Gravity Versus Quantum Seen Through SIMPLICIAL DECONSTRUCTION. Relations With Oligarchy.
[Lots Of Physics For Inquiring Minds.]
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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.
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I MEEK, THEREFORE I GOOD:
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!)
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DECONSTRUCTION AS SIMPLICIAL STRIPPING:
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.)
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EINSTEIN’S THEORY OF GRAVITATION, IN FIRST ORDER :
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).
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I TAUTOLOGIZE, THEREFORE I LOGICAL:
“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.)
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QUANTUM FIELD THEORY GETS FORCE FROM A LAGRANGIAN:
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…)
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WHY GRAVITONS? BECAUSE ONE CAN VIEW QFT AS EXCHANGING VIRTUAL PARTICLES:
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).
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FORCE AS GEODESICS’ DISTANCIATION:
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).
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LAPLACE’S BLACK HOLE DISCOVERY:
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.
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IF THERE IS NO GRAVITATIONAL FORCE, WHY SHOULD PARTICLES CARRY IT?
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.
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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.
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Patrice Ayme
