Newtonian Constant of Gravitation

International Consortium

I. BACKGROUND

Recent measurements of the Newtonian constant of gravitation G are in disagreement,

with discrepancies that are roughly ten times the quoted uncertainties in some cases. This

is clearly an unsatisfactory situation for one of the most basic fundamental constants in

classical physics.

The disagreement calls into question our ability to measure small forces on a laboratory

scale. It also raises the question of whether the Newtonian force law is a complete description

of gravity at these distances.

This issue was recently discussed at a Royal Society scientific meeting entitled The Newtonian constant of gravitation, a constant too difficult to measure? [1] The conclusions of

that meeting are included as the appendix to this proposal.

Given the history of discrepancies, it is unlikely that one or two more experiments will

resolve the situation even if they are done with the oversight of an advisory committee.

Instead possible sources of bias, not previously tested for, should be checked. In addition

there needs to be redundancy and tests for reproducibility order to determine a reliable

value for G. This proposal describes an approach to arrive at such a value.

II. METHOD

As an effort to resolve this situation, a consortium will be formed consisting of capable

individuals and institutions willing to collaborate on a large-scale project to determine a

reliable value for G. Participants would either produce the necessary apparatus and make

measurements of G, or they would use an apparatus made at another institution and repeat

the measurements. In some cases, participants that produce an apparatus might also make

measurements with a different apparatus produced at another institution. It is expected that

different institutions will produce different types of apparatus to implement independent

experimental approaches.

In contrast to previous projects, it is proposed that two identical copies of each type

of apparatus be produced and used to make the measurements. Work will continue until

consistency is achieved between the two devices by the institution that produced them.

Then, each of the two devices will be taken apart and loaned to two other members of the

consortium who will repeat the measurements using their own procedures and data analysis.

Basic instructions for putting the device back together will be provided, but to avoid bias,

operating procedures and data analysis will be done independently. Details of how the

apparatus will be distributed will depend on the number of members in the consortium and

their availability to make the measurements.

When the experiments are completed, the results will be compared. If they agree, then

a valid value for G will have been obtained. If not, then there will be multiple results that

could uncover a pattern for the disagreements to guide the search for possibly overlooked

systematic effects.

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This approach will test for possible systematic bias associated with the location of the

measurement, the design of the apparatus, and the personnel carrying out the measurement,

which have not previously been fully tested.

III. PARTICIPANTS

NIST will consider being one of the institutions where two copies of an apparatus will be

produced and new measurements of G will be carried out. Simultaneously with NIST, other

institutions might each make two copies of an apparatus based on a different design and

carry out the proposed measurement and redistribution procedure. Participants could also

collaborate by repeating measurements with either of the two copies already made at one of

the primary institutions. Another role for participants who are experienced in doing such

experiments would be as members of an international advisory board to act as consultants

for the groups making the measurements.

IV. JOINING THE CONSORTIUM

People considering participating in this project are invited to apply for a collaborative

partnership. A statement of possible interest and intended level of participation may be

sent to bigg@nist.gov.

V. WORKSHOP

To refine the plan for the project and exchange ideas for experiments, a workshop will

be held at NIST on 9-10 October 2014. Potential participants are invited to attend. To

register and for detailed information see the website at pml.nist.gov/bigg.

The workshop is intended to cover the following topics:

• Methods of measuring G.

• Timescale of the overall project.

• Procedures for carrying out the cross comparisons.

• Whether there should be blind offsets until all measurements are done.

• Drafting of a joint article on the project for Metrologia.

[1] Website: royalsociety.org/events/2014/gravitation/.

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Appendix: Outcome of the Royal Society meeting on G held at Chicheley Hall

on 27th and 28th February 2014

Terry Quinn, 7 March 2014

A broad consensus was reached on the following main points;

1. The problem of arriving at a reliable value for G in the face of the wide dispersion of

recent results (some 450 ppm, more than ten times the sigma of the individual results)

is unlikely to be resolved by one or two additional results obtained, as in the past, by

teams working independently.

2. There is nevertheless an urgent need to resolve this situation, unprecedented in the

determination of one of the fundamental constants of physics. Although at present

there is no pressing problem in theoretical physics that requires an accurate value of G,

accurate values of the fundamental constants are an essential part of the foundations

of physics. In almost all areas of the physical sciences, determinations of fundamental

constants are at the frontiers of science. This is so in experimental gravitational physics

where one of the characteristics of the work is the need to measure extremely small

forces. The science and techniques used in the determination of G are those also used

in tests of the equivalence principle, in tests of the inverse square law and in the search

for other non-Newtonian forces. Quite apart from the results of such measurements,

whether they are null experiments or ones leading to a value of a constant, the training

of young scientists who participate has always been an important product of high

metrology. The wide disagreement among recent measured values of G must cast

some doubt on our abilities in this crucial area of small-force measurement and in

other areas where similar techniques are used. This is an unsatisfactory situation.

3. There are a number of key parameters some or all of which have to be measured with

the highest accuracy in determinations of G. These include mass, density, length,

time, electric current, voltage, capacitance and angle. In some experiments there may

be others. Measurements of these must be traceable to verified national and international standards with evaluated uncertainties with respect to the SI. The experiments

themselves must be carried out in laboratories having the highest quality of temperature and environmental control. All of this strongly points to a national metrology

institute, or a laboratory closely associated with a national metrology institute, as

being the most appropriate place for future experiments to take place.

4. Thus, instead of simply calling for new determinations of G, it is suggested that an

international advisory board be created, made up largely of those who have already

carried out a G experiment, to advise on the choice of method or methods, on the

design of the experiment, on its construction and finally on the interpretation of the

data and calculation of the results. This would be in contrast to the present situation

in which outside criticism and comments can be brought to bear only when the experiment is finished and published when it is too late to affect the outcome. It is only by

proceeding in this way that one might hope to obtain results that are demonstrably

reliable.

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