sea level rise or…

Despite previous assurances^ about the rock-solid stability of the earth’s dimensions, further analysis of satellite altitude data suggests that there may still be a bit of life in the old girl (Mother Earth) yet.* :-)

The following abstract suggests that some minimal expansion activity can still be discerned today insofar as some of the observed satellite altitude variation that is usually explained as sea level rise is actually the result of earth expansion.

Evidences of the expanding Earth from space-geodetic data over solid land and sea level rise in recent two decades
Wenbin Shena, Ziyu Shena, Rong Sunc, Yuri Barkind
30 June 2015

According to the space-geodetic data … vertical variation of the Earth’s solid surface suggests that the Earth’s solid part is expanding at a rate of 0.24 ± 0.05 mm/a in recent two decades.

In another aspect, the satellite altimetry … demonstrate the sea level rise (SLR) rate 3.2 ± 0.4 mm/a, of which 1.8 ± 0.5 mm/a is contributed by the ice melting over land. This study shows that the oceanic thermal expansion is 1.0 ± 0.1 mm/a due to the temperature increase in recent half century, which coincides with the estimate provided by previous authors. The SLR observation by altimetry is not balanced by the ice melting and thermal expansion, …, in this study we infer that the oceanic part of the Earth is expanding at a rate about 0.4 mm/a.

Combining the expansion rates of land part and oceanic part, we conclude that the Earth is expanding at a rate of 0.35 ± 0.47 mm/a in recent two decades. If the Earth expands at this rate, then the altimetry-observed SLR can be well explained. …

^ From the linked report, … The scientists estimated the average change in Earth’s radius to be 0.004 inches (0.1 millimeters) per year, or about the thickness of a human hair, a rate considered statistically insignificant. …

* By way of explanation, my current view is that most of the expansion occurred in the past when mantle conditions were radically different to present day norms, …and that the activity was both rapid and episodic.

crust mobility conundrum. how does the earth move?

Until comparatively recently, the only crustal movements worth the name were thought to be either post glacial rebound, where surface ice melting induces crust rebound until a new equilibrium is established, or gravitational collapse, such as weathering  and erosion. Both are gradual, isostatic processes.

The many extensional features such as rifts, horst/graben faulting, uplift, tilted blocks and basin formation were seen to be part of these isostatic processes, occurring over geologic time scales and with any lateral movement being a localized event.

However mounting geographical, geological, paleontological and botanical evidence was pointing to continental mobility on a global scale, and by the sixties the Isostatic Tectonics view was finally rejected in favour of a globally mobile surface with most opting for a surface plate model driven by mantle convection currents, …Plate Tectonics.

Others concluded that the abundant extensional features, the spreading ridge that surrounds Antarctica being one of many such examples, … such features could only be accounted for by an increase in the surface area, and thus radial expansion, of the earth, …Expansion Tectonics.

‘Surface’ mobilists espoused Plate Tectonics while the ‘surface area’ mobilists advocated Expansion Tectonics. The ‘facts’ could be made to fit both explanations. But the absence of a plausible expansion mechanism was an insurmountable problem for Expansion Tectonics, and Plate Tectonics was adopted to replace the Isostatic model.

To recap, Plate Tectonics prevailed over Expansion Tectonics because Plate Tectonics requires less energy, no mass/volume variation, and, more importantly, it has a plausible mechanism to drive the process, i.e. convection. Earth expansion was a contender process in the sixties but is now considered a discredited theory.  It has been considered, and, largely due to the absence of any causal mechanism, rejected by most, but not all,  right-thinking geo-folk. This is despite the fact that much of the geological/geographical/botanical/fossil/seismic evidence for plate tectonics can be used to support the expansion model. The evidence is also consistent with a sub-crustal increase in mantle or core/mantle volume so that the increased surface area consists of primordial crust separated by recent ocean crust.

Both Plate and Expansion theories assume that the process occurs continuously over geological time spans. Whatever its driving mechanism, tectonic movement is considered to slow but inexorable process.

But recent work on the structure of the world that lies beneath our feet, specifically 3-D images of the crust and mantle generated by supercomputer processed, earthquake induced, seismic wave data,  reveals that there is no obvious evidence for the simple convective system that one might expect from the tectonic model. From the link…

… One could a priori expect such [tomographic ] images to reflect a very simple convective system, where the ascending currents are found under mid-ocean ridges, and the descending currents are found at subduction zones, where the tectonic plates slide back into the mantle. In fact, seismic tomography … reveals a more complex situation that cannot yet be very clearly interpreted. …
– Physics of the Earth’s Interior. Barbara Romanowicz.

The images,10060010002800From the maps it is evident that Mid-Ocean Ridge spreading centers do not persist below 600 kms. What emerges at deeper levels are ocean sized blobs located under the southerly region of the Pacific and African plates to create a more or less balanced global distribution of these low density/high temperature features.

This configuration does not support the simple convection model of a continuous column of ascending or descending material originating near the core-mantle boundary and extending to the base of the, …according to the Plate Tectonic model, very mobile and actively subducting crust.

Convection is an important part of the Plate Tectonics narrative in that it is the proposed mechanism that supplies the enormous amount of energy needed maintain the currents necessary to drive the plates across the surface of the earth. Without it, Plate Tectonics has difficulties with its energy budget as it assumes that surface plate mobility is powered by energy from below. Without convection, plate mobility is left without a plausible driving mechanism. It could not be maintained, let alone initiated. Something else would be required to explain the obvious separation of pieces of continental crust that both Plate Tectonics (and Expansion Tectonics) seek to explain.

The lack of  evidence for simple convection in the tomographic data has prompted modifications to the model by way of the introduction of a stratified two-stage convection model. This is roughly analogous to a pot filled with water and oil, with separate convection cells in both oil and water layers and a conductive energy transfer process at the interface.of the liquid layers. The modifying effects of uncontained convection, regional lateral temperature variations and other tweaks are also being considered.

The picture that emerges, …a chemically stratified mantle with variable-depth chemical boundaries near 1,000 and 2,000 km and a lower mantle depleted in radioactive elements appears to satisfy available geochemical and geophysical constraints. … suggests a major revision of the Plate Tectonics energy budget and itself appears to be somewhat at odds with what one might expect were convection currents present. Convection is not generally associated with stratification.

The tomographic picture may offer more support to a model where the plates are relatively static with any relative movement due an increase in the overall surface area of the globe together with accompanying isostatic adjustment and curvature modification.

Separation by surface area expansion still doesn’t have a causative mechanism, but the lack of evidence for simple convection also casts doubt on the viability of the surface plate mobility claimed by Plate Tectonics.

a rapid expansion event?


This is an  ESA Rosetta Navcam image of comet 67P/C-G taken on Feb 3 2015.

It may be just a trick of the light, so to speak :-), but from this perspective it sure looks like something popped, …well it does to me at least.


The current view is that the lobed shape of this and other comets is a product of ‘binary contact’ but this view of the comet seems more indicative of separation than evidence of a contact event.

Picture: Copyright: ESA/Rosetta/NAVCAM, CC BY-SA IGO 3.0
licensed under a Creative Commons Attribution-ShareAlike 3.0 IGO License.




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.^

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 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 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.

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 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,

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 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 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 with the gravitational geodesic assertions of relativity. Much time and effort has been devoted to resolving the issue and a number of addons 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.

^ 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. …

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



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 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.