Friday, July 25, 2014

Is G, The Newtonian Gravitational Constant Variable?


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Gradiometer method for measuring the Newtonian gravitational constant G - a take off on the simple pendulum.

Newton’s law of universal gravitation:

F = G M1 M2/ r 2


Is one of the most important in physics, as is his constant G, of universal gravitation. But now, according to a new article  (Newton’s Constant) recently appearing in Physics Today, (July, p. 27)  it appears new measurements of G are arousing more questions than answers. Why? Because although G  is considered a constant of nature, “experiments have yet to yield a consensus on the constant’s value”.

In other words, 'G'  may not be a true constant at all.

This is not a new concept, and indeed, my former professor in mathematical methods of physics – Carl Brans – was one of the first to propose a variable G along with his co-contributor Robert H. Dicke. What they did is propose a scalar-tensor theory whereby gravitational interaction is mediated by a scalar field (in which the reciprocal of G is replaced by f  )  which can vary over time and from place to place.

In an earlier blog post,


I also examined a test of the Brans-Dicke  theory using solar oblateness.

According to the Committee on Data for Science and Technology which issues recommended values of scientific constants every 4 years, their last value from 2010 was:

G = 6.67384(80) x 10-11 kg-1m3 s-2.

This value reflects “nearly a  dozen experimental measurements made during the past three decades.”  Interestingly, though many of the individual measurements have an uncertainty of less than 50 parts per million their collective spread is nearly ten time larger.   The graphic shown below

gives a number of the recent G measurements made with different instruments.
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The torsion balance results are in maroon, beam balance are in green- and the year made is given too. (To see the basis of the torsion balance, go to:


A beam balance form of measurement is depicted below, based on apparatus used by a team in Zurich, and the comparison of the weights of two 1.1  kg test masses. (By switching between the left and right configurations, the differential weight or M2 – M1 changes by an amount equivalent to a millimeter sized drop of water.


The error bars shown in the measurements graphic correspond to one standard deviation, and the shaded area indicates the assigned uncertainty of the value as recommended by the Committee on Data for Science and Technology.
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What is most noteworthy is that the apparent uncertainty is extremely large compared to that of other physical constants, many of which are known to a few parts in 108.

How much does this uncertainty and variation matter, if at all? According to the authors (op. cit., p. 28):


The actual numerical value of G is of little consequence to physics. For example, planetary orbits in our solar system are known to follow Newton’s law and can be used along with G to estimate the mass of the Sun. Revising G upward by say 0.05 % would simply reduce the Sun’s mass by the same fraction.”

 In other words, by about:

(1.99      x 10 30 kg) (0.0005) = 9.95 x 10 26  kg

Then subtracting:

(1.99 x   10 30 kg -  9.95 x 10 26  kg) =  1.989 x 10 30 kg


In other words, a negligible difference.

The authors add correctly:


At present we do not have models of the Sun that usefully constrain its mass at such small levels.”

Indeed! And the typical  class 4 optical solar flare will hurl out vastly more mass than this differential.

So in other words, what matters isn’t G’s actual value but “to show that it is, in fact, constant.”

Sadly, unless nature “misbehaves” in a radical way (say Earth’s surface gravity value suddenly diminishes by 5 %) , so it is of such magnitude to allow all the metrology to exhibit it, we are stuck with these variations. But as the authors also point out:

Discrepant measurements of G may signal we do not understand the metrology of measuring weak forces, which may in turn imply that the experimental tests establishing the inverse square law (and universality of free fall) are flawed in some subtle fashion.”

This, in fact, is what I take to be the actual case, so we may have to refine our techniques away from suspending 1.1. kg masses or the like to obtain the best  measurements of G. Perhaps some future genius can devise a far more sophisticated method that’s  not so ham handed, i.e. using gravitational waves. Who knows?

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