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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.20351064 |
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Table of Contents:
- <p>This work introduces an energy-causal criterion to determine when an electromagnetic excitation in electrical and electronic circuits admits effective proper time. Based on the distinction between fundamental phase,<br>\[<br>\phi_{\rm fund}=\frac{S}{\hbar},<br>\]<br>and phase observed by circuits and filters,<br>\[<br>\phi_{\rm obs}=\phi_{\rm fund}+\Phi(\omega,A),<br>\]<br>it is shown that group delay is an operational signal temporality, but it does not, by itself, constitute electromagnetic proper time.<br>The proposed criterion is<br>\[<br>\Delta_{\rm circ} = u_{\rm circ}^{2} - \frac{|S_{\rm circ}|^{2}}{c_{\rm circ}^{2}}.<br>\]<br>When \(\Delta_{\rm circ}>0\), the energy current is time-like, and it is defined that<br>\[<br>d\tau_{\rm circ} = dt\,\frac{\sqrt{\Delta_{\rm circ}}}{u_{\rm circ}}.<br>\]<br>When \(\Delta_{\rm circ}=0\), the excitation is effective null and \(d\tau_{\rm circ}=0\).<br>For lossless lines, one obtains<br>\[<br>d\tau_\ell = dt\, \frac{|C'V^2-L'I^2|} {C'V^2+L'I^2}.<br>\]<br>The formulation preserves Maxwell, does not redefine group delay, and does not attribute proper time to the free photon; it provides a measurable criterion to classify circuital electromagnetic excitations as null or time-like.</p>