Gravest Gravity

Tim Cullen, who writes the ‘Malaga Bay’ blog, and I seem to be singing from the same hymn book though I am not sure what page he is on, let alone what page I am on either after reading his latest effort about “All Gyre and No Gimbals”. The reason I write this is because during the last few days I have been mulling over Newton’s theory of gravitation as a result of having finished reading Hilton Ratcliffe’s latest book, “Stephen Hawkings Smoked My Socks …” which I mentioned here. Hilton’s thesis is that science in general has wandered off into a mathematical fantasy world in which maths has become truth, and physical reality something to be avoided, or if it can’t, then explained away with some ad hocery.

I have published some measurements of gravity and magnetics of a down-hole survey of a diamond cored hole drilled into a deeply buried magnetic anomaly interpreted as a magnetite deposit in the Archaean folded sediments east of the Pilbara town of Port Hedland, on De Grey Station. This survey produced incomprehensible gravity data from the first 90 metres or so of drilling along which the inclination of the hole, (described as a negative dip) was positive and hence, according to the measurements, coming out of the ground. This is not possible, or both the driller and I were hallucinating rather badly, which considering the safety regulation etc involved with doing any geological field work these days, was also not a possibility. And my consulting geophysicists were quite speechless when confronted with this data although they did aver that these results meant explicitly that there was a gravitating mass sitting above the drilled, diamond cored, hole. So unless one believes in invisible UFO’s hovering above one’s drilling operation, this survey result remains inexplicable. Note the emphasis on belief; it’s important.

(I should mention that prior to drilling a field gravity survey was completed to refine the earlier airborne data that the targetting was based on, and no anomalous surficial gravity values were observed. Incidentally the drilling intersected banded iron formations that were magnetically fairly uniform but certainly not due to a concentration of magnetite in the BIF’s as implied by the magnetic anomaly. Another lovely geophysical interpretation killed by an unfortunate fact called a drill-hole — the scientific method in its purest application).

So the politest comment one could offer on the drill hole survey results is that Newton’s Law of Gravitation seems to be incomplete; a conclusion which Tim Cullen and others have also reached via other means.

Newton’s Law of Gravitational Force, however, is simplicity itself, F=(GM1M2)/(D^2), the force being the product of the two masses M1 and M2, divided by the square of the distance separating them, and the result multiplied by G, the gravitational constant that is a rather small number when you think about it, 6.67384 x 10^-11 cubic metres per kilogram per second.

The down-hole survey instrument measures drill hole inclination by reference to a small pendulum like mechanism in the instrument, and in terms of Newton’s equation, would be M2, while the the earth is M1. For the drill hole inclination to be positive (convention is that negative is measured down from horizontal, while positive is measured up from horizontal) a third mass, M3, had to be above the instrument in order to counter act the attraction the test object M1 experiences from the Earth M2.

As these inverted drill hole inclinations also occurred within the overlying geologically younger Cretaceous sediments of the Canning Basin, and which sediments also host a source of artesian water, then one suspects that these younger sediments must have some or other unknown gravitational property. Simply weird, to say the least.

And what was I mulling over? The obvious implication that if the distance separating two objects is zero, then there isn’t any gravitational attraction between the two objects.

Que? What has this to do with the drill hole survey and bizarre drill hole dips?

Remember that Newton originally described his law in terms of two objects separated by empty space, or vacuum in that there isn’t any ‘matter’ between the two objects. Objects are thus simply independent, non contiguous clumps of matter be they small ball bearings, moons or planets, separated by ‘space’. The trouble is that space is not devoid of matter, as was believed by Newton, and even the case of a falling cannon ball dropped from the top of a building is never isolated in ‘space’ per se but is always in contact with contiguous matter, here the Earth’s atmosphere. So when does a physical object become an object in the Newtonian sense? This is not a trivial question I need to add.

So imagine a cube of lead measuring 1 metre by 1 metre by 1 metre, a cubic metre of lead, resting on the surface of the earth. There is no distance between the cube of lead and the Earth. There’s also no movement between the Earth and the lead cube which appears as if glued to the Earth. So what is the gravitational force acting on this cube of lead? That depends on what the value of “D” is, (in metres). It has to be zero as the Earth and lead-cube are spatially contiguous.

But mathematically dividing something by zero, since that is the actual distance between the Earth and the lead cube, is impermissible and if we make it an extremely small number, say 0.0000000000001 metres then F, per the formula above, approaches infinity or if it doesn’t, is an extremely large, perhaps incomprehensibly large, number. This is not physically realistic either but if we define the distance as the distance between the centre of gravity of the lead cube and the centre of gravity of the earth, then we end up with a more plausible number for distance and hence the gravitational force but we then have the nonsense of having all the matter of the object concentrated in a point which is dimensionless and hence has no volume. Centre of gravity is essentially a computational simplification, not an actual physical fact, as was drummed into me in Physics 1 all those years ago at University. (I studied Physics 1, Geology 1, Chemistry 1 and Mathematics 1 during those days). However we will find ourselves in deep intellectual waters if we reify these computational abstractions as physically real things. And that’s when maths starts to render science as something surreal.

I also need to stress that I am not asserting Newton’s Law of Gravitation is intrinsically problematical, since it works splendidly for independent non contiguous objects like satellites, airplanes and cannon shells etc. It just becomes problematical when we extrapolate the theory into situations that do not involve mutually independent objects such as the Earth-lead-cube example. The implication is that Newton’s law seems not applicable to sub-objects making up an object. So what is a sub-object? In terms of the Earth it is made of the following sub-objects, internal core, outer core, mantle and crust, in its simplest form. (We should add the following outer shells of liquid, the oceans etc, and the enveloping atmosphere, which then blends into the ionosphere, but all these things remain sub-objects of the main object, the Earth).

Is therefore gravitational attraction between the various sub-objects that make the earth responsible for the observed pressures and temperatures? But when one starts to think about this problem in detail, difficulties arise, especially when the only data one has are remote geophysical surveys that are intrinsically untestable.

So what causes the inferred pressures and high temperatures interpreted inside the Earth’s core and mantle? Gravity? But if two objects are not separated by distance, so together they appear as, say, a heterogenous object, then no gravitational attractive force is being applied by either on the other, or if you believe in UFO’s, the force is actually infinity and just as silly. It is sort of like internal gravitation. Do we observe this? No but we do seem to ‘believe’ it because mathematically we can compute it.

However just because it is mathematically possible does not mean it is physically possible; the Earth’s core does not move independently of the rest of the Earth, does it. The problem seems to lie in understanding what objects M1 and M2, in the equation above, mean physically because in exploration and mining geology we routinely have to understand these concepts when we sample a body of mineralisation and produce aliquots of material known as samples, which end up being treated as ‘objects’ either with chemical or physical properties; otherwise known as the sample-volume-variance problem.

Think of it as a collection of billiard balls of which we have 100. We thus have N=100 individual and independent objects that have specific physical properties such as volume, colour, and mass. The number N is an integer, by the way, and N can never be a fraction since that implies one has partitioned one billiard ball into smaller components. So independent objects are always countable as integers since one can only have whole objects. But this is not the problem, for we are dealing parts of the earth as sub-objects that have, obviously, differing physical properties such as buried magnetite deposits producing anomalies in the magnetic field, or massive objects producing anomalies in the gravitational field. And this is at the stage when belief comes into play.

Consider the case when we complete a geophysical modelling exercise for a geophysical ground survey and mathematically postulate that a magnetic or gravitating object is causing the observed anomaly in the magnetic or gravitic fields, we actually believe this as opposed to knowing this. It is only when we drill a hole into the position of the supposed target and actually indentify it in the here and now, that belief transforms into knowledge. It’s when this in-situ testing is not possible that problems arise.

The problem with geophysical gravity modelling is the assumption of the centre of gravity of a gravitating object. So as long as the centres of mass of two or more objects are assumed to exist, then there is a ‘distance’ between each ‘object’ and hence a gravitational force. But a centre of gravity is not a physical object but a mind trick to ease numerical calculation. It’s when these mind tricks become reified that problems appear. And to muddy waters a little more, only an ‘object’ can have a centre of gravity, so it also depends on what we understand an ‘object’ to be. If we assume the previous cubic metre of lead sitting on the Earth and along with the Earth as one single object, then these two contiguous objects have a single centre of gravity that is derived from each of them. It also means that if we think of the Earth as having a core, outer-core, mantle and crust, then these four contiguous ‘object’s have but one centre of gravity. They might individually have their own specific centres of gravity, but they cannot be considered as ‘objects’ in a classical Newtonian sense, because in the Newtonian sense objects are independent clumps of matter separated by ‘space’, initially assumed to be a vacuum, to give us distance of separation. The distance between two centres of gravity, incidentally, is unreal because the centres of gravity are not physically real, especially when the two objects are spatially contiguous; that is the physical distance between them is zero, so there cannot be any gravitational attraction. If there is then that is because the proponents of this idea are dealing with imaginary mathematical constructs. Or are they?

The essential point, however, is deciding whether contiguous clumps of matter are independent objects, or collectively one object. This distinction is crucial. Mathematically the Earth’s internal partitioning on the basis of velocity, and hence density, can be distinguished individually as ‘objects’ or rather as sub-objects, core, outer core, mantle and crust, but is this physically realistic? And if we view the spherical shells of the outer core, mantle and crust as individual ‘object’s then their centres of gravity are actually all at the same location at the geometric centre of the core itself. If this is the case then there cannot be any gravitational attraction at all between the core and the enveloping shells of matter outwards since their centres of gravity have no distances between them.

(The underlying assumption here is that the core, outer-core, mantle and crust, and for that matter the enveloping ocean and atmosphere, are, from a density perspective, homogenous; they are not of course since if they were, seismic tomography would not be possible, or it would be but would not show any ‘density’ variations within the Earth’s interior; and often anomalies in these fields point to un-normal concetrations of potentially useful minerals or rocks. But in the case here for discussion I am assuming homegenity on the scale that allows us to discriminate between these gross parts of the Earth’s interior).

What this argument is leading to is that the high pressures and temperatures inside the earth are not caused by gravitational attraction by the weight of the overlying material but most likely from the mechanism that produced the protoplanet in the first place. As the standard model of planetary formation is solar accretion that is wholly gravity driven, it should be clear that gravity actually cannot compress matter into more dense forms, so an alternative mechanism is needed. That mechanism is the plasma Z-pinch process that is quite capable of compressing matter into very high density minerals and hence rocks. But where protoplanets are being formed in the here and now remains unanswered though one might consider Venus being a recently formed planet and whose birth was apparently witnessed by our ancestors not that long ago. And that path leads us to beliefs and how these affect our interpretations of historical accounts, and for that one would need to read Hilton Ratcliffe’s latest book.

Finally one might define a belief as a fixed pattern of thinking that when repeated often enough becomes a habit and thus dogma; dogma could be likened as fossilised thoughts.

About Louis Hissink

Retired diamond exploration geologist. Trained by Western Mining Corporation and polished by De Beers.
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