Posts Tagged ‘Gravitation’

Discrepancy In Universe’s Expansion & Quantum Interaction

January 17, 2018

In “New Dark Matter Physics Could Solve The Expanding Universe Controversy“, Ethan Siegel points out that:

“Multiple teams of scientists can’t agree on how fast the Universe expands. Dark matter may unlock why.
There’s an enormous controversy in astrophysics today over how quickly the Universe is expanding. One camp of scientists, the same camp that won the Nobel Prize for discovering dark energy, measured the expansion rate to be 73 km/s/Mpc, with an uncertainty of only 2.4%. But a second method, based on the leftover relics from the Big Bang, reveals an answer that’s incompatibly lower at 67 km/s/Mpc, with an uncertainty of only 1%. It’s possible that one of the teams has an unidentified error that’s causing this discrepancy, but independent checks have failed to show any cracks in either analysis. Instead, new physics might be the culprit. If so, we just might have our first real clue to how dark matter might be detected.

20 years ago it was peer-reviewed published, by a number of teams that we were in an ever faster expanding universe (right). The Physics Nobel was given for that to a Berkeley team and to an Australian team. There are now several methods to prove this accelerating expansion, and they (roughly) agree.

Notice the striking differences between different models in the past; only a Universe with dark energy matches our observations. Possible fates of the expanding Universe which used to be considered were, ironically enough, only the three on the left, which are now excluded.  Image credit: The Cosmic Perspective / Jeffrey O. Bennett, Megan O. Donahue, Nicholas Schneider and Mark Voit.

Three main classes of possibilities for why the Universe appears to accelerate have been considered:

  1. Vacuum energy, like a cosmological constant, is energy inherent to space itself, and drives the Universe’s expansion. (This idea comes back to Einstein who introduced a “Cosmological Constant” in the basic gravitational equation… To make the universe static, a weird idea akin to crystal sphere of Ptolemaic astronomy; later Einstein realized that, had he not done that, he could have posed as real smart by predicting the expansion of the universe… So he called it, in a self-congratulating way, his “greatest mistake”… However, in the last 20 years, the “greatest mistake” has turned to be viewed as a master stroke…).
  2. Dynamical dark energy, driven by some kind of field that changes over time, could lead to differences in the Universe’s expansion rate depending on when/how you measure it. (Also called “quintessence”; not really different from 1), from my point of view!)
  3. General Relativity could be wrong, and a modification to gravity might explain what appears to us as an apparent acceleration. (However, the basic idea of the theory of gravitation is so simplest, it’s hard to see how it could be wrong, as long as one doesn’t introduce Quantum effects… Which is exactly what I do! In my own theory, said effect occur only at large cosmic distances, on the scale of large galaxies)

Ethan: “At the dawn of 2018, however, the controversy over the expanding Universe might threaten that picture. Our Universe, made up of 68% dark energy, 27% dark matter, and just 5% of all the “normal” stuff (including stars, planets, gas, dust, plasma, black holes, etc.), should be expanding at the same rate regardless of the method you use to measure it. At least, that would be the case if dark energy were truly a cosmological constant, and if dark matter were truly cold and collisionless, interacting only gravitationally. If everyone measured the same rate for the expanding Universe, there would be nothing to challenge this picture, known as standard (or “vanilla”) ΛCDM.

But everyone doesn’t measure the same rate.”

The standard, oldest, method of measuring the Hubble cosmic expansion rate is through a method known as the cosmic distance ladder. The simplest version only has three rungs. First, you measure the distances to nearby stars directly, through parallax, the variation of the angle of elevation during the year, as the Earth goes around its orbit. Most specifically you measure the distance to the long-period Cepheid stars like this. Cepheids are “standard candles”; they are stars whose luminosities vary, but their maximum power doesn’t, so we can know how far they are by looking how much they shine. Second, you then measure other properties of those same types of Cepheid stars in nearby galaxies, learning how far away those galaxies are. And lastly, in some of those galaxies, you’ll have a specific class of supernovae known as Type Ia supernovae. Those supernovae explode exactly when they accrete 1.4 solar mass, from another orbiting star (a theory of Indian Nobel Chandrasekhar, who taught at the University of Chicago). One can see these 1a supernovae all over the universe. Inside the Milky Way, as well as many of billions of light years away. With just these three steps, you can measure the expanding Universe, arriving at a result of 73.24 ± 1.74 km/s/Mpc.

The other methods makes all sorts of suppositions about the early universe. I view it as a miracle that it is as close as it is: 66.9 km/s/Megaparsec…

Ethan concludes that: “Currently, the fact that distance ladder measurements say the Universe expands 9% faster than the leftover relic method is one of the greatest puzzles in modern cosmology. Whether that’s because there’s a systematic error in one of the two methods used to measure the expansion rate or because there’s new physics afoot is still undetermined, but it’s vital to remain open-minded to both possibilities. As improvements are made to parallax data, as more Cepheids are found, and as we come to better understand the rungs of the distance ladder, it becomes harder and harder to justify blaming systematics. The resolution to this paradox may be new physics, after all. And if it is, it just might teach us something about the dark side of the Universe.”


My own starting point is a revision of Quantum Mechanics: I simply assume that Newton was right (that’s supposed to be a joke, but with wisdom attached). Newton described his own theory of gravitation to be absurd (the basic equation, F = M1 M2/dd. where d was the distance was from a French astronomer, Ishmael Boulliau, as Newton himself said. Actually this “Bullaldius” then spoiled his basic correct reasoning with a number of absurdities which Newton corrected).

Newton was actually insulting against his own theory. He said no one with the slightest understanding of philosophy would assume that gravitation was instantaneous.

Newton’s condemnation was resolved by Laplace, a century later. Laplace just introduced a finite speed for the propagation of the gravitational field. That implied gravitational waves, for the same reason as a whip makes waves.

We are in a similar situation now. Present Quantum Physics assumes that the Quantum Interaction (the one which carries Quantum Entanglement) is instantaneous. This is absurd for exactly the same reason Newton presented, and Laplace took seriously, for gravitation.

Supposing that the Quantum Interaction has a finite speed (it could be bigger than 10^23c, where c is the speed of light.

Supposing this implies (after a number of logical and plausible steps) both Dark Matter and Dark Energy. It is worth looking at. But let’s remember the telescope (which could have been invented in antiquity) was invented not to prove that the Moon was not a crystal ball, but simply to make money (by distinguishing first which sort of cargo was coming back from the Indies).

We see what we want to see, because that’s we have been taught to see, we search what we want to search, because that’s what we have been taught to search. Keeping an open mind is great, but a fully open mind is a most disturbing thing… 

Patrice Aymé

Black Hole & “French Theory”

September 9, 2015

“French Theory” is how American humanists qualified the body of work of a great number of 1960s French philosophers. “French Theory” puts under suspicion all and any mental work.

French Theory is an American observation. “French Theory” is not known to the French as such: the expression was born, and thrived, in the USA. Some professors in the USA love it, others hate it (the resulting conflict is called the culture wars).

According to those Americans who defined it, French Theory is supposed to emanate from  an impressive assemblage of disparate French philosophers (and, as we will see in a further essay, increasingly desperate).  That exotic assemblage is the most surprising part to the French, as many of those philosophers did not agree with each other’s work.

"French Theory" Says Something About Black Hole Theory, Or Lack Thereof

“French Theory” Says Something About Black Hole Theory, Or Lack Thereof

It goes without saying that the herd of physicists whose entire religion is “Shut Up And Calculate” hate “French Theory” with a passion. This went on until they finally understood that hatred from intellectual to intellectual did not serve the honor of the human spirit, nor the intellectual cause, in the eye of the increasingly suspicious public.

“French Theory” was influenced (in my idiosyncratic opinion) by a formidable array of deep thinkers: Sade, Herder, Hugo, Nietzsche. According to them, following even earlier authors such as Julius Caesar (who walked the talk, or rather fought his way through), much human psychology is explained by the “Will To Power”. “French theory” insists that much social and institutional organizations, theories, and countless “truths” are truly all about the will to power. Society, its institutions, works, and art, come to be viewed as a generalized calculus of power.

The principal architects of French Theory are:

Louis Althusser , Jean Baudrillard, Simone de Beauvoir, Hélène Cixous, Gilles Deleuze, Jacques Derrida, Michel Foucault, Félix Guattari, Luce Irigaray, Julia Kristeva, Jacques Lacan, Claude Lévi-Strauss, Jean-François Lyotard, Jacques Rancière, Monique Wittig. I would add to this traditional list Alain Badiou.

What does “French Theory” see? Not just suspicious motives all over. Not just suspicious structures all over. Suspicious neurology all over.


When The Will to Power Darkens Black Holes:

A particularly controversial aspect of “French Theory” has been its suspicion of established science.

Let me give a sharp personal example of French Theory in action: when I exposed to some of the best Black Hole theorists in the world, that Black Holes, by a particular strand of logic, ought to drop out of the universe gravitationally, I was teasing them (out of their self-satisfied complacency). From that particular point of view (which is what theory means in Greek), which I rolled out, Black Hole theory leaves much to be desired.

If those gentlemen had been sincerely interested primarily by the science, they ought to have engaged me in a passionate debate. Instead, they ignored the subject, after showing signs of impotent rage. Why? All what those famous brains could feel, and see, was that their position is society was compromised by my idiotic theory.

My theory was idiotic, because, should it become widely known, it may have compromised the standing of Black Hole theory, hence of Black Hole theorists, in the eyes of the public. Should my observation disseminate, those worthies were in danger, those sacred monsters, to turn, in the public eye, from great gurus, mysterious oracles, to uncomprehending toddlers. Thus it was safer to ignore the problem altogether, while giving a warning that it ought not to be broached again, with a discrete show of deep rage. So Black Hole theorists kept on thinking of Black Holes as gathering geodesics, a very classical picture.

This personal example (and I came across a few others) told me that, for many of these professors who are household names, social standing was more important than real understanding. If anything, I have come across way worse since: watch economists ignoring plutocracy and the banking system, when they ponder what’s wrong with the world socioeconomy.

The Will to Power is all over learning, and sometimes, it reduces to the will to money. Academic editions sell books at outrageous prices, which nobody can afford… except the taxpayer supported libraries. And in the USA (followed by the UK) private or pseudo-public “universities” universally serve the richest class, by providing taxpayer supported exclusive education to the very few.

And so on. Black Hole theory may not be clear, but the Dark Side is pretty transparent. By making the will to power in all the metaphysics that counts, it reduces humanity to a crab basket, solving all problems in one stroke. Indeed, what do crabs know about problem? Nothing. Thus, no problem!

Patrice Ayme’

Constructing TIME

June 3, 2014

How does one usually define time? Well, I will argue, it’s constructed by machines.

This has major consequences in physics, to be evoked some other time: Cosmic Inflation theory uses time, but has forgotten to define it. Thus a philosophical-historical review is in order.

The concept of time was developed experimentally over several millennia.  Time was important in agriculture: it allowed predicting when to do some specific activities essential to agriculture (planting, irrigation works, etc.).

Mayan Calendar: No Time, No Hydraulic Civilizations

Mayan Calendar: No Time, No Hydraulic Civilizations

The Mayas, and the Babylonians discovered that astronomy, observing stars and planets, allowed to predict the seasons. Thus, they defined time. The Mayan civilization depended upon highly technological seasonally constrained hydraulics, so time was of the essence. The Mayans thrived for millennia before an inordinate drought brought ecological catastrophe and the consequential mayhem (7C to 9C).

Shortly after the equal sign was invented (circa 1500 CE), time appeared in the equations of the Seventeenth Century physics. Time was fundamental to the equations of classical mechanics that described both how mechanical forces and gravitation-imparted trajectories: every dynamical phenomenon was a function of time, and its acceleration, the double derivative relative to time, was the force.

This classical time allowed to determine longitude in navigation. The more precise the time, the more precisely navigators knew where they were in the middle of the ocean. This (new) mechanical notion of time had grown from astronomical time, and was found, de facto, to be identical with astronomical time.

Mathematics and physics were deeply entangled. Time is truly an injection of the Real Line into the space(s) the equations are about. The concept of Real Line is implicitly central to calculus. Calculus was developed for physics.

However, in the Nineteenth Century, equations were derived for a force that was not found in Classical Mechanics, Electromagnetism.

(17 C) Gravitation is what one could call (until 1916!), a “point force”: a planet of mass M can be replaced by a point of mass M (that’s Gauss theorem; it caused lots of trouble to Newton).

Electromagnetism was more complex than gravitation.  Faraday drew lines of force lovingly (and was despised for it). Maxwell transformed them into “field” equations.

A “field”, just as a field of wheat. The Electromagnetic field could turn in circles on itself, or make lobes.

Sometimes, electric charges behave like “point forces” too. But magnetic charges could not be found: they were never like point (“monopoles” in modern jargon). However, electricity would turn into magnetism, and varying magnetism into electricity. Electromagnetism was exasperatingly complicated.

A journalist asked Faraday what use the fact that a varying magnetic field created electricity had. Faraday retorted: ”What’s the use of a new born baby?

All our industry now rests on this new born baby. (By the way, Michael Faraday was directly supported personally by the top plutocrat in Britain, the king.)

A field is non local. Whereas it looked as if gravitation did not need to be described by a field (an impression Einstein would change, but that’s besides the points made here), it was certainly not the case for electromagnetism.

Any force generates an acceleration, hence a dynamic, hence a trajectory. So classical mechanics generated a notion of time (it had turned out that time from a mechanical force, a spring, was the same as from gravitation).

Similarly for electromagnetism: it’s a force, so it defines a notion of time. However, even classically, electromagnetism was non-local. So the clocks defined by electromagnetism are non-local. I call them holonomic. (Adjusting classical time to electromagnetic time is called Special Relativity; it turned out that gravity needed to be made into a field, and that time needed to vary with speed so that physics was independent of speed.)

This notion of non-local time, it turned out, was another excellent torpedo against Cosmic Inflation, and the naivety that helped built it. More later…

Patrice Aymé



May 28, 2011

Gravity Versus Quantum Seen Through SIMPLICIAL DECONSTRUCTION. Relations With Oligarchy.

[Lots Of Physics For Inquiring Minds.]


Abstract: Once, long ago, some unknown author gave a joint physics-mathematics conference in Stanford on Black Holes. Some math-physics celebrities were in attendance. The author concluded that General Relativity cannot be used to demonstrate  singularities in spacetime, because of Quantum effects. At the time, the author was accused of “meditation”.

Several years later, Hawking (in a “Brief History of Time”), adopted that conclusion, that Quantum overwhelmed Relativity. It seems to have become standard. The source of ideas are not always where they seem. But, to those for whom thinking is the prime motivation, it does not matter, they proceed, through fire, objections, dejections, the ashes of illusions washed away…

Present physics abound in deep paradoxes in plain sight. I ponder here another: Why are Black Holes not Total Holes? Indeed if photons cannot come out of a Black Hole, how come gravitons do? The Theory of Gravitation and the Quantum contradict each other.

Here I search for truth through simplicial deconstruction. If the logical skeleton makes no sense, how could the logical body around it survive?

This complex essay ponders the nature not just of nature, but also of the scientific oligarchy, and how it connects with the plutocracy. This explains the insufficient funding for deep science, when deep questions lay all around, untouched. The usual suspects are brought out for the traditional perp walk.




There ought to be such a thing as a theory of theories. The philosopher (and scientist!) Karl Popper said that falsification was important in science, but he did not present a new technique of falsification. When Derida proclaimed deconstruction, he did not really forge a new insight, either, as thinkers have been busy falsifying and deconstructing, as this is what thinking is all about.

Falsification does not reduce to computation: only parts of science are amenable to computation. Most of the most important falsifications, historically speaking, did not rest on computation.

For example the heliocentric theory was proven right computationally by Kepler. Kepler followed pointed advice from Tycho, who thought, rightly so, that Ptolemy and his friends had cheated. However, both followed the work of Buridan, 250 years earlier (rehabilitated by Copernicus), or even Aristarchus and his predecessors, 19 centuries before.

Those theoreticians had already falsified the geocentric theory by presenting something more plausible. Buridan hinted, and Copernic said, that heliocentrism was true, before excruciating computations could verify it (that certainty was the motivation for the expensive multi decades effort to establish the orbit of Mars). And Ptolemy had cheated, to prove the opposite, through the sophistry of mathematical lies.

By the same token, even though Kepler had demonstrated, in his “War On Mars“, that Mars followed an ellipse with the sun on a focus, he was not believed. Until about 1700 CE, in spite of Galileo, Newton, and all their numerous fellow travelers, most scientists did not believe in the heliocentric theory.

Why? Because the scientific establishment is an oligarchy which is mostly anxious to find out who is in, and who is out (as Feynman put it, before he resigned from the academy in protest). The Bible said that the sun turned around the Earth, and the Bible was the foundation of established order. That was good enough a reason for the scientific oligarchy.

The scientific oligarchy augments its power to the max by ingratiating itself with the plutocracy in command. And plutocracy prefers its rabble meek and reeking of the same old thoughts, and the more inconsequential, uncontroversial, and incoherent, the better. If the meek and weak venerates incoherence, they will never make sense and the mastery of force will elude them. They will stay meek and weak. Coherence is what gives a laser its punch. If yesterday’s venerated idea can reveal itself a lie, could not all the evidences which make Plutocracy’s throne also reveal themselves to be lies? 

The Catholic Church, forced by a Parisian students strike, in 1200 CE, to embrace Aristotle, embraced him with a vengeance, as a new rigidity, a new definition of evidence. That was all the more judicious, since Aristotle, brought up in the highest circle of Philippe’s Macedonian court, was most attentionate to fascism and plutocracy.

Some will scoff that it is not like that nowadays. That now reign super scientists, super qualified, super selected, the ones and only, the finest flowers of thought among 7 billion.

However, as I already showed in other essays, and will do some more, there are major problems, even blatant contradictions, in today’s physics (contrarily to the idyllic picture often haughtily presented).  This is true in theoretical physics, and thus, a fortiori, in applied physics. (Out of dozens of thousands of possible materials for  batteries, only a few hundreds have been tested in decades!)

The correct consequence to be drawn is that there are way too few physicists, and way too few experiments conducted in physics (an experiment alluded to below on the dragging of frames from a rotating mass, was mostly organized by some physicists at Stanford University, and took more than 40 years to reach orbit, from dearth of funding; the 2010 Nobel was given to physicists who made a major discovery, a new state of matter, by peeling graphite… with scotch tape!)



I demonstrate a total hole in the union of the two most prestigious pillars of physics. Usually this is done in a way which is not only incomprehensible to non specialists (gravity is found to be “non renormalizable”), but also not logically compelling.

The union of the two most celebrated theories in contemporary physics, “General Relativity” (GR) and “Quantum Field Theory” (QFT) does not appear incompatible with energy conservation. My first order reasoning is ridiculously simple.

An approach to falsification uses the meta-idea of stripping down theories to lower dimensional simplicity, and see if what’s left still makes sense.

I view any theory as a simplicial topology made of simplicial complexes (I will detail that theory of theories some other time). The reason for doing this is that complex reasonings can hide simpler, more fundamental truths, just as a WWI destroyer could hide behind a smoke screen. If the lower dimensional part of a theory cannot be reorganized so as to make sense,  danger signals should go up. Not only this gives some punch to Popper’s and Derida’s vague slogans, but it is worthy to remake all of science and mathematics that way. The essences come out…

This approach deserves a name: SIMPLICIAL STRIPPING (roll over Derrida!). Simplicial Stripping does not have to be restricted to science. It works even better throughout politics, ethics, philosophy. Look at Israel: a contradiction onto itself (and putting it back into its 1967 cage won’t change that!). Or look at the economic rescue plan since 2008: save the plutocrats! (From themselves.)   



Here is the skeleton of Einstein’s Theory of Gravitation, so called “General Relativity”. The idea is actually not Einstein’s, but Riemann’s, in 1860 CE: gravitation is  inertia in an elaborated geometry defined by mass-energy.

In its most primitive form, the idea that inertia can replace force originated with Buridan, around 1320 CE. Buridan brandished the disappearance of force to explain that planets, submitted to no force, were going around the sun. It was a big progress over the completely silly Aristotle, who thought force was needed to keep on going (so things would stop in vacuum, according to him and his clueless followers).

If you never heard of Buridan, Johannes Buridanus, please thank the fascist plutocrats of the Inquisition for simplifying your mind. Buridan, an adviser to kings, head of the university, mathematician, physicist, philosopher, and teacher to major mental heavy weights such as Oresme, was much more famous, and inflected civilization much more than a modest contributor to thinking such as Einstein. That is precisely why the Inquisition forbid his works, more than a century after his death, just when Copernicus was a young man. 

Whether gravitation is no force (Buridan-Riemann-Einstein) or whether it is a battle between the centrifugal force and Ismaël Bullialdus’ inverse square law, as Newton had it, was solved in the favor of the first… By Einstein. The zero order reason for the switch is that the concept of “centrifugal force” is not clear (it has no Lagrangian).



“The Foundation of the General Theory of Relativity”, by Albert Einstein, Annalen der Physik, 49, 1916 contains the following revealing statement by Einstein:

“It will be seen from these reflections that in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to “produce” a gravitational field merely by changing the system of co-ordinates.”

OK, fine, so everything is relative, and out pops gravity. I can reflect too. From my point of view, Einstein described everything, and explained nothing. He was proud to have identified acceleration with gravitation, but the problem is that any force, including gravitation, shows up as acceleration.  If the sheep formally identifies grass as food, did anything happen?

(Some are bound to scoff that General Relativity is well checked, GPS, bla, bla, bla; indeed, such is the property of any tautology! Tautologies are the definition of absolute truth. The non trivial effects of GR can be obtained directly; for example the prediction of gravitational waves is immediate from the belief that gravity is a field. The slowing down of the clocks next to a mass is caused by energy conservation, etc.)



Riemann’s insight, as implemented by Einstein, Hilbert and company looked fine. Until an interloper showed up on the scene. Studying elementary particle collisions, physicists discovered an unending zoo of particles accelerating here and there, thus exhibiting new forces in action.

These were new notions of force, same as the old one, the one before Einstein. Indeed the same old notion of force as in the seventeenth century, by Bullialdus, or electricity, in the eighteenth century, by Coulomb. Namely anything which causes an acceleration.

This can of worms was a deviously obscure scheme, Quantum Field Theory, QFT. Einstein got lessons from one of the top early practitioner of that dark art, and gave up.  Einstein believed in the big idea, whereas QFT was a bunch of cooking recipes with stuff found in bubble and spark chambers.

The basic scheme of QFT is to guess a Lagrangian (an expression depicting force), taking consideration of what has been found experimentally (such as the strong force, or the weak force, or what has been imagined, such as the inflaton force, etc… It’s like a modern salad). 

Thus there is no big idea: force is whatever acts funny. To accommodate all the new forces, according to the basic Riemannian scheme, one would have to augment considerably the number of dimensions of the universe.

It was found possible to add just one dimension to accommodate electromagnetism (Kaluza-Klein), but electromagnetism, as Bullialdus had already (knowingly) pointed out, is similar to gravitation, whereas the strong force is very strong, and very short range, and the geometry for that, obscure.

As it turns out the strong force is described best by curvature in an SU(3) fiber bundle over spacetime, Quantum Chromo Dynamics, QCD. Beautiful math, but spacetime found itself relegated to playing the role of base space of a fiber bundle (“base” here has both a technical, and poetic meaning…)



When people think of science, especially physics, they think of irresistible logic. And so it is for very well established physics. But when it’s really not well established at all, on the theoretical edge, anything goes (see the deeply grotesque “multiple infinite universe” theory). And, as Bohr said, nothing presented yet is crazy enough. (Although I am trying my best!)

The most intuitive and handy way to depict the development in series of Lagrangians has been through a pictorial scheme found by Feynman, Feynman Diagrams. De facto, it depicts interactions as exchanges of particles, which are called “virtual particles”. Whether those virtual particles really happen is a matter of debate (rigorists refuse the abstraction of “virtual particles” as they cling to equations, like infant monkeys to their mummies). Feynman himself was coy on the subject, as behooves a higher type. However, in practice, experimental physicists view forces as particle exchanges, this is the essence of QFT.

More exactly, the essence of QFT is the Lagrangian. As one tries to develop it in series, virtual particles show up, exploiting, and allowed, thus “caused” by the time-energy uncertainty of Quantum Mechanics (higher dimensional idea).  The higher the mass, hence energy, of said virtual particle, the less time it can stay directly undetected, thus big mass, short range (and big force too, to create said mass). 

So QFT says, in practice, that forces are depicted by particle exchanges. It certainly looks so for all forces known, thus so should it  be for gravitation (it’s an emotional reasoning: physicists are human beings too).



OK, let’s go back to how Einstein’s theory of gravitation is an implementation of Riemann’s proposition that all forces can be viewed as suitably curved spacetime geometries.

What is this splendid idea? (“Riemannian”) geodesics are defined by the distance function (aka “metric”). In a curved space, geodesics, if close enough, will either converge, or diverge (contrarily to Euclid’s straight lines).

In Einstein’s 4 dimensional spacetime, crawling along the geodesics correspond to the flow of time, and particles follow said geodesics. Thus, according to whether geodesics diverge or converge, particles will either approach each other, or flee each other. But that is exactly how an acceleration, and thus a force is detected: how the distance varies in the fullness of time. In other words, how the distance between geodesics varies describe a force.

Some mathematics then show that how the distance between geodesics varies is equivalent to curvature. [Here is a philosophico-mathematical proof of that: both curvature and how the distance between geodesics varies are the only two infinitesimal variables of the geometry, but it’s relatively easy to prove that there is only one connection, id est only one geometry compatible with the Riemannian distance, so they have to be the same, because, if they were not, there would be two different geometries!]

Hence, to describe the gravitational force, one needs a space with the appropriate curvature. Newton, following Ismaël Bullialdus’ inverse square law, plus Huyghens’ balance of centrifugal and attractive, and contributions from Hooke and Borelli exploited the notion that gravitation was proportional to the mass.

Thus Einstein (in collaboration with Hilbert, among others) needed an equation such as:

curvature = mass. This is, basically, Einstein’s gravitational equation.

That’s all (the rest is complicated details; including that ‘mass’ is mass-energy, and that’s a 16 dimensional tensor, whereas, at first sight, the left hand side of the equation is a 256 dimensional tensor; so one needs tricks to reduce the dimensions on the left to write an equation…by making the riemannian tensor into a lower dimensional Ricci tensor).



The nature of matter is not clear, because the nature of particles is not clear, and that’s not clear because particles are always Quantum Mechanically entangled, and entanglements are non local. But today, we will, exceptionally, ignore that fascinating subject, which is more fundamental than space and time, and is what the true order of the universe is really made of (the realm of my pet, TOW).

The Greeks thought matter was made of atoms. That was confirmed 20 centuries later. However, what atoms were made of revealed Quantum Mechanics. Atoms were made of protons, electrons, and, first of all, vacuum. It turned out that the electrons were found where their waves added up nicely (Bohr-De Broglie).

And what was light made of? Huyghens in the seventeenth century suggested waves, Newton suggested particles. A century later, Laplace arrived on the scene. Assuming that light was made of particles, he observed that they would be submitted to gravitational attraction. Thus, if a star was massive enough, it would pull on light, and light would lose energy (that’s known as the “Gravitational redshift” in Einstein’s gravitation). If the star was dense enough, the pull would be so hard that no light could escape. Laplace (and a less well known English polymath named Mitchell) concluded that the brightest objects in the universe may well not be seen. They had discovered Black Holes. At least Black Holes in the light-as-massive-particle theory. Development in the subject stopped when Young (another english polymath1) and Poisson (another French matematician!) demonstrated, beyond any suspicion, that light was “made” of waves. Waves were thought impervious to gravity (curious, because it is not so in the ocean). 

The prediction of Black Hole in Einstein’s gravitation is not much different. The photons have no mass, so they follow spacetime geodesics perfectly. But mass pulls on the geodesics, and if it pulls hard enough, those will spiral in. Thus light can’t escape.


In conventional physics, a force is anything that accelerates. According to the essence of QFT, a force is enacted by an exchange of particles. Thus gravitation is caused by an imagined, hypothetical particle, the graviton.

Notice that this logic makes no sense in Einstein’s theory of gravitation, since, according to said theory, its essence is that gravitation is just inertia. (Said inertia is determined by geodesics, determined in turn by the mass-energy field, and if the mass-energy moves, as when it rotates, the sense of inertia should be dragged around, an effect verified in 2011 by gyroscopes in low Earth orbit.)

So if there is no force, so why should there be a particles exchange depicting said force?

Some sophisticated, mathematically competent physicists, will have a sophisticated piece of sophistry to answer that one. They will argue that interactions are wavy fields, and particles are their lowest excited states. So, be it gluon or photon, or W or Z boson, by “particles” we mean those primary excitations, these “virtual particles”.

By the same token, those sophisticated types would define the graviton as the lowest excited state of the wavy field known as spacetime geometry.  

Thus, the Theory of Gravitation, looked at face value, cannot be a force, and thus exchange virtual gravitons, but, looked at as a Quantum metatheory, it has both! The smallest conceptual incorporation of the simplest piece of QFT in the Theory of Gravitation generalizes the concept of “force”. Usually a force displaces an object, within a geometry, here the force deforms geometry itself. A meta-objection to that meta-interpretation is that this destroys the intuition of Riemann. But of course, nowadays, geometry of geometries are a standard tool: that’s what the Ricci Flow is all about, a flow from one geometry to the next, until a sphere is reached.  


Conclusion: THE MORE WE KNOW, THE MORE QUESTIONS: The edge of physics is stuffed with questions of the deepest philosophical nature. In his lectures on physics, Feynman whined that philosophers are always around, talking a lot and having nothing important to say. An immediate consequence was that Feynman’s son graduated in philosophy. Feynman should also have realized that the closest mirror would bring to light a philosopher he knew all too well. Actually, he obviously did.

But, of course, in one sense Feynman is right, because all too many of today’s philosophers are ignorant of science. Can one be ignorant and wise? Socrates thought so, exhibiting his ignorance. And driving civilization into the ground.

In first order of understanding, if gravity respected the basic principles of Quantum Field Theory, a gravitational field which is strong enough will prevent gravitational quanta to come out. Just as it prevents  electromagnetic quanta (photons) to come out, and for the same reason.

A major problem has been whether “virtual particles” are real or not.  The abstraction of virtual particles brings into question the very notion of existence,  what “real” means, and even what abstraction is, and how the mind works.

Let’s make a joke mathematicians will get. Are complex numbers “real” or not? The human brain makes abstraction “real”, because real means the way the brain is.

Kant had decided that there was such a notion of “thing in itself” “das Ding an sich“, causing a great disservice to philosophy, by declaring it unknowable. As it is, the greatest task of the edge of physics is to figure out what exists, and what does not. The line between essence and appearance is where the edge of science is. By claiming it is obvious, an entire school of philosophy made itself ridiculous (philosopher-physicists such as Mach, also disagreed with Kant).

Does gravitation exist? Obviously it does, a monkey could tell you that. Is it just inertia, as Einstein had it? If it is, and gravitons follow spacetime geodesics, how come gravitons come out of Black Holes? Or do Black Holes, when sufficiently black, all together drop off the universe? That would violate (local) energy conservation.

As I pointed in “Dark Demon Energy” energy conservation is probably violated (it is a well known problem that Cosmological Expansion violates energy conservation, in a global fashion, let it be said in passing, and I know of no convincing hand waving that explains that away).

I will explore some of these questions later. Science teaches modesty to those who learn it well, but also the pride and elation of reason well deployed.

There are not enough scientists, and not enough science made. Just as there is not enough common sense deployed in government (example: the refusal of the Japanese government to consider virtual tsunamis real, which is seconded by the same attitude on the West Coast of the USA, by the way).

The dearth of science, scientists, and common sense are related phenomena: after all, science is just common sense, thoroughly deployed. Plutocracy can be achieved only when enough common sense has been reduced to the bleating of sheep. That is exactly why the West is deploying just enough science to survive, but not enough to thrive. 

The tragi-comical spectacle of a few lawyers, “elected” to decide in secrecy the fate of the world at a French resort, flows along the same geodesics, the inertia of plutocracy and its servants, attracted by the darkest side, imprisoning even light. What do those know, and what are they talking about? And it’s all too real.

If the major Western countries had dozens of millions of scientists, it’s unlikely that the  plutocrats and their lawyer-servants could keep on hypnotizing the masses with tales for children. That works well only with a scientific oligarchy, where the few scientists can be bought off with enough toys and ribbons.

One can buy a few people all the time, and all the people some of the time, but not all the people, all the time. A scientific massocracy cannot be bought (if I dare to borrow the term “massocracy” from my nemesis Libyan dictator Qaddafi).

Where to find the resources, the money? Agricultural subsidies ought to be reduced. Those who want to live dangerously will propose, as the foolishly bold Dominique Strauss Kahn did, to augment government and tax and regulate the pirates of finance into oblivion. But who wants the New York Attorney paid by Goldman Sachs and its partners in crime, accusing them of attempted rape on the closest tall mammal that they can find?

“Power is the ultimate aphrodisiac.” said Kissinger in 1973. Plutocracy is all about the obsession with power. But power is what physicists study.  Let’s not forget that the most powerful Soviet dissidents, Solzhenitsyn, a mathematician, or Sakharov, a master of the H bomb, and a top theoretical physicist, were scientists. That was no coincidence. Honing the capability to distinguish what is real, and what is not, and how energy flows, is intrinsically revolutionary.


Patrice Ayme

Dark Matter, Dark Energy, Gravitation, etc.

December 24, 2009


Abstract: A few basic considerations on Dark Matter, Dark Energy, Gravitation, and how science proceeds. For once, nearly no statement here is in any way controversial… (OK, except a few snide remarks on the motivations of some revered physicists, and some tenets of physics requiring experimental proof, rather than blind acceptance…)


Deep mine experiments look for WIMPs (Weakly Interacting Massive Particles). In Europe and the USA, the world’s two largest elementary particle accelerators have targeted their beams towards detectors in said mines, through hundreds of Kilometers of Earth’s mantle. Claims have been made for tentative events. It’s all very tentative, although tantalizing.

The idea for the WIMP search is a bit the same as with neutrino detection: bury deep underground, so that only WIMPs should be left.

Neutrinos are traditionally supposed to have mass zero (neutrino means the small neutral one, an Italian neologism invented by Enrico Fermi, Nobel prize winner, refugee from Mussolini, and scientific head of the nuclear bomb project in the USA; the concept was from Wolfgang Pauli, to explain the continuous spectrum of beta decay). But it turns out that neutrinos have mass, and they oscillate between types. A whole slew of experiments will try to know more soon. So neutrinos are a type of WIMPs, except that they are very light.

It has been known since 1933 (by the Swiss astronomer Zwicky, a supernova specialist, discoverer of the concept of neutron star) that galaxies and clusters of galaxies are missing mass by a factor of at least ten, if one uses straight Newtonian gravity on the observed motions of galaxies or their disks.

Now Newtonian gravity is the first order of the modern ("Einstein’s") theory of gravitation. Both theories differ only at very high speeds or fields. Hence the observed discrepancy would mean that our theory of gravitation is false. A class of modification of Newtonian theory was proposed (MOND = MOdified Newton Dynamics, where the gravitational attraction is the same for high acceleration, proportional to the inverse of the square of the distance, but slips into simply the inverse of the distance for weak accelerations).

But the way science proceeds is to milk a theory to death, until it dies. The Newton-Einstein theory of gravitation is correct in the Earth’s neighborhood, as far as we can see. So the reflex of experimentalists was to look for missing mass under the form of WIMPs. The search was on well before it became obvious neutrino had mass. Now that later fact is a game changer, since supernovas emit copious quantities of neutrinos. Indeed there is less of a missing mass now (maybe only a factor of five instead of ten…)

The apparent Dark Matter is concentrated in strange ways: halos, lobes…


Apparent Dark Matter Ring. Located in the "Fish" galactic cluster, 5 billion light-years away, and 2,6 million light-years across. Gravitational lensing can be seen (by looking carefully) and exhibits the enormous mass of the Dark Matter halo.


Please remark that in today’s physics, photons have mass zero. All other particles have some mass. The mass zero of the photon has been turned into religion by Relativity theory, but, ultimately, it ought to be considered an experimental fact, to be continually verified. If photons did have a mass, that would be much more of a game changer. It would most probably imply that gravitons have mass too, so gravity would have to be recomputed…

However, for reasons of logical completeness, Pauli (again!) noticed that Quantum Field Theory would work well if and only if each particle had a symmetric partner across the fermion-boson line. This is called SUSY ("SUperSYmmetry"). That would give plenty of WIMPs. So the search is on. 2010 will bring on line plenty of experiments worldwide, and the LHC in Geneva will ramp up in power.

As the preceding indicates, Dark Matter could be something radically new (new WIMPs), or simply explained: say by massive neutrinos (?).

Or then may be gravity was not as we extrapolated it to be, from around our little blue and white spaceship.

But the real mystery is DARK ENERGY. That, if confirmed, is way out of imagined physics (although it could be claimed that the ad hoc "cosmological inflation" used to explain the homogeneity of the Big Bang was just such a possible prediction!). The universe is expanding, as if there was out there a mysterious anti-gravity. There is no mechanism to explain this (although it can be written down in Einstein’s gravitation equation by re-introducing a scalar term, the cosmological constant, Einstein had introduced to make the universe static, before Hubble discovered the expansion, leading an opportunistic Einstein to declare the cosmological constant was "his greatest mistake").

In conclusion, we are extremely far from a final "theory of everything", contrarily to what some physicists have claimed with profit motivated outrageous naivety (there is great profit in books and fame). Profit is most often a bad adviser to the sharpest thinking (something profit obsessed American regressive economists fail to integrate).

Verily, in 25 centuries or so of official physics history, I do not know of one period when so much has been officially not known, and blatantly darkly mysterious. Anything could happen. For example, there is not one force theory, but two, and they do not agree conceptually. The explanatory scheme in gravitation (no force, just inertia), is completely different from the explanatory scheme for forces in Quantum Field Theory (whatever that mystery wrapped in an enigma, shrouded by immense Lagrangians, renormalized by reality turns out to want to say).

Patrice Ayme