What Neutrinos have to do Faraday Rotation? QTT Explains

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

$ \theta_{\rm F} = V\,B\,L, $

where:

$\theta_{\rm F}$ is the rotation angle,
$B$ is the magnetic field (in Tesla),
$L$ is the length of the sample,
$V$ is the Verdet constant, a material-dependent number that tells you how “strongly” that material rotates light.

In standard physics, $V$ 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 (Dy $_2$ O $_3$ ), 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 $V$ 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 $T$ : the “ledger” the Universe uses to keep track of capacity and creation.
Our lab time $t$ 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 $\theta$ . QTT’s postulate is that this angle is not random: it’s locked to a discrete value

$ \theta_\star = \frac{\pi}{8} \quad\Rightarrow\quad I_{\rm clk} = \cos\!\Bigl(\frac{\pi}{8}\Bigr) \approx 0.9239. $

Here $I_{\rm clk}$ 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 $I_{\rm clk}$ 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 $I_{\rm clk}$ . 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:

$\Delta m^2_{21} = m_2^2 - m_1^2$ ,
$\Delta m^2_{31} = m_3^2 - m_1^2$ .

Experiments measure the ratio

$ R_\nu \;\equiv\; \frac{\Delta m^2_{31}}{\Delta m^2_{21}}. $

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:

$ R_\nu \;=\; 4\pi^2\,I_{\rm clk}^2, \qquad I_{\rm clk} = \cos\widehat\theta_\nu. $

Taking $R_\nu$ from data and solving for $\widehat\theta_\nu$ gives an angle

$ \widehat\theta_{\nu} \approx 22.8^\circ \pm 1.8^\circ, $

which is fully consistent with

$ \frac{\pi}{8} = 22.5^\circ. $

In other words: neutrinos act like a cosmic protractor, pointing to the same $\pi/8$ 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 Dy $_2$ O $_3$ , we can split the Verdet constant into a “magnetic plateau” piece and everything else:

$ V(\lambda) = V_{\rm mag}^{\rm plateau} + V_{\rm dispersive}(\lambda). $

QTT is interested in the plateau piece $V_{\rm mag}^{\rm plateau}$ , 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

$ S_{\rm mag} \;\equiv\; V_{\rm mag}^{\rm plateau} \;\frac{v_g}{n_{\rm ion}\,\mu_{\rm eff}}, \qquad v_g \simeq \frac{c}{n}, $

where:

$v_g$ is the group velocity of light in the medium,
$n_{\rm ion}$ is the spin density (ions per volume),
$\mu_{\rm eff}$ is the effective ionic magnetic moment.

Empirically, for TGG and Dy $_2$ O $_3$ in their plateau regions, one finds

$ S_{\rm mag}^{\rm (TGG)} \sim 0.8\times10^{-20}, \qquad S_{\rm mag}^{\rm (Dy_2O_3)} \sim 1.8\times10^{-20}, $

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

3.2 QTT’s capacity–holonomy law

QTT does not treat $V_{\rm mag}^{\rm plateau}$ as a random constant. Instead, it comes from a capacity holonomy between the light field and the spins.

The key relation is:

$ \boxed{ \theta_{\rm mag} = 2\pi\,I_{\rm clk}\, \frac{H_{\rm cap}}{N_{\rm SQ}^{(S)}} } $

where

$H_{\rm cap}$ is the capacity carried by the optical magnetic field,
$N_{\rm SQ}^{(S)}$ is the spin capacity, the number of “spin quanta” available to align.

More explicitly:

$ H_{\rm cap} = \frac{1}{E_\ast} \int_{\mathcal V_{\rm pulse}} \frac{B_{\rm opt}^2}{2\mu_0}\,d^3x\,dT, $ $ N_{\rm SQ}^{(S)} = \frac{1}{E_\ast} \int_{\mathcal V_{\rm spin}} u_S\,d^3x\,dT \;\sim\; \frac{n_{\rm ion}\,\mu_{\rm eff}\,B_{\rm sat}\,L}{E_\ast}. $

Here:

$E_\ast$ is the endurance quantum (QTT’s fundamental capacity unit),
$B_{\rm opt}$ is the optical magnetic field,
$u_S$ is the spin alignment energy density,
$B_{\rm sat}$ 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

$ \theta_{\rm mag} = V_{\rm mag}^{\rm plateau}\,B_{\rm ext}\,L, $

or via the holonomy formula above. Comparing the two gives a direct relation between $V_{\rm mag}^{\rm plateau}$ and the ratio $H_{\rm cap}/N_{\rm SQ}^{(S)}$ .

3.3 Minimal quanta and the geometry factor

QTT’s Axiom A6 ties the endurance quantum $E_\ast$ to Newton’s constant $G$ , the speed of light $c$ , and Planck’s constant $\hbar$ via a “Planck four-cell”:

$ V_4 = 4\pi \tilde\ell^4, \qquad E_\ast = \frac{\hbar c}{\tilde\ell}, \qquad G = \frac{\tilde\ell^2 c^3}{\hbar}. $

Solving these means there are no extra free microscopic scales once $(G,\hbar,c)$ 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 $S_{\rm mag}$ must have the QTT form

$ \boxed{ S_{\rm mag}^{\rm (QTT)} = \mathcal C_{\rm geom}\,I_{\rm clk}, } $

where $\mathcal C_{\rm geom}$ is a pure number built only from:

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

Once $\mathcal C_{\rm geom}$ is fixed by QTT’s geometric prescription, the Faraday experiment itself measures the clock factor:

$ \boxed{ I_{\rm clk}^{\rm (Faraday)} = \frac{S_{\rm mag}^{\rm (exp)}}{\mathcal C_{\rm geom}}. } $

3.4 What the numbers say

Using the same QTT geometry for both TGG and Dy $_2$ O $_3$ , the experimental plateau values $S_{\rm mag}^{\rm (exp)}$ lead to a common clock factor

$ I_{\rm clk}^{\rm (Faraday)} \sim 0.9 \pm 0.1. $

The uncertainty here is not in QTT itself; it’s in the spin modelling (Van Vleck mixing, precise $\mu_{\rm eff}$ , plateau extrapolation).

Within these uncertainties, this is totally consistent with

$ \cos\!\Bigl(\frac{\pi}{8}\Bigr) = 0.9239\ldots $

So we now have:

Neutrinos giving $I_{\rm clk}^{(\nu)} \approx \cos(\pi/8)$ ,
Faraday plateaus giving $I_{\rm clk}^{\rm (Faraday)} \approx \cos(\pi/8)$ .

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:

Neutrinos measure a precise ratio of mass-squared splittings. QTT reads that ratio as a clock ratio and extracts an angle $\widehat\theta_\nu \approx \pi/8$ .
Faraday rotation in TGG and Dy $_2$ O $_3$ shows a magnetic plateau, where a dimensionless combination $S_{\rm mag}$ becomes nearly universal. QTT’s capacity-holonomy law ties this directly to the same clock factor $I_{\rm clk}$ .
When you invert the Faraday law, the plateau becomes a direct measurement of $I_{\rm clk}$ , 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 $I_{\rm clk} = \cos(\pi/8)$ .

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.

What Neutrinos have to do Faraday Rotation? QTT Explains

1. The simple story: magnets as cosmic clocks

1.1 What is the Faraday effect?

1.2 The mysterious “magnetic plateau”

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

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

2.1 Neutrino mass splittings

2.2 QTT’s neutrino–clock relation

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

3.1 From Verdet constants to a universal plateau

3.2 QTT’s capacity–holonomy law

3.3 Minimal quanta and the geometry factor

3.4 What the numbers say

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

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1. The simple story: magnets as cosmic clocks

1.1 What is the Faraday effect?

1.2 The mysterious “magnetic plateau”

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

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

2.1 Neutrino mass splittings

2.2 QTT’s neutrino–clock relation

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

3.1 From Verdet constants to a universal plateau

3.2 QTT’s capacity–holonomy law

3.3 Minimal quanta and the geometry factor

3.4 What the numbers say

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

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Published by Quantum Traction Theory

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