The Existence Boundary: A Foundational Principle in Cosmology and Quantum Physics ?

[ovidiu t]

7 hours ago, Markus Hanke said:

But this is functionally identical to the ordinary field equations with cosmological constant, thus Eμν=λgμν . There is nothing new here.

This is not a valid tensor equation, and thus quite meaningless. 

The other thing of course is that we know from experiment and observation that the motion of free-fall particles outside local masses (eg Earth) is very well described by vacuum solutions to the ordinary Einstein equations without cosmological constant. This puts very stringent limits on whatever modification to the field equations you propose.

PS. The forum software here supports LaTeX, I’d suggest you use it instead of embedded pictures.

 

1. Core Idea: Absolute Nothingness vs. Localized Nothingness

• My proposal emphasizes a fundamental principle: absolute nothingness is impossible. While localized nothingness (e.g., a node in a wavefunction or an isolated vacuum region) can exist, the entire framework—the universe or physical reality—always contains something.
• This idea is rooted in well-established physics:
  • Quantum Mechanics: Wavefunction normalization ensures total probability is always 1, even if parts of the system have zero probability:(overleaf issues while transporting it here, until I figure it out I will put capture screens, I appologize) 
  • Quantum Field Theory: Vacuum fluctuations mean even “empty” space is never truly empty:
  • General Relativity: Baseline spacetime curvature (e.g., from a cosmological constant) ensures the universe retains structure even in the absence of matter:
  • These principles converge into a single boundary condition: nothingness is possible only in localized regions, but never globally across the entire framework.

2. Response to  Adds Nothing New

 

• If EμνE_{\mu\nu}Eμν were merely a constant multiple of the metric (λgμν\lambda g_{\mu\nu}λgμν) at all scales, it would indeed replicate the behavior of a cosmological constant (Λgμν\Lambda g_{\mu\nu}Λgμν) and add no new physics.
• However, my proposal introduces a scale-dependent transformation of E:
  • At quantum scales, E acts as a scalar condition enforcing global normalization (or conservation of existence).
  • At macroscopic scales, EμνE_{\mu\nu}Eμν emerges as a tensorial contribution to spacetime curvature.
• This is conceptually similar to a phase transition, where the same principle (e.g., H₂O) manifests in different forms (liquid vs. vapor) depending on external conditions. The novelty lies in this transition across scales.

3. Addressing the Valid Tensor Criticism (with Thermodynamic Analogy)

• I acknowledge the concern that an equation like:

  

• is not tensorially valid as written. It was meant as a conceptual shorthand for how EEE shifts from a scalar role to a tensorial one depending on the scale ℓ\ellℓ.

• To clarify this transition, I propose the thermodynamic analogy:

  • In thermodynamics, a substance like water undergoes phase transitions depending on external conditions, such as temperature and pressure.
  • For instance:
    • Below 100∘100^\circ100∘C (at standard pressure), water exists in the liquid phase, with distinct properties like incompressibility.
    • Above 100∘100^\circ100∘C, it transforms into a gas phase, with entirely different properties like diffusivity.
    • Despite these differences, the underlying substance (H₂O) remains the same—it simply exhibits different behaviors in different regimes.

• Similarly, in my framework:

  • Below the Planck scale (ℓ≪ℓPlanck\ell \ll \ell_\text{Planck}ℓ≪ℓPlanck), EEE behaves as a scalar condition (e.g., E=1E = 1E=1), ensuring global wavefunction normalization and prohibiting absolute void at the quantum level.
  • Above the Planck scale (ℓ≫ℓPlanck\ell \gg \ell_\text{Planck}ℓ≫ℓPlanck), EμνE_{\mu\nu}Eμν emerges as a tensorial contribution to spacetime curvature, ensuring a baseline structure even in macroscopic “vacuum” regions.
  • The Planck scale acts as a tipping point, analogous to the boiling point of water, where the underlying principle of existence (like the substance H₂O) remains constant but manifests differently depending on the regime.

• Rigorous Mathematical Path Forward:

The transition can be formalized using a scale-dependent parameter λ(ℓ)\lambda(\ell)λ(ℓ), which smoothly interpolates between the two regimes:

4. Experimental Constraints on Vacuum Solutions

• I recognize the strength of observational data supporting standard GR with a small or negligible Λ\LambdaΛ in local vacuum solutions. My framework is consistent with these constraints because:
  • At everyday and astrophysical scales, the effects of EEE (or λ(ℓ)\lambda(\ell)λ(ℓ)) are negligible, ensuring no observable deviations from standard GR.
  • Only under extreme conditions—such as near singularities or at the Planck scale—does EEE deviate significantly from classical GR, potentially preventing singularities or explaining pre-Big-Bang states.

    5. Absolute Nothingness in Cosmic Contexts

  • This principle offers a fresh perspective on two major questions:

    1. Before the Big Bang: If absolute nothingness is impossible, then the Big Bang could not have emerged from void. Instead, some precursor state must have existed—whether as a quantum phase, a bounce, or another structure within the Existence Boundary framework.
    2. End States of the Universe: Even in extreme scenarios like heat death, the Big Crunch, or the Big Rip, the universe cannot vanish entirely. Nonzero vacuum energy, quantum fluctuations, or baseline curvature ensure a persistent “something.”

  • Much like water retains a molecular structure in all phases (solid, liquid, gas), the universe retains a minimal existence across all cosmic scenarios. This ensures continuity of existence even in extreme conditions.

  • ---

    6. Value of the Proposal

  • While the mathematical refinement and rigorous predictions are still in development, the concept offers:
    • Unification: A single boundary condition linking quantum, relativistic, and cosmological domains.
    • Inspiration: A framework for addressing questions like singularity resolution and the nature of pre-Big-Bang existence.
    • Potential for Novel Predictions: For example, detecting signatures of a cosmic bounce in the CMB or deviations in gravitational wave spectra near black holes.

  • ---

    Conclusion

    I recognize the need to refine the mathematical structure of EEE and its tensorial formulation. However, the central principle—that absolute nothingness is impossible, and existence persists across all scales—is a meaningful unification of existing physical insights. By focusing on the transition of EEE between quantum (scalar) and macroscopic (tensorial) regimes, this framework offers a novel lens on some of the universe’s biggest questions: the origins of the Big Bang, the fate of the cosmos, and the resolution of singularities.

     

[swansont]

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Moderator Note

If all you can do is repeat what you’ve posted, we’re done. You haven’t presented a way to test your idea in any quantifiable way, so it does not meet the criteria of speculations.