There is a rigorous mathematical proof for the energy-time uncertainty principle
Rigorous mathematical formulations and proofs exist for specific interpretations of the energy-time uncertainty principle, such as the Mandelstam-Tamm inequality.
The retrieved literature includes specific papers (such as [0] and [2]) that demonstrate rigorous mathematical formulations and derivations of the energy-time uncertainty principle, supporting the claim.
John E. Gray, Andrew Vogt. Mathematical analysis of the Mandelstam–Tamm time-energy uncertainty principle. 2005. https://doi.org/10.1063/1.1897164
Paper [0] provides mathematical analysis and confirms that the Mandelstam–Tamm time-energy uncertainty inequality can be established rigorously, achieving equality for certain observables.
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Mirza Wasif BAig. Time Energy Uncertainty Principle and Vacuum Fluctuations. 2019. https://doi.org/10.20944/preprints201901.0292.v1
Paper [2] mathematically models and derives the time-energy uncertainty principle by calculating the variance of energy and time for wave functions.
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