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Docta Complutense author Fernández-Rañada, Antonio 2023-06-20T03:38:45Z 2023-06-20T03:38:45Z 2012-10 0008-4204 10.1139/P2012-086 https://hdl.handle.net/20.500.14352/44143 http://dx.doi.org/10.1139/P2012-086 http://www.nrcresearchpress.comhttp://digital.csic.es It is usually assumed that the t parameter in the equations of dynamics can be identified with the indication of the pointer of a clock. Things are not so simple, however. In fact, because the equations of motion can be written in terms of t but also in terms of t' = f(t), f being any well-behaved function, any one of those infinite parametric times t' is as good as the newtonian one to study classical dynamics in hamiltonian form. Here we show that, as a consequence of parametric invariance, one of the foundations of classical dynamics, the relation between the mathematical parametric time t in the equations of dynamics and the physical dynamical time sigma that is measured with a particular clock (which is itself a dynamical system) requires the characterization of the clock that is used to achieve a complete treatment of dynamical systems. These two kinds of time, therefore, must be carefully distinguished. Furthermore, we show that not all the dynamical clock-times are necessarily equivalent and that the observational fingerprint of this nonequivalence has, curiously, the same form as that of the Pioneer anomaly. This suggests, therefore, that an acceleration to one another of the astronomical and the atomic times, t(astr) and t(atom), can contribute to the total amount of the anomaly. eng Parametric invariance and the Pioneer anomaly journal article URL https://docta.ucm.es/bitstreams/a973bcc9-a780-4f57-bc63-5d339606a59a/download File MD5 a8db00bdcb55afc54756a1647d3cf971 290180 application/pdf RañadaAF 02 preprint.pdf URL https://docta.ucm.es/bitstreams/6274d313-1bdc-4e85-a64d-40411282640e/download File MD5 f27bca21e0a88f3f0a5f7f3c074d9b0d 39645 text/plain RañadaAF 02 preprint.pdf.txt