[Paper Review] Comments on "Measuring the Gravity Speed by VLBI"

Hideki Asada|arXiv (Cornell University)|Aug 20, 2003

Geophysics and Gravity Measurements1 references3 citations

TL;DR

This paper argues that the 2002 VLBI measurement of Jupiter's gravitational influence, claimed by Kopeikin and Fomalont to measure the speed of gravity, actually measures only the speed of light due to light-cone effects in post-Newtonian approximations. The analysis shows the observed time delay excess arises from light propagation, not gravity, with gravity effects appearing only at higher-order $O(c^{-4})$ terms, which are negligible in this context. The conclusion is that the experiment did not measure the speed of gravity, despite claims to the contrary.

ABSTRACT

Einstein gravity with extra dimensions or alternative gravity theories might suggest that the gravity propagation speed can be different from the light speed. Such a difference may play a vital role in the primordial universe. In recent, Kopeikin and Fomalont claimed the first measurement of the gravity speed by VLBI. However, the measurement has no relevance with the speed of gravity as I had shown before the observation was done. It seems that our conclusion has been established well by re-examining recent papers with great care.

Motivation & Objective

• To challenge the interpretation of the 2002 VLBI experiment as a measurement of the speed of gravity.
• To clarify that the observed time delay excess in the experiment originates from light propagation, not gravitational propagation.
• To demonstrate that gravity propagation effects appear only at $O(c^{-4})$ in post-Newtonian expansions, while the observed effect is at $O(c^{-3})$.
• To correct misinterpretations in Kopeikin's subsequent papers that incorrectly attributed the delay to gravity speed using flawed Green's function choices.
• To reaffirm that the high-precision VLBI measurement, while not measuring gravity speed, still provides valuable astrophysical constraints on gravity theories and stellar motion.

Proposed method

• Uses post-Newtonian approximation of general relativity, expanding in inverse powers of the speed of light $c$.
• Derives the Shapiro time delay in retarded time formalism using null geodesics on past light cones.
• Applies expansions to the baseline vector $\mathbf{B}$, position vectors $\mathbf{r}_{iJ}$, and velocity $\mathbf{v}_J$ of Jupiter, retaining terms up to $O(c^{-2})$.
• Expresses the time delay difference $\Delta(t_1,t_2)$ in terms of $\mathbf{B}$, $\mathbf{v}_J$, and angular parameters like $\theta$ between Jupiter and the quasar.
• Identifies the dominant excess delay as proportional to $\mathbf{n} \cdot \mathbf{B} / (r_{1J} \theta)$, which is a light-cone effect, not gravity propagation.
• Critically analyzes Kopeikin’s use of artificial time $\tau$ and advanced Green functions, showing they lead to incorrect conclusions due to inconsistent causal structure.

Experimental results

Research questions

• RQ1 Does the observed time delay excess in the 2002 VLBI Jupiter experiment reflect the propagation speed of gravity?
• RQ2 What is the correct order of magnitude of gravitational effects in post-Newtonian theory, and how do they compare to the observed delay?
• RQ3 Why do Kopeikin’s claims of measuring gravity speed fail when analyzed using standard post-Newtonian formalism?
• RQ4 How does the use of advanced Green functions instead of retarded ones affect the interpretation of time delay in gravitational experiments?
• RQ5 What are the astrophysical implications of the high-precision VLBI measurement, even if it did not measure gravity speed?

Key findings

• The observed time delay excess in the 2002 VLBI experiment is at $O(c^{-3})$, while gravity propagation effects appear only at $O(c^{-4})$, making the former irrelevant to gravity speed.
• The excess delay is entirely due to light-cone effects and the velocity of Jupiter, not the propagation of gravity.
• Kopeikin’s use of artificial time $\tau$ and $c_g$ in place of $c$ is misleading because $V/c_g$ is equivalent to $v/c$ in the final expression, thus depending on light speed, not gravity speed.
• The use of advanced Green functions in Kopeikin’s second paper leads to unphysical signature changes in the delay, which are artifacts of incorrect light-cone treatment (future vs. past cone).
• Correctly applying retarded time and past light cones shows that the sign of the excess delay does not change when switching Green functions, invalidating claims of gravity-speed dependence.
• Despite not measuring gravity speed, the VLBI measurement achieved sub-microarcsecond accuracy (~10 μas), enabling tighter constraints on scalar-tensor gravity theories and precise parallax and proper motion measurements for stars up to a few kpc.