A close association

The behemoth lies under the lotus tree.

embraced imperceptibly
by the slightest of brushes
with the nebulous aether,
in tidal synchronicity with its inscrutable motions,
…we spin and weave our way,
to come what may.

in all rolls and rotations,
and loops and orbits,
we hum to the tune
of our live companion
via intimate connection
with each tiny spark that makes up our quarks.


Is gravity losing its grip on reality?

Everything in the universe appears to be moving relative to something else, and the majority of that motion appears to be curved, as in a planet moving in an orbit about a central point. Some people, Johannes Kepler for example, thought that this demonstrated that natural motion is circular. Others, like René Descartes favoured the idea that natural motion is rectilinear, i.e. that matter is naturally inclined to move in a straight line, only deviating from this natural straight path if some other external force is acting on it (which is usually the case).

It could be argued that this difference is just a semantic issue, that the forces that cause deviation from the straight and narrow are part of the natural order so that the rectilinear idea is an unreal ideal state as far as matter is concerned. But Descartes’ idea got a lot of traction when Isaac Newton proposed that the observed curved motion could be attributed to the existence of two separate, very unequal and unrelated types of motion, firstly inertia or linear momentum which is a pre-existing state of motion and a second one which has its origin in mass itself and which acts on other matter causing the direction of the inertial component to constantly change. The earlier concept of angular motion or momentum was also recognized by Newton but only in the context of spinning bodies. He seems to have been the first to propose that it was conserved.

“A top, whose parts, by their cohesion, are perpetually drawn aside from rectilinear motions, does not cease its rotation otherwise than it is retarded by the air. … greater bodies of the planets and comets, meeting with less resistance in more free spaces, preserve their motions both progressive and circular for a much longer time”
– Axioms; or Laws of Motion, Law I. in The Mathematical Principles of Natural Philosophy. (See here)

This division of motion into two separate, unrelated, vastly unequal components was helped along by the new-at-the-time idea that curved motion could be represented by two motion components or vectors (h/t Robert Hooke et al.). Curved motion could be divided into two components, one tangential to the curved track and the other perpendicular to the curve.

Once two components have been identified then the way is open to assign two different origins to the motion. And that, via Newton, is what happened. He identified the perpendicular component as originating in the center of a mass and he went further with this line of thinking by proposing that separate masses are influenced by this component of motion, that they attract one other. The rectilinear component or vector was assumed to be inherent and lately it has been proposed that this inherent motion (it is called inertia) is a result of the event that set everything in motion, the proposed cosmological big bang. Note the if a curved motion has more than two components, as is the case for helical motion (which has three components) then the set of components is called a tensor, but still involves separating the complete motion into component parts.

To bolster his idea, Newton came up with a suitable expression that enabled the observed motion of a falling body, called g (little g), to be calculated from the mass of the earth and the distance between the center of the earth and the falling body. However, in order to obtain the correct result it is necessary to apply an adjustment factor (also known as a constant) to the mass/distance relationship. This adjustment factor is written as G (big G) and is called the universal gravitational constant. (See note below for details on how the value of G is determined)

Because this constant must possess dimensions , i.e. length, mass and time (the expression is not valid if the constant doesn’t have the dimensions of length^3 *, mass^-1, time^-2) it is called a dimensioned constant. This is in contrast with the arguably more fundamental constants (such as pi, which is just a number), which are called dimensionless constants. The other thing to note about G is that when everyday units are used to describe the masses and distance involved, it has an extremely small value. G’s value is hard to pin down precisely but depending on the units chosen for length, mass and time it is something like 0.00000000000676 m^3 kg^-1 t^-2.

Newton’s expression can be written as the force acting between two masses in the form,

F = GMm/r^2,

M and m are the gravitational masses involved and r is the distance between their centers. Note that, unlike length, where the product of two lengths can give an area, by itself, the product of two masses does not yield useful information. The more intuitive combinations of M + m or M – m do not work.

And note also that this form of the expression is similar to the expression for the force between two electrical charges (Coulomb’s Law), F = Kq1q2/r^2, with K being the constant and q1 and q2 the charges. (In contrast to the gravitation constant which is very small, Coulomb’s constant is large, 8.99×10^9 N m^2 C^−2 where N is a unit of force, the Newton and C is a unit of charge, the Coulomb. Note also that Coulomb’s constant has structure in that it is inversely proportional to another constant, ε0, the permittivity of free space.)

From this expression the acceleration due to the force between the two bodies, called little g, can be derived. We do this by substituting mg for F (this relationship between force and the product of inertial mass and acceleration is another one of Newton’s insights and is known as Newton’s Second Law, which, incidentally, was contra Aristotle who proposed mass and velocity as the elements of force) so that the expression becomes,

mg = GMm/r^2,  ** (see below)

and from there it is just a matter of using the simple mathematical expedient of removing the little m’s from both sides of the expression to obtain

g = GM/r^2.

Here we see that little m has been removed from the expression, hence the independence of little g from the (as we perceive it) falling mass.

And if we plug in the right values for big G, M and r we get the right (observed) value for little g, i.e. about ten meters/second/second.
No one knows exactly how Newton came up with this expression.

Note that Kepler himself was no slouch when it came to figuring things out. Wikipedia tells us that, …His work led to the modern laws of planetary orbits, which he developed using his physical principles and the planetary observations made by Tycho Brahe. Kepler’s model greatly improved the accuracy of predictions of planetary motion, years before Isaac Newton developed his law of gravitation in 1686.

About a century ago a new idea was proposed by Albert Einstein. This still involved the mass of the large body, but instead of the mass directly influencing motion it was here proposed that there was a more indirect effect with the mass now influencing spacetime causing it to curve so that any other masses would then follow the now curved shape of space (this curved track becomes the shortest distance between two points and is called the geodesic). The motion, both inertial and gravitational components, becomes a function of this curvature of spacetime rather than direct mutual attraction between the masses.

This necessitated the designation of gravity as a pseudo force (the motion itself can be “transformed away” by switching frames of reference ***) as opposed to a real force. In my opinion, this idea is significant because it includes spacetime into the mix as well as the masses themselves.

However recent observations of the cosmos have upset this apple-cart 🙂 and cast doubt on the relationship between gravity and mass. It has been found necessary to propose the existence of at least five times more mass than we can see to account for the observed motions of some galaxies. This affects both of the mass related causes discussed above. Because we cannot see this mass it is called dark matter. Unlike ordinary matter, dark matter, by definition, does not radiate energy. One could perhaps imagine dark matter to be like a very cold non-radioactive rock or gas that does not reflect or re-radiate incident (incoming) energy. Strange stuff, no?

Relativity at least finds a place for gravity in the contours of the the spacetime geodesic but it doesn’t fare so well when it comes to the other recent big thing in physical theory, Quantum Mechanics. This very successful model is strangely muted when it comes to gravity.

Quantum Mechanics deals with energy levels that give matter its structure and properties. These energy magnitudes overwhelm any effect that gravity might exercise and as a result it just doesn’t rate, everything works fine without it. But nevertheless it is dogged by demands that it be ‘unified’ with the gravitational geodesic assertions and transformations of relativity. Much time and effort has been devoted to resolving the issue and a number of add-ons such as Loop Quantum Gravity and String Theory have been developed in the attempt to include gravity in the picture. But all are problematic in some way, for example,

…1) Loop quantum gravity is a way to quantise space time while keeping what General Relativity taught us. It is independent of a background gravitational field or metric. So it should be if we are dealing with gravity. Also, it is formulated in 4 dimensions. The main problem is that the other forces in nature, electromagnetic, strong and weak cannot be included in the formulation. Nor it is clear how loop quantum gravity is related to general relativity.

2) … String theory is a quantum theory where the fundamental objects are one dimensional strings and not point like particles. String theory is “large enough” to include the standard model and includes gravity as a must. The problems are three fold, first the theory is background dependant. The theory is formulated with a background metric. Secondly no-one knows what the physical vacuum in string theory is, so it has no predictive powers. String theory must be formulated in 11 dimensions, what happened to the other 7 we cannot see? …

Quantum mechanics has a hard time ‘seeing’ gravity and doesn’t really need it to exercise its quantitative talents. It goes about its quantum scale business quite successfully without it. Perhaps Quantum mechanics is trying to tell us something about the nature of gravity, …that maybe it doesn’t exist as a discrete entity but is somehow an integral part of the geodesically guided inertial motion inherent in all matter, its motion groundstate. And whose origin is perhaps not based in matter itself. Maybe one needs to consider the geodesic energy state (if there is such a thing) rather than the matter energy state so that the raising of a finger changes the energy state of its surroundings rather than the energy state of the finger itself.

To recap, is it possible that the energy considerations of gravity are related to the alteration of the geodesic of spacetime, …where the energy variation is necessary to reconfigure the local geodesic, …because different locations require different inherent energy levels? That, together with a tendency for things to attempt to occupy the lowest motion groundstate in the local system, the center, may provide a more useful picture of this mysterious phenomenon. It may also lead to an understanding as to why gravity is only discernible at larger scales in that at quantum scale most matter does occupy its local groundstate where gravitation potential is a function of the state of the local geodesic rather than the mass itself.

It could also be that the current understanding of gravity may be returning anomalous results (via dodgy mass estimates) for the density of some of the components of the solar system. For example, although photographic evidence suggests a rocky composition, the latest estimate for the density of comet 67P is about 0.5 which is similar to the density of fluffy snow. Others think that the hydrogen sun model is obsolete and that iron is its most abundant element but the density is calculated to be about 1.5 which doesn’t allow for much iron content.

Given this state of affairs others have looked for a different origin for the cause of this strange phenomenon we identify as the force due to gravity. And given the similarity of the force expressions between two masses and two charges, some have proposed an alternative mechanism, that being the influence of the electron field. This idea still treats the perpendicular vector as a separate force but invokes the electron field rather than the proton (field?) which contains the majority of the thing we call mass. The neutron is a sort of hybrid of a proton and an electron so its mass is also proton related. Recall too that (at some scales?) the force associated with the electron field is about thirty-seven orders of magnitude greater than the gravity field (that is assuming that gravity does actually constitute a separate field) so their is plenty of scope for it to hide in the electron field.

It is also possible that gravity is mass related but operates differently at different scales, sometimes attracting, sometimes repelling. But nevertheless until we positively identify this extra hidden mass then the concept of mass related gravity has to be on shaky ground. 🙂

Apart from an aside, I haven’t mentioned spin in this polemic. That’s because gravity is not thought to play any role in this type of motion, it being due solely to primordial angular momentum and the conservation thereof which is balanced by self-adhesion of the mass. As I understand it, gravity only plays a part in the accretion of the body from the primordial disk.


* Note that length cubed is the unit for volume. It may be worth looking into why G has a volume component in its dimensions.

** Note that with this substitution, Newton has equated gravitational little m with inertial little m. This equivalence is justified by the remarkable equivalence of earthly gravitational mass with inertial mass.

… gravitational mass, is something that responds to the pull of gravity, tending to accelerate a body in a gravitational field. The other, inertial mass, is the property of a body that opposes any acceleration. That makes it rather odd that a large chunk of modern physics is precariously balanced on a whopping coincidence. This coincidence is essential to the way we view and define mass. …  – New Scientist

But this equivalence of gravitational and inertial mass only applies on earth’s surface. Anywhere else like the Moon or Jupiter or wherever this remarkable feature does not apply, as even though inertial mass is the same, gravitational mass varies according to the mass of the body in question.

Because weight is directly dependent upon gravitational acceleration, things on the Moon will weigh only 16.6% of what they weigh on the Earth.

*** … Inertial forces can be “transformed away”, as physicists say. Specifically, they can be made to vanish by simply making the transition from one observer to another (in our example, by making the transition from a rotating observer to a non-rotating one). The same is true for gravity, which can be made to vanish, at least locally and approximately, if you just let yourself fall freely. …

This transformation process is informed by Einstein’s Equivalence principle which equates inertial mass with gravitational mass.

… The starting point for general relativity is the equivalence principle, which equates free fall with inertial motion, and describes free-falling inertial objects as being accelerated relative to non-inertial observers on the ground. …

Determining the value of G.
The value of this constant was determined about a century after Newton proposed it by Henry Cavendish using an apparatus designed and constructed by a geologist , Michel, who passed away before he had the opportunity to use it. The machine consisted of two small identical weights suspended at each end of a beam which was in turn suspended from a wire attached to the substantial housing intended to reduce temp fluctuations, vibration etc. The idea was that when large masses were moved into close proximity to the suspended masses the smaller object would move toward the large masses causing a small torque or twisting of the wire which would translate to movement of a suitably amplified motion indicator. The indicator, somewhat like a horizontal pendulum, oscillates about the point which indicates the attraction between the two bodies.  (Presumably the oscillation pattern differs from the way the pointer would react were it under the influence of, say, a magnetic field where the oscillation would perhaps be more rapidly damped than the more elastic? gravitational attraction/field.) The amount of deflection of the pointer can be used to determine the force as the magnitude of the mass(es) are also accurately known.

The force acting to twist the suspending wire appears to exert a real force on the suspended masses, although it is not clear how one might distinguish between a physical force and the more recent idea of gravity as a pseudo force of distorted spacetime.

Below are two versions of how the results are used to calculate the value of G.


The next one is an abbreviated version of the full derivation outlined in the linked pdf.




There is an alternate opinion about what Cavendish actually determined from his observation,

… Most physics books state that Cavendish performed the Cavendish experiment and measured the value of G, or the gravitational constant. However historical evidence suggests that Cavendish used the experiment to measure Earth’s density and did not actually calculate G – not until much later were Cavendish’s results used to calculate the value of G. …

– Updated on 14/10/17 to include discussion of inertial vs. gravitational mass (a.k.a. weight)




I find it somewhat puzzling that no-one in authority ever gets fired (or heaven forbid, offers to resign 🙂 ) when one of these incidents occurs.

Maybe the following report gives some insight as to why that might be the case.

14 June 2013
A sends:
Traffic Accident with Deep Connections

On February 15, 2013, Mr. Yasin Kadi*, [was] having a meeting with Mr. Hakan Fidan, Undersecretary of Turkish National Intelligence Agency (MIT), in Ankara and then moving to Istanbul, had an interesting traffic accident together with his business associate and close relative Usame Kutub, and Ibrahim Yildiz, Police Lieutenant at Prime Ministry’s Guard Office while they were traveling by official vehicle in Bakirkoy, Istanbul, on February 16, 2013. …

The accident was immediately reported to the Prime Minister by Mustafa Latif Topbas (very close friend of A. Kadi). The Prime Minister then asked his son Bilal Erdogan to go to the hospital. A. Kadi and Kutub did not have any serious injuries, but that was not the case for Lieutenant Yildiz. For several days, Lt. Yildiz stayed in the hospital under medical observation.

However; the original report was replaced with a new report to cover up such seemingly unexplainable togetherness in the accident. The new report claimed “as if Lt. Ibrahim Yildiz was alone during the accident”, but he was actually not.

* From the wikipedia entry on Kadi

… OFAC relied on Kadi’s involvement in Muwafaq and, in particular, activities claimed to have occurred in Bosnia, Albania, Sudan and Pakistan, to conclude that “Kadi financially supported terrorist activities, primarily through Muwafaq, but also through other Kadi-owned entities.” …

Kadi was among nine defendants sued by the Lloyd’s of London insurance syndicate on 8 September 2011 in a “landmark legal case against Saudi Arabia, accusing the kingdom of indirectly funding al-Qa’ida and demanding the repayment of £136m [$215 million] it paid out to victims of the 9/11 attacks.

Erdogan: “I know Mr. Kadi. I believe in him as I believe in myself. For Mr. Kadi to associate with a terrorist organization, or support one, is impossible.”

And the latest note,

… US Unblocks Property and Interests
On September 11, 2014, OFAC unblocked the property and interests in property of Yassin Kadi pursuant to E.O. 13224, “Blocking Property and Prohibiting Transactions With Persons Who Commit, Threaten To Commit, or Support Terrorism.”

Io’s mountains

With about 400 active volcanoes Io is, according to Wikipedia, the most geologically active object in the Solar System. And as it has very few craters (which are assumed to be impact related), the conventional interpretation is that it has been resurfaced comparatively recently. A recent story at phys.org points out that as well as volcanoes and extensive lava plains, Io also has about 100 mountains which take the form of isolated peaks of great height that jut up out of nowhere. These “pull apart” mountains are described as part of a group of “extensional” tectonic features.

The researchers postulate that the mountains are the result of a squeezing out process. It is speculated that heat induced compression, …thermal stress, in the lower crust is the source of both the volcanic activity which vents magnesium-rich silicate magmas (liquid rock) to the surface and, if the volcanic activity is for some reason restricted, then these thermal stresses are thought to be responsible for crustal displacement processes such as mountain building.

… It’s not just the increasing weight of the overlying lava that puts the deep crust in compression McKinnon said, but also the increasing temperature. “Heating at depth causes the rocks to want to expand, and since there’s no room to expand, you again get compressive forces,” he said.

As long as the volcanoes are erupting, they carry this heat away and thermal stresses are low, reducing the likelihood of mountain formation. But if volcanism stops, the crust heats up, thermal stresses increase, and mountain formation becomes more likely. …

Alternatively, as extensional/uplift related geological activity in crustal material could conceivably result from forces produced by a sub-crustal based expansion process which could be regional or general, it may be that these jutting mountains were the result of a more widespread inflation initiated crustal disturbance that also initiated the magma flows to the surface and the ongoing residual volcanic activity.

Note that plate tectonic/constant radius theory proposes that Earth’s volcanic activity is mainly associated with plate subduction activity but this process is not given consideration in the thermal stress theory and there is no apparent visual evidence (e.g. extensive mountain ranges) for it on Io.

Anomalous Comet Dust

The following quotes are from Are fractured cliffs the source of cometary dust jets? Insights from OSIRIS/Rosetta at 67P.

From Pg 5
… With a mass of 1 x 1013 kg and a density of 470 kg/cubic meter … we obtain a effective gravity* of … , typically .0004 m/s² at the cliff’s foot. …

and from Pg 8
… Dust velocities are measured by GIADA … . The cumulative distribution shows a mean velocity equal to 3.75 m/s, [about] 4 times the escape velocity. The average dust density is 1900 kg/cubic meter. …

Coincidentally the density of the dust (1900 kg/cubic meter) is also about four times greater than the comet’s density (470 kg/cubic meter), …which is similar to that of lightly packed or windblown snow (about 500 kg/cubic meter). The dust density is also somewhat less than that of Silicon dioxide (Quartz) which has a density of about 2600 kg/cubic meter (Silicon carbide is even denser at about 3200 kg/cubic meter). Silicate or carbide coated with ice would probably fit the bill, although ice, and fluffy ice at that, appears to be in short supply, …on the surface of the comet at least. Note however that other silicate compounds such as Calcium silicate have a density of around 290 kg/cubic meter which is even less than the overall density of the nucleus. Not sure though how the comet might produce its relatively heavy dust from a Calcium silicate like compound, or if Calcium has been detected.

The paper also notes that the maximum angle of repose (slump angle) of unconsolidated surface material on comets and asteroids is about 30°. This is at the lower end of of slump angle values for various materials here in the earth’s gravity field. The comet’s gravity is of course substantially less than earth’s gravity so one could expect a higher slump angle for a similar type of material on the comet, e.g. according to the wiki, on earth, snow which has a density similar to the comet, has a slump angle of 38°. So why don’t we see steeper piles of sand/dust on the comet?

The other odd thing is the average velocity of the dust, 3.75 meter/sec (presumably that is relative to the comet). That seems to be a bit high for a heating/photolysis based process.

* In contrast, the earth’s gravity is 9.8 m/s² and for the moon it is 1.6 m/s².

Speaking of Whitehead…

Here is a quote from the man about his conception of God,

“It does not emphasize the ruling Caesar, or the ruthless moralist, or the unmoved mover. It dwells upon the tender elements in the world, which slowly and in quietness operates by love; and it finds purpose in the present immediacy of a kingdom not of this world. Love neither rules, nor is it unmoved; also it is a little oblivious as to morals. It does not look to the future; for it finds its own reward in the immediate present.”

-Alfred North Whitehead, Process and Reality (New York: The Free Press, 1978), 343

The Geodesic

The geodesic is the shortest path between any two points, …from point a, to point b. Most of the time we understand this shortest path to be a straight line, …it is obvious that any deviation from that arrow straight line will add some length to the path traveled so it will not be a geodesic. It will still get you from a to b, but it will not be the shortest, least energetic path.

This is all fair enough but what if it is not possible to traverse from a to b via said straight line? That is something that we earthlings (who live on the surface of a sphere) have to contend with as soon as we start to increase the distance between a and b. It doesn’t take long for the straight line option to become untenable as, short of boring a tunnel between a and b, we find that the shortest path has acquired some curvature, …we are restricted to following the curve of the earth’s surface.

Once we traverse more than a few kilometres, we find that due to restrictions imposed by the spherical nature of the earth, the shortest path to our destination, the geodesic, is curved.

One could say that the curved geodesic emerges from the actual scale of the geodesic itself, …with small scale shortest paths being for all intents and purposes a straight line and the largest scale paths being curved, …with a complete circumnavigation having the shape of a circle, …which in turn is about as far away from a straight line as one can get. The circle being closed, a and b end up as the same location, whereas with the line, the distance between a and b just keeps increasing. In the everyday world here on earth, the straight line geodesic is limited to the shorter length traverses and the curved geodesic emerges as the distance between a and b increases.

Curved geodesics are notable in that they create horizons or interfaces which limit visibility and, due to things like temperature/density zoning and what have you they are often associated with diffractions, reflections, mirages, projections and the like.

And when we venture from our spherical surface home into outer space we again find that, due to matters over which we have very limited control, i.e the observed circular (ok, elliptical) nature of traverses in the solar system (and our galaxy as a whole), …we find that beyond some limit of measurement, shortest paths are necessarily curved and eventually form a closed loop or orbit.

We once thought that an invisible force that seems to emanate from the centres of planetary and solar objects, called gravity, was responsible for these unavoidable deviations from the straight line geodesics that we are familiar with at ordinary human scales. But it has been shown to the satisfaction of many that there is something else that needs to be considered in that, at the planetary scale at least, the objects, which are themselves 99.9% nominally empty space (this inner space housing just a more energetic/more concentrated version of the electromagnetic electron field that pervades outer space) cause the very space surrounding them to also become curved, …so that even light itself, which is renowned for its ability to travel in straight lines, must accommodate itself to the curved geodesic of the space that it traverses. It can no longer follow its innate straight line path and the very region that provides toll-free passage to all traversing radiation will nevertheless cause it to deviate from its usual straight-line motion (at ‘normal’ scales) and instead track along the curved geodesic of space that is itself modified by the various heavenly bodies in the vicinity. And of course this mass induced curvature also obliges any adjacent mass in the region (which will also generate curvature of space) to follow the curved geodesic that results from the presence of the other mass in the region, so to speak. So perhaps one could view gravity as emerging from the interaction between matter and the space that surrounds it.

The above invites number of questions about the nature of the process that causes electromagnetic radiation to follow a curved geodesic, e.g. how does the light ‘know’ the disposition of the local geodesic? is there any relationship between the matter electron fields (bound electrons) and space electron fields (energetic free electrons)? or, does e/m radiation itself have a reciprocal effect on the configuration of space such that it also influences the motion of matter and other e/m radiation? So that motion becomes a property of the interactions between things? Perhaps it is time to revisit the ideas of Alfred Whitehead who suggested that interactions between things are more significant than the objects themselves.

And if the geodesic of space is curved in various ways it raises the interesting possibility that, given a large enough scale and providing it is not absorbed along the way, that light may also eventually return to somewhere near its source, albeit somewhat stretched out and drained of energy by the (postulated) expansive nature of the space that it has traversed. Could it be that the cold radiation (CMB Cosmic Microwave Background radiation etc.) that we detect is well traveled light returning to its source. 🙂