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Directional Density of Gases Under FitzGerald-Lorentz Contraction: Predictions for Optical Interferometry

Alvydas Jakeliunas

Published Feb 26, 2026• 0 citations
Publisher

Abstract

In Lorentz Ether Theory, FitzGerald-Lorentz contraction affects all matter — containers, molecules, and the electromagnetic interactions between them. In a static gas, the anisotropic collision cross-sections of contracted molecules drive the density distribution toward the same anisotropy as in a solid, restoring the SR/LET equivalence. However, this equilibration proceeds at the diffusion timescale τ_diff ~ L²/D — hundreds to thousands of seconds for a laboratory gas cell. In a continuously rotating experiment with period T_rot ~ 5–60 s, the anisotropy cannot keep pace with the changing contraction direction: the gas density remains isotropic while the solid tracks the contraction instantaneously. This timescale separation creates a measurable difference: the directional density of a gas (molecules per unit length) is isotropic, while that of a solid is anisotropic. The resulting fringe shift on rotation is ΔN = k(L/2λ)(n−1)(v/c)², where k is the number of passes. The signal scales linearly with gas pressure — providing a built-in calibration. We predict null results for solid-dielectric interferometers regardless of refractive index.

DOI
10.5281/zenodo.18782803

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In Lorentz Ether Theory, FitzGerald-Lorentz contraction affects all matter — containers, molecules, and the electromagnetic interactions between them. In a static gas, the anisotropic collision cross-sections of contracted molecules drive the density distribution toward the same anisotropy as in a solid, restoring the SR/LET equivalence. However, this equilibration proceeds at the diffusion timescale τ_diff ~ L²/D — hundreds to thousands of seconds for a laboratory gas cell. In a continuously rotating experiment with period T_rot ~ 5–60 s, the anisotropy cannot keep pace with the changing contraction direction: the gas density remains isotropic while the solid tracks the contraction instantaneously. This timescale separation creates a measurable difference: the directional density of a gas (molecules per unit length) is isotropic, while that of a solid is anisotropic. The resulting fringe shift on rotation is ΔN = k(L/2λ)(n−1)(v/c)², where k is the number of passes. The signal scales linearly with gas pressure — providing a built-in calibration. We predict null results for solid-dielectric interferometers regardless of refractive index.
From a macroscopic viewpoint, atomic vapours appear homogeneous and isotropic. As we have seen during the discussion of the microscopic dynamics that light induces in atomic systems, however, the interaction with light as well as external fields can break the rotational and translational symmetries and make the system both inhomogeneous and anisotropic. This microscopic anisotropy appears directly in the optical properties of the system. This chapter discusses the propagation of light in such a medium and describes experiments that analyse the transmitted light to obtain information about the microscopic state of the medium. Isotropic atoms The Lorentz–Lorenz model Outline The interaction of electromagnetic radiation with matter, in particular light, has inspired philosophers of nature for many centuries and has led to heated debates like the one between Newton and Goethe. The original interest was with the difference in absorption of various materials as a function of the optical wavelength and with the refraction of light, i.e., its dispersion. The first theoretical analysis that connected these macroscopic effects to microscopic properties of the material was the Lorentz–Lorenz theory of dispersion (Lorentz 1880; Lorenz 1881), which was put forward shortly after the Maxwell equations and published in the year after Maxwell's death. (See Figure 6.1.) This theory models the material as a collection of dipoles, driven by the electromagnetic wave. We give here a brief summary of the theory, since its physical content is still the foundation of today's description although the mathematical formalism has changed significantly.
A microscopic description of the zero-energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole-dipole interaction, on the energy per particle, comparing the results with mean-field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to the polarization field. We present a series expansion of the solution of the zero-energy two-body problem, which allows us to find the scattering length of the interaction and to build a suitable Jastrow factor that we use as a trial wave function for both a variational and diffusion Monte Carlo simulation of the infinite system. We find that the anisotropy has an almost negligible impact on the ground-state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions.
A collection of ultracold atoms has an index of refraction that varies depending on the spatial density distribution of the gas. For many confined gases commonly found in ultracold atom experiments, there can be a substantial gradient in the spatial density distribution and hence the index of refraction. In addition, these gases can have a smaller spatial extent than that of the cross section of a laser beam that illuminates them. With a sufficient gradient in density under these conditions, the resulting index variation leads to frequency-dependent focusing or defocusing of incident near-resonant light as demonstrated by the calculations in this work. Nonintuitive intensity pattern formations result within the gas from the combination of refraction and diffraction of the incident light, including focusing effects that substantially increase the intensity of the light as compared to its incident value despite the nominally absorptive nature of the gas.
We report the first measurements of the index of refraction of gases for lithium waves. Using an atom interferometer, we have measured the real and imaginary parts of the index of refraction n for argon, krypton, and xenon as a function of the gas density for several velocities of the lithium beam. The linear dependence of (n-1) with the gas density is well verified. The total collision cross section deduced from the imaginary part of (n-1) is in very good agreement with traditional measurements of this quantity. Finally, the real and imaginary parts of (n-1) and their ratio rho exhibit glory oscillations, in good agreement with calculations.
A rarefied gas of neutral atoms cooled and trapped by means of the resonance light pressure forces’ is an example of a system when n λ3 ≤ 1, but Nα ≥1. Here N denotes the density of atoms, λ is the light wavelength, a is the microscopic polarizability. It means that local field effects are essential, whereas Lorentz–Lorenz relation between α and refractive index n already, generally speaking, is not applicable. For rarefied gas even the question of the method integral equation2 applicability in itself is not evident, but in any case its application implies that the Lorentz’s sphere radius must be much larger than wavelength, which is incompatible with the traditional approach. With the choice of a large Lorentz sphere the variables substitution method3 allowed to calculate simultaneously linear and nonlinear medium characteristics and to obtain a connection between local and macroscopic fields when the spatial dispersion is taken into account. These characteristics essentially depend on the interaction law between the particles. In the no-interaction condition (ideal gas) Lorentz-Lorenz formula is valid for arbitrary densities, including the case Nλ3<< 1. It has been revealed that for repulsive forces between the atoms in a case Nα ≥ 1 an effect of the optical transparency (n2− 1 << 1) takes place.