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The standard model of particle physics forms a consistent system for universe description. After following quantum mechanics, it derives particles from relativistic quantum fields. Since it does not include gravitation, it describes only one aspect of the universe. In extension of general relativity, Einstein had proposed a symmetrical and complementary approach of physics. In his program, he privileged a relativist field based on representations for physical phenomena, before a precise mathematical description. It allows completing and unifying the universe description, like both eyes for relief vision, and both ears for stereophonic audition. We propose to show it with many simple examples.

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<p class="1Body">The Einstein’s program forms a consistent system for universe description, beside the standard model of particles. It is founded upon a scalar field propagating at speed of light c, which constitutes a common relativist framework for classical and quantum properties of matter and interactions. Matter corresponds to standing waves. Classical domain corresponds to geometrical optics approximation, when frequencies are infinitely high, and then hidden. Quantum domain corresponds to wave optics approximation. Adiabatic variations of frequencies yield electromagnetic interaction. They lead also to Classical and Quantum Mechanics equations, with unification of first and second quantifications for interactions and matter, and to the wave-particle duality, by space reduction of the introduced space-like amplitude function u(r,t), which completes the usual time-like function ψ(r,t).</p>

For a scalar field propagating at light velocity c, we show that kinematic and dynamic properties of almost monochromatic standing waves, with frequency Ω(x, t) = ω ± δΩ(x, t), where ω is constant, and δΩ (x, t) ω, are formally identical with mechanical properties of matter. They are both described by equations with the same mathematical structure. The energy conservation stems from stability in time, while the variational principle stems from stability in space. In classical mechanics of a particle, the relativist equations correspond to the geometrical optics approximation as ω → ∞. The quantum mechanical equations correspond to the wave optics approximation, in which wave homogeneous Fourier relations are replaced by the material Heisenberg relations.