Special relativity · The opening asymmetry
The same relative motion,
two accounts of one current.
Why does moving the magnet instead of the conductor create an explanatory asymmetry, and how does the transformation remove it? Both descriptions are internally coherent. They agree on what is measured to first order in v/c.
SR-02 · Magnet and conductor
Magnet and conductor
The same relative motion of magnet and conductor can be told two ways; nature does not care which body we call at rest.
In the magnet's rest frame the charges in the moving conductor feel q(v × B). In the conductor's rest frame those charges feel qE', and E' is the transform of the magnet's field. The two electromotive forces along a path across the motion differ by the factor gamma.
A path across the boost has endpoint events with Δx = 0, so they are simultaneous in both frames and the length is unchanged. Then the magnet-frame electromotive force is vBℓ and the conductor-frame value is gamma vBℓ. The excess gamma − 1 is computed as gamma²β²/(gamma+1), never as a float64 ratio minus one.
The paper's first paragraph states the classical asymmetry. Section 6 removes it: electric and magnetic forces do not exist independently of the state of motion of the coordinate system. Lorentz's ether plus local time produces the same first-order formulae; that account is empirically equivalent at the speeds of real apparatus, not declared refuted here.
Choose which body is described as moving, type a speed, and inspect both accounts of the same current. No dragging is required. The ether-plus-local-time account is not declared refuted; at the speeds of real apparatus it agrees to first order in v/c.
Accepted snapshot
| B (magnet rest) | 1 T |
|---|---|
| E (magnet rest) | 0 V/m |
| E′_y (conductor rest) | -10 V/m |
| Force on q (magnet rest) | -1.6022e-18 N |
| Force on q (conductor rest) | -1.6022e-18 N |
| Electromotive force, magnet rest | 1 V |
| Electromotive force, conductor rest | 1 V (slice: magnet rest K) |
| Excess γ − 1 | 5.5633e-16 |
| Endpoint offset | 0 s |
| Circuit current | Current in a real circuit is not modeled; SR-02 has no circuit. |
Not modeled: conductor resistance and induced currents; self-inductance; magnetization dynamics and extended-magnet fields beyond the ideal dipole; time-varying flux of extended circuits; edge fields; radiation; unipolar machines; electromotive-force comparison across frames for a path with a component along the direction of motion, which needs a declared simultaneity slice this model does not supply.
Open the two descriptions
A path across the motion is comparable
An electromotive force is work per unit charge along a stated path, not a field component. The default segment lies along ŷ, across a boost along x̂, so the endpoint events have Δx = 0. They are simultaneous in both frames, the length is unchanged, and the ratio of the two electromotive forces is exactly γ.
At 10 m/s with B = 1 T and ℓ = 0.1 m the magnet-frame value is 1 V. The excess γ − 1 is 5.563×10⁻¹⁶ from the cancellation-free form; a float64 evaluation of γ − 1 is not that number. At 0.6c the ratio is 1.25. Those two electromotive forces are not the same number, and they are not supposed to be: the correct comparison is the transformation law. Lorentz's ether plus local time produces the same first-order formulae and is not declared refuted here.