So from an experimental viewpoint, Newtons law runs into various problems even right here on Earth. Who knows what problems it faces when extrapolated to the large scale constituents of the universe.
Since gravity was related by Einstein to the geometry of space-time (whatever the hell that physically is) gravity has received support from various tests, such as the perihelion of mercury, and others. However, the following quote from a very popular book on astronomy, is quite remarkable:
Galactic dynamics (page 635)
"It is worth remembering that all of the discussion so far has been based on the premise that Newtonian gravity and general relativity are correct on large scales. In fact, there is little or no direct evidence that conventional theories of gravity are correct on scales much larger than a parsec or so. Newtonian gravity works extremely well on scales of ∼ 10^14cm (the solar system).
(...) It is principally the elegance of general relativity and its success in solar system tests that lead us to the bold extrapolation that the gravitational interaction has the form GM/r2 on the scales 10^21 − 10^26cm..."
[....]
The above cited 'bold extrapolation' of gravity seems to have encountered problems even in the solar system now, with the pioneer and voyager anomalies, so it seems very naive to presume that gravity functions how we currently model it when applied to much larger scales.
Many tests show that gravity obeys an inverse square law in terms of distance, but little work has been done on observations that test the dependence on the field mass, M. Since mass estimates of the whole universe depend on it, determining the absolute value of G is kinda important. The thing is that they all tend to give different values for G, and whereas other (fundamental) constants in nature achieve an accuracy of over 12 decimal places the value of the gravitational constant lags behind with far greater uncertainty, with only about 3-4 decimal places remaining undisputed by various methods. This indicates that we still have a lot to learn about the true nature of gravity.
A lot of work has been done on determining the value of G. What seems lacking however are test which test the spatial and temporal dependence of G, which can also be used to test Newtons law as well. At the atomic level, although you can work out the ratio of electric and gravitational forces at 2.27x10
39 (respectively), this has never been measured as particles this size are too light to be used as field masses. Gravity is amazingly illusive at this small scale, and remains so right up to much larger scales. At the standard laboratory scale the torsion balance is the usual method, done usually over a distance of 10 – 30 cm, which is the method used by originally by cavendish, which has changed very little to this day. One further method is by using a superconducting gravimeter and a moving mass (see
http://www.iop.org/EJ/abstract/0957-0233/10/6/311).
And that’s about it from methods of determining G directly. We only have direct confirmation of this law over a very small scale range, from laboratory to geological size, it is presumed from this that it applies exactly to all other scales. Other larger scale methods like satellite based experiment’s to find the value of G, such as LLG, are in fact finding the product M
EG, using the mass of the Earth, under the presumption it is correct, and other larger scale estimates use generally use the mass of the sun (inferred from the mass of the Earth) to determine G.
Another interesting way to test gravity would be check the dependency of Newtons law on the amount of field mass in question. Which is an idea lacking much experimental verification too. When M = m (in F=GMm/r
2) the law becomes symmetric, but a deviation for large masses would not violate the equivalence principle, at least within its experimental constraints which apply mostly to test masses. It is often claimed that any physical theory has to be linear in the weak-field-limit, but this cannot be definitively proven, mainly due to the amazingly weak nature of gravity making tests for this very hard. We just perform an extrapolation of our mathematical methods, which should be tested. There are plenty of ways to test the r
2 term in Newtons law, but testing the exponent 1 on M is much more difficult to prove.
Torsion balance experiments typically use masses in the range 5 – 20 Kg, and this is the mass at which we base our most accurate measurements of G. And this mass range goes up to about 10
7 Kg with lake experiments to measure gravity (see:
Determination of the gravitational constant with a lake experiment.), which achieved results close to laboratory values, but not to such a high degree of accuracy. Generally, the more mass is used the less reliable the value becomes. And when you get to the solar system scale satellite data of planetary orbits can not be used to find the field mass dependence of Newtons law (ie, the exponent of M not equal to 1 in F=GMm/r
2) as the same data is used to measure the mass. You can use Keplers law to test the validity of the inverse square relationship, but this can not reveal an exponent of M different from 1. This problem stems from not being able to find independent mass estimates of these larger scale objects (apart from some very crude methods with a very high amount of uncertainty), and so from the mass range of the moon \earth (10
23 kg) all the way up to sun, no accurate test for this exists. When dealing with the galactic scale (from 10
39 to 10
44) you run into the same problem of not having independent mass estimates. And this applies to all scales above the solar system. Solar mass to light ratio measurements for galaxies do not fit the dynamically determined mass, and so dark matter is invented to explain this failure of Newton’s law. And right up on the cosmological scale Newtons law fails, and so dark energy is invoked to explain the anomalies. So over time Newtons law has been patched up with numerous ad hoc solutions, but maybe instead of just assuming these entities exist and can explain away everything we should just consider that the law of gravity is plain wrong when applied to large scales. This is where theories like MOND and others come in. And while MOND presents more problems than it solves (in my opinion), it has been very useful in pointing out another problem with Newtons law, that it is poorly tested for accelerations below 10
−10ms
−2.
I think that it is highly likely that the hierarchy of structures in the universe, the lab, earth, solar system, galactic, cosmic does not stop at the laws that we use in the solar system but requires a corresponding hierarchy of theories. Inventing new entities and new free parameters to simulations will not be sufficient; this type of approach seems to me to be a modern day version of the
epicycles of Ptolemy. Extrapolating theories beyond their true testable scope should be avoided, unless we want to walk down the path of ever more complex theories piled up ontop of each other in an attempt to try to hold on to the basic law underlying them all,
this type of approach merits a warning from history.
The amount of research that is done in cosmology based on this unverified extrapolation of gravity over some 14 orders of magnitude is quite a remarkable spectacle.
There are considerable gaps in our knowledge about how gravity functions at large scales. Take a look at this graph for example;
http://img502.imageshack.us/img502/6536/gravityvd8.jpg
Generally objects fall into three groups at different scales. The group on the left are the only area where direct absolute measurements of G are possible, from tiny scales up to geological scales. Everything else on this table, from our satellites up to super-massive black holes are extrapolations of Newtons law that remain to be tested, as even the middle group are testing Keplers law rather than Newtons. For the group on the right, none of them offer any sort of undisputable evidence for Newtons law, without having to invoke quantities such as dark matter or energy. To put it simply, tests of the field mass dependence are entirely determined by only 1-2 independent types of experiments on the small scale. The extrapolation to the other larger objects is assumed.
The interesting thing about Maxwells electromagnetism is that it is not like gravity, it is scale invariant. Gravity has no effect on that atomic scale. But it does on the solar scale. And it is
assumed to be the only force that can effect even larger scales. But the sheer amount of large scale objects that do not obey Newtons law by their shape and structure, certainly imply that other forces are at work on the large scale. And now we know that plasma is so pervasive in the universe, something not known when most gravitational models were invented back when they thought that space was a void of empty space, EM forces in plasma are the obvious candidate to explain these objects.
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