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Relativistic Interferometer and Lightspeedometer Based on Relativistic Nonlocality

Gajendra Singh Solanki

Published Feb 1, 2021• 0 citations
OpenAlex

Abstract

This paper, the eleventh in the series of rudiments of relativity revisited, extends our efforts to speed up or slow lightspeed in a vacuum using relativistic non-localization of new relativity. In the previous paper namely ‘Ultra lightspeed travel using relativistic non-localization’ we had developed theory and experimental setups to realize supra and infra lightspeed travel. However, all the experimental setups were bulky to realize and their sensitivity was also low. In this paper, we design a highly sensitive interferometer and a lightspeed manipulator that work on the presumption that reflection or refraction may lead to the total collapse of the relativistic non-localized state of a photon, and the reflected or refracted beam bears no memory of the relativistic non-localized state of the incident beam.

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Recent experiments on ultra slow light in strongly dispersive media by several research groups reporting slowing down of the optical pulses down to speeds of a few metres per second encourage us to examine the intriguing possibility of detecting a deflection or fall of the ultra slow light under Earth's gravity, i.e., on the laboratory length scale. In the absence of a usable general relativistic theory of light waves propagating in such a strongly dispersive optical medium in the presence of a gravitational field, we present a geometrical optics based derivation that combines {\it the effective gravitational refractive index} additively with the usual optical dispersion. It gives a deflection, or the vertical fall $Δ$ for a horizontal traversal $L$ as \[ Δ= \frac{L^2}{2}\big(\frac{R_{\oplus G}}{R_\oplus^2}\big) n_g \big(\frac{1}{1+n_g\frac{R_{\oplus G}}{R_\oplus}}\big), \] where $R_{\oplus G}/R_\oplus$ is the ratio of the gravitational Earth radius($R_{\oplus G}$) to its geometrical radius $R_\oplus$, and $n_g$ is the group refractive index of the strongly dispersive optical medium. The expression is essentailly that for the Newtonian fall of an object projected horizontally with the group speed $v_g=c/n_g$, and is tunable refractively through the index $n_g$. For $L \sim 1 m$ and $n_g = c/v_g \sim 10^8$ (corresponding to the ultra-slow pulse speed $\sim few \times 1 ms^{-1}$), we obtain a fall $Δ\sim 1 μm$, that should be measurable $-$ in particular through its sensitive dependence on the frequency that tunes $n_g$.

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The authors are developing a high precision inertial sensor. This device uses cold Caesium atoms manipulated by stimulated Raman transitions (Berman, 1997). As this setup is sensitive to both acceleration and rotation, two counter-propagating beams of cold atoms are used to discriminate between the two contributions. The last experimental results will be presented here

Conference on Precision Electromagnetic Measurements•Jun 1, 2004•1 citation
This paper, the eleventh in the series of rudiments of relativity revisited, extends our efforts to speed up or slow lightspeed in a vacuum using relativistic non-localization of new relativity. In the previous paper namely ‘Ultra lightspeed travel using relativistic non-localization’ we had developed theory and experimental setups to realize supra and infra lightspeed travel. However, all the experimental setups were bulky to realize and their sensitivity was also low. In this paper, we design a highly sensitive interferometer and a lightspeed manipulator that work on the presumption that reflection or refraction may lead to the total collapse of the relativistic non-localized state of a photon, and the reflected or refracted beam bears no memory of the relativistic non-localized state of the incident beam.
This paper, the tenth in the series of ‘Rudiments of relativity revisited’, explores superluminal communication based on relativistic non-localization of new relativity. The new relativity preserves the lightspeed like the current one but also digs deeper into the mechanism behind this constancy. The relativistic non-localization as a superstate is one of the explanations: a photon exists in a superstate of relativistic non-localization, which collapses on detection such that the lightspeed is preserved in the frame of detection. Is it possible to trick this mechanism for the light to supersede its own speed using one or more cross-frame interruptions meant to collapse its superstate in one frame and relaying another burst of light to be detected in another? The two subsequently relayed light-bursts individually preserve lightspeed in their respective frames of detection, but the net result of the two cross-frame flights can be fast or slow travel in a vacuum. Various caveats, assumptions, and experiments to explore supra or infra luminal communication under new relativity are discussed.
Relativistic non-localization enables a moving particle such as a photon to exist at different positions in different frames at an instant and gives rise to an experimentally distinguished physics of relativity. A photon exists in a relativistic non-localized superstate until it is encountered by a detector which results in the collapse of the superstate so as to preserve the lightspeed across frames because the motion state of the detector affects the position of detection. But the current relativity inadvertently assumes the photons to be relativistically localized and invents the relativity of simultaneity. The relativistic non-localization, which is the nonlocality across frames, remained hidden so far under the mathematical elegance of Lorentz transform but is readily revealed by the real domain transform.
Recent experiments on ultra slow light by several research groups reporting slowing down of the optical pulses down to speeds of a few metres per second encourage us to examine the intriguing possibility of detecting a fall of the ultra slow light under Earth's gravity, i.e., on the laboratory scale. In the absence of a usable general relativistic (e.g., post-Newtonian) theory of light waves propagating in the presence of a gravitational field in such a strongly dispersive optical medium, we present a geometrical-optics based derivation that incorporates 'the effective gravitational refractive index' additively to the usual optical dispersion. It gives a deflection, or the vertical fall Δ for a horizontal traversal L as Δ=L 2 /2(R ⊕G /R ⊕ 2 )n g (1/1+n g R ⊕G /R ⊕ ), where R ⊕G /R ⊕ is the ratio of the gravitational Earth radius to its geometrical radius R ⊕ , and n g is the group refractive index of the strongly dispersive optical medium. The expression is essentailly that for the Newtonian fall of an object projected horizontally with the group speed v g =c/n g , and is tunable refractively thorugh the index n g . For L~1 m and n g = c/v g ~10 8 (corresponding to the ultra-slow pulse speed ~few × 1 ms -1 ), we obtain a fall Δ~1μm, that should be measurable-in particular through its sensitive dependence on the frequency that tunes n g .
In the quest to develop viable designs for third-generation optical interferometric gravitational-wave detectors (e.g., LIGO-III and EURO), one strategy is to monitor the relative momentum or speed of the test-mass mirrors, rather than monitoring their relative position. A previous paper analyzed a straightforward but impractical design for a speed-meter interferometer that accomplishes this. This paper describes some practical variants of speed-meter interferometers. Like the original interferometric speed meter, these designs in principle can beat the gravitational-wave standard quantum limit (SQL) by an arbitrarily large amount, over an arbitrarily wide range of frequencies. These variants essentially consist of a Michelson interferometer plus an extra ``sloshing'' cavity that sends the signal back into the interferometer with opposite phase shift, thereby cancelling the position information and leaving a net phase shift proportional to the relative velocity. In practice, the sensitivity of these variants will be limited by the maximum light power Wcirc{W}_{\mathrm{circ}}Wcirc​ circulating in the arm cavities that the mirrors can support and by the leakage of vacuum into the optical train at dissipation points. In the absence of dissipation and with squeezed vacuum (power squeeze factor ${e}^{\ensuremath{-}2R}\ensuremath{\simeq}0.1)$ inserted into the output port so as to keep the circulating power down, the SQL can be beat by ${h/h}_{\mathrm{SQL}}\ensuremath{\sim}\sqrt{{W}_{\mathrm{circ}}^{\mathrm{SQL}}{e}^{\ensuremath{-}2R}{/W}_{\mathrm{circ}}}$ at all frequencies below some chosen ${f}_{\mathrm{opt}}\ensuremath{\simeq}100\mathrm{Hz}.$ Here ${W}_{\mathrm{circ}}^{\mathrm{SQL}}\ensuremath{\simeq}800\mathrm{kW}{(f}_{\mathrm{opt}}/100\mathrm{}\mathrm{Hz}{)}^{3}$ is the power required to reach the SQL in the absence of squeezing. (However, as the power increases in this expression, the speed meter becomes more narrow band; additional power and reoptimization of some parameters are required to maintain the wide band. See Sec. III B.) Estimates are given of the amount by which vacuum leakage at dissipation points will debilitate this sensitivity (see Fig. 12); these losses are 10% or less over most of the frequency range of interest $(f\ensuremath{\gtrsim}10\mathrm{Hz}).$ The sensitivity can be improved, particularly at high freqencies, by using frequency-dependent homodyne detection, which unfortunately requires two 4-km-long filter cavities (see Fig. 4).
Recent experiments on ultra slow light in strongly dispersive media by several research groups reporting slowing down of the optical pulses down to speeds of a few metres per second encourage us to examine the intriguing possibility of detecting a deflection or fall of the ultra slow light under Earth's gravity, i.e., on the laboratory length scale. In the absence of a usable general relativistic theory of light waves propagating in such a strongly dispersive optical medium in the presence of a gravitational field, we present a geometrical optics based derivation that combines {\it the effective gravitational refractive index} additively with the usual optical dispersion. It gives a deflection, or the vertical fall ΔΔΔ for a horizontal traversal LLL as Δ=L22(R⊕GR⊕2)ng(11+ngR⊕GR⊕), Δ= \frac{L^2}{2}\big(\frac{R_{\oplus G}}{R_\oplus^2}\big) n_g \big(\frac{1}{1+n_g\frac{R_{\oplus G}}{R_\oplus}}\big), Δ=2L2​(R⊕2​R⊕G​​)ng​(1+ng​R⊕​R⊕G​​1​), where R⊕G/R⊕R_{\oplus G}/R_\oplusR⊕G​/R⊕​ is the ratio of the gravitational Earth radius(R⊕GR_{\oplus G}R⊕G​) to its geometrical radius R⊕R_\oplusR⊕​, and ngn_gng​ is the group refractive index of the strongly dispersive optical medium. The expression is essentailly that for the Newtonian fall of an object projected horizontally with the group speed vg=c/ngv_g=c/n_gvg​=c/ng​, and is tunable refractively through the index ngn_gng​. For L∼1mL \sim 1 mL∼1m and ng=c/vg∼108n_g = c/v_g \sim 10^8ng​=c/vg​∼108 (corresponding to the ultra-slow pulse speed ∼few×1ms−1\sim few \times 1 ms^{-1}∼few×1ms−1), we obtain a fall Δ∼1μmΔ\sim 1 μmΔ∼1μm, that should be measurable −-− in particular through its sensitive dependence on the frequency that tunes ngn_gng​.