An Analysis of the Speed of Gravity Measurement by Jupiter Scientific including a suggested resolution to the criticism concerning the experiment.| Home | Books | Reports | Reviews | Contact Us | Press Releases | Submissions |

Top Box: c

Because the speed of gravity is infinite for the bottom box,

one does not see gravity propagating; the effect is instantaneous.

The black disk represents Jupiter. The open circle O is a point of observation. The important questions are: what is the strength of gravity at O at a particular time due to Jupiter when it is moving toward O, and how does it depend on the speed of propagation of gravity? Recall that Jupiter is creating gravity by causing a curvature of spacetime in its vicinity. As Jupiter moves, its effect on spacetime propagates at c

Let v denote the speed of Jupiter. Then the differences between the various distances r

Suppose, however, that a new reference frame is chosen that moves along with Jupiter. In other words, suppose we, as observers, just happen to be moving at the same velocity as Jupiter so that Jupiter does not appear to us to be moving at all. Since, for short times, Jupiter is almost moving in a straight line with constant speed, its acceleration is small, and such a reference frame is, according to Einstein's special theory of relativity, an equally good one to make measurements and observations.

If we now consider the situation in the new reference frame, Jupiter is now motionless but O is moving toward Jupiter and arrives at r

One concludes that, if the speed of gravity is not equal to the speed of light, then measurements of the strength of gravity are reference frame dependent.

Part of the problem is that it is not known how to modify Einstein's theory of gravity to accommodate a speed of gravity different from c. In the frame of reference for which Jupiter is moving, it is natural to substitute v/c

If c

If the graviton, the hypothetical particle that is supposed to be exchanged to produce gravity, has a mass, then the effect of gravity propagates at a speed less than c. It is not easy to produce a consistent theory of massive gravitons, but it is known that Newton's inverse square law (the weakening of gravity as the distance squared) would be violated with gravity being eventually exponentially (highly) suppressed. The current bound on the graviton mass is that it must be exceedingly small – about 10

The observation that the binary pulsar 1913+16 loses energy due to the generation of gravitational waves also validates Einstein's theory at the one percent level. Indirectly, this supports that gravitational waves propagate at c.

The above theoretical and experimental evidence for c

In this frame, it is the Earth that appears to be moving.

The computation for an observer on Earth can be done by using the results for the static observer s if differences between the two systems are related.

There are two effects. First, if

Second, if

Thus to compute the effect of a moving Jupiter, one can proceed as in the static case of a motionless Jupiter carefully noting the dependence of formulas on

In summary, if a speed of gravity parameter is introduced into general relativity that differs from the speed of light then measurements become observer dependent thereby rendering the theory inconsistent. The interpretation that the Jupiter/quasar experiment is a measure of the speed of gravity is valid only in a frame for which Jupiter is moving. In the frame in which Jupiter is not moving, the measurement is only sensitive to the speed of light. This issue undermines the thesis that the Jupiter/quasar measurement is a test of the speed of gravity.

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