BeeTheory · Challenge & Conclusion · 2025

BeeTheory vs Galaxy Rotation Data: Challenge, Best Parameters & Conclusion

Challenging BeeTheory against two independent rotation-curve references: the Newby/Rubin canonical flat rotation curve and the Gaia 2024 Milky Way kinematic data.

This page tests whether a wave-based 3D Yukawa dark-mass kernel can reproduce both the classical flat-rotation picture and the more recent declining Milky Way rotation curve.

BeeTheory.com · Newby, Temple University, 2019 · Ou et al., MNRAS 528, 2024

0. Results — Best Parameters and Equation

The BeeTheory 3D Yukawa integral over all galactic disk rings is fitted simultaneously on two datasets: the Newby/Rubin canonical rotation curve, which is approximately flat near 220 km/s, and the Gaia 2024 Milky Way data, which declines beyond about 20 kpc.

The best-fit dark mass density equation is:

\(\rho_{\mathrm{dark}}(r)=K\int_0^{R_{\mathrm{max}}}\Sigma_0e^{-R’/R_d}\frac{(1+\alpha D)e^{-\alpha D}}{D^2}\,2\pi R’\,dR’\) \(D=\sqrt{r^2+R’^2}\)

The kernel is not inserted arbitrarily. It is derived from the corrected BeeTheory force law:

\(F(D)=-\frac{K_0(1+\alpha D)e^{-\alpha D}}{D^2}\)

Inside the coherence length, the force becomes Newton-like:

\(D\ll\ell=\frac{1}{\alpha}\quad\Longrightarrow\quad F(D)\approx-\frac{K_0}{D^2}\)

The best combined fit gives:

\(K=0.038\,\mathrm{kpc}^{-1}\) \(\alpha=0.074\,\mathrm{kpc}^{-1}\) \(\ell=\frac{1}{\alpha}=13.4\,\mathrm{kpc}\) \(\lambda=K\ell^2\approx6.8\)

1. The Two Datasets

Tension between the datasets

The Newby/Rubin curve is a canonical model-like reference, while Gaia 2024 is a direct kinematic measurement. BeeTheory must reproduce both: a flat region inside the coherence length and a decline beyond the coherence length.

2.1 Hypothesis Challenge: Is K Universal?

BeeTheory predicts that the coupling K and the coherence length ℓ should not be freely redefined for every galaxy. They should follow scaling relations linked to the disk structure and wave-mass coupling.

For the Milky Way, the combined fit gives:

\(K=0.038\,\mathrm{kpc}^{-1},\qquad \ell=13.4\,\mathrm{kpc}\)

For a larger spiral galaxy with disk scale length R_d = 5 kpc, a simple proportionality would predict:

\(\ell\approx5.2R_d\approx26\,\mathrm{kpc}\)

Testing this across the SPARC galaxy sample is an immediate next step.

Robustness result

The two BeeTheory parameters shift only moderately when moving from Gaia-only to combined data. This is a sign that the model is not simply overfitting one dataset.

4. Best Formulas and Justified Coefficients

4.1 Complete Equation Set

1. Particle wave function

\(\psi(r)=\frac{\alpha_0^{3/2}}{\sqrt{\pi}}e^{-\alpha_0r}\) \(\alpha_0=\frac{1}{a_0}\ \mathrm{(atomic)}\quad\mathrm{or}\quad\alpha_0=\frac{1}{\ell}\ \mathrm{(galactic)}\)

2. Corrected BeeTheory force law

\(F(D)=-\frac{K_0(1+\alpha D)e^{-\alpha D}}{D^2}\) \(\alpha D\ll1\quad\Longrightarrow\quad F(D)\approx-\frac{K_0}{D^2}\)

3. Dark mass density

\(\rho_{\mathrm{dark}}(r)=K\int_0^{R_{\mathrm{max}}}\Sigma_0e^{-R'/R_d}\frac{(1+\alpha D)e^{-\alpha D}}{D^2}\,2\pi R'\,dR'\) \(D=\sqrt{r^2+R'^2}\)

4. Baryonic velocity with physical truncation

\(V_{\mathrm{bar}}(R)=\sqrt{(1-w)V_{\mathrm{Freeman}}^2+w\,\min(V_{\mathrm{Freeman}},\sqrt{GM_{\mathrm{bar}}/R})^2}\) \(w(R)=\frac{1}{2}\left[1+\tanh\left(\frac{R-R_{\mathrm{trunc}}}{\sigma}\right)\right]\) \(\sigma=1.5\,\mathrm{kpc}\)

5. Total circular velocity

\(V_c(R)=\sqrt{V_{\mathrm{bar}}^2(R)+V_{\mathrm{dark}}^2(R)}\) \(V_{\mathrm{dark}}(R)=\sqrt{\frac{GM_{\mathrm{dark}}(4.2 Numerical Coefficients

Parameter	Value	Units	Physical justification
K	0.038	kpc⁻¹	Wave-mass coupling amplitude. Stable across datasets.
α	0.074	kpc⁻¹	Inverse coherence length. Controls transition from flat to declining rotation.
ℓ	13.4	kpc	Coherence length. Approximately 5.2 times the Milky Way disk scale length.
λ = Kℓ²	6.8	dimensionless	Possible universal BeeTheory coupling.
Rd	2.6	kpc	Milky Way thin disk scale radius.
Rtrunc	10.4	kpc	Physical disk edge, approximately 4Rd.
Mbar,tot	4.7 × 10¹⁰	M⊙	Disk plus bulge baryonic mass.
G	4.302 × 10⁻⁶	kpc km² s⁻² M⊙⁻¹	Newton’s constant in the working unit system.

6. Opening — The Potential of BeeTheory

If the wave-mass exponential mechanism is real, then dark matter as a separate substance may be unnecessary. What appears as missing mass would be the cumulative effect of the wave field of ordinary matter extending beyond its visible boundaries.

This reframes the dark matter problem. Instead of asking what particle constitutes dark matter, the question becomes: what is the coherence length of the gravitational wave field?

Galaxy clusters. Clusters such as the Bullet Cluster are the next critical test. In BeeTheory, the wave field of galaxies could propagate independently from hot gas during a collision, potentially explaining offsets between baryonic gas and gravitational lensing mass.

The cosmic web. At large scales, BeeTheory predicts that hidden mass should trace the accumulated wave field generated by baryons within the relevant coherence length, creating filaments and voids linked to ordinary matter.

Gravitational waves. A deeper derivation of ℓ from fundamental constants could connect atomic, galactic, and cosmological coherence lengths into a single theory.

The Hubble tension. If gravitational coherence changes with scale, it may affect the effective gravitational behavior at cosmological distances and could offer a new angle on the Hubble tension.

The single most important open question

Why is λ = Kℓ² approximately 4–7 across scales from the hydrogen molecule to the Milky Way? If this dimensionless coupling is universal, it should be derivable from fundamental constants. Finding this relation would turn BeeTheory from a powerful empirical framework into a deeper theory of gravity.

BeeTheory.com — Wave-based quantum gravity · From the hydrogen atom to the Milky Way

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