The literature notes that electromagnetics is the unification of electricity, magnetism, and optics. Although not noted in the literature, quantics is the unification of mechanics and optics. (Historical background.) By the antitone, we can shown similarity of pattern.

• The basic equation of optics is ln = c, which is antitonic.
• A primary equation of mechanics is implicitly antitonic: T = K + P, where T is total enerygy; K is kinetic energy; P is potential energy. Let T = log S; K = log J; P = log O. Then, T = K + P Û log S = log J + log O Û S = JO, another antitonic form.
• Momentum can be derived from kinetic energy, K = 1/2(mv²): p = m(2K)^1/2 = m(2(T - P))^1/2.
• The mixture of the optical and mechanical antitones results in
  • the Planck-Einstein Law: E = hn, recast antitonically as El = ch,
  • and the de Broglie Law pl = h.

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Both the De Broglie Law and the Planck-Einstein Law cn be derived from the optics law (using action, h) by dimensional algebra

DERIVATION OF DE BROGLIE LAW:
• [ln] = [c] = [L T^-1];
• [h] = [M L² T^-1];
• the dimensional part [M L T^-1] is that for momentum: [p] = [M LT^-1];
• hence, we have [h] = [p L];
• and we can connect back to photonic law by using its wavelength for [L];
• hence, we have h = pl, de Broglie's Law.
DERIVATION OF PLANCK-EINSTEIN LAW:
• knowing light involves energy, we wish to introduce this to some part of photonic law;
• [E] = [M L² T^-2];
• if we put frequency from the photonic law with energy, we have: [E l];
• we consider "absorbing" some of this by action: [h] = [M L T^-1];
• so we have: [Eln] = [h L T^-1];
• and we see that we can "absorb" the [L T^-1] on right above by taking, from photonic law, [c] = [L T^-1];
• hence, we have: El = hc;
• and, this, by the photonic law is equivalent to E = nh, the usual form of the Planck-Einstein Law.

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"Where did we get that [Schrödinger's equation] from? It's not possible to derive it from anything you know. It came out of the mind of Schrödinger." Richard Feynman in The Feynman Lectures on Physics. Wrong! as shown below.
• A quanton displays its wave aspect in free space, but its particulate aspect in side an atom -- an "outide-inside" aspect which is definitely topological.
• One of the two basic laws of quantum theory is the Planck-Einstein "relation": E = hn, recast as El = ch, the form of an antitonic (ordinological) process, and topology can be derived from ordinology.
• The other basic law is the de Broglie "relation": pl = h, also antitonic.
• Correcting Feynman's viewpoint, satisfaction of both of these conditions shows Schrödinger's equation to be the proper differential equation