Reply to ‘Dynamic phase shift within a falling glass cube is negligible: comment on ‘Relativistic theory of the falling cube gravimeter’’

Abstract

In the subject paper Ashby (2018 Metrologia 55 1-10) of the comment Svitlov (2018 Metrologia 55 609-13), light propagation through an absolute gravimeter was analyzed, including the propagation delay through the falling retroreflector and through the vacuum. The resulting expression for the interference signal applies without any subsequent 'speed of light' correction. Other corrections appeared for the three fitting parameters Z 0 , V 0 and g, which are, respectively, the initial position and velocity, and the acceleration of gravity at the reference point. The comment assumes the value of Z 0 is known a priori; this case was not addressed in Ashby (2018 Metrologia 55 1-10). Also, the comment misunderstands statements made in Ashby (2018 Metrologia 55 1-10) regarding the derivation of the relativistic/non-relativistic parts of the corrections (equation (47) of Ashby (2018 Metrologia 55 1-10)), and mistakenly claims they apply to the undifferenced interference signal. In this reply we show why, because of inapplicable assumptions, approximations and misunderstandings, the comment does not apply to the results of Ashby (2018 Metrologia 55 1-10).

Use of the relativistic phase-time equation in absolute ballistic gravimetry

“…According to (7), the error affecting the estimated ḡ value in a real operational condition, i.e. D = 0.0175 m, was 7.76 × 10 −5 µGal and 7.83 × 10 −5 µGal (1 µGal = 1 × 10 −8 m s −2 ) in the direct free-fall and symmetric rise-and-fall case, respectively, whereas in the fictitious operational condition, i.e.…”

“…The subject was extensively discussed in several comments and replies without reaching a final agreement [2][3][4][5][6][7].…”

Comparison of Open and Solid Falling Retroreflector Gravimeters

“…( 1) is the basis for the present study. The apparently large effect on g arising from dimensions and refractive index of the cube resulted in several critical comments [2,3,4], and replies [5,6,7], without throwing light on the real issues.…”

“…This expression is the basis for the present study. The apparently large effect on g arising from dimensions and refractive index of the cube resulted in several critical comments [2][3][4], and replies [5][6][7], without throwing light on the real issues. D'Agostino [8] simulated dropping of glass and open retroreflectors using only the difference ϕ(t)−ϕ(0) for the interference observations.…”

On the effect of the light propagation within the corner-cube reflector of absolute gravimeters

“…Assuming D=1.75 cm, γ = 307 E ‡, n=1.57, d = D/4 [1], the effect reaches the value of 7 µGal §. Several authors have found problems with the reasoning substantiating the effect [2,3,4], but the arguments of the critique were declined [5,6,7,8]. The discussed issue directly affects the realisation of the new definition of the base SI unit of mass, the kilogram [9,10], therefore, the question of the existence of the effect needs to be resolved.…”