Primordial Fields and Gravity in QFunity

Primordial Fields and Gravity

Relics of the Emergent Pre-Temporal state

Overview of Primordial Fields and Gravity

« Constraints on Primordial Magnetic Fields from the Lyman-𝛼 Forest » (DOI: https://doi.org/10.1103/77rd-vkpz) detects weak primordial magnetic fields (~10⁻¹⁵ T). QFunity interprets these and gravitational fields as EPT relics, explained by rotational and scale-dependent dynamics.

Chronology of Events: From EPT to Micro-Magnetic Fields Post-Big Bang

  1. Pre-Transition State: EPT Equilibrium (t < 0)

    Time: Before the Big Bang (t = 0, conventionally defined as the Planck epoch, \(\sim 10^{-43} \, \text{s}\)).

    State: The universe exists as the EPT, a pre-spacetime foam governed by \(\left[ \hat{\mathbb{B}}_\epsilon, \hat{\mathbb{V}}_\epsilon \right] \Psi_{\text{EPT}} = 0\). Fluctuations in \(\hat{\mathbb{B}}_\epsilon\) produce a spectrum of rotational vortices, while \(\hat{\mathbb{V}}_\epsilon\) sets a fractal energy density \(\rho_{\text{vac}}(\epsilon)\).

    Field Origins: – Magnetic: \(\hat{\mathbb{B}}_\epsilon\)’s vortices are the precursors to magnetic fields, with local amplitudes potentially on the order of Planck-scale fields (\(\sim 10^9 \, \text{T}\)). – Gravitational: \(\hat{\mathbb{V}}_\epsilon\)’s geometry seeds curvature fluctuations, the precursors to gravitational fields, encoded in \(g_{\mu\nu}^{\text{LQG}}\).

    Dynamics: Acausal and non-local, with no defined time or space, only a scale-dependent rotational structure.

  2. Transition Phase: Symmetry Breaking and Big Bang (t ≈ 0 to 10⁻³⁶ s)

    Time: The Planck epoch, where \(\epsilon \to \ell_P\), marking the transition from EPT to spacetime.

    Process: The master equation \(\lim_{\epsilon \to 0^+} \left[ \hat{\mathbb{B}}_\epsilon \hat{\mathbb{V}}_\epsilon – \hat{\mathbb{V}}_\epsilon \hat{\mathbb{B}}_\epsilon^2 \right] \Psi = \Lambda \cdot \frac{\Psi}{\|\Psi\|^2 + \epsilon^2}\) becomes active. The commutator turns non-zero, breaking the rotational symmetry of the EPT.

    Field Evolution: – Magnetic: EPT vortices (\(\hat{\mathbb{B}}_\epsilon\)) are « frozen » into primordial magnetic fields \(\mathbf{B}\). The \(\epsilon^2\) term ensures these fluctuations persist, with initial amplitudes diluted by symmetry breaking. – Gravitational: \(\hat{\mathbb{V}}_\epsilon\)’s fractal geometry transitions into \(g_{\mu\nu}^{\text{LQG}}\), initiating spacetime curvature. The \(\Lambda\) term redistributes energy, some into gravitational waves.

    Outcome: Emergence of a causal spacetime with a time arrow, where \(\Psi\) evolves into localized wave packets representing field precursors.

  3. Inflation and Freezing (t ≈ 10⁻³⁶ to 10⁻³² s)

    Time: The inflationary epoch, driven by rapid expansion (\(a(t) \propto e^{Ht}\), where \(H\) is the Hubble parameter).

    Process: The universe expands exponentially, stretching the frozen EPT fluctuations. The scale-dependent metric \(g_{\mu\nu}(\epsilon)\) shifts as \(\epsilon\) increases, with \(g_{\mu\nu}^{\text{LQG}}\) diminishing relative to \(g_{\mu\nu}^{GR}\).

    Field Evolution: – Magnetic: \(\mathbf{B} \propto 1/a^2\) due to flux conservation, reducing amplitudes from Planck-scale to \(\sim 10^{-5} \, \text{T}\) by the end of inflation. The \(\langle \hat{B} \rangle_{\epsilon_O}\) equation begins to average these fields over growing \(\epsilon_O\). – Gravitational: Curvature fluctuations amplify into gravitational waves, with \(g_{\mu\nu}^{\text{interactions}}\) emerging as matter interactions begin.

    Outcome: Fields are diluted but retain a fractal signature from the EPT.

  4. Recombination and Structure Formation (t ≈ 10³ to 10¹³ s)

    Time: From the recombination era (\(\sim 380,000 \, \text{years}\)) to galaxy formation (\(\sim 1 \, \text{billion years}\)).

    Process: The universe cools, and matter decouples from radiation. Simulations (e.g., the article’s 250,000) model perturbation growth via gravitational instability.

    Field Evolution: – Magnetic: \(\mathbf{B}\) fields are further diluted to femto-Tesla levels (\(\sim 10^{-15} \, \text{T}\)) as \(\epsilon_O\) reaches galactic scales (\(\sim 10^{20} \, \text{m}\)). \(\langle \hat{B} \rangle_{\epsilon_O}\) smooths local variations, matching Lyman-𝛼 forest observations. – Gravitational: Curvature evolves into large-scale structure, with gravitational fields (\(\mathbf{g} \propto \nabla \phi\)) amplified by matter clustering.

    Outcome: Magnetic fields become observable relics, while gravitational fields shape cosmic web formation.

  5. Present Day Observation (t ≈ 13.8 billion years)

    Time: Current epoch, with observations via radio telescopes and Lyman-𝛼 forest data.

    Process: The \(\langle \hat{B} \rangle_{\epsilon_O}\) equation governs the measured field strength, with \(\epsilon_O\) reflecting modern observational scales.

    Field Evolution: – Magnetic: Detected at \(\sim 10^{-15} \, \text{T}\), their weakness reflects dilution and scale averaging, with EPT fractal origins confirmed by simulations. – Gravitational: Observed as galactic and cluster potentials, tracing back to \(g_{\mu\nu}^{\text{LQG}}\)’s EPT roots.

    Outcome: Both fields are EPT fossils, testable via scale-dependent measurements.

1. Origin in EPT Fluctuations

\[ \left[ \hat{\mathbb{B}}_\epsilon, \hat{\mathbb{V}}_\epsilon \right] \Psi_{\text{EPT}} = 0 \] where \(\hat{\mathbb{B}}_\epsilon = \epsilon^2 (\nabla \times \boldsymbol{\omega})\), \(\hat{\mathbb{V}}_\epsilon = -\frac{\hbar^2}{2\epsilon^2} \nabla^2 + \frac{\rho_{\text{vac}}(\epsilon)}{\epsilon^2}\), \(\rho_{\text{vac}}(\epsilon) = \rho_0 \epsilon^{-4} e^{-\epsilon/\ell_P}\)

Interpretation:

At \(\epsilon \to \ell_P\), \(\hat{\mathbb{B}}_\epsilon\) generates magnetic vortex precursors (\(\mathbf{B} = \nabla \times \mathbf{A}\)), while \(\hat{\mathbb{V}}_\epsilon\) seeds gravitational curvature (\(g_{\mu\nu}^{\text{LQG}}\)).

Proof Request:

Predict \(P_B(k) \propto k^{-n}\) and gravitational wave spectra from EPT.

2. Transition via Big Bang

\[ \lim_{\epsilon \to 0^+} \left[ \hat{\mathbb{B}}_\epsilon \hat{\mathbb{V}}_\epsilon – \hat{\mathbb{V}}_\epsilon \hat{\mathbb{B}}_\epsilon^2 \right] \Psi = \Lambda \cdot \frac{\Psi}{\|\Psi\|^2 + \epsilon^2} \]

Interpretation:

Symmetry breaking freezes EPT vortices into \(\mathbf{B}\) and curvature into \(g_{\mu\nu}\), with \(\epsilon^2\) ensuring persistence.

Proof Request:

Simulate with varying \(\Lambda\) to test field and gravity evolution.

3. Inflation and Freezing

Interpretation:

Expansion (\(\mathbf{B} \propto 1/a^2\)) dilutes fields, with \(g_{\mu\nu}(\epsilon)\) shifting to \(g_{\mu\nu}^{GR}\).

Proof Request:

Measure field dilution rates during inflation.

4. Recombination and Structure Formation

\[ \langle \hat{B} \rangle_{\epsilon_O} = \frac{\langle \Psi | \hat{B} | \Psi \rangle}{\langle \Psi | \Psi \rangle + \epsilon_O^2} \]

Interpretation:

At \(\epsilon_O \sim 10^{20} \, \text{m}\), \(\mathbf{B} \sim 10^{-15} \, \text{T}\), while gravitational fields shape structure.

Proof Request:

Test \(\langle \hat{B} \rangle_{\epsilon_O}\) at different scales.

5. Present Day Observation

\[ g_{\mu\nu}(\epsilon) = g_{\mu\nu}^{GR} + \frac{\ell_P^2}{\epsilon^2} g_{\mu\nu}^{\text{LQG}} + \alpha’ g_{\mu\nu}^{\text{interactions}} \]

Interpretation:

Fields are EPT fossils, with \(g_{\mu\nu}^{\text{LQG}}\) tracing gravity’s origin.

Proof Request:

Compare EPT-predicted spectra with Lyman-𝛼 observations.

Conclusion

Magnetic and gravitational fields are EPT relics, validated by QFunity’s rotation and scale principles. These proof requests invite cosmic tests.

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