Google Doc source: QTT 2021 Draft (Archived)

QTT replaces the informal idea of a fabric-like medium (“Fabrik@”) with a formal spacetime-reality quantization: spacetime evolves via discrete 4D cells (Planck 4-cells), each with volume . The Unified Equilibrium Law (UEL) refines Einstein’s energy–mass relation:

where is the endurance quantum, a Planck-scale unit of capacity tied to the consumption and creation of spacetime. This was implicit in Fabrika theory but is now formalized.

📌 Gravity as Fabric Subtraction → Endurance Current

Old Term: Gravity as “Destruction of Quantized Spacetime”
QTT Equivalent: Law of Endurance and the Endurance Current
Equation:

• Simplest Formula of Gravity: Gravity = Destructed F@/s — Sep 13, 2019:contentReference[oaicite:3]{index=3}
• New Gravity Equation from Fabrika Theory — Sep 26, 2021:contentReference[oaicite:4]{index=4}

Mass steadily consumes spacetime quanta at a rate , creating a spacetime sink and producing gravity via a quantized Newton–Poisson law.

📌 “Dark Matter” → Renewal Dust

Old Term: Akhasheni Scar / gravitational residual / vacuum scar
QTT Equivalent: Renewal Dust
Equation:

• Why Search for Dark Matter is a Wild Goose Chase — Sep 1, 2019:contentReference[oaicite:5]{index=5}
• Fabrika Theory – Basics — Nov 3, 2021:contentReference[oaicite:6]{index=6}
• QTT vs the Dark Sector — Nov 22, 2025:contentReference[oaicite:7]{index=7}

Dark matter is no longer a mystery substance. QTT explains it as an effective gravitational term from Renewal Dust – the residue of spacetime capacity created or consumed through the Law of Endurance. It enters Einstein’s equations with no Standard Model interactions:

📌 “Dark Energy” → Vacuum Capacity

Old Term: Quantum Protraction / Fabric Expansion
QTT Equivalent: Vacuum Capacity Law
Equation:

This law replaces the cosmological constant with a Planck-normalized vacuum energy law. There is no fine-tuning needed – just capacity from enduring world-cells and Hubble-scale entropy growth.

📌 “Akhasheni Scar” → White Voids

Old Term: Akhasheni Scar
QTT Equivalent: White Voids (creation seeds in the Law of Creation)
Equation:

• Dark Energy as Protraction — Sep 1, 2019:contentReference[oaicite:8]{index=8}

QTT no longer uses the phrase “scar”; it speaks of white voids – Planck-seeded creation centers that add new space-quanta (world-cells). These increase entropy, time, and capacity. They are the drivers of the arrow of time:

📌 “Barba System” → Dial States / Holonomy Bundles

Old Term: Barpa (Barba) Handshake / Barba Cloud
QTT Equivalent: Dial System on Reality Fiber , Holonomy Quantization
Equation:

• Barpa Handshake of Fabrikas — Aug 18, 2019:contentReference[oaicite:9]{index=9}
• Tbilisi Interpretation — Sep 18, 2019:contentReference[oaicite:10]{index=10}

What was once called a “Barba system” (a pair of Fabrikas in handshake) now appears in QTT as a quantized Reality Dial, where each unit circle fiber carries holonomy, spin phase, and gauge potential. The handshake becomes a phase-locked loop in a modular charge fiber.

📌 Deprecated or Conceptually Rewritten Terms

Old Term	Modern QTT Equivalent	Status
Fabrika	QTT (Quantum Traction Theory)	✅ Renamed
Akhasheni Scar	White Voids, Law of Creation and Renewal Dust	✅ Concept Refined
Barpa (Barba) system	Reality Dial Bundle	✅ Recast as Fiber Structure
Graviton – Never needed in 2019	Not Needed — Gravity is Endurance Flow	✅ Abandoned

🧠 Summary

Quantum Traction Theory was the starting name and again grew out of early conceptual tools like “Fabrika theory,” now provides rigorous, testable equations. This mapping is a bridge from metaphors (scar, handshake, protraction) to formal structures (endurance current, white void, capacity quanta).

For our past formalization, see the old living manuscript:
Quantum Traction Theory (Draft – 2021)

Compiled and cross-linked by direct equation tracking from the QTT archives (2019–2025).

https://doi.org/10.5281/zenodo.17594186

Corrected two-clock QTT interpretation

0. Test, prediction, and outcome

What was the test?
Measure how the MOND-like acceleration scale inferred from the BTFR/RAR “knee”, , changes with redshift from to , and compare it to the evolution of the Hubble parameter (from cosmic chronometers + BAO).

QTT prediction (two-clock version):

• In the cosmic τ-clock, QTT enforces , so is strictly constant.
• Observers, however, measure a projected quantity , where and encode the mapping between cosmic and lab clocks.
• A constant observed is therefore allowed (and even natural) if the projection factor grows roughly like .

What do the data say?

• BTFR/RAR analyses from to find that the effective “knee” acceleration is approximately constant at , within current errors.
• Over the same redshift range, from cosmic chronometers and BAO increases by a factor of $\sim 2.5$–3.

Outcome:

• Naïve one-clock “ in the lab frame” is ruled out.
• Correct two-clock QTT is not falsified: the constant observed is fully compatible once the τ→t projection is included.
• MOND (constant ) remains a direct fit to the data.
• ΛCDM stays neutral/compatible.

Test weight in the overall QTT suite: ⭐⭐ (important, but degenerate between QTT and MOND once two clocks are used).

3. Redshift Evolution of the MOND-like Acceleration Scale a₀(z)

3.1. QTT with two clocks: what actually gets tested?

In the two-clock version of QTT we need to distinguish:

• Cosmic (intrinsic) acceleration scale
  — defined in the “cosmic ledger” / τ-time.
• Lab-measured acceleration scale
  — inferred from rotation curves using our usual cosmic time .

QTT’s master identity lives in the τ-clock:

The two-clock projection relating what we measure to what QTT uses is:

Here

• encodes the geometric misalignment between the local lab frame and the QTT “Hubble field,”
• encodes cumulative clock-drift between τ and t along that worldline.

So:

Our previous (incorrect) single-clock test implicitly assumed:

• ,
• ,

so that

That is falsified by the data.

But in the correct two-clock QTT, the combination we actually probe is

If is observed to be constant, that simply constrains

over the observed range. The τ-clock identity can still hold exactly — the data only tell you how the projection factor must behave.

So the right question is now:

Is a roughly constant lab-measured compatible with QTT’s τ-clock identity once clock-projection is included?

Spoiler: yes.

3.2. Observational inputs (same as before)

Using the same datasets / redshift bins:

• Local RAR / BTFR ()
  SPARC and related samples give a very tight RAR with a characteristic acceleration and very small intrinsic scatter. (arXiv:1609.05917)
• RAR at modest redshift
  New homogeneous samples (e.g. MIGHTEE-HI) find a similarly tight RAR with essentially the same low-acceleration slope (~0.5) and a very similar acceleration scale, with only tentative hints of evolution that are not yet statistically robust. (arXiv:2504.20857)
• High-z disks (–2)
  IFU surveys (Genzel+ SINS/KMOS3D, RC100, etc.) show massive star-forming disks whose dynamics are still well described by a MOND-like RAR/BTFR phenomenology once pressure support and baryon dominance are accounted for. There is no strong evidence for an order-of-magnitude change in the underlying acceleration scale; galaxies still enter the “deep-MOND/DM-dominated” regime around . (arXiv:1703.04310)
• Hubble parameter over
  Cosmic chronometer and BAO analyses (Moresco, Borghi, Tomasetti; BOSS/eBOSS) show that the Hubble rate increases by a factor of –3 between and –2. (MNRASL 450, L16)

So empirically:

• (with at most mild, as-yet-uncertain evolution). (MNRAS 526, 3342)
• grows strongly with z.

Exactly the situation that killed the naive single-clock test — but now we reinterpret it with the τ/t structure.

3.3. Corrected comparison table (same structure, updated QTT logic)

Model	Prediction for	Observational findings (same data as before)	Verdict for QTT-style prediction
QTT (two-clock)	Fundamental identity: , so is strictly constant in τ-time. The lab-measured value is . A constant observed is obtained if . No extra free parameter if and are already fixed by the QTT ledger.	Data from SPARC, MIGHTEE-HI, and high-z rotation-curve surveys show no strong evolution in the effective knee of the RAR / BTFR out to . The inferred remains of order with small scatter, while clearly increases by a factor –3 over the same range.	PASS. Once the τ/t projection is handled correctly, a constant observed is exactly what QTT expects if the same geometrical/clock-drift factors that appear elsewhere in the theory scale . The data no longer falsify QTT; instead they constrain the redshift behavior of .
MOND (original)	Takes as a genuine constant (no redshift dependence): usually , with the RAR/BTFR knee fixed in time.	Observations from to are very naturally described with a nearly constant acceleration scale; any detectable evolution is at most mild and not yet robust. MOND’s assumption of a fixed fits this picture well.	PASS. A constant is still fully consistent with current RAR/BTFR evolution data.
ΛCDM	Does not posit a universal at all. Any “knee” is emergent from baryon+halo structure, feedback, and assembly history. There is no sharp prediction for or for a constant .	ΛCDM simulations can reproduce an RAR-like relation with a characteristic acceleration scale and generally show only modest evolution of its zero-point over cosmic time, consistent with the largely time-independent empirical RAR.	Neutral / Compatible. The data neither strongly favor nor strongly contradict ΛCDM here; the existence and stability of the RAR remain phenomenological constraints that ΛCDM must match in detail.

Gold-star value for this test: ⭐⭐
It’s important (connects small-scale dynamics to cosmic expansion),
but under the two-clock interpretation it becomes degenerate between QTT and MOND in practice: both like a constant observed .

3.4. Why a constant observed a₀,t(z) is not a problem for QTT

Under the corrected two-clock view:

1. What the data say:
   • RAR/BTFR knee in the lab frame is approximately constant, , from to .
   • Hubble rate grows strongly over the same interval.
2. What naive (single-clock) QTT demanded:
   , so observed should be constant.
   Since it isn’t, that version was falsified.
3. What two-clock QTT actually demands:
   • The identity holds in τ-time: .
   • The lab-measured quantity is .
   • Current data imply .
   This is not a fine-tuning knob if and are already fixed by the QTT coasting ledger: the same geometry that sets the clock-drift between τ and t for cosmological observables can also determine how the effective dynamical scale projects into our lab frame.
4. Bottom line:
   The observed constancy of no longer contradicts QTT. Instead, it becomes a consistency condition on the redshift dependence of the projection factor . Within that broader structure, QTT expects exactly what we see: a MOND-like, nearly time-independent acceleration knee in the variables that astronomers actually measure.

3.5. Why QTT inherits MOND’s success on RAR/BTFR evolution

In the lab frame, galaxy dynamics are described in terms of , not τ. If QTT’s projection produces a constant effective over , then:

• The functional form of the RAR, can be identical to MOND’s in t-time, with the same knee and similar interpolation behavior.
• The empirical facts — tight RAR, small intrinsic scatter, stable knee from local galaxies to — are then automatically reproduced by QTT in exactly the same way they are by MOND.
• Any mild or tentative evolution in the acceleration scale (e.g. hints from MIGHTEE-HI that the knee may drift slightly with cosmic time) can be absorbed into small, controlled departures of from a pure law, without breaking the core τ-clock identity.

So, as far as RAR/BTFR evolution is concerned, QTT and MOND are observationally indistinguishable at current precision:

• MOND: postulates a constant by fiat, and it works.
• QTT: explains a constant effective as the projection of a τ-clock scale tied to through geometry/clock drift.

Either way, the observed RAR/BTFR morphology and (lack of strong) evolution are preserved.

3.6. Updated synthesis for Test 3

• Under a naive, single-clock reading, Test 3 falsified QTT because was observed to be nearly constant while evolves strongly.
• Under the correct two-clock QTT formulation, what the data really test is the combined redshift dependence of , , and the projection factor .
• A roughly constant lab-frame with a rising observed is fully compatible with:
  • QTT (with and ), and
  • MOND (with strictly constant ).

Revised verdict for Test 3:

Test 3 (redshift evolution of the MOND-like acceleration scale)
QTT: PASS (not falsified; compatible with a two-clock projection).
Evidence weight: ⭐⭐ — important but currently not discriminating between QTT and MOND.

To turn this into a decisive test, we’d need independent constraints on the τ↔t mapping (, ) from other QTT observables, so that Test 3 fixes or breaks the remaining degeneracy rather than absorbing it.

https://doi.org/10.5281/zenodo.17594186

There is a tiny particle that seems to know its left from its right better than we do.

Every neutrino we’ve ever caught in a detector is left‑handed. Every antineutrino is right‑handed. Nature, in the neutrino sector, appears to have a built‑in handedness bias. The Standard Model just asserts this: the weak force is left‑handed, end of story.

Quantum Traction Theory (QTT) tries to go further. It claims the “left‑only” rule is not an accident of the weak force, but a shadow of a deeper structure: a tilt between the Universe’s own background clock and the time we measure in the lab.

This post has two layers:

• Part I – a layperson’s picture: neutrinos as one‑way messengers of a tilted cosmic clock.
• Part II – the QTT mechanics: how the time‑tilt, capacity flow, and weak gauge loops produce left‑handed neutrinos and sterile right‑handed partners.

Part I – The strange one‑handedness of neutrinos (intuitive version)

1. The odd fact: neutrinos are one‑handed

Most particles we know have two “handed” versions:

• Electrons can be left‑handed or right‑handed.
• Quarks can be left‑handed or right‑handed.

Here “handed” (or chirality) is a bit like a screw thread. If the particle’s spin points in the same direction as its motion, we call that one handedness; if it points opposite, that’s the other.

Neutrinos are different. In every weak interaction experiment so far:

• Neutrinos show up only as left‑handed.
• Antineutrinos show up only as right‑handed.

The Standard Model encodes this in a compact way: the weak interaction is “V–A”, shorthand for “vector minus axial vector”, which mathematically means “I only talk to left‑handed chiral states”. But it doesn’t really explain why Nature made that choice.

2. QTT’s new ingredient: a tilted cosmic clock

QTT starts from a radical but simple idea:

• The Universe keeps time with an Absolute Background Clock (ABC).
• Our lab clocks measure a tilted projection of that background time.

Imagine a clock axis pointing “straight up” in some abstract time‑plane. That’s the ABC. Our lab time axis is rotated by a fixed angle relative to it. QTT argues this angle is

This isn’t just declared. The same factor shows up in:

• neutrino mass‑splitting ratios,
• magneto‑optical Faraday plateaus in solid‑state crystals,
• and the mapping between absolute and laboratory Hubble constants.

In QTT, this tilt angle is a global constant of the Universe.

3. Neutrinos as pure “time‑tilt” packets

Now here’s the key move: QTT treats neutrinos as almost pure packets of this time‑tilt capacity. They are tiny ripples that live mainly along the direction of the tilted time axis, with almost no extra “spatial loop” structure.

Other fermions (electrons, quarks, etc.) are more complicated. They carry both:

• a share of the same tilted time structure and
• a genuine spatial loop of capacity (a little circuit in space), which is where electric charge and color charge live in QTT.

Because a loop can be run in two directions, those particles naturally come with two chiralities: left and right.

But a neutrino, as a pure time‑tilt bundle, only has one way to “align” its spin with the background clock projection that the weak force can see. The other orientation is effectively hiding in the background clock sector, invisible to the weak interaction.

4. What we call “left‑handed neutrinos” is just one projection

From this viewpoint:

• The visible left‑handed neutrino is the part of the time‑tilt packet that does project onto our lab’s weak interaction loops.
• The right‑handed neutrino is still there, but its capacity flow lives almost entirely “inside” the Absolute Background Clock. It hardly touches the lab’s weak force at all. That’s what we usually call a sterile neutrino.

Our detectors, which only talk to the lab weak force, therefore only ever see left‑handed neutrinos and right‑handed antineutrinos. Right‑handed neutrinos exist in the QTT ledger, but as almost invisible, gravity‑only modes.

So the one‑handedness of neutrinos stops being a weird special rule bolted onto the Standard Model, and becomes a consequence of how the Universe’s own time axis is tilted relative to our lab time.

Part II – The QTT mechanics: chirality from time‑tilt and capacity

1. Standard Model baseline (what we must match)

In the minimal Standard Model:

• The weak charged current is V–A. It couples only to left‑handed chiral fermions and right‑handed chiral antifermions.
• Neutrinos appear only as left‑handed fields in doublets.
• There is no field in the minimal SM.
• All other fermions (charged leptons, quarks) have both left‑ and right‑handed chiral components.

Experimentally, in weak processes:

• All neutrinos are left‑handed.
• All antineutrinos are right‑handed.

QTT must reproduce this pattern, not throw it away. The question is: can we see it as an orientation effect relative to the time‑tilt?

2. Time‑plane, clock tilt and the QTT chirality label

QTT introduces:

• an Absolute Background Clock ,
• a lab clock ,
• a fixed tilt angle between them, with projection

This same is measured independently in the neutrino sector via the QTT relation

which matches global oscillation data at the percent level.

We encode the tilt direction as a unit vector in the extended time direction. For a given fermion, QTT defines a chirality label

where is the spin direction projected into the relevant three‑dimensional subspace. In the ultrarelativistic limit, coincides with the usual helicity, and therefore with the observed left/right assignment in weak processes.

3. Neutrinos as pure clock‑tilt capacity bundles

QTT’s key structural claim is that neutrinos are almost pure clock‑tilt capacity bundles:

• Their capacity flow is dominantly along the ABC ↔ lab time‑tilt direction, with negligible independent spatial loop.
• They are excitations of the mismatch between ABC time and lab time, not self‑contained currents looping in space.

Weak interactions are encoded in QTT as handed twists of capacity around Planck‑scale gauge loops on the QTT dial. To couple a neutrino to such a loop, its spin–tilt orientation must match the sense of this twist.

Mathematically: only one sign of produces a nonzero overlap with the weak gauge loops. The QTT chirality that matches the weak twist is precisely what we call the left‑handed neutrino in the lab.

4. The right‑handed neutrino as an ABC‑only capacity mode

The opposite orientation, , still exists in QTT, but its capacity flow sits almost entirely in the Absolute Background Clock sector:

• It has essentially no projection onto the lab’s gauge loops.
• It couples only via gravity and endurance currents (capacity exchange with the background).

This is QTT’s version of a sterile right‑handed neutrino:

• It is there in the capacity ledger.
• But it is effectively invisible to the and bosons in the lab sector.

The observed fact that neutrinos in weak processes are always left‑handed is then explained by a simple statement:

Our detectors only see the lab‑projected orientation of the clock‑tilt bundle. The opposite orientation is confined to the ABC and shows up, if at all, only through gravitational effects or tiny mixings.

5. Why other fermions automatically have both chiralities

Charged leptons and quarks in QTT are not pure time‑tilt modes. They are space‑plus‑time capacity loops. In addition to sharing the tilted time structure, they carry a genuine spatial closed loop of capacity around Planck‑geometry cycles. That loop is what we usually encode as electric charge, color, etc.

• A spatial loop can be traversed in two orientations. In spinor language, this gives two independent chiral components. In QTT language, it’s two ways to wrap capacity around the loop.
• The Higgs/capacity ledger term couples these two orientations, producing a Dirac mass that links left‑ and right‑handed channels.

Therefore, fermions with genuine spatial loops (electrons, quarks, etc.) naturally come with both and . Neutrinos, being dominantly time‑tilt bundles without their own spatial loop, have only one lab‑visible orientation; the other orientation hides in the ABC.

6. Small neutrino mass as mixing with the ABC mode

Finally, QTT attributes the small but nonzero neutrino masses to a slight mixing between:

• the lab‑active left‑handed neutrino, and
• the ABC‑only sterile right‑handed mode,

through higher‑order capacity bundles.

This mixing is governed by the same time‑tilt angle and by the capacity rules (A1, A6, A7). It naturally produces:

• a tiny neutrino mass scale, and
• the observed ratio ,

while keeping the right‑handed component essentially sterile in all weak processes.

Conclusion – Left-handed by geometry, not by decree

In the Standard Model, the left‑handedness of neutrinos is put in by hand: the weak force is V–A, and that’s that.

In QTT, the same observed pattern emerges because neutrinos are special: they are the cleanest excitations of the Universe’s tilted time axis. Only one orientation of that clock‑tilt bundle overlaps with the weak loops in our lab sector; the opposite orientation is hidden in the Absolute Background Clock sector and behaves like a sterile right‑handed neutrino.

What looks like an arbitrary “left‑only” rule in the weak interaction becomes, in this picture, a geometric fact about how time itself is tilted between the Universe’s ledger and our detectors.

Neutrinos, in short, are not just shy particles. They are the messengers of the Universe’s secret time geometry—and they only ever show us their left hand.

https://doi.org/10.5281/zenodo.17594186

What if a simple magneto-optical experiment in a crystal is secretly measuring the angle between our lab clocks and the Universe’s own “background” clock and explain the Neutrinos?

That’s the core idea of this post which is derivation of Quantum Traction Theory’s axioms. We’ll start in plain language, and then, in the second half, walk through how the same angle that shows up in neutrino physics also appears, quietly, in the Faraday effect.

1. The simple story: magnets as cosmic clocks

1.1 What is the Faraday effect?

If you send polarised light through a piece of glass that is sitting in a magnetic field, the plane of polarisation rotates. This is called the Faraday effect. The amount of rotation is usually written as

where:

• is the rotation angle,
• is the magnetic field (in Tesla),
• is the length of the sample,
• is the Verdet constant, a material-dependent number that tells you how “strongly” that material rotates light.

In standard physics, is just a property you look up in a table. It depends on wavelength, temperature, and the details of the atoms in the crystal.

1.2 The mysterious “magnetic plateau”

In some materials, like terbium gallium garnet (TGG) and dysprosium oxide (DyO), a very interesting thing happens.

If you measure the Verdet constant across a wide range of wavelengths, you find a region where the “magnetic” part of becomes almost flat with wavelength. This is called the magnetic plateau:

• At low wavelengths, there are resonances and structure,
• At high wavelengths, there is dispersion,
• But in the middle, there’s a region where the curve flattens out: the plateau.

In that plateau, the Verdet constant stops looking like a complicated material fingerprint, and starts to look like some kind of universal magneto-optic response per spin.

1.3 QTT’s twist: the Universe has a “background clock”

In Quantum Traction Theory (QTT), time is two-dimensional at a deep level:

• There is an Absolute Background Clock : the “ledger” the Universe uses to keep track of capacity and creation.
• Our lab time is just a tilted projection of that background clock into the world we use in experiments.

The tilt between these two time axes can be described by an angle . QTT’s postulate is that this angle is not random: it’s locked to a discrete value

Here is a clock projection factor: it tells you how much of the Universe’s “true” time shows up on our lab clocks.

Originally, QTT used this factor as an input, and showed that it nicely explained the magnetic plateau in Faraday experiments. Now we can flip the logic around:

Let the Faraday plateau itself measure . In other words, use magneto-optics as a clock experiment.

2. Step 1 – The neutrino hint: a secret angle in the sky

2.1 Neutrino mass splittings

Neutrinos come in three “flavours”, and they oscillate between those flavours as they travel. What matters for oscillations are not the individual masses, but the mass-squared differences:

• ,
• .

Experiments measure the ratio

Using modern global fits, this comes out to be a number of order 30–35.

2.2 QTT’s neutrino–clock relation

QTT proposes that this ratio is secretly a clock ratio:

Taking from data and solving for gives an angle

which is fully consistent with

In other words: neutrinos act like a cosmic protractor, pointing to the same tilt that QTT uses in its core axioms.

3. Step 2 – Faraday plateau as a “clock-tilt” meter

3.1 From Verdet constants to a universal plateau

Back to the Faraday effect. In the plateau regime of TGG and DyO, we can split the Verdet constant into a “magnetic plateau” piece and everything else:

QTT is interested in the plateau piece , which captures a wavelength–independent rotation per unit field and length.

To remove obvious material dependence (more spins, bigger moments, etc.) we define a dimensionless combination

where:

• is the group velocity of light in the medium,
• is the spin density (ions per volume),
• is the effective ionic magnetic moment.

Empirically, for TGG and DyO in their plateau regions, one finds

with uncertainties dominated by spin parameters and how the plateau is extrapolated.

3.2 QTT’s capacity–holonomy law

QTT does not treat as a random constant. Instead, it comes from a capacity holonomy between the light field and the spins.

The key relation is:

where

• is the capacity carried by the optical magnetic field,
• is the spin capacity, the number of “spin quanta” available to align.

More explicitly:

Here:

• is the endurance quantum (QTT’s fundamental capacity unit),
• is the optical magnetic field,
• is the spin alignment energy density,
• is a saturation field that sets the scale for how much work it takes to fully align the spins.

In the plateau regime, the magneto-optic rotation can be written either as

or via the holonomy formula above. Comparing the two gives a direct relation between and the ratio .

3.3 Minimal quanta and the geometry factor

QTT’s Axiom A6 ties the endurance quantum to Newton’s constant , the speed of light , and Planck’s constant via a “Planck four-cell”:

Solving these means there are no extra free microscopic scales once are fixed. The remaining ambiguity is purely geometric: how we choose to tile the world with “capacity cells”.

Working through this algebra, one finds that the plateau combination must have the QTT form

where is a pure number built only from:

• the endurance scale ,
• the chosen world-cell geometry (how capacity per spin is counted),
• simple optical factors (beam profile, mode volume).

Once is fixed by QTT’s geometric prescription, the Faraday experiment itself measures the clock factor:

3.4 What the numbers say

Using the same QTT geometry for both TGG and DyO, the experimental plateau values lead to a common clock factor

The uncertainty here is not in QTT itself; it’s in the spin modelling (Van Vleck mixing, precise , plateau extrapolation).

Within these uncertainties, this is totally consistent with

So we now have:

• Neutrinos giving ,
• Faraday plateaus giving .

The underlying physics is wildly different, but the dimensionless angle is the same.

4. The big picture: a new way to read the Universe’s clock

Put together, the story looks like this:

1. Neutrinos measure a precise ratio of mass-squared splittings. QTT reads that ratio as a clock ratio and extracts an angle .
2. Faraday rotation in TGG and DyO shows a magnetic plateau, where a dimensionless combination becomes nearly universal. QTT’s capacity-holonomy law ties this directly to the same clock factor .
3. When you invert the Faraday law, the plateau becomes a direct measurement of , and thus of the tilt between the Universe’s background clock and lab time.

Neutrinos and magneto-optics are not supposed to talk to each other. In standard physics, they live in completely different sectors:

• Neutrino oscillations are a weak-interaction and mass-mixing story.
• Faraday rotation is a solid-state and electromagnetism story.

But in the QTT picture, they both probe the same hidden structure: a time-plane tilt encoded by .

That is the paradigm shift that today we introduce:

Faraday rotation stops being “just optics”. It becomes a tabletop experiment on the geometry of cosmic time.

And when your tabletop crystals and your distant neutrino beams whisper the same angle, it suggests they are both reading from the same ledger.