Weber’s Universe | One Force. 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Independent Research · Sweden · 2026

Weber’s UniverseOne Force. One Field.

A unified framework combining Wilhelm Weber’s velocity-dependent electrodynamics, a variable speed of light, and quantum mechanics — explaining all fundamental forces through a single electromagnetic principle.

Weber’s Force Law

F = (q₁q₂)/(4πε₀r²) × [ 1 − ṙ²/2c(t)² + r·r̈/c(t)² ]

where c(t) is the dynamical speed-of-light scalar field

4→1

Forces unified

c(t)

Dynamic light speed

α(t)

Fine structure varies

e

Only true constant

A Simpler Story for the Same Universe

Rather than adding invisible scaffolding — colour charge, gluons, dark energy, inflaton fields — this framework asks whether existing entities have been described with sufficient generality.

01

Weber’s Electrodynamics

Wilhelm Weber (1804–1891) showed that the force between charged particles depends on their relative velocity and acceleration — not just distance. This richer law predicts nuclear-scale attraction without invoking new particles.

02

Variable Speed of Light

Promoting c to a dynamical scalar field c(t, φ) resolves the horizon problem, explains fine-structure constant drift in quasar spectra, and serves as the c-wave — the physical carrier of quantum probability amplitudes.

03

Quantum Mechanics Reinterpreted

Quantum uncertainty need not be irreducible mystery. In a fluctuating c-field, every charged particle sits in a trembling electromagnetic environment. The probability cloud is a statistical description of deterministic motion.

Historical Background

1785

Coulomb’s Law

Charles-Augustin de Coulomb establishes the inverse-square law for electrostatic force — distance only.

1845

Fechner’s Hypothesis

Gustav Fechner proposes that currents consist of equal positive and negative charges moving in opposite directions — the seed of Weber’s insight.

1846

Weber’s Force Law

Wilhelm Weber publishes his velocity- and acceleration-dependent force law, unifying electrostatics and Ampère’s induction law in a single formula.

1856

Weber–Kohlrausch Constant

Weber and Kohlrausch measure the ratio c_W = c√2 — the first derivation of the speed of light from pure electrical measurements, predating Maxwell by years.

1864

Maxwell’s Equations

Maxwell independently derives c from electromagnetic constants — but in a field-based framework that abandons Weber’s action-at-a-distance approach.

1937

Dirac’s Large Numbers

Paul Dirac notes that the ratio of electromagnetic to gravitational force (~10⁴⁰) matches cosmic age ratios — suggesting G and other ‘constants’ evolve with the universe.

1993

VSL Cosmology

John Moffat proposes a variable speed of light to solve the horizon problem without inflation. Magueijo and Albrecht extend this in 1998–1999.

2026

Weber-VSL Unification

This framework: Weber’s law + c(t) scalar field + quantum reinterpretation = a single unified description of all four fundamental forces.

by the Weber attractive regime (sub-femtometre). The net charge is zero but the residual Weber interaction gives the strong nuclear binding.

Particle Spin in a Variable c-Field

In the Weber-VSL framework, spin angular momentum is not an intrinsic, structureless property — it is a consequence of the charge orbiting within the c-field vortex at the Planck scale.

Two electrons with the same spin (↑↑) have co-rotating c-field vortices that interfere destructively — producing a repulsive pressure (Pauli exclusion). Electrons with opposite spin (↑↓) have counter-rotating vortices that interfere constructively, allowing closer approach and Cooper-pair-like binding.

When c(t) decreases over cosmic time, both ℏ and α co-evolve because all three are linked through the single relation α(t) = e²/(4πε₀·ℏ(t)·c(t)). The Bohr radius a₀ = ℏ²/(m_e·e²·k) shifts measurably, producing detectable atomic spectral drift. This is a direct, falsifiable prediction: neither ℏ nor α is truly constant.

α(t) = e² / (4πε₀·ℏ(t)·c(t))
ℏ(t) = e² / (4πε₀·α(t)·c(t))
→ Δα/α ≈ Δc/c − Δℏ/ℏ (coupled drift)

Beta Decay in the Weber Framework

Before: Neutron

A neutron is a Weber-bound (e⁻ + p⁺) composite. The sub-femtometre Weber attraction holds them together at the current value of c(t).

n = e⁻ ⊕ p⁺ r < r_c(c₀)

Trigger: c-field fluctuation

A local c-field fluctuation momentarily increases c, which expands r_c beyond the neutron radius. The Weber binding weakens below the zero-point energy threshold.

δc/c > threshold r_c → r_c·(c+δc)/c

After: Proton + Electron

The Weber binding breaks: the electron is emitted as β⁻ and the proton remains free. A neutrino carries the momentum imbalance — reinterpreted here as a c-field wave packet.

n → p⁺ + e⁻ + ν̅_e (c-wave packet)

What Really Doesn’t Change

Modern physics assumes c, ℏ, G, and α are eternal constants. The Weber-VSL framework shows only the elementary charge e is truly invariant — c, ℏ, G, and α are all derived from it and the evolving scalar field c(t).

c VARIABLE

Speed of Light

Standard Model: fixed at 299,792,458 m/s. Invariant.

Weber-VSL: c = c(t, φ), a dynamical scalar field. Decreases smoothly over cosmic time. Its drift is the root cause of all other ‘constant’ variations.

VARIABLE

Planck’s Constant

Standard Model: fixed at 1.055×10⁻³⁴ J·s. Fundamental quantum of action.

Weber-VSL: ℏ(t) = e²/(4πε₀·α(t)·c(t)). As both c and α evolve, ℏ is doubly derived — not fundamental at all.

α VARIABLE

Fine Structure Constant

Standard Model: α = e²/(4πε₀ℏc) ≈ 1/137.036. Dimensionless, exact, the coupling strength of electromagnetism.

Weber-VSL: α(t) = e²/(4πε₀·ℏ(t)·c(t)). As c(t) decreases, α drifts if ℏ does not compensate exactly. Quasar spectra confirm Δα/α ≈ −5.7×10⁻⁶ over 10 Gyr — the primary observational window into the VSL field.

G VARIABLE

Gravitational Constant

Standard Model: fixed at 6.674×10⁻¹¹ N·m²/kg². No derivation from other constants.

Weber-VSL + Mach: G ∝ c²(t)/M_universe. As the universe expands and c decreases, G evolves. Dirac predicted exactly this: G changes by ~5 parts in 10¹¹ per year.

e TRUE CONSTANT ✓

Elementary Charge

Standard Model: e = 1.602×10⁻¹⁹ C. One of the fundamental constants.

Weber-VSL: e is the ONE true constant. The electric charge of the electron/proton does not evolve with c or cosmic time. All other ‘constants’ are functions of e and c(t).

The α–ℏ–c Triangle: How the Three Variables Are Linked

Definition of α

α(t) = e² / (4πε₀·ℏ(t)·c(t))

α is derived — not fundamental

Planck’s constant from α and c

ℏ(t) = e² / (4πε₀·α(t)·c(t))

ℏ tracks both α and c

Observed drift (quasars)

Δα/α ≈ −5.7×10⁻⁶ / 10 Gyr

Murphy, Webb & Flambaum 2003

In the Weber-VSL framework, α, ℏ, and c are not three independent constants — they form a coupled system where only e is free. A change in c(t) at the cosmological scale propagates through this triangle, producing correlated drifts in α and ℏ. The fact that α appears to drift (quasar absorption spectra) while ℏ appears stable at laboratory precision is naturally explained: the two drifts are partially compensating — Δα/α ≈ Δc/c − Δℏ/ℏ.

Dirac’s Large Number Hypothesis

In 1937, Paul Dirac noticed a remarkable numerical coincidence: the ratio of the electromagnetic force to the gravitational force between an electron and proton (~10⁴⁰) is approximately equal to the age of the universe in atomic units (~10⁴⁰). This could not be coincidence — it implies that at least one of the ”constants” involved (G, e, m, c) must change with cosmic time.

F_em/F_g ≈ 10⁴⁰

EM/gravity force ratio

T_universe ≈ 10⁴⁰ t_atomic

Age of universe (atomic units)

G ∝ 1/t

Dirac’s prediction: G decreases

The Double-Slit Experiment: c-Wave as Probability

In standard quantum mechanics the wave function Ψ is a purely mathematical object with no agreed physical interpretation. In the Weber-VSL framework it acquires a concrete identity: the c-wave is a real fluctuation of the local speed-of-light field, and |Ψ|² is the squared amplitude of that fluctuation.

When a single electron passes through a double slit, it is the c-field that passes through both slits simultaneously, forming an interference pattern. The electron, as a point charge, follows a definite trajectory — but lands at a position drawn from the probability distribution set by the c-wave amplitude.

This resolves the measurement problem without collapse postulates: ”measurement” is simply a strong local c-field perturbation that localises the particle’s trajectory.

P(x) = |Ψ(x)|² — Ψ = ?

P(x) = |c-wave(x)|²

c-wave = δc(x)/c₀

Physical, measurable, deterministic

Heisenberg Uncertainty from c-fluctuations

If c fluctuates stochastically on microscopic scales, the variance in particle position follows:

⟨(Δx)²⟩ ~ ℏ / (m · δc² / c³)

Requiring consistency with ΔxΔp ≥ ℏ/2 constrains c-fluctuation amplitude to δc/c ~ 10⁻³⁵ at the Planck scale — a natural bridge between quantum and gravitational domains.

Experimental Predictions

The Weber-VSL framework is not a philosophical curiosity — it makes three families of precise, near-term falsifiable predictions.

Test 01

Fine-Structure Constant Drift

Instrument

ESPRESSO / ELT-HIRES

Prediction

Monotonic decrease of α(t) with look-back time (Δα/α ≈ −5.7×10⁻⁶ per 10 Gyr). α and ℏ drift together as c(t) decreases.

Tentative evidence reported (Murphy, Webb, Flambaum 2003)

Test 02

Atomic Clock Comparison

Instrument

Al⁺ vs Hg⁺ optical clocks

Prediction

Non-zero dα/dt ≈ 10⁻²⁰/yr across different atomic species

Current sensitivity: 10⁻¹⁹ (Brewer et al. 2019) — just within reach

Test 03

Nuclear Binding Anomalies

Instrument

Penning trap mass spectrometry

Prediction

Sub-percent Weber correction to ⁴He binding energy: ΔE ≈ 10 keV

Within reach of current Penning trap precision (Blaum 2006)

Author

Johan Hägglund

Independent Researcher, Sweden

”Weber’s Force and Variable Speed of Light: A New Approach to Unification in Physics”

Contact Author