Posts Tagged ‘Black Holes’

Not An Infinity Of Angels On Pinheads

July 1, 2016

Thomas Aquinas and other ludicrous pseudo-philosophers (in contradistinction with real philosophers such as Abelard) used to ponder questions about angels, such as whether they can interpenetrate (as bosons do).

Are today’s mathematicians just as ridiculous? The assumption of infinity has been “proven” by the simplest reasoning ever: if n is the largest number, clearly, (n+1) is larger. I have long disagreed with that hare-brained sort of certainty, and it’s not a matter of shooting the breeze. (My point of view has been spreading in recent years!) Just saying something exists, does not make it so (or then one would believe Hitler and Brexiters). If I say:”I am emperor of the galaxy known as the Milky Way!” that has a nice ring to it, but it does not make it so (too bad, that would be fun).

Given n symbols, each labelled by something, can one always find a new something to label (n+1) with? I say: no. Why? Because reality prevents it. Somebody (see below) objected that I confused “map” and “territory”. But I am a differential geometer, and the essential idea there, from the genius B. Riemann, is that maps allow to define “territory”:

Fundamental Idea Of Riemann: the Maps At the Bottom Are Differentiable

Fundamental Idea Of Riemann: the Maps At the Bottom Are Differentiable

The reason has to do with discoveries made between 1600 and 1923. Around 1600 Kepler tried to concretize that attraction of planets to the sun (with a 1/d law). Ishmael Boulliau (or Bullialdius) loved the eclipses (a top astronomer, a crater on the Moon is named after him). But Boulliau strongly disagreed with 1/d and gave a simple, but strong reasoning to explain it should be 1/dd, the famous inverse square law.

Newton later (supposedly) established the equivalence between the 1/dd law and Kepler’s three laws of orbital motion, thus demonstrating the former (there is some controversy as whether Newton fully demonstrated that he could assume planets were point-masses, what’s now known as Gauss’ law).

I insist upon the 1/dd law, because we have no better (roll over Einstein…), on a small-scale.

Laplace (and some British thinker) pointed out in the late 18C that this 1/dd law implied Black Holes.

In 1900, Jules Henri Poincaré demonstrated that energy had inertial mass. That’s the famous E = mcc.

So famous, it could only be attributed to a member of the superior Prussian race.

The third ingredient in the annihilation of infinity was De Broglie’s assertion that to every particle a wave should be associated. The simple fact that, in some sense a particle was a wave (or “wave-packet”), made the particle delocalized, thus attached to a neighborhood, not a point. At this point, points exited reality.

Moreover, the frequency of the wave is given by its momentum-energy, said De Broglie (and that was promptly demonstrated in various ways). That latter fact prevents to make a particle too much into a point. Because, to have short wave, it needs a high frequency, thus a high energy, and if that’s high enough, it becomes a Black Hole, and, even worse a Whole Hole (gravity falls out of sight, physics implodes).

To a variant of the preceding, in: Solution: ‘Is Infinity Real?’  Pradeep Mutalik says:

July 1, 2016 at 12:31 pm

@Patrice Ayme: It seems that you are making the exact same conflation of “the map” and “the territory” that I’ve recommended should be avoided. There is no such thing as the largest number in our conceptual model of numbers, but there is at any given point, a limit on the number of particles in the physical universe. If tomorrow we find that each fermion consists of a million vibrating strings, we can easily accommodate the new limit because of the flexible conceptual structure provided by the infinite assumption in our mathematics.

***

I know very well the difference between “maps” and territory: all of post-Riemann mathematics rests on it: abstract manifolds (the “territories”) are defined by “maps Fi” (such that, Fi composed with Fj is itself a differential map from an open set in Rx…xR to another, the number of Real lines R being the dimension… Instead of arrogantly pointing out that I have all the angles covered, I replied:

Dear Pradeep Mutalik:

Thanks for the answer. What limits the number of particles in a (small enough) neighborhood is density: if mass-energy density gets too high, according to (generally admitted) gravity theory, not even a graviton could come out (that’s even worse than having a Black Hole!)

According to Quantum Theory, to each particle is associated a wave, itself computed from, and expressing, the momentum-energy of said particle.

Each neighborhood could be of (barely more than) Planck radius. Tessellate the entire visible universe this way. If too each distinct wave one attaches an integer, it is clear that one will run out of waves, at some point, to label integers with. My view does not depend upon strings, super or not: I just incorporated the simplest model of strings.

Another mathematician just told me: ‘Ah, but the idea of infinity is like that of God’. Well, right. Precisely the point. Mathematics, ultimately, is abstract physics. We don’t need god in physics, as Laplace pointed out to Napoleon (“Sire, je n’ai pas besoin de cette hypothese”). (I know well that Plato and his elite, tyrant friendly friends and students replied to all of this, that they were not of this world, a view known as “Platonism”, generally embraced by mathematicians, especially if they are from plutocratic Harvard University… And I also know why this sort of self-serving, ludicrous opinion, similar to those of so-called “Saint” Thomas, a friend of the Inquisition, and various variants of Satanism, have been widely advocated for those who call for self-respect for their class of haughty persons…) 

The presence of God, aka infinity, in mathematics, is not innocuous. Many mathematical brain teasers become easier, or solvable if one assumes only a largest number (this is also how computers compute, nota bene). Assuming infinity, aka God, has diverted mathematical innovation away from the real world (say fluid flow, plasma physics, nonlinear PDEs, nonlinear waves, etc.) and into questions akin to assuming that an infinity of angels can hold on a pinhead. Well, sorry, but modern physics has an answer: only a finite number.

Patrice Ayme’

 

Gravitational Waves Directly Detected

February 11, 2016

How Were Gravitational Waves detected?

By two detectors in the USA, one in Washington State, the other in Louisiana (detecting in one place would have been enough; in two places at the same time, the finding is overwhelming certain; the National Science Foundation of the USA had spent $1.1 billion, over 40 years, on that research). The detectors were simplicity themselves in concept: just a light interferometer to measure the distance between mirrors: light is split, sent in two perpendicular directions, and then re-united with itself. If one of the branches vary slightly in length relative to the other as a gravitational waves passes, an interference will show up. However mirrors hanging from pendulum hanging from pendulums five times, the whole thing in an anti-vibration machine had to be realized in half a dozen places in a chain of reflections and interference.

What are these Gravitational Waves?

As far as existing gravitation theory has it, distortion in space (and, thus time: time and space are related by the speed of light, c).

A Field Carries Away A Wave Just As A Whip Does

A Field Carries Away A Wave Just As A Whip Does

What Was Detected:

Einstein’s Gravitation Theory says that gravitation “is” the deformation of space(time) it brings. It is this deformation which was directly detected: a part of space in one direction was made shorter than in another direction. That meant a huge gravitational wave had passed.

The formidable event that caused it was the crash and collapse of two black holes into each other, each around 30 solar masses (much more details are known).

Gravitational Waves Were Certain Theoretically, & Already Detected:

We already had evidence for the existence of gravitational waves, both theoretical and experimental. Einstein’s name was rolled out, naturally enough. Because Einstein contributed to the present Theory of Gravitation (I am not anti-Einstein, far from it, but he closely worked with a number of other people, including the towering mathematician David Hilbert, who published his own approach to gravity within weeks of Einstein).

Einstein tends to appear as the cherry on many a cake. Those who celebrate the photogenic cherry, and ignore the cake, will go hungry.

WAVES ARE PREDICTED BY FINITE SPEED FIELD THEORY:

Actually, once one has hypothesized that gravitation is a field propagating at a finite speed, the apparition of waves is automatic.

The reasoning was made first by British and French Eighteenth Century physicists, in the framework of electromagnetic force; the mathematics is exactly the same with gravitation, as both fields vary with the inverse square of the distance. This is what happens in a radio antenna, with electrons going back and forth: the electric field that those electrons create is deformed in such a way that it moves other electron at a distance, back and forth.

The Gravitational Energy Loss Detection Method:

Thus, how do the waves show up? By shaking things at a distance. Using conservation of energy, it means that the field creating system, by moving just so, loses energy to its waves. An obvious case is two neutron stars (“pulsars”) rotating around each other: as they move back and forth, because of said rotation, they create gravitational waves which carry energy away from their system, As this happens, their system loses energy, the two stars should spiral into each other, thus rotate ever faster, and this should be observable, and computable exactly. This, indeed, was thoroughly observed, so we knew the waves were there.

Einstein’s Gravitation Theory is a sleight of hand:

It affects to identify space(time) deformations with gravitation. The idea actually originated with the awesome German mathematician Bernard Riemann, who invented manifold theory in part to point out that any force could be viewed as convergence, or divergence of geodesics (this is an idea that physics has been milking ever since).

This, though, does not answer Newton’s deeper query about the nature of gravitation (see below). It’s a bit as if a creature asked:’What is an arm?’ And one answered:’An arm is what pushes things, and we can detect the deformation the arm brought.’

What is the discovery good for?

Well, first, one has to make sure. Science is about making 100% sure. The present experiment improved some technology far out what anything else required (but then it does open some possibilities!) Just an importantly, now we will be able to check the details of the Gravitation Theory (the big picture was not in doubt; the details are). Ultimately it may be possible to communicate through gravitational waves, etc (although right now the deformation are only of the size of the fraction of a nucleus, and we could detect them!)

Who were the originators of that idea? First Newton himself pointed out that his own theory of gravitation was grotesque (I am paraphrasing). Newton:

“that one body may act upon another at a distance thro’ a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it.”

There were actually two problems: that the action was instantaneous, and that it was at a distance without intermediaries. Newton paid attention to the second one, physics, in the last two centuries, solved the first (which was implicit in Newton’s observations).

As I mentioned in passing above, part of Newton’s worries were addressed by the invention of the concept of field. And then by the realization that fields carried energy away in waves. At that point, gravitational waves were automatic… Riemann’s introduction of manifolds, and how to conceptualize forces in them gave the manifestation of its nature to gravitation we presently have, a distortion of space metric (once again, time follows automatically).

It’s important to know who invented what, and contributed most. Because it unveils how ideas appear and evolve. Then, in turn, one can make theories of that, accelerating innovation (don’t forget there is a horse race between innovation and oblivion, on the scale of the entire biosphere!)

Curiously, this is all very useful; GPS with a precision of 30 centimeters has allowed to find out that baboon society is more democratic than ours, in fundamental ways. “General Relativistic” effects (the fact clocks run slow in a gravitational field) make crucial corrections to the GPS computations (otherwise GPS would be pretty useless). So this is not all academic. GPS will soon allow robotic agriculture… among other things.

We still don’t know what gravitation is. However, we can predict more things than Newton did… Even if he did not suspect they were there. This is just the beginning of what could be revealed, if our satanic impulses are kept in check.

Patrice Ayme’

Black Holes Are Not Black

January 31, 2014

NOR ARE EQUATIONS EVERYTHING.

Hawking’s claim to fame has been to show that, considering what we held to be true in physics in 1970, Black Holes are not really black. So it’s not surprising that he wants to advertise that fact.

Basically Quantum Field Theory assumes that there are (“virtual”) pairs of particle-antiparticle that come into existence, not long enough to be observed directly, but long enough to change (“renormalize”) the Field (whatever the “Field” is). These quantitative changes are observed, so these “virtual” pairs are assumed to exist.

Next to a Black Hole, one of the pair could fall in the Hole, and then the other could escape. Hence the Hole would radiate. That’s Hawking radiation (my way). There are lots of hidden hypotheses, though. That means, it could be wrong. Anyway, this is the largest Black Hole within two million light years:

Giant Black Hole Sagittarius A*, Core Of Milky Way

Giant Black Hole Sagittarius A*, Core Of Milky Way

Does it look dark to you?

As stuff falls into Black Hole (see the “threads”in the real picture above), immense energy is gathered by the fall (as in a hydroelectric plant), and then most of it is thrown back out as violent radiation. As you can see, the Black Hole is not black at all. Actually the giant Black Holes at the core of galaxies are periodically exploding with greater force than hyper novas. And that means that life in many volumes of the galaxies has not possibility to evolve in sophisticated forms as we did.

A whole cloud is expected to fall into our giant Sagittarius A*, within weeks).

Even in Black Hole theory itself could be wrong: it’s full of holes, I demonstrated grandly once to a prestigious audience at Stanford (Yau, Susskind, Penrose were in the audience among other celebrities).

I was looked at as cows watch a high speed train. In the meantime, though, Black Hole theory has become decidedly gray, and, decades later, many of these celebrities became famous for precisely what I talked about. First.

(That little feat did nothing for my career, indeed, as this opinion, that Black Holes were full of holes,  was viewed as thoroughly iconoclastic at the time).

The kind Matt Strassler, in his excellent blog, got all excited about Hawking’s latest pronouncements.

“Media absurdity has reached new levels of darkness with the announcementthat Stephen Hawking has a new theory in which black holes do not exist after all.

No, he doesn’t.

First, Hawking does not have a new theory… at least not one he’s presented. You can look at his paper here — two pages (pdf), a short commentary that he gave to experts in August 2013 and wrote up as a little document — and you can see it has no equations at all. That means it doesn’t qualify as a theory. “Theory”, in physics, means: a set of equations that can be used to make predictions for physical processes in a real or imaginary world. When we talk about Einstein’s theory of relativity, we’re talking about equations. Compare just the look and feel of Hawking’s recent note to Einstein’s 1905 paper on the theory of special relativity, or to Hawking’s most famous 1975 paper on black holes; you can easily see the difference without understanding the content of the papers.”

That was too good to let pass. I sent the following comment, which was published immediately:

Equations are just very precise sentences, nothing more, nothing less. They are not the Golden Calves.

Equations are crucial to distinguish two exquisitely close theories (as in BH physics… to be distinguished from BS physics).

However, not only equation fetishism, but exquisitely precise physics can itself become a trap, if the conceptual foundations of the theory are wrong. Some have said that equations are necessary to validate concepts. That, too, is wrong.

The best known example of precise, but erroneous theory is the geocentric theory. It became a prisoner of its precise mathematics (Fourier analysis in disguise). It took 19 centuries (Kepler) to make the math of heliocentrism precise enough to contradict geocentrism (but Kepler’s mentor, Tycho was handsomely financed because he had a hunch that ancient astronomers had cheated, especially about Mars).

Earlier, Buridan (1320 CE) had contradicted Aristotle, by discovering inertia (“Newton’s First Law”), and pointing out that it made heliocentrism as valid as geocentrism (but for the little problem of “scripture”…. the specialists of which put all of Buridan’s work at the “Index of Prohibited Books”, a century after his death… Although he was part of mandatory teaching in Cracow, where Copernic studied…. thanks to Hus, earlier burned to a crisp, alive, by the highest cardinals).

Ideas are more general than equations. Equations, like sentences, are written with concepts (root: becoming pregnant)… and pre-conceptions. “Shut up and calculate” goes only that far (my gaze is turning towards “superstrings”).

With the wrong concepts, it does matter how many equations one writes. (The same happens in other fields, such as economics!… or philosophy, or psychology!)

***

Anon (January 31, 2014) objected that:

“Equations are not just precise sentences, they are precise *quantitative* sentences. Equations are how you figure out if your concepts are right or wrong, by comparing them to empirical reality. 

Without equations, it doesn’t matter whether you think your concepts are “right” or “wrong”. With equations, then if the concepts are sufficiently wrong then it’s the equations that will show that. If the equations do not show that, then what is your basis for saying that the concept is wrong?…

It’s easy for you to sit here with all that history behind us and say that they should have just realized that ellipses were the right concept to begin with, but it’s only obvious to you because of the precise math that went into showing that this was indeed the right concept to describe reality. 

For things where we don’t already know the right answer, then equations are how you figure that out. Trying to declare which concept is “right” before working out the equations and seeing if it matches reality is bass-ackwards.”

Anon: I did not say ellipses were easy to figure out, nor that concepts can be dissociated from equations. Ellipses were not easy to figure out. Kepler tried something like 100 different curves. However, clearly Buridan knew that the heliocentric theory was right. Heliocentrism is no more about ellipses than Kepler’s theory was about the 1/d in gravitation.

Kepler mad a “30 year war on Mars” (as he put it). And he won. However, he believe erroneously, that gravity went as the inverse of the distance (instead of the inverse of the square of the distance).

A French astronomer got the 1/dd, and Newton exploited it. The point is: theories have degrees.

For example, Einstein Theory of Gravitation is a modest, pretty obvious extension of Newton’s theory of gravitation. (One that Newton partly called for.)

Geometry did without equations until Bolyai and Lobachevsky. Even then, the (re)”discovery” of Non Euclidean geometry was, fist of all, a philosophical phenomenon, the realization that geometry was a local computation, or modelization.

Riemann’s shattering ideas were in a paper (Habilitationsschrift)… With just one (sort of) equation. His paper was all about concepts, including some erroneously attributed to Einstein.

Speaking of Einstein (Matt started it, see above) his Special Relativity work of 1905 was just a neat repackaging of what was already known (that means Einstein 1905 strictly did not have ONE new equation).

Considering the history of the last 5,000 years of science, Descartes having invented algebraic geometry less than 4 centuries ago, to equate science and equations is unwise. And soon to be irrelevant, thanks to computing power. After all, equations are digital, and the universe is not.

An inkling of this: there is a field called combinatorial topology. General topology (which is… more general) does not rest on numbers. Ironically the Black Hole problem is all about Quantum Topology (we don’t know what that is, the crux of the problem).

It gets better than that: the essence of the Incompleteness Theorems of mathematical logic is precisely that any formal expression belongs to a countable world… And the universe does not. To which I have added the further twist that the available energy if finite (and that obviously impact expressions, hence computations).

Theory is hard, but it is the law. Of nature.

Patrice Ayme

Black Hole INEQUALITY

September 12, 2013

Krugman rightly denounces “toxic inequality“. One can say much more. Inequality has poisoned civilizations, before. Now it’s even poisoning the planet itself. And much worse will come if corrective measures are not applied.

Inequality is not just a political problem, it’s also a mathematical problem, with dynamics similar to the mathematics of Black Holes. If one falls too deep into it, there is no coming back. Contrarily to what obsolete philosophies said.

Black Hole Plutocracy?

Black Hole Plutocracy?

Here are the three ingredients of this mathematical situation:

a) the fascist instinct. The group pulls together as one mind once the group is under attack. That instinct is more than 50 million years old. It turned primate troops into effective superorganisms able to hold off predators, armed with war minds rather than dangerous bodies.

b) the plutocratic phenomenon. The exponentiation of capital plays a crucial role: the more capital one has, the easier it’s to get more, everything else being equivalent.

Rousseau observed: “Everywhere one looks, man is in chains“. Yet, total democracy is the natural state of man. Indeed, groups in nature are not under attack every day. Thus the fascist state (everybody goose-stepping behind the chief, and thinking, and feeling what the mind of the chief does) ought to be rare, as they ought to appear only in unnatural situations.
Hence, monarchies, tyrannies, aristocracies, theocracies, all types of plutocracies, are not natural states. So how come they keep on appearing? When the Roman Republic grew, it was continually at war, for centuries. Why? because it was fighting to death all sorts of plutocracies surrounding it. Not just Carthage and Hellenistic kingdoms.

When Rome was sacked by Gallic invaders in 387 BCE, the chiefs of that Celtic army were on a giant kleptocratic adventure; Rome struck them as a rich agricultural and herding area, ripe for plunder. Kleptocracy is also a form of plutocracy.

(After Rome paid a huge ransom, the Gallic invaders, were defeated and later annihilated, by the dictator Camillus.)

Plutocracies kept on appearing within civilizations, in the last 7,000 years, from an abuse of the fascist instinct and plutocratic phenomenon out of control. Both fascism and plutocracy are exponential phenomenon. Moreover, they are entangled: plutocrats discover readily enough that fascism is their friend, and that they can foster it with a state of perpetual war. A recent demonstration of this is the Bush’s Patriot Act. The instauration of this state of siege corresponds to rising inequality in the USA.

(In 1979 the income of the top 0.01% was 1.5% of all income in the USA; now it is 5.5%. This means that the wealth of the top .01% in income has been multiplied by a factor of 3.67. In the same period the income of the top 1% went from 9% of all income to 23% of all income. Hence the top 1% are 2.55 times richer. This is all paid by having the lower classes poorer than they used to be.)

The most successful societies were aware of the preceding pitfall, that deadly exponential of wealth and fascism. Thus the Roman Republic put an absolute limit on wealth. It’s no accident that the same Camillus above who defeated the Gallic plutocrats allowed the passage in 376 BCE of the Lex Licinia Sextia that put a limit on the public land (held by the army) that could be acquired by one individual (to a measly 1.3 square kilometer). There was cheating, though, by major plutocrats, and things came to a head under Tiberius Gracchus in 134 BCE. Basically, plutocracy was not lawful in the Republic, and the Gracchi tried to make it so. They failed, and the result was 2,000 years of plutocracy.

However, We The People, when ruled by the few, tend to revolt: see the American and French revolutions. Both succeeded, though, because their oppressors were too civilized. Lack of civilization has allowed the oppression to perdure more in the Orient, all the more as it is entangled there with theocracy. (In the West the break with theocracy occurred when the Roman army of the franks took control in 486 CE: it was a Pagan army!)

So indeed, to keep control, enters:
c) The Dark Side. The oligarchs, threatened by revolution, react by doing whatever it takes to stay in control. No brutality is high enough. See Syria. At that point, “plutocracy” takes its full meaning, as the rule of the worst, the rule of Pluto in all its splendor, the rule of the liar and the invisible, as the Greeks had it, and the astutely vicious as the French had it.

The USA is early in this general degeneracy. However, it is a massive society, and a model. Its faltering is thus of great consequence.

Faced with the infamy of the Dark Side Unchained, the people used to revolt. No tyranny ruled a Greek polis for more than three generations. then it was back to revolution, democracy, etc.

Polybius spoke of this cycling, 22 centuries ago, going through seven stages, as if the mathematics of psychohistory were rigorous. However, History does not always repeat itself. Polybius ought to have known this.

After the well named Macedonian fascist Antipater took control of Greece, Macedonian rule went on until the Roman legions defeated the Macedonian phalanx. Twice. So Greece did not self-liberate (although Greek armies helped the Romans). And indeed Polybius himself was taken hostage by the Romans (before he became friends with the .001% there!)

When plutocrats took control of the Roman republic, they were anxious to keep a republican façade. It would take more than eighteen centuries for constitutional democracy to return (in 1789 CE, simultaneously in France and the USA, the entangled revolutions; yes, no, Britain is NOT the “closest ally” of the USA).

Another example of non cyclicality is what happened to Egypt; after rabid men in black, the Christian monks ravaged Egypt around 400 CE, and burned the world’s largest library, Egypt, which had been a creator of civilization for 3,000 years, never recovered.

Passed a point, the Dark Side overwhelms all. This is what happened in Syria. Syria, fundamentally was just a very bloody hereditary plutocracy. Yet, offered the possibility of fleeing, and enjoying billions stashed away, as Tunisia’s ex-dictator Ben Ali does in Saudi Arabia, Assad chose to escalate the ferocity, well beyond what his father already did.

The same stickiness of horror happened during the Spanish Civil war, originally just a revolt by the Spanish army in the Canaries and Morocco (then leveraged by Hitler, Mussolini, Texaco, and countless American corporations).

After millions were killed, the return to normal in Spain was enforced by a decapitation of the fascist regime by assassination (when ETA executed admiral Carrero Blanco in Operation Ogro, the partial launch into orbit of the dictator), plus an incorporation in the European Union, under severe conditions (a similar scheme, a combination of force and negotiation, could be extended further around the Mediterranean to many a horrendous regime).

Nevertheless we have to keep in sight that the Dark Side, like Black Holes, cannot just suck everything up, but can be indefinitively stable. Whether we like it or not, and be it only because we want to survive, we are in a run-away tech society.

Hence the return of total plutocratic control now would be no cycle, but termination of civilization. Yet, plutocrats are solidly entrenched: just look at Putin, the ex-head of the Soviet KGB, now the hope of masses of naïve fools, just as his (spiritual) grandfather Stalin was in the 1930s.

Why would plutocracy be the end? Because, ultimately plutocracy reigns as the mind of one (or a few), and is no more intelligent than that one (or those few). Whereas democracy is the exact opposite: to exist it has to encompass millions of minds intelligently debating. (That’s why Obama, considering the sorry state of the democracy in the USA, has turned into the Professor In Chief, educating millions so that they can acquire enough intelligence to debate destiny in a half sentient way.)

And that mind of one will have to call to the Dark Side, darker than ever before, to master billions. There would be no limit to how dark things could get.

Plutocracy, entangled with fascism, is this world great Black Hole, and great temptation. See China rushing back to it under Xi. Plutocracy, entangled with fascism, will be resisted through massive force only. be it only intellectually massive force. As Obama just pointed out (in a particular case).

Many philosophies in the past, from Ancient India to the Mayas, to common men wising up, have argued for the Eternal Return of the Same, as Polybius did. This sort of metaphysics is in a way reassuring; do everything wrong, and it will turn out OK in the long run. However science has now debunked this completely: be it geological evolution, atmospheric evolution, biological evolution, or cosmological evolution, the only thing that does not change is change.

Change is your only chance, think accordingly.

***

Patrice Ayme

RELATIVITY + QUANTUM = CRAZY

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.

***

***

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