Binary flow hypothesis

Dual Energy Universe: A Speculative Model with Falsifiable Predictions

Author's note: The mathematical formulation proposed in this hypothesis has not been duly reviewed by experts in the field. Any conclusion drawn from the reading of this work must be thoroughly contrasted.

1. Simple universe: electron + positron

Schrödinger's equation for two bodies

Reduced mass:

μ = \frac{m_{e}}{2}

i ℏ \frac{\partial Ψ (r, t)}{\partial t} = [- \frac{ℏ^{2}}{2 μ} \nabla^{2} - \frac{e^{2}}{4 π ϵ_{0} r}] Ψ (r, t)

Bound States: Positronium

E_{n} = - \frac{μ e^{4}}{2 (4 π ϵ_{0})^{2} ℏ^{2}} \cdot \frac{1}{n^{2}} = - \frac{6.8 eV}{n^{2}}

Duration

Para-positronium (singlet,

S = 0

τ \approx 1.25 \times 10^{- 10} s

Ortho-positronium (triplet,

S = 1

τ \approx 1.42 \times 10^{- 7} s

Annihilation Energy

E_{annihilation} = 2 m_{e} c^{2} = 1.022 MeV

2. Simple universe: photon + "antiphoton"

The photon is its own antiparticle → two identical photons.
They do not interact linearly (Maxwell is linear in vacuum).
In QED, weak interaction via Euler-Heisenberg:

L_{EH} \sim \frac{α^{2}}{90 m_{e}^{4}} [(F_{μ ν} F^{μ ν})^{2} + \frac{7}{4} (F_{μ ν} {\tilde{F}}^{μ ν})^{2}]

Duration: infinite (photons do not decay).
If

E_{C M} > 2 m_{e} c^{2} = 1.022 MeV

, can create a pair

e^{-} e^{+}

and then they are annihilated.

3. Dual matter-antimatter universe with black/white hole

3.1 Refined model: bidirectional black/white hole

A single object connects

U_{M}

and

U_{A}

Black hole on one side, white hole on the other.
Bidirectional.
Hawking radiation is the leftover from matter-antimatter annihilation in the center of the throat.

3.2 Net Flow

Φ = \frac{E_{γ}}{τ_{transit}} = \frac{h ν}{τ}

Φ_{net} = Φ_{M \to A} - Φ_{A \to M}

Φ_{effective} = (1 - η) \cdot | Φ_{net} |

3.3 Differential equations

\frac{d E_{M}}{d t} = - Φ_{M \to A} + Φ_{A \to M} - \frac{E_{Hawking}}{2}

\frac{d E_{A}}{d t} = - Φ_{A \to M} + Φ_{M \to A} - \frac{E_{Hawking}}{2}

Where

E_{Hawking} = η (Φ_{M \to A} + Φ_{A \to M})

Total energy loss:

\frac{d E_{total}}{d t} = - E_{Hawking} = - η (Φ_{M \to A} + Φ_{A \to M})

3.4 Characteristic times

Equilibrium Time:

t_{balance} \approx \frac{E_{0} \cdot τ_{transit}}{2 h ν (1 - η / 2)}

Evaporation Time:

t_{death} \approx \frac{E_{0} \cdot τ_{transit}}{η \cdot h ν}

Frequency of Transit:

f_{transit} = \frac{1}{τ_{transit}} \approx \frac{c^{3}}{4 G M_{BH}}

Frequency of Hawking radiation (annihilation):

ν_{Hawking} = \frac{2 m c^{2}}{h}

4. Exotic matter and photonic dark matter

4.1 Exotic matter to stabilize the throat

Condition: violate the Null Energy Condition (NEC):

ρ + p < 0

Options: Phantom Scalar Field, Casimir Energy, Negative Cosmic Strings.

4.2 Photons with collective mass

Invariant mass of a system of

N

Photons:

M^{2} c^{4} = {(\sum_{i} E_{i})}^{2} - {| \sum_{i} p_{i} c |}^{2}

\sum p_{i} \approx 0

(Isotropic directions):

M_{system} \approx \frac{E_{total}}{c^{2}} \neq 0

Proposal: Dark matter is clouds of photons confined in swirls with zero net momentum.

5. Maxwell's Formalism for Energy

There is only energy

E

. Everything emerges from its flow.

5.1 Maxwell-type equations

Electromagnetism	Dual energy model
Electric Charge $q$	Power Charging $Υ$
Electric field $E$	Concentration flow $C$
Magnetic field $B$	Circulation flow $R$
Potential $A^{μ}$	Flow potential $Ψ^{μ}$

\nabla \cdot C = \frac{Υ}{ϵ_{E}}

\nabla \cdot R = 0

\nabla \times C = - \frac{1}{c_{E}} \frac{\partial R}{\partial t}

\nabla \times R = \frac{1}{c_{E}} \frac{\partial C}{\partial t} + μ_{E} J_{E}

Where

c_{E} = 1 / \sqrt{ϵ_{E} μ_{E}}

is the speed of propagation of energy waves.

5.2 Dual pressure confinement

Energy Polarization Tensor:

Π^{μ ν} = (\begin{matrix} ρ_{E} & P_{E} \\ P_{E} & σ_{E} \end{matrix})

Pressure Transfer Matrix:

\frac{d}{d t} (\begin{matrix} P_{M} \\ P_{A} \end{matrix}) = (\begin{matrix} - α & β \\ β & - α \end{matrix}) (\begin{matrix} P_{M} \\ P_{A} \end{matrix})

Self-values:

λ_{\pm} = - α \pm β

Stable confinement condition (Fixed Point):

α \approx β

The rate of dissipation equals the rate of exchange.

5.3 Compton-Schwarzschild confinement ratio

Compton Length of Swirl:

λ_{C} = \frac{ℏ}{M_{effective} c}

Schwarzschild Radio:

λ_{R} = \frac{G M_{effective}}{c^{2}}

Equalizing:

M_{effective} = \sqrt{\frac{ℏ c}{G}} = M_{Planck}

For arbitrary masses, we enter coupling parameter

ξ

λ_{C} \cdot λ_{R} = ξ \cdot ℓ_{P}^{2}

with

ξ \sim N_{photons in the vortex}

6. Wave and mass spectrum solutions

6.1 Free waves

In the void (

J_{E} = 0

\nabla^{2} C - \frac{1}{c_{E}^{2}} \frac{\partial^{2} C}{\partial t^{2}} = 0

\nabla^{2} R - \frac{1}{c_{E}^{2}} \frac{\partial^{2} R}{\partial t^{2}} = 0

→ Photons free.

6.2 Swirl solutions (vortex)

Cylindrical symmetry,

R = R_{ϕ} (r) \hat{ϕ}

C = C_{r} (r) \hat{r}

R_{ϕ} (r) = \frac{μ_{E} ω}{3} ρ_{0} r^{2} (r < r_{0})

R_{ϕ} (r) = \frac{μ_{E} ω ρ_{0} r_{0}^{3}}{3 r} (r > r_{0})

6.3 Effective mass of the eddy

Total Energy:

E_{vortex} = \frac{1}{2 μ_{E}} \int (| C |^{2} + | R |^{2}) d V

Effective mass:

M_{vortex} = \frac{E_{vortex}}{c_{E}^{2}} = \frac{2 π ρ_{0}^{2} r_{0}^{3}}{3 μ_{E} c_{E}^{2}} (1 + \frac{3 μ_{E}^{2} ω^{2} r_{0}^{2}}{10})

6.4 Quantization of angular momentum

L = \int ρ_{E} ω r^{2} d V = n ℏ

L = \frac{4 π}{5} ρ_{0} ω r_{0}^{5} = n ℏ

Quantized Angular Frequency:

ω = \frac{5 n ℏ}{4 π ρ_{0} r_{0}^{5}}

6.5 Mass spectrum

M_{n} (r_{0}) = \frac{2 π ρ_{0}^{2} r_{0}^{3}}{3 μ_{E} c_{E}^{2}} [1 + \frac{3 μ_{E}^{2}}{10} {(\frac{5 n ℏ}{4 π ρ_{0} r_{0}^{4}})}^{2}]

For

n = 0

M_{0} \propto r_{0}^{3}

For

n \geq 1

and

r_{0}

small:

M_{n} \approx \frac{15}{16 π} \frac{μ_{E} n^{2} ℏ^{2}}{ρ_{0} c_{E}^{2} r_{0}^{5}} \propto \frac{1}{r_{0}^{5}}

Critical radius minimizing mass:

r_{0}^{*} = {(\frac{5 n^{2} ℏ^{2} μ_{E}}{16 π^{2} ρ_{0}^{2}})}^{1 / 8}

Discrete spectrum:

M_{n}^{mín} \propto n^{3 / 4}

7. Falsifiable observational predictions

Prediction 1: Discrete mass spectrum for dark matter halos

Spacing:

\frac{M_{n + 1}}{M_{n}} \approx {(1 + \frac{1}{n})}^{3 / 4}

Test: Mass function of satellite galaxies with "steps". → LSST, Euclid.

Prediction 2: Gamma line series with logarithmic spacing

A whirlpool that loses a quantum of angular momentum (

Δ n = 1

) Broadcasts:

E_{γ} (n \to n - 1) \approx \frac{3}{4} \frac{ℏ^{2}}{ρ_{0} r_{0}^{5}} \propto n^{- 5 / 4}

Logarithmic relationship:

\log E_{γ}^{(n)} \approx cte - \frac{5}{4} \log n

Test: Find gamma line series with this pattern in the galactic center. → Fermi-LAT, CTA.

Prediction 3: Excess in the cosmic infrared background (CIB)

Non-Planckian Hawking radiation with excess in 10-100

μ

ν F_{ν} \propto ν^{1.3}

Test: Compare with Galactic Dust Spectrum. → Planck, Herschel, SPHEREx.

Prediction 4: Deviation from the Tully-Fisher ratio

Modified centripetal force:

\frac{v_{rot}^{2}}{r} = \frac{G M (< r)}{r^{2}} + \frac{1}{μ_{E}} | C |

Prediction:

v_{rot}^{4} = a M_{b} + b

with

b > 0

for galaxies with low surface mass.

Test: Rotation curves of dwarf and ultra-diffuse galaxies. → WEAVE, DESI.

Prediction 5: Asymmetry in gravitational lensing due to frame dragging

Additional spin displacement of the swirl (

J = n ℏ

Δ ϕ_{lens} = \frac{4 G M}{c^{2} b} + \frac{4 G J}{c^{3} b^{2}}

Position difference between images:

δ θ \approx 10^{- 6} (\frac{n}{10^{60}}) {(\frac{b}{1 kpc})}^{- 2} arcsec

Test: VLBI in galactic lenses. → EHT, VLBI.

8. Prediction Summary

#	Prediction	Instrument	¿Differentiable from $Λ$ CDM?
1	Discrete mass spectrum for DM halos	LSST, Euclid	Yes
2	Gamma line series $E_{γ} \propto n^{- 5 / 4}$	Fermi-LAT, CTA	Yes (Only)
3	CIB Excess with $ν F_{ν} \propto ν^{1.3}$	SPHEREx, Planck	Yes
4	Tully-Fisher deviation for dwarfs	WEAVE, DESI	Yes
5	Asymmetry in lenses due to frame dragging	VLBI, EHT	Yes

9. Conclusion

A self-consistent framework has been constructed where:

Energy is the only fundamental quantity.
Two dual fields

C

(concentration) and

R

(circulation) describe all phenomena analogous to

E

and

B

.
3. The lockdown emerges from a fixed point

α \approx β

.
4. The masses of the eddies follow a discrete spectrum

M_{n} \propto n^{3 / 4}

.
5. Dark matter is naturally clouds of confined photons with collective mass.

5 falsifiable predictions are proposed with current and future missions.

The cleanest and most unique prediction is number 2: a series of gamma lines with logarithmic spacing. Its detection would be an irrefutable signature of this model.

"Energy is the only currency of the universe. Everything else is exchange."

10. Explanation for laypeople

If you're left with the impression that you haven't understood anything, don't worry. Mathematics is powerful, but not very appealing. Despite appearances, what it expresses is very simple, and I can summarize it in a few lines.

The creation of the universe is currently explained by the inflationary Big Bang model, but certain elements have appeared that we do not understand: dark energy and dark matter, of which we were unaware and which, without knowing exactly what they are, become essential to explain how the universe moves.

In this hypothesis, I propose an alternative creation of the Universe to the Big Bang, based on a dual equilibrium between matter and antimatter, which could resolve the observed mysteries and provide a more effective and cleaner solution to many of the processes we observe in the Universe.

As key points of novelty, what I explicitly suggest is that energy is balanced in a way that creates a cyclical process without a defined beginning or end. In this model, gravity is not determined by matter, as we currently think, but by an energy drag flow originating from black holes. Think of the Earth and the Moon as "pebbles" carried by the current of a river (light) flowing toward a waterfall (black hole).

Matter itself is made up of light, or, to continue the analogy, of a "calcareous residue" that it leaves behind as it swirls along its path.

I'm aware of how strange it seems, but if I'm not terribly mistaken, both mathematics and observations seem to predict it this way.

What do you think?...

Could this be how our Universe works?

Loading results...