Vacuum Energy Calculator
The vacuum catastrophe — the 10121-order discrepancy between quantum field theory’s prediction for vacuum energy and the observed value — is resolved by the ether’s physical UV cutoff at the healing length. Adjust the ether quantum mass to explore.
Viable window: 0.3–3.0 eV (Section 9.3, Table 9.3)
ZPF Spectral Density — The Physical Cutoff
Move the slider: the teal cutoff line shifts as ξ changes. The ether integrates only the teal area. QFT continues 30 orders of magnitude further to the Planck scale (off-screen to the right).
Derived Parameters at me = 1.00 eV
- Healing length ξ (Eq 4.103)
- 8.73 μm
- Chemical potential μ̂
- 0.256 meV
- Sound speed cs (Eq 4.109)
- 4.794e+6 m/s
- Number density n0 (Eq 9.19)
- 1.248e+9 m−3
Vacuum Energy Densities
- Ether ZPF density (Eq 4.122)
- 6.366e-10 J/m³
- Observed dark energy (Eq 4.99)
- 6.360e-10 J/m³
- QFT prediction — Planck cutoff (Eq 4.101)
- 2.934e+111 J/m³
- Ether / Observed
- 1.001Exactly 1 for all m_e — this is the constraint, not a coincidence
- QFT / Observed
- 4.61e+120The vacuum catastrophe
- QFT / Ether
- 4.61e+120How much the healing length cutoff reduces the prediction
- Equation of state w (Theorem 4.2)
- -1 (exact)Uniquely Lorentz-invariant — not a fit parameter
Why doesn’t ρZPF change? Constraint I (Eq 9.13) fixes me3/2·μ̂5/2 = CΛ = const, which is exactly the combination appearing in the Bogoliubov integral (Eq 4.122). The constraint guarantees ρZPF = ρΛ for every me. The slider shows that the resolution of the vacuum catastrophe is robust — it does not depend on the specific value of the free parameter.
How This Works
- 1. Standard QFT sums zero-point energies up to the Planck frequency — an arbitrary cutoff with no physical justification. Result: 10111 J/m³.
- 2. The ether framework models the vacuum as a superfluid BEC. Phonon modes only exist above the healing length ξ — a physical cutoff determined by the condensate’s equation of state.
- 3. The integral over the Bogoliubov dispersion relation (Eq 4.108) with cutoff at kmax = 1/ξ gives a finite, exact result (Eq 4.122) — no renormalisation, no cancellation, no fine-tuning.
- 4. The spectrum ρ(ω) ∝ ω³ is uniquely Lorentz-invariant (Theorem 4.2), giving w = −1 exactly — the equation of state of a cosmological constant.
Beta Tools are under active development. Equations are verified against the monograph but outputs may be refined. Report an issue