Electric and magnetic frame change

export function evaluateSr08(input: Sr08Input): Sr08Snapshot {
  const c = C_SI;
  const v = input.boost;
  const eventId = "event-test-charge-0";

  const packScalar = (
    key: keyof typeof SR08_ROWS,
    make: (id: string, unit: string, kind: string, owner: string) => ScientificResult,
  ) => {
    const r = SR08_ROWS[key];
    return make(r[0], r[1], r[2], r[3]);
  };

  const refuseAll = (reason: string, condition: string): Sr08Snapshot => {
    const out = (key: keyof typeof SR08_ROWS) =>
      packScalar(key, (id, unit, kind, owner) =>
        asOutside(id, unit, kind, owner, condition, reason),
      );
    return Object.freeze({
      beta: v / c,
      gamma: Number.NaN,
      electricFieldStationary: out("Em"),
      electricFieldMoving: out("Ec"),
      magneticFieldStationary: out("Bm"),
      magneticFieldMoving: out("Bc"),
      fieldInvariantEDotB: out("id"),
      fieldInvariantE2MinusC2B2: out("iv"),
      lorentzFactor: out("g"),
      chargeVelocityStationary: out("um"),
      chargeVelocityMoving: out("uc"),
      transverseForceLaboratory: out("Fm"),
      transverseForceComoving: out("Fc"),
      eventId,
    });
  };

  const inputsValid = [
    input.electricField.x,
    input.electricField.y,
    input.electricField.z,
    input.magneticField.x,
    input.magneticField.y,
    input.magneticField.z,
    input.chargeVelocity.x,
    input.chargeVelocity.y,
    input.chargeVelocity.z,
    input.boost,
    input.testCharge,
  ].every(Number.isFinite);

  if (!inputsValid) {
    return refuseAll(
      "All field, velocity, boost, and charge inputs must be finite numbers.",
      "finite inputs",
    );
  }

  if (Math.abs(v) >= c) {
    return refuseAll("Observer boost speed must satisfy |v| < c.", "|v| < c");
  }

  const uSpeed2 =
    input.chargeVelocity.x * input.chargeVelocity.x +
    input.chargeVelocity.y * input.chargeVelocity.y +
    input.chargeVelocity.z * input.chargeVelocity.z;
  if (uSpeed2 >= c * c) {
    return refuseAll("Test charge speed must satisfy |u| < c.", "|u| < c");
  }

  const beta = v / c;
  const g = gamma(beta);
  if (g.status !== "value") {
    return refuseAll("Lorentz factor undefined for |v| >= c.", "|v| < c");
  }
  const γ = g.value;

  const E0 = input.electricField;
  const B0 = input.magneticField;
  const u0 = input.chargeVelocity;
  const q = input.testCharge;

  // Transformed fields under boost v along x
  const transformedSI = transformSI({ E: E0, B: B0, boost: v, c });
  const Eprime = transformedSI.E;
  const Bprime = transformedSI.B;

  // Invariants
  const inv0 = fieldInvariants(E0, B0, c);

  // Transformed velocity of test charge
  const uprime = transformVelocity3D(u0, v, c);

  // Forces
  const F_lab = lorentzForce(q, E0, B0, u0);
  const F_comoving = lorentzForce(q, Eprime, Bprime, uprime);

  const valScalar = (key: keyof typeof SR08_ROWS, val: number) =>
    packScalar(key, (id, unit, kind, owner) => asValue(id, unit, kind, owner, val));
  const valVec = (key: keyof typeof SR08_ROWS, vec: Vec3) =>
    packScalar(key, (id, unit, kind, owner) => asVectorValue(id, unit, kind, owner, vec));

  return Object.freeze({
    beta,
    gamma: γ,
    electricFieldStationary: valVec("Em", E0),
    electricFieldMoving: valVec("Ec", Eprime),
    magneticFieldStationary: valVec("Bm", B0),
    magneticFieldMoving: valVec("Bc", Bprime),
    fieldInvariantEDotB: valScalar("id", inv0.eDotB),
    fieldInvariantE2MinusC2B2: valScalar("iv", inv0.e2MinusC2B2),
    lorentzFactor: valScalar("g", γ),
    chargeVelocityStationary: valVec("um", u0),
    chargeVelocityMoving: valVec("uc", uprime),
    transverseForceLaboratory: valVec("Fm", F_lab),
    transverseForceComoving: valVec("Fc", F_comoving),
    eventId,
  });
}

export function transformSI(input: {
  E: Vec3;
  B: Vec3;
  boost: number;
  c?: number;
}): Readonly<{ E: Vec3; B: Vec3; gamma: number }> {
  const c = input.c ?? C_SI;
  const v = input.boost;
  const g = gamma(v / c);
  if (g.status !== "value") {
    return Object.freeze({ E: input.E, B: input.B, gamma: Number.NaN });
  }
  const γ = g.value;
  const { E, B } = input;
  return Object.freeze({
    gamma: γ,
    E: Object.freeze({
      x: E.x,
      y: γ * (E.y - v * B.z),
      z: γ * (E.z + v * B.y),
    }),
    B: Object.freeze({
      x: B.x,
      y: γ * (B.y + (v * E.z) / (c * c)),
      z: γ * (B.z - (v * E.y) / (c * c)),
    }),
  });
}