Abstract
To perform any physical measurement it is necessary to identify in a non ambiguous way both the observer and the observable. A given observable can be then the target of different observers: a suitable algorithm to compare among their measurements should necessarily be developed, either formally or operationally. This is the task of what we call “theory of measurement,” which we discuss here in the framework of general relativity.
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- 1.
We have adopted the \(\nabla \)-convention differently from a \(;\)-convention also widely used.
- 2.
A Lie spatial Riemann tensor can be defined similarly, replacing the Fermi–Walker structure functions \(C_\mathrm{(fw)}{}^f{}_b\) with the corresponding Lie structure functions \(C_\mathrm{(lie)}{}^f{}_b\) according to Eq. (42).
- 3.
In fact the Euclidean space definition involves spatial orbits parameterized by the (spatial) curvilinear abscissa.
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Acknowledgments
I’m indebted to my “teachers,” Profs. R.T. Jantzen and F. de Felice, for a more than 20 years of collaboration and friendship. I also acknowledge the numerous useful discussions with Dr. A. Geralico. Finally, I warmly thank the organizers of this wonderful meeting in Prague for all their work.
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Bini, D. (2014). Observers, Observables and Measurements in General Relativity. In: Bičák, J., Ledvinka, T. (eds) General Relativity, Cosmology and Astrophysics. Fundamental Theories of Physics, vol 177. Springer, Cham. https://doi.org/10.1007/978-3-319-06349-2_3
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DOI: https://doi.org/10.1007/978-3-319-06349-2_3
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