Cavendish Experiment

The Cavendish Experiment, performed in 1797–1798 by British scientist Henry Cavendish, was alleged to be the first experiment to measure the force of gravity between masses in the laboratory. The results of the experiment were used to determine the masses of the Earth and celestial bodies. The Cavendish Experiment is often held up as evidence for the universal attraction of mass, and as a proof for gravity. The experiment involves two spherical lead balls attached to a torsion balance, which is alleged to detect the faint gravitational attraction between the masses.

When institutions have reproduced this experiment with modern methods involving lasers and instruments of the highest precision, however, the detection of gravity has been fraught with difficulty, giving erratic results. Oddly, modern repetitions of the Cavendish Experiment tell us that the readings deviate over ten fold from their expected uncertainties when observed at different times.^{1, 2} It is admitted that the experiment is dominated by effects which are not gravity.^{3, 4}

The use of this experiment as demonstration of the universal attraction of mass is further faulted at its premise. This experiment is a matter of observation and interpretation. In this experiment a slight attraction with the force equivalent of the weight of a few cells is observed ⁵ and conclusions are then made about the strength of gravity for the entire universe. Those observations are used to estimate the masses of the celestial bodies, rather than using the theory of gravity and the size of the earth to determine the amount of attraction which should have been seen in the experiment. It is assumed that the attraction seen must originate from the universal attraction of mass rather than any other cause which could cause attraction with the weight of a few cells at close range. Different values seen in the experiment would produce different conclusions for the masses of the earth and celestial bodies.

Gravity Not a Constant

Scientific American provides an assessment of a large number of Cavendish Experiments conducted by prestigious laboratories and institutions and explains that, unlike other fundamental forces in physics, gravity cannot be accurately measured.

Puzzling Measurement of "Big G" Gravitational Constant Ignites Debate - Scientific American (Archive)

“ Gravity, one of the constants of life, not to mention physics, is less than constant when it comes to being measured. Various experiments over the years have come up with perplexingly different values for the strength of the force of gravity, and the latest calculation just adds to the confusion.

The results of a painstaking 10-year experiment to calculate the value of “big G,” the universal gravitational constant, were published this month—and they’re incompatible with the official value of G, which itself comes from a weighted average of various other measurements that are mostly mutually incompatible and diverge by more than 10 times their estimated uncertainties.

The gravitational constant “is one of these things we should know,” says Terry Quinn at the International Bureau of Weights and Measures (BIPM) in Sévres, France, who led the team behind the latest calculation. “It’s embarrassing to have a fundamental constant that we cannot measure how strong it is.”

In fact, the discrepancy is such a problem that Quinn is organizing a meeting in February at the Royal Society in London to come up with a game plan for resolving the impasse. The meeting’s title—“The Newtonian constant of gravitation, a constant too difficult to measure?”—reveals the general consternation. ”

Measuring the Very Faint

In the article Physicist Jens Gundlach (bio) explains that gravity is very hard to measure and would require measuring the force equivalent of the weight of a few human cells on two one-kilogram masses that are one meter apart:

“ Although gravity seems like one of the most salient of nature’s forces in our daily lives, it’s actually by far the weakest, making attempts to calculate its strength an uphill battle. “Two one-kilogram masses that are one meter apart attract each other with a force equivalent to the weight of a few human cells,” says University of Washington physicist Jens Gundlach, who worked on a separate 2000 measurement of big G. “Measuring such small forces on kg-objects to 10-4 or 10-5 precision is just not easy. There are a many effects that could overwhelm gravitational effects, and all of these have to be properly understood and taken into account.” ”

Gundlach explains that there are many effects that could overwhelm the gravitational effects. Static attraction, air viscosity, air particles, static drag, other forces, &c, can easily overcome such gravitational attraction.

“ This inherent difficulty has caused big G to become the only fundamental constant of physics for which the uncertainty of the standard value has risen over time as more and more measurements are made. “Though the measurements are very tough, because G is so much weaker than other laboratory forces, we still, as a community, ought to do better,” says University of Colorado at Boulder physicist James Faller, who conducted a 2010 experiment to calculate big G using pendulums. ”

Wildly Erratic

The article explains that the results are wildly erratic.

“ Through these dual experiments, Quinn’s team arrived at a value of 6.67545 X 10-11 m3 kg-1 s-2. That’s 241 parts per million above the standard value of 6.67384(80) X 10-11 m3 kg-1 s-2, which was arrived at by a special task force of the International Council for Science’s Committee on Data for Science and Technology (CODATA) (pdf) in 2010 by calculating a weighted average of all the various experimental values.These values differ from one another by as much as 450 ppm of the constant, even though most of them have estimated uncertainties of only about 40 ppm. “Clearly, many of them or most of them are subject either to serious significant errors or grossly underestimated uncertainties,” Quinn says ”

The values of these sophisticated laboratory experiments differ from one another by as much as 450 ppm of the gravitational constant. The uncertainty for measuring the gravity of the opposite mass with the equipment should be only about 40 ppm, yet the values observed are far more erratic—over ten times their estimated uncertainties.

Cannot Be Measured

“ “Either something is wrong with the experiments, or there is a flaw in our understanding of gravity,” says Mark Kasevich, a Stanford University physicist who conducted an unrelated measurement of big G in 2007 using atom interferometry. “Further work is required to clarify the situation.”

If the true value of big G turns out to be closer to the Quinn team’s measurement than the CODATA value, then calculations that depend on G will have to be revised. For example, the estimated masses of the solar system’s planets, including Earth, would change slightly. Such a revision, however, wouldn’t alter any fundamental laws of physics, and would have very little practical effect on anyone’s life, Quinn says. But getting to the bottom of the issue is more a matter of principle to the scientists. “It’s not a thing one likes to leave unresolved,” he adds. “We should be able to measure gravity.” ”

The end sentence is plain in its understanding, admitting that they cannot measure gravity.

Forbes Article

From a Forbes piece titled Scientists Admit, Embarrassingly, We Don't Know How Strong The Force Of Gravity Is (Archive) by astrophysicist Ethan Siegel, Ph.D. (bio), we read the following about the issue:

“ While the other fundamental constants are known to precisions of anywhere between 8 and 14 significant digits, uncertainties are anywhere from thousands to billions of times greater when it comes to G.

The gravitational constant of the Universe, G, was the first constant to ever be measured. Yet more than 350 years after we first determined its value, it is truly embarrassing how poorly known, compared to all the other constants, our knowledge of this one is. We use this constant in a whole slew of measurements and calculations, from gravitational waves to pulsar timing to the expansion of the Universe. Yet our ability to determine it is rooted in small-scale measurements made right here on Earth. The tiniest sources of uncertainty, from the density of materials to seismic vibrations across the globe, can weave their way into our attempts to determine it. Until we can do better, there will be an inherent, uncomfortably large uncertainty anywhere the gravitational phenomenon is important. It's 2018, and we still don't know how strong gravity actually is. ”

We are told that, compared to other fundamental constants, the uncertainties with G are thousands to billions of times greater. We are also told that the strength of gravity for the celestial bodies across the universe are all reliant on this inconsistent experiment.

AIP Review

AIP Review of Scientific Instruments
Invited Review Article: Measurements of the Newtonian constant of gravitation, G

“ By many accounts, the Newtonian constant of gravitation G is the fundamental constant that is most difficult to measure accurately. Over the past three decades, more than a dozen precision measurements of this constant have been performed. However, the scatter of the data points is much larger than the uncertainties assigned to each individual measurement ”

Futurism

From a Futurism Article Is the Gravitational Constant Really a Constant? by astrophysicist Colin Robson (bio):

“ So far as we can tell, the gravitational constant has remained constant throughout the entire history of the universe. This has, however, been VERY difficult to prove! Measurements of the gravitational constant over the past 200 years have been erratic. Even as the techniques that we use now are far more advanced and sensitive than were used two centuries ago, the true value of the gravitational constant remains elusive.

In 2013, a group of researchers working out of France took the measurement of the gravitational constant, using the same machine that they’d used some 2 years earlier. Improvements were made on the machine to improve the sensitivity and give a more accurate result. The machine, which uses two independent methods to calculate the constant, averages the results of the two. This, in theory, should help reduce systematic errors. What did they find? A different result!

At first it may seem strange that the gravitational constant is so hard to determine. There are four fundamental forces in the universe:

Strong Force
Weak Force
Electromagnetism
Gravity

Gravity is by far the weakest of the four forces, which, may also sound a little strange considering what we see in the universe. When looking out into the cosmos, gravity appears to be the reigning king of all. Gravity is so strong that it causes stars to fuse hydrogen into helium, collapses stellar cores into neutron stars and black holes, creates quasars and dictates the flow of matter within the entire universe.

On a large scale, gravity wins. But, as was previously mentioned, gravity is the weakest of the four forces. The reason for this discrepancy is, as a force, gravity travels further and has a slower fall off. The strongest of the four forces, the Strong Force, becomes almost non-existent at distances outside of a nucleus. What makes gravity stronger in macro circumstances is that it is accumulative. The more matter there is, the more gravity. But still, gravity is weaker. Therefore, when trying to measure it, the other forces can cause systematic errors. It is akin to trying to measure the weight of a feather, outdoors, in a slight breeze, with an old pair of scales. ”

Physics World

Physics World provides a graphic, showing that the measurements often do not overlap and are spread out across a range of over ten times the estimated uncertainties:

https://physicsworld.com/a/the-lure-of-g/ (Archive.is)

Figure 1:

“ Low precision alone is enough to keep a metrologist up all night. But in recent years, a much more serious problem has arisen: measurements of big G are in wild disagreement with one another (figure 1). Since the turn of this century, values recorded by some of the best labs in the world have been spread apart by more than 10 times their estimated uncertainties. Something is amiss – yet no-one is quite sure what. “You go over it, and over it, and over it,” says Speake. “And there comes a time when you say, I just can’t think of anything we’ve done wrong.” ”

Terrance Quinn

Terence Quinn (bio) is a British physicist who spent many years studying gravity and was emeritus director of the International Bureau of Weights and Measures.

Significant Errors

In a Scientific American article Quinn says the errors are significant:

https://www.scientificamerican.com/article/puzzling-measurement-of-big-g-gravitational-constant-ignites-debate-slide-show/ (Archive)

“ These values differ from one another by as much as 450 ppm of the constant, even though most of them have estimated uncertainties of only about 40 ppm. “Clearly, many of them or most of them are subject either to serious significant errors or grossly underestimated uncertainties,” Quinn says ”

Quinn is also quoted in the article as saying that "we should be able to measure gravity":

“ But getting to the bottom of the issue is more a matter of principle to the scientists. “It’s not a thing one likes to leave unresolved,” he adds. “We should be able to measure gravity." ”

If Quinn is stating that we should be able to measure gravity, then this may imply that Quinn does not think that he measured gravity in his years of studying it in the laboratory.

Science of Meteorology

In a Nature article Quinn says that the published range undermines the science of metrology:

https://www.nature.com/articles/nphys3651?proof=t (Archive)

“ Who needs a more accurate numerical value of G (the current recommended value6 is 6.67408 ± 0.00031 × 10−11 kg−1 m3 s−2)? The short answer is, nobody, for the moment, but being apparently unable to converge on a value for G undermines our confidence in the metrology of small forces. Although it is true that the orbits of the planets depend on the product of G and the mass of the Sun — the structures of all astrophysical objects are determined by the balance of gravity and other forces produced by, for example, gas, photon or degeneracy pressure — ab initio models of the Sun are still an order of magnitude away from predicting a value of G at a level comparable with laboratory determinations. We do not need a value of G to test for departures from the inverse square law or the equivalence principle. There is as yet no prospect of a theory of quantum gravity that would predict a value for G that could be tested by experiment. ”

In the above quote we see a statement that the recommended range undermines their science in the metrology of small forces, showing that he is certainly not endorsing it. Quinn clearly suggests the recommended range is questionable.

Quinn also speaks about about the practical purpose for the such a measurement, in non-cavendish situations and measurements. He is correct that G is not needed for the Equivalence Principle tests. This is something else, showing that gravity does not depart in laboratory experiments from the concept that the Earth is accelerating upwards. The EP tests are highly and accurately verified.

New Physics

In an article The Newtonian constant of gravitation—a constant too difficult to measure?, a title which suggests that Quinn believes that Gravity has not been satisfactorily measured, he suggests that it could be that gravity isn't truly universal and that it mainly applies on astrophysical scales:

https://royalsocietypublishing.org/doi/10.1098/rsta.2014.0253 (Archive)

“ What matters then is not the actual value of G itself (give or take a percentage or so) but its uncertainty. The real importance of the accuracy of G is arguably that it can be taken as a measure, in popular culture, of how well we understand our most familiar force: the discrepant results may signify some new physics, or they may demonstrate that we do not understand the metrology of measuring weak forces. Owing to the lack of theoretical understanding of gravity, as alluded to earlier, there is an abundance of respectable theories that predict violations of the inverse square law or violations of the universality of free fall. In fact, a growing view is that G is not truly universal and may depend on matter density on astrophysical scales, for example. A misunderstanding of the metrology of weak force physics may in turn imply that the experimental tests that have established the inverse square law and the universality of free fall thus far are flawed in some subtle fashion. This makes for a potentially exciting situation and perhaps explains the general interest shown in our apparently mundane and painstaking work on G. ”

Whether the science of metrology is misunderstood or the physics of gravity are different than envisioned, the result is the same: The Cavendish Experiment is not a demonstration of gravity.

Gravity 'Oscillates'

Due to the mysterious readings and problems, some are now calling gravity part of "Dark Energy."

https://www.newscientist.com/article/dn24180-strength-of-gravity-shifts-and-this-time-its-serious/ (Archive)

“ An oscillating G could be evidence for a particular theory that relates dark energy to a fifth, hypothetical fundamental force, in addition to the four we know – gravity, electromagnetism, and the two nuclear forces. This force might also cause the strength of gravity to oscillate, says Padilla. “This result is indeed very intriguing." ”

History

According to physicist George T. Gillies the difficulties in measuring G has been a recurring theme in the study of gravity.

The Newtonian gravitational constant: recent measurements and related studies (1996) (Archive)
George T. Gillies

Abstract: “ Improvements in our knowledge of the absolute value of the Newtonian gravitational constant, G, have come very slowly over the years. Most other constants of nature are known (and some even predictable) to parts per billion, or parts per million at worst. However, G stands mysteriously alone, its history being that of a quantity which is extremely difficult to measure and which remains virtually isolated from the theoretical structure of the rest of physics. Several attempts aimed at changing this situation are now underway, but the most recent experimental results have once again produced conflicting values of G and, in spite of some progress and much interest, there remains to date no universally accepted way of predicting its absolute value ”

Concluding Remarks - p.212

“ The spread in the values of G obtained by the recent high-precision determinations of it attests to the difficulty of the experiments. Interestingly, the differences in the published results replicates a similar situation that arose almost 140 years ago (Jacobs 1857), and which seems to have repeated itself every few decades since then. As discussed at length in section 4, determinations of G are fraught with difficulty because of the universality of the gravitational force, its weakness compared to the other fundamental interactions and the sensitive nature of the apparatus used to make the measurements. ”

The Newtonian Gravitational Constant: An Index of Measurements (1983) (Archive)
George T. Gillies

Introduction - p.1

“ If one were to catalog the tools of precision measurement, an unusually high number of the listings would claim as their genesis the precision measurement of the Newtonian Gravitational Constant, herein simply referred to as "G". These tools would include the torsion balance, the optical lever, the quartz fiber, synchronous detection techniques, ultra-high precision rotations and many others. Yet G stands alone as the only fundamental constant currently known to little better than one part in a thousand although there are three measurements claiming accuracies of one part in ten thousand. In parallel with these efforts to measure the absolute value of G, there has also been a wide variety of experiments aimed at linking the gravitational force to the other forces of nature. All such efforts to date have had the singularly unique result of demonstrating that gravity, indeed, stands alone - the last of the great classical mechanisms - in spite of its modernized presentation via general relativity.

Classical gravitational physics has been like this, and foreseeably will continue to be like this. The reason why is that, to this date, no one has succeeded in isolating sufficiently well the gravitational interaction between laboratory masses to the point where other disturbing forces or experimental uncertainties do not dominate the measurement, at least at levels above those at which other phenomena might be expected to occur. ”

Addendum

As suggested by the references above; until physics is able to isolate the gravitational interaction between laboratory masses to the point where other disturbing forces do not dominate the measurement, the Cavendish Experiment should be regarded for what it is: An inconsistent experiment which is admittedly disturbed and dominated by unknown or unmitigated effects, and which might or might not include "gravity" in the results seen.

A found attraction somewhere around the force equivalent of the weight of a few cells is considered by popular thought to be an impeachable proof for gravity and the universal attraction of mass. Accordingly, anything which seems to support it does support it, no matter how imprecise, no matter how many other effects may be dominating the results of the experiment, and the absurdity of equivocating the detection of such a slight effect to one cause above any other possibility in nature is put out of the mind and ignored entirely. It is through such inherent fallacy that one hypothesis is built upon another. Deductions and conclusions are given, but the foundations remain essentially undemonstrated. It is deemed sufficient to observe and interpret rather than to prove and demonstrate.

A Small Effect

One attempted justification of the issues with the Cavendish Experiment is to point out that the deviation in the experiment is "small". Specifically, the Forbes article above references discrepancies on a 0.15% level.

“ As you might expect, the values got better and better through time, with the uncertainties dropping from 0.1% to 0.04% all the way down to just 0.012% in the late 1990s, owing mostly to the work of Barry Taylor at NIST...

This is why it was such a shock, in 1998, when a very careful team got a result that differed by a spectacular 0.15% from the previous results, when the errors on those earlier results were claimed to be more than a factor of ten below that difference....Multiple teams, using different methods, were getting values for G that conflicted with each other at the 0.15% level, more than ten times the previously reported uncertainties. ”

It is argued that this 0.15% deviation is small, and so the problems with the Cavendish Experiment should be ignored on that basis.

However, this argument is insufficient. The range of deviations dominates the result. As these "small" effects dominate the still smaller effect of gravity that should be measured by the equipment, causing deviations of over 10 times the expected uncertainties, it is still questionable whether the experiment is measuring gravity. In the Futurism article astrophysicist Colin Robson compares the issues with the Cavendish Experiment to an analogy^[1] of trying to measure the weight of a feather on a crude pair of scales in a slight breeze. This "small" effect from the slight breeze dominates the smaller effect of the feather's weight. Under such a situation if the view of the feather was obscured from observers, and only the readings on the scale were seen, varying because of the breeze, it would be reasonable to question whether the feather was there at all. Likewise, any situation which dominates the effect of gravity must necessarily call the existence of gravity into question.

A dominating noise invalidates the detection of a smaller effect. The range of results is over ten fold the determined uncertainties of the equipment. One cannot merely assume that the experiment is detecting a number of admittedly stronger effects to cause the inconsistent results, but maintain that "gravity is in there somewhere."

A Statistical Approach

Another common approach to justifying the results of the Cavendish Experiment is to assert that we need only find the closest mean, median, or mode of the results, and to declare that this is the value of 'gravity'. Yet, minimal introspection on this approach will show that finding a statistical average value of the effects which are dominating the experiment would tell us only what the average is for the dominating effects, and not about 'gravity'.

Proof by Contradiction

As a proof by contradiction, similar experiments which have attempted measure gravity at larger scales than the shorter ranges of the Cavendish Experiment have been unable to detect gravitational influence. There is a reason for why the Cavendish Experiment is cited as one of the very few proofs of gravity. It is typically neglected mention in the classroom that a great amount of effort has gone into searching for gravitational variations from either the earth or external bodies, with negative results. See: Variations in Gravity