# On the Possibility of Observing Negative Shapiro-like Delay Using Michelson–Morley-Type Experiments

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## Abstract

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## 1. Introduction

## 2. Gravitational Time Advancement

## 3. Gravitational Negative Time Delay for Small Distance Travel from the Earth’s Surface

## 4. Possibility of Experimental Detection of the Negative Time Delay

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Michelson, A.A. The relative motion of the Earth and the Luminiferous ether. Am. J. Sci.
**1881**, 22, 120–129. [Google Scholar] [CrossRef] - Michelson, A.A.; Morley, E.W. On the Relative Motion of the Earth and the Luminiferous Ether. Am. J. Sci.
**1887**, 34, 333–345. [Google Scholar] [CrossRef] - Michelson, A.A.; Morley, E.W. On the relative motion of the earth and the luminiferous aether. Philos. Mag.
**1887**, 5, 449–463. [Google Scholar] [CrossRef] - Lipa, J.A.; Nissen, J.A.; Wang, S.; Stricker, D.A.; Avaloff, D. New Limit on Signals of Lorentz Violation in Electrodynamics. Phys. Rev. Lett.
**2003**, 90, 060403. [Google Scholar] [CrossRef] - Müller, H.; Herrmann, S.; Braxmaier, C.; Schiller, S.; Peters, A. Modern Michelson-Morley Experiment using Cryogenic Optical Resonators. Phys. Rev. Lett.
**2003**, 91, 020401. [Google Scholar] [CrossRef] [PubMed] - Wolf, P.; Bize, S.; Clairon, A.; Santarelli, G.; Tobar, M.E.; Luiten, A.N. Improved test of Lorentz invariance in electrodynamics. Phys. Rev. D
**2004**, 70, 051902. [Google Scholar] [CrossRef] - Stanwix, P.L.; Tobar, M.E.; Wolf, P.; Susli, M.; Locke, C.R.; Ivanov, E.N.; Winterflood, J.; van Kann, F. Test of Lorentz invariance in electrodynamics using rotating cryogenic sapphire microwave oscillators. Phys. Rev. Lett.
**2005**, 94, 040404. [Google Scholar] [CrossRef] - Stanwix, P.L.; Tobar, M.E.; Wolf, P.; Locke, C.R.; Ivanov, E.N. Improved test of Lorentz invariance in electrodynamics using rotating cryogenic sapphire oscillators. Phys. Rev. D
**2006**, 74, 081101. [Google Scholar] [CrossRef] - Herrmann, S.; Senger, A.; Kovalchuk, E.; Müller, H.; Peters, A. Test of the Isotropy of the Speed of Light Using a Continuously Rotating Optical Resonator. Phys. Rev. Lett.
**2005**, 95, 150401. [Google Scholar] [CrossRef] - Antonini, P.; Okhapkin, M.; Göklü, E.; Schiller, S. Test of constancy of speed of light with rotating cryogenic optical resonators. Phys. Rev. A
**2005**, 71, 050101. [Google Scholar] [CrossRef] - Müller, H.; Stanwix, P.L.; Tobar, M.E.; Ivanov, E.N.; Wolf, P.; Herrmann, S.; Senger, A.; Kovalchuk, E.; Peters, A. Tests of Relativity by Complementary Rotating Michelson-Morley Experiments. Phys. Rev. Lett.
**2007**, 99, 050401. [Google Scholar] [CrossRef] [PubMed] - Kostelecky, V.A.; Mewes, M. Signals for Lorentz violation in electrodynamics. Phys. Rev. D
**2002**, 66, 056005. [Google Scholar] [CrossRef] - Kostelecky, V.A.; Mewes, M. Sensitive Polarimetric Search for Relativity Violations in Gamma-Ray Bursts. Phys. Rev. Lett.
**2006**, 97, 140401. [Google Scholar] [CrossRef] - Müller, H.; Stanwix, P.L.; Herrmann, S.; Peters, A.; Lümmerzahl, C. Electromagnetic cavities and Lorentz invariance violation. Phys. Rev. D
**2003**, 67, 056006. [Google Scholar] [CrossRef] - Müller, H. Testing Lorentz invariance by the use of vacuum and matter filled cavity resonators. Phys. Rev. D
**2005**, 71, 045004. [Google Scholar] [CrossRef] - Eisele, C.; Nevsky, A.Y.; Schiller, S. Laboratory Test of the Isotropy of Light Propagation at the 10
^{−17}Level. Phys. Rev. Lett.**2009**, 103, 090401. [Google Scholar] [CrossRef] - Shapiro, I.I. Fourth Test of General Relativity. Phys. Rev. Lett.
**1964**, 13, 789. [Google Scholar] [CrossRef] - Bhadra, A.; Nandi, K.K. Gravitational time advancement and its possible detection. Gen. Relativ. Gravit.
**2010**, 42, 293–302. [Google Scholar] [CrossRef] - Shapiro, I.I.; Pettengill, G.H.; Ash, M.E.; Stone, M.L.; Smith, W.B.; Ingalls, R.P.; Brockelman, R.A. Fourth Test of General Relativity: Preliminary Results. Phys. Rev. Lett.
**1968**, 20, 1265. [Google Scholar] [CrossRef] - Desai, S.; Kahya, E.O. The Galactic One-Way Shapiro Delay to PSR B1937+21. Mod. Phys. Lett.
**2016**, 31, 1650083. [Google Scholar] [CrossRef] - Desai, S.; Kahya, E.O.; Woodard, R.P. Reduced time delay for gravitational waves with dark matter emulators. Phys. Rev. D
**2008**, 77, 124041. [Google Scholar] [CrossRef] - Cromartie, H.T.; Fonseca, E.; Ransom, S.M.; Demorest, P.B.; Arzoumanian, Z.; Blumer, H.; Brook, P.R.; DeCesar, M.E.; Dolch, T.; Ellis, J.A.; et al. Relativistic Shapiro delay measurements of an extremely massive millisecond pulsar. Nat. Astron.
**2020**, 4, 72. [Google Scholar] - Ghosh, S.; Bhadra, A. Influences of dark energy and dark matter on gravitational time advancement. Eur. Phys. J. C
**2015**, 75, 494. [Google Scholar] [CrossRef] - Bertotti, B.; Iess, L.; Tortora, P. A test of general relativity using radio links with the Cassini spacecraft. Nature
**2003**, 425, 374–376. [Google Scholar] [CrossRef] - Will, C.M. Theory and Experiment in Gravitational Physics; Revised ed.; Cambridge University Press: Cambridge, UK, 1993. [Google Scholar]
- Ghosh, S.; Bhadra, A.; Mukhopadhyay, A. Probing dark matter and dark energy through gravitational time advancement. Gen. Rel. Grav.
**2019**, 51, 54. [Google Scholar] [CrossRef] - Deng, X.-M.; Xie, Y. Gravitational time advancement under gravity’s rainbow. Phys. Lett. B
**2017**, 772, 152. [Google Scholar] [CrossRef] - Tuleganova, G.Y.; Karimov, R.K.; Izmailov, R.N.; Potapov, A.A.; Bhadra, A.; Nandi, K.K. Gravitational time advancement effect in Bumblebee gravity for Earth bound systems. Eur. Phys. J. Plus
**2023**, 138, 94. [Google Scholar] [CrossRef] - Tartaglia, A.; Ruggiero, M.L. Angular Momentum Effects in Michelson–Morley Type Experiments. Gen. Rel. Grav.
**2002**, 34, 1371–1382. [Google Scholar] - Misner, C.W.; Thorne, K.S.; Wheeler, J.A. Gravitation; Freeman: San Francisco, CA, USA, 1973. [Google Scholar]
- Richter, G.W.; Matzner, R.A. Second-order contributions to relativistic time delay in the parametrized post-Newtonian formalism. Phys. Rev. D
**1983**, 28, 3007. [Google Scholar] [CrossRef] - Zhang, Y.Z. On the Theory of the Michelson-Morley Experiment in the Earth’s Gravitational Field. Europhys. Lett.
**1987**, 3, 1251. [Google Scholar] [CrossRef] - Lipa, J.A.; Buchman, S.; Saraf, S.; Zhou, J.; Alfauwaz, A.; Conklin, J.; Cutler, G.D.; Byer, R.L. Prospects for an advanced Kennedy-Thorndike experiment in low Earth orbit. arXiv
**2012**, arXiv:1203.3914. [Google Scholar]

**Figure 1.**Schematic view of gravitational time delay/advancement: (

**a**)—Light motion in the horizontal direction; (

**b**)—Light motion in the vertical direction.

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**MDPI and ACS Style**

Bhadra, A.; Izmailov, R.N.; Nandi, K.K.
On the Possibility of Observing Negative Shapiro-like Delay Using Michelson–Morley-Type Experiments. *Universe* **2023**, *9*, 263.
https://doi.org/10.3390/universe9060263

**AMA Style**

Bhadra A, Izmailov RN, Nandi KK.
On the Possibility of Observing Negative Shapiro-like Delay Using Michelson–Morley-Type Experiments. *Universe*. 2023; 9(6):263.
https://doi.org/10.3390/universe9060263

**Chicago/Turabian Style**

Bhadra, Arunava, Ramil N. Izmailov, and Kamal K. Nandi.
2023. "On the Possibility of Observing Negative Shapiro-like Delay Using Michelson–Morley-Type Experiments" *Universe* 9, no. 6: 263.
https://doi.org/10.3390/universe9060263