Archive for April 11th, 2019

Black Hole For Dummies: An Old Illuminating Story

April 11, 2019

Black Hole Seen At Core Of Galaxy Messier 87 

Black Holes were predicted at the end of the Eighteenth Century. I am not here campaigning for justice or historical precision, by giving Michell and Laplace the honor due to them. I am also defending physics, and promoting understanding. The guy with the bushy hairdo didn’t launch understanding of Black Holes. That means Black Hole theory arose for DEEPER reasons than in Einstein’s theory of gravitation. Deeper reasons is what science is all about.

Black Holes are indeed an effect of the most basic theory of gravity which was elaborated in the 1560-1800 CE period by Tycho, Kepler, Galileo, Bullialdus, Hookes, Newton, and finally Laplace. That basic theory of gravitation is the first order of the present theory of gravitation. The Black Hole effect, per se, has nothing to do with Jules Henri Poincaré’s Theory of Relativity (translated into German by Einstein).

In 1796 marquis Pierre-Simon de Laplace,mathematician, physicist, astronomer and philosopher (of course) rediscovered the idea of John Michell, a cleric and independent scholar. Michell has noticed that a body falling from far away onto something big enough, would exceed the speed of light. Thus, supposing that light would be made of particles, those particles would lose as much speed, trying to escape that big body, and thus, would fall back onto that body.  Laplace wrote:

Un astre lumineux, de la même densité que la Terre, et dont le diamètre serait 250 fois plus grand que le Soleil, ne permettrait, en vertu de son attraction, à aucun de ses rayons de parvenir jusqu’à nous. Il est dès lors possible que les plus grands corps lumineux de l’univers puissent, par cette cause, être invisibles.

(...because of this, it’s possible that the greatest luminous bodies of the universe would be invisible.)

Here I will follow Laplace’s proof.

Laplace on top. Don’t pay much attention to the text (not from me) which is a bit confusing

The Black Hole effect comes from the fact that the gravitational attraction is proportional upon the mass of an object, but also inversely proportional to the distance of said object, while the energy of an object necessary to escape the gravitation, is simply proportional to its mass. So, if too close, the gravitation will overwhelm any escape energy.  

Here is a bit more detailed reasoning  Supposing a particle of light has mass m, 1/2 mvv is its kinetic energy. If situated at x from the gravitational center, the energy to bring it to infinity is Gm/x. (G is aM, where a is some constant and M the central mass.)

Equating, we get 1/2 mvv = Gm/x

Thus, cancelling m, changing the constant: v^2= bM/x

But now, as early as the late 17C, the speed of light became known, by observing carefully Jupiter’s satellites.  It’s c, a constant. So we get: x= bM/cc.

Hence, if x is smaller than bM/cc, the potential gravitational energy Gm/x is TOO BIG to become 1/2 mcc.

Let’s put it in words only. Suppose light is a particle of mass m.  

OK, let me wait for the laughter of professional physicists to die off… Indeed, those simple souls will object that I neglected Relativity and its guru, Einstein. Well, my reply is that I know very well what I am doing, and they don’t. Meanwhile, here is the Black Hole:

Matter Falling into the Black Hole or running crazy orbits around it at relativistic speeds generate lots of heat, by collision and sheer acceleration (like a super enormously incredibly humongously giant circular particle accelerator, CERN on unimaginable steroids…). With 6.5 BILLION Solar Masses, this is one the largest Black Holes known.

OK, this reasoning was in Laplace. The incredibly famous Laplace, after whom Laplacians are named, made gravitation into a field theory, predicting thus gravitational waves (said waves were relativized by Jules Henri Poincaré… Modern Quantum Field Theory is all about manipulating Laplacians…

So is light a particle? Einstein said so (following Newton) [I have my doubts: SQPR changes the game!] Does light have mass? Definitely yes, according to E = mcc, a relation first demonstrated and taught by Jules Henri Poincaré in 1899 at the Sorbonne (the Einstein cult omits this little detail). There is a simple reasoning for that… simple once one knows Maxwell equations, or observe light momentum…

Here is the simplest proof of E = mcc. Light pushes, it has momentum. So light acts as if it had what’s called “inertial mass”. Now the “Equivalence Principle”  says that inertial mass = gravitational mass. Thus, light behaves as if it were endowed with a gravitational mass m, as used above.  

(The EP is truly an experimental observations, last checked excruciatingly a year ago, in a French satellite launched for that purpose)

So what’s the next problem in my hare brain derivation of Black Hole? None, really. The modern gravitation theory (aka General Relativity) integrates the LOCAL TIME theory of Lorentz-Jules Henri Poincaré into the gravitation theory of Newton. Local time runs slow in a gravitational field, and the deeper the gravitational well, the slower the time. Thus, if I wanted to ameliorate the hare brain Black Hole theory, I would have to add that….

The full Einstein gravitation theory simply says that: Ricci Tensor = Mass-Energy Tensor.

The Italian Ricci, starting in 1890, simplified the full Riemann Curvature tensor. It’s applied to the spacetime metric g. We see immediately that, the more mass-energy, the more curvature. In the limiti of small masses, this is Newton’s equation…

The preceding is very simple, thus ironclad.  

So here it is: physics is not that complicated.

***

Many scientists present science as more complicated than it is, so they appear to be great sorcerers or shamans. An example is the claim made by Darwin that man arose in East Africa (then a UK dominion). There was evidence for this, as the Brits digged in East Africa. When the Chinese digged in China, they begged to differ. Humans had originated in China too, they insisted.

Now another human species was just discovered, in the Philippines… ‘Homo luzonensis’ boasted an eclectic mix of features comparable to, but distinct from, different species of hominins. So this is another human species which lived 50,000 to 60,000 years ago. We now have five. It’s clearly a different species as they have three root teeth where we have just two.

Contemporary humans have genetic material from three human species: ancestral Sapiens, Neanderthals and Denisovans…

Science is both simple, and complex. Often the lack of simplicity, and the grandiloquent style in exposition, is just an attempt to hide ignorance, and leveraging said ignorance in awe for the perpetrators of pseudo-scientific obscurantism.  

Physicists are particularly culprit of this in recent decades. Consider titles such as: “The First Three Minutes”, “The Theory of Everything”, “A Universe Out Of Nothing”, “The God Particle”, etc… The more fatuous physicists became, the less the theory progressed. Now, right, they couldn’t probably have done better. Fortunately, experimental physics, and especially astronomy has kept on advancing, ever more spectacularly… cornering the fatuous ones, even when adorned with Nobel Prizes, into irrelevance…

Decades ago, I caused a scandal at an integrated physics-mathematics seminar at Stanford by exposing the shortcoming of Black Hole Theory… I was coming from the mathematical, hyper-logical side, unearthing all the little problems, which weren’t so little… Namely I claimed it didn’t take into account enough Quantum Theory. (Following my generously provided orientation, has brought a cottage industry of quantized “Black Holes” theory… Some not really black, just frozen…)

Many surprises await… Stay tuned…

Patrice Ayme