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## Does G vary because of Mach's Principle?

Does G with r vary because of Mach's Principle?

A Solar System Test of Mach's Principle with Gravimetric Data
 We present a new test for a possible Mach-Sciama dependence of the Gravitational constant G. According to Ernst Mach (1838-1916), the gravitational interaction depends on the distribution of masses in the universe. A corresponding hypothesis of Sciama (1953) on the gravitational constant, $c^2/G = \sum m_i/r_i$, can be tested since the elliptic earth orbit should then cause minute annual variations in G. The test is performed by analyzing the gravity signals of a network of superconducting gravimeters (SG) which reach a precision of $10^{-10} m/s^2$.
The result?
 After reducing the signal by modelling tidal, meteorologic and geophysical effects, no significant evidence for the above dependence is found
Unless, that is, M also varies with G such that GM is constant.........

http://arxiv.org/abs/gr-qc/0405094
 this variation (in G) is normally ’hidden’ by the compensating change in atomic masses that causes GM to be constant.
Garth
 Recognitions: Gold Member Science Advisor I think it begs the the question Garth. What testable predictions does this model produce?

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 Quote by Chronos I think it begs the the question Garth. What testable predictions does this model produce?
The OP was simply reporting on the non-detection of a varying G.
I pointed out that actually all such determinations of variations of G are also convoluted with a possible variation in rest mass as we can only test for GM.

SCC, in which both G and m vary such that GM is observed to be constant is of course being tested by Gravity Probe B and we only have another 6 months to wait for the results!

Garth

## Does G vary because of Mach's Principle?

Its correspondent experiments do seem to set an upper limit on the variation of G.

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 Quote by Loren Booda Its correspondent experiments do seem to set an upper limit on the variation of G.
Agreed - but only if particle masses do not vary, as in GR.

In fact they have set an upper limit on the variation of GM.

Garth
 Recognitions: Gold Member Science Advisor If GR is correct, distant observers should always be able to reconcile their measurements [observations] by calibrating their clocks. To make the case for variable G, or C, it is, IMO, necessary to show a discrepancy that cannot be explained by calibrating clocks.

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 Quote by Chronos If GR is correct, distant observers should always be able to reconcile their measurements [observations] by calibrating their clocks. To make the case for variable G, or C, it is, IMO, necessary to show a discrepancy that cannot be explained by calibrating clocks.
Such as the Pioneer Anomaly?

The Pioneer anomaly as acceleration of the clocks

Garth
 Recognitions: Gold Member Science Advisor Grumbles, kicks at stones on the road, and ponders whether it is more civilized to tar witches before setting them afire . . . That dang pioneer anomaly is troublesome. I wish you would just ignore it like most other civilized scientists . . .

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 Quote by Chronos Grumbles, kicks at stones on the road, and ponders whether it is more civilized to tar witches before setting them afire . . . That dang pioneer anomaly is troublesome. I wish you would just ignore it like most other civilized scientists . . .
Careful now - otherwise we'll might get this thread locked!

Garth
 I am still with Mach, my trouble is the figures don't quite support my hypothesis (YET). If the universe is expanding then its overall density is decreasing this has to mean a decrease in the universe's gravity, it also means that time must accelerate. Can anyone work out how we operate a relative frame of reference instead of an inertial frame of reference? The basic construction is an iterated polynominal that varies according to our position in time as well as in space and with regard to relative velocity. Everything is variable and relative (to our position in time) even the speed of light.

 Quote by Chronos That dang pioneer anomaly is troublesome. I wish you would just ignore it like most other civilized scientists . . .
It is troublesome! Based on what reviewed papers I've read, the data just isn't the least bit conclusive.. I wish they'd hasten sending a probe to properly test the effect, but I'm guessing the expense of sending something right out of the solar system will have us waiting quite some time.
 Recognitions: Gold Member Science Advisor I think it is too far beyond the error bars to be ignored. The usual suspects have been ruled out rather conclusively, IMO. Few at NASA think it is a systematic measurement error [according to my sources]. Even fewer have a viable guess as to what it means. Neither MOND or dark matter can be ruled out, or ruled in, but more data is required. A lasar ranging type experiment on any of the outer planets would be helpful. Precision measurements [within a few meters] would helpful.
 Recognitions: Gold Member Science Advisor A second interesting anomaly may exist. As reviewed by Leslie Morrison and Richard Stephenson, [1998, Astronomy & Geophysics Vol. 39 October], The Sands of Time and the Earth’s Rotation and again by Stephenson, [2003, Astronomy & Geophysics Vol. 44 April], Historical eclipses and Earth’s rotation. Their analysis of the length of the day from ancient eclipse records discovered that in addition to the tidal contribution there is a long-term component acting to decrease the length of the day, which equals: △ T/day/cy = −6 x 10−4 sec/day/cy. This component, which is consistent with recent measurements made by artificial satellites, is thought to result from the decrease of the Earth’s oblateness following the last ice age. Although this explanation may be correct, and it is difficult to separate the various components of the Earth’s rotation, it is remarkable that this value of △T/day/cy is equal to H if H = 67km.sec−1/Mpc! The question is; why should this spinning up of the Earth’s rotation have a natural time scale equal to the age of the universe rather than the natural relaxation time of the order of that of the Earth’s crust or the periodicity of the ice ages? This anomaly also may therefore be cosmological rather than geophysical in nature. If this is the case then again, as with the PA, it is a phenomena not explicable by the standard theory. I mention this because again it could be explained by a clock drift between physical clocks (the Earth's rotation as a 'balance wheel') and ephemeris clocks (the Moon's orbital period). These clock drifts could be one way of observing an otherwise convoluted and hidden variation in G. Garth

 Quote by cesiumfrog It is troublesome! Based on what reviewed papers I've read, the data just isn't the least bit conclusive.. I wish they'd hasten sending a probe to properly test the effect, but I'm guessing the expense of sending something right out of the solar system will have us waiting quite some time.
There are already other probes which have exited the solar system and, as far as I know, there has been no report of similar anomalies with them, although they didn't follow the same trajectory and had higher velocities if I remember correctly, so they aren't a perfect comparision.

If we do not see similar anomalies in future probes it might be a sensible assumption to say that the original anomaly was due to equipment malfunction or some transient phenomenon. Although I am fairly optimistic that if it was an equipment malfunction that we would have had a complete working model of it already...

(EDIT: I have just looked this up and I am totally wrong so ignore that please. Its seems there is similar data from Galileo and Cassini, its seems that the only reason for no Voyager data was that they used a more complicated method to stabilise the craft than was used with the others which prevented the collection of good data. Also, according to the wikipedia page the ESA has plans for a dedicated probe to investigate the effect :) )