Study on data analysis for Ives-Stilwell-type experiments

TL;DR

The paper identifies a fundamental inconsistency in how the relativistic Doppler effect has been tested in Ives-Stilwell-type experiments, showing that the commonly used combined-accuracy metric $\\varepsilon=\\sqrt{\\nu_a\\nu_p/(\\nu_1\\nu_2)}-1$ cannot confirm Einstein's Doppler formula for a single beam. It proposes two first principles and derives single-beam accuracies $\\varepsilon_{a1},\\varepsilon_{p2}$ (and symmetric forms) from the Doppler shifts $\\nu_{a\\textrm{-sh}}=\\gamma(1+\\beta)\\nu_a$ and $\\nu_{p\\textrm{-sh}}=\\gamma(1-\\beta)\\nu_p$, applying them to Botermann et al.'s data to show $\\mathcal{O}(10^{-4})$ precision per beam rather than $10^{-9}$ for the combined metric. By constructing discriminants and reanalyzing Ives-Stilwell eight cases, the work finds that no single beam satisfies the relativistic Doppler relation, implying the original test did not confirm Einstein's Doppler effect. The result provides a rigorous framework for testing Lorentz invariance via the Doppler effect and clarifies why previous analyses overinterpreted the data.

Abstract

Ives-Stilwell experiment in 1938 is a historic experiment for confirming Einstein's special relativity, and various modern types have been repeated by use of laser technology. However in this paper, we reveal and solve a fundamental issue that the data analysis for all those experiments is not consistent with Einstein's definition of the relativistic Doppler effect so that the Doppler effect and its associated time dilation have not actually been confirmed. For example, in the Letter [Phys. Rev. Lett. 113, 120405 (2014)] the definition of the measurement accuracy of Doppler effect, given by $\varepsilon=\sqrt{ν_aν_p/(ν_1ν_2)}-1$, is not physical because Einstein's Doppler formula cannot be confirmed even when $\varepsilon = 0$ holds. We argue that there are two first principles for analyzing and confirming Einstein's Doppler effect, stating: (i) Einstein's Doppler effect refers to the same photon (or laser beam) exhibiting different frequencies observed in different inertial frames, and (ii) the quantity (or measurement accuracy) used as a measure to confirm the effect must be able to confirm Einstein's Doppler formula itself. Unfortunately, the data analysis for the 1938 Ives-Stilwell experiment does not comply with the first principles, so it fails to confirm the relativistic effect, although this data analysis has been mimicked by quite a few generations of physicists. (It should be emphasized that in fact, Ives-Stilwell data analysis and the experimental test itself both fail to confirm Einstein's Doppler effect.) Based on the first principles, we propose a justified data analysis and correctly confirm the Doppler effect in the Ives-Stilwell-type experiment, thus resulting in a great advance in the experimental verification of Lorentz invariance via the Doppler effect.

Figures (13)

• Figure 1: Schematic diagram of Ives-Stilwell-type experiment based on optical-optical double resonance (OODR) spectroscopy r7. Two laser beams are aligned antiparallel $(\nu_a)$ and parallel $(\nu_p)$ relative to an ion beam moving at $\beta$. The ion beam has two transition frequencies $\nu_1$ and $\nu_2$, functioning as Doppler-shifted laser frequency detector.
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