View Full Version : Fomalont-Kopeikin experiment; Gravity Propigation questions:

2007-Jan-15, 06:44 PM
After reading these posts (http://www.bautforum.com/showthread.php?t=52024), I've been googling and thinking (dangerous stuff) and come up with some conjectures and questions:

1. Fomalont-Kopeikin experiment:

I've read about the Fomalont-Kopeikin experiment using a quasar and Jupiter to measure the propigation speed of gravity. (They postulated that you could measure the speed of gravity by observing the effect of gravitational lensing as Jupiter passed in front of a quasar. If the lensing effect matched the observed position, then gravity must propigate no faster than the speed of light...) I've also read a criticism stating that what they really measured was the propigation of light rather than gravity. (I'm trying to understand the experiment, so please bear with me...)

A. Conjecture: Jupiter's orbital speed is too slow for this experiment to work. Presuming gravity propigates at a different speed than that of light, to work properly, the reference object (Jupiter) has to move far enough for its actual (gravitationally significant) position to be offset from its observable position.

Jupiter has an equitorial radius of 71492 km. Its average orbital speed is 13.056 km/s. Its minimum distance to the Earth is @ 588 million km. At that distance, it would take light passing Jupiter (and the light Jupiter reflects back to us) @ 1961.4 seconds to reach the earth. By the time we see Jupiter, it has moved 25,615.9 km. - or a little over 1/3 of its diameter. The overlap is too great. Using the extremes of my propigation examples:

- If gravity propigates instantly, the lensing phenomena would only appear to "lead" Jupiter by a sliver equalling 1/3 of its apparent diameter.
- If gravity propgates at c, the lensing phenomena matches the observed location of the planet.
There is a 2/3 apparent diameter overlap here (I don't have the math handy to work out the arc/second - but its gotta be miniscule) and I suspect that any differences are going to be swallowed up by the error rate.
Had a later thought (told you this was dangerous!):

Is it possible this experiment could not work with a planet at all, simply because the moment Jupiter's mass is in a position to affect the passing light from the quasar, the sun's light reflected off Jupiter "matches velocity" with the passing light and both reach the observer at the same instant? --Are any of these ideas correct?

B. Question:Would the experiment I describe above work if the lensing object were independently radiant (like a star or galaxy)? Would a misalignment between observed gravitational lensing effect and the observed radiant mass location allow for a measurement of the speed by which gravity propigates? (Presuming we could find a distant enough, fast enough radiant mass to create the lens and a distant enough emission source beyond the mass to be lensed)?

Tim Thompson
2007-Jan-15, 07:15 PM
I don't know the answers. But I have a suggestion (in the event you have not already done this). The original Fomalont - Kopeikin paper is available through the NASA/ADS database: The Measurement of the Light Deflection from Jupiter: Experimental Results (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2003ApJ...598..704F&db_key=AST&d ata_type=HTML&format=&high=4366fa465103067), Astrophysical Journal 598(1): 704-711, November 2003. You can download a copy of the paper by following the arXiv eprint link (http://arxiv.org/abs/astro-ph/0302294). You can also follow the link to the 36 papers (http://adsabs.harvard.edu/cgi-bin/nph-ref_query?bibcode=2003ApJ...598..704F&refs=CITATIO NS&db_key=AST) which cite the original. Those 36 papers encompass the published discussion of the Fomalont-Kopeikin claim. There are several authors, including Carlip & Will, who dispute the claim by Fomalont & Kopeikin; they claim that the problem is still degenerate, and the Fomalont-Kopeikin experiment cannot distinguish between the speed of light and the speed of gravity (i.e., they say the claim that the experiment shows that gravity propagates with the speed of light is false). Many of these 36 papers are probably not available online, but at least you can track them down this way.

I have not followed the discussion in any detail, so I really don't know how to answer your questions. But I am guessing that a study of the back & forth between the proponents & critics will be educatuional in that respect.

2007-Jan-15, 08:11 PM
You are already more in the details of this experiment than I am, but as Tim noted, this is still being hotly disputed. Kopeikin is adamant that he did measure the speed of gravity, while other, very much GR heavyweights, are certain he did not.

I tend to agree with Carlip and the others based on this simple reasoning: From the earth's perspective Jupiter was moving, and its gravity well was therefore moving as well. That was the idea behind the experiment.

However, transform into Jupiter's rest frame and then look at the picture. Jupiter's gravity well is completely static there, and all that is happens there is how light between a moving source and moving receiver propagates through that stationary gravity well. Any effects can just be seen as that of motion through a static field, and not as the effects of a dynamic field.

So what you need for a "really" dynamic field is a situation where there is no frame where the field is static, and effects on light propagation depend on how the gravitational field is changing from any frame.

An accelerating mass will give you that -- and actually, considering how gravity compensates for acceleration, you may need a *jerking* mass, time-varying acceleration to actually get what can be considered a truly dynamic field. But this is all getting well ahead of my understanding.

In short, this is a very tricky subject!