Optics as the Unification Paradigm in Fundamental Physics and the Possibility of Gravito-Inertial Engineering

Introduction

There exist compelling hints (for example ) which point towards the notion that the branches of fundamental physics, including gravity, “quantum mechanics”, and their overlapping domain are already unified. I argue that this paradigm is optics (understood as the science of propagation of perturbations within a medium) in its various declinations and specialization to particular cases (geometrical, wave, nonlinear, diffractive) and that the various branches or regimes of fundamental physics are special cases of this broader framework.

The Vision

What I propose is to look at known, but puzzling, phenomenology such as wave-particle duality, single-particle diffraction and interference, “curved spacetime” as manifestation of some general theory of propagation of “disturbances” within a medium. The disturbances can either take the form of extended undulation regions with expanding wave-fronts (that is waves in the most natural sense), or the form of highly-localized self-confined dynamic configurations of the medium, which propagate as impulses maintaining their shape (“solitons”), or anything in between these two extremes.

The propagation of these waves, these localized dynamic configuration and of these something-in-between is assumed to be governed by the Principle of Least Action, which declined in various special cases gives rises to specific phenomenology.

The Medium

The medium which could realize such internal motions is an ether in the sense specified by Larmor-Lorentz-Poincaré-Bell with some modification to allow for some large-scale inhomogeneity (to account for “gravity”) and some nonlinearity (to account for “particles”).

What is a massive particle?

Material massive particles can be understood as portions of ether in which some radiant electromagnetic energy is confined (this is the true sense of \(E=mc^2\), or better: \(m=E/c^2\)). I am not yet sure of which is the confinement mechanism, but I am betting on the local modification of the electric permittivity and magnetic permeability tensors by the high intensity of the radiation field, a manifestation of the medium nonlinearity as in Kerr effect for example. In other words, I argue that massive particles are solitons characterized by internal, periodic, cyclic, “effective” spatially-limited motions, which also must include spin. The characteristic frequency of this internal motion is \(\Omega_0 = \frac{\hbar}{c^2}m\), while the period is \( \tau_0 = 2\pi/\Omega_0 \).

What is a photon?

In this paradigm, photons must be local, circularly polarized perturbations of the ether which propagate at the locally defined characteristic speed, which in turn is a function of of the local values of the electric permittivity tensor \(\stackrel{\leftrightarrow}{\varepsilon}\), the magnetic permeability tensor \(\stackrel{\leftrightarrow}{\mu}\), and the antisymmetric magneto-electric coupling tensor \(\stackrel{\leftrightarrow}{\alpha}\) of the ether . Photons carry around units of energy and angular momentum between massive particles (which are themselves lumps of confined photons).

How do photons and massive particles propagate?

The propagation of photons or lumps of confined photons (“massive particles”) is determined by the PLA applied within portions of a generally inhomogeneous and anisotropic ether including the potential obstacles that the particle (or a ray of light) may find along its possible paths.

What is gravity and how do photons and massive particles generate it?

In this paradigm “gravity” is just a local perturbation of the “inertial field” or “refractive field” given by the triplet \((\stackrel{\leftrightarrow}{\varepsilon}(\vec{x},t),\stackrel{\leftrightarrow}{\mu}(\vec{x},t),\stackrel{\leftrightarrow}{\alpha}(\vec{x},t))\). In fact the physical significance of general relativity and its core principle (the Principle of Equivalence (in its Einsteinian form)) rests not so much on the “geometrization” of gravity, but rather in the unification of inertia and gravitation in a single gravito-inertial field, as explained by Einstein himself .

At the time of writing, the most plausible constructive mechanism for the generation of gravity that I can think of, is considering that the mass-energy distribution (that is the distribution of solitons and photons and extended waves) must act as sources of perturbation of an acousto-optic modulation signal of the triplet \((\stackrel{\leftrightarrow}{\varepsilon}(\vec{x},t),\stackrel{\leftrightarrow}{\mu}(\vec{x},t),\stackrel{\leftrightarrow}{\alpha}(\vec{x},t))\) exactly as what happens in so-called spacetime modulated metamaterials .

It has been demonstrated, that accurate spacetime modulation of \((\stackrel{\leftrightarrow}{\varepsilon}(\vec{x},t),\stackrel{\leftrightarrow}{\mu}(\vec{x},t),\stackrel{\leftrightarrow}{\alpha}(\vec{x},t))\) can simulate any known spacetime metric (flat or curved) plus any other exotic ones, like “white holes” for cloaking applications .

If this is really the case (and I think it is), it could be possible in principle to discover what kind of signal the masses are emitting, how to control, amplify, focus, and direct it so to manipulate “spacetime curvature” at will, realizing what could be called gravito-inertial or metric engineering . The possibilities are mind-boggling.

Correspondence between the limits of optics and different fundamental physical theories

The critical parameters which distinguish the various limits of the general framework are the following:

• Spatial scale of observation w.r.t characteristic length of a particle (\( \lambda_{dB}/L \))
  • For \( \lambda_{dB}/L \sim 1\) we must consider the particle(s) as spatially extended system(s).
  • For \( \lambda_{dB}/L \rightarrow 0\) we can consider the particle(s) as point-like.
• Temporal scale of observation w.r.t characteristic period of a particle (\( \tau_0/T \))
  • For \( \tau_0/T \sim 1\) we must consider the particle(s) as oscillating system(s).
  • For \( \tau_0/T \rightarrow 0\) we can consider the particle(s) as a time-averaged and stationary.
• Number of particles considered (\( N \))
  • For \( N \sim 1 \) we have “few particles mechanics”.
  • For \( N \gg 1 \) we have a “many-particle-mechanics”.
• Characteristic dimensions of slits, holes, impact parameters w.r.t. characteristic length of a particle (\( D/\lambda_{dB} \))
  • For \( D/\lambda_{dB} \rightarrow \infty\) we have the geometrical optics limit (ballistic straight-line propagation, reflection, refraction).
  • For \( D/\lambda_{dB} \sim 1 \) we have the diffraction-interference optics limit (ballistic straight-line propagation, reflection, refraction, diffraction, interference).
• Homogeneity or in homogeneity of opto-electro-magnetic parameters of the ether \((\stackrel{\leftrightarrow}{\varepsilon},\stackrel{\leftrightarrow}{\mu},\stackrel{\leftrightarrow}{\alpha})\)
  • For \((\stackrel{\leftrightarrow}{\varepsilon}\rightarrow\varepsilon_0,\stackrel{\leftrightarrow}{\mu}\rightarrow\mu_0,\alpha_{jk}\rightarrow [ijk]v_i)\) we have an homogeneous (but in general anisotropic) ether. This is the ether of (weak) special relativity. The anisotropy (parametrized by the vector \( \vec{v} \)) has an effect on the one-way-speed-of-light (which is empirically inaccessible) but leaves the two-way speed of light invariant (as it should).
  • For \((\stackrel{\leftrightarrow}{\varepsilon}(\vec{x},t),\stackrel{\leftrightarrow}{\mu}(\vec{x},t),\stackrel{\leftrightarrow}{\alpha}(\vec{x},t))\) we have (in general) an inhomogeneous and anisotropic ether. The inhomogeneities in the parameters are a function of the distribution of matter-energy. This is the ether of general relativity.

Some examples of combinations of limits

• Case A.1 Geometrical optics + few particles + homogeneous ether \(\rightarrow\) special relativity
  • \( \lambda_{dB}/L \rightarrow 0\) (point particles)
  • \( \tau_0/T \rightarrow 0\) (fast internal motions)
  • \( N \sim 1 \) (few particles)
  • \( D/\lambda_{dB} \rightarrow \infty\) (large slits, distant obstacles)
  • \((\stackrel{\leftrightarrow}{\varepsilon}\rightarrow\varepsilon_0,\stackrel{\leftrightarrow}{\mu}\rightarrow\mu_0,\alpha_{jk}\rightarrow [ijk]v_i)\) (homogeneous ether)
    In this case we have single massive particles and single photons which propagate in straight lines unless acted upon by a force (a.k.a. potential gradient), which corresponds to the unmodified principle of inertia (as stated by Leonardo, Galileo, Newton) and therefore to the massive point mechanics of Newton-Euler-Lagrange and (for high speeds) special relativity without considering gravity.
    
• Case A.2 Geometrical optics + few particles + inhomogeneous ether \(\rightarrow\) general relativity
  • \( \lambda_{dB}/L \rightarrow 0\) (point particles)
  • \( \tau_0/T \rightarrow 0\) (fast internal motions)
  • \( N \sim 1 \) (few particles)
  • \( D/\lambda_{dB} \rightarrow \infty\) (large slits, distant obstacles)
  • \((\stackrel{\leftrightarrow}{\varepsilon}(\vec{x},t),\stackrel{\leftrightarrow}{\mu}(\vec{x},t),\stackrel{\leftrightarrow}{\alpha}(\vec{x},t))\) (inhomogeneous, anisotropic ether)
    In this case we have single massive particles and single photons which propagate in curved spacetime geodesic unless acted upon by a force (a.k.a. potential gradient), which corresponds to the modified principle of inertia (Einstein’s geodesic equation) and therefore to the massive point mechanics of Newton-Euler-Lagrange including high-speed effects and gravity, that is general relativity.
    
• Case B.1: Wave optics + few particles + homogeneous ether \(\rightarrow\) “de Broglie mechanics”
  \( \lambda_{dB}/L \rightarrow 0\) (point particles)
  \( \tau_0/T \rightarrow 0\) (fast internal motions)
  \( N \sim 1 \) (few particles)
  \( D/\lambda_{dB} \sim 1\) (small slits, near obstacles)
  \((\stackrel{\leftrightarrow}{\varepsilon}\rightarrow\varepsilon_0,\stackrel{\leftrightarrow}{\mu}\rightarrow\mu_0,\alpha_{jk}\rightarrow [ijk]v_i)\) (homogeneous ether)
  In this case we have the diffractive optics limit in a homogeneous, isotropic medium, where massive particles and photons propagate in straight lines unless acted upon by a force (a.k.a. potential gradient) and/or unless they pass through a slit, or a hole or close enough to an obstacle so that they deviate their path, which corresponds to the modified principle of inertia advocated by de Broglie in 1923 and therefore to the yet-to-be-developed mechanics of de Broglie which should include the single-particle or low-number-of-particles diffraction in its equations of motion .The state of the art is a probabilistic recipe based on signal-analysis in 3N-dimensional configuration space which can calculate stationary states and interference patterns without reference to 3D Euclidean space. We call this “quantum mechanics“, even if it is neither quantum, nor mechanics.

One can go on and play with all the different combinations to find different physics regimes (even “new physics”). An example would be to make the ether inhomogeneous in B.1 so to obtain a “quantum gravity” regime combining “quantum effects” (diffraction and interference) with “gravitational” ones (refraction). If one takes again B.1 and sets \( N \gg 1 \) one ends up in the classical wave optics limits (which means the propagation of a classical Maxwell field (for photons) and a classical Dirac field (for electrons)), if one then releases the ether homogeneity hypothesis one obtains the propagation of Maxwell or Dirac fields within a “curved spacetime”). One could also play with the spatio-temporal observation scale and see what happens (for example) when we have a macroscopic particle like a Bose-Einstein condensate \( \lambda_{dB}/L \sim 1\) interacting with a gravitational field (local perturbation of \((\stackrel{\leftrightarrow}{\varepsilon}(\vec{x},t),\stackrel{\leftrightarrow}{\mu}(\vec{x},t),\stackrel{\leftrightarrow}{\alpha}(\vec{x},t))\)). In fact there are good reasons to expect that new physics might pop up , and maybe already has .

Conclusions and Outlook

Optics as understood in the modern sense as the study of propagation of perturbations within a medium stands out as an all-encompassing, unifying vision for all branches of fundamental physics, even if the specific details of some regimes are not worked out yet. In fact, this vision can serve as a guide in constructing new specialized theories in the “quantum gravity” regime, in the “macroscopic quantum gravity” regime, or even in a causal, microscopic “emergent” explanation for the perturbation of the gravito-inertial field by the masses based on testable, reproducible phenomena.

Acknowledgements

Special thanks to M. De Solda for his infinite patience in questioning, correcting, criticizing, proofreading my innumerable attempts at finding a path to unification over a span of 14 years. This time it really seems that “there is a path” after all.

References