Doppler spectroscopy on relativistic particle beams in the light of a test theory of special relativity

Abstract

Modern experimental techniques based on collinear laser spectroscopy have led to greatly improved versions of the classical Ives-Stilwell experiment. The new experiments employ collinear laser beams and measure the Doppler shift as it is seen in the rest frame of a relativistic particle beam. This note analyzes these experiments in the framework of a test theory of special relativity due to Mansouri and Sexl. It is found that the experiments can test the coefficient function a(v 2) (responsible for time dilation), but are insensitive to b, d and e. While the Mansouri-Sexl theory in principle allows for an anisotropy of the velocity of light with respect to a moving reference frame, anisotropy effects cancel out in Ives-Stilwell type experiments. These experiments by themselves are not sufficient for a direct observation of such an anisotropy.

A test of special relativity with stored lithium ions

“…The ion velocity of v = 6.4% c. A precision of {Z < 9-10'° has been obtained, which sets saturation spectroscopy as a test of the time dilatation factor 7 = (1 --U°)"1'° at an optical A type three level system of 7Li+ the Doppler shift has been measured by precision experiments testing the limits of the special theory of relativity. [12] using the analysis of reference [8] and [9] OCR Output modulation. The previous version of the present experiment has resulted in 504 S 1.5-105 a < 1.6 · 10`6 1 for an absolute limit and 6:1 < 1.…”

Measurement of the transverse Doppler shift using a stored relativistic7Li+ ion beam

“…Hypothetical deviations of a test experiment from the predictions of SRT are usually expressed in terms of the Mansouri-Sexl test theory [7,8]. Within this test theory, which allows for a preferred frame of reference (ether system), in which light propagates rectilinearly and isotropically with a constant speed c, and which admits rather general clock synchronization procedures, the Doppler shift formula is found to be given by (8) where v (v') denotes the velocity of the ion restframe (the laboratory system) with respect to the ether system.…”

“…Hypothetical deviations of a test experiment from the predictions of SRT are usually expressed in terms of the Mansouri-Sexl test theory [7,8]. Within this test theory, which allows for a preferred frame of reference (ether system), in which light propagates rectilinearly and isotropically with a constant speed c, and which admits rather general clock synchronization procedures, the Doppler shift formula is found to be given by (8) where v (v') denotes the velocity of the ion restframe (the laboratory system) with respect to the ether system. Using the modified Doppler shift formula (8) and expressing the velocity difference (v2-v'2)/c2 in terms of the ion velocity fl in the laboratory system, and the normalized velocity ,8' of the laboratory system relative to the ether frame, retaining only terms up to (velocity) 2, one finds for the A-resonance frequency [8], v~'v2 (1 +25c~(/3e+2(,B fl'))) (9) Via es = __ .…”

“…Using e.g. the framework of the test theory of SRT due to Mansouri and Sexl [7,8] and assuming the ion velocity in the laboratory system to be large compared to the velocity of the laboratory against a possible ether frame (estimations from the 3 K background radiation leads to an earthether velocity of 10-3c as compared to an ion velocity of 64-10-3 c), the resultant Doppler-shift formula reads again as (1) with y (/32) being replaced by Yus(/32)= y (/32)(1 +6c~fl 2+---)…”

Systematic approach to the relativistic Doppler effect based on a test theory

“…Based on the MS framework, some detailed theoretical analyses have been made to see the effect of ε on experimental results [12,13]. It was seen that the relativistic Doppler shift is independent of ε , through approximate analysis for some test results [12] and by using a Doppler shift formula in the special case of a wave of light propagating parallel or antiparallel to the direction of motion of the detector's inertial frame [13].…”