Posts Tagged ‘Schwarzschild Radius’

Photon, Graviton, Contradiction

May 8, 2013

 Abstract: No need to dig very deep to find glaring contradictions in today’s physics. A discreet warning to those who act as if everything important is already understood.  I exhibit a few elementary reasonings where basic physics ominously implodes like an overstuffed star. Among other implosions, the “Planck Length” is derived, not from dimensional analysis, but through an outrageously simple analysis.

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EVEN THE BRIGHTEST CIVILIZATIONS CAN MAKE THE GROSSEST ERRORS:

 May 8, 1945, the 68th anniversary of the defeat of Nazi Germany. A big deal in France. Starting in 1934, the French republic armed itself to the teeth to crush fascism. It took a while, but it worked. At this point, fascism is only history in Europe (and don’t forget the collapse of the USSR).

 Keeping May 8 as a mandatory vacation day helps to remind the young generations that for the Republic to fight racial fascism cost, over 31 years, more than four million dead, in the French empire alone. (More than 100 million, 5% of the world’s population, died, all together. More if one counts the (“Spanish“) flu epidemics that hitched a hike on the military situation)

 Fascism was an erroneous system of thoughts and emotions. All the more striking as it struck mostly the country with the most intellectual hubris, namely the “German Reich“. The basic mental deviations inciting such errors are best studied in pure science, or aeronautics; as the  situations are clearer.

 When looking at history on the largest scale, what counts are optimal results. If one gets optimally to a disastrous result, it’s still disastrous. The Greeks had tremendous physics. At least, they built excellent ships. Roman cements were astounding; they made siphons on such a scale, aqueducts could cross valleys this way.  

 Yet, both Greek optics and Greek were full of correct, intricate considerations. Yet, both were not just false, but inside out, the exact opposite of the truth in the most fundamental message.

 How did it happen? The Greeks had overlooked the obvious. It should have been obvious that the Sun, being so much more enormous than the Earth, did not turn around it: that contradicted intuitive notion about centrifugal forces (say when launching a stone from a sling), and the fact the much smaller moon rotated around the Earth.

 In optics, simplistic experiments would have shown light came from the observed objects, not conversely.

 The Greeks had overlooked the obvious in physics. I will talk about something that maybe similar. Now. Keeping in mind that the Greeks overlooked the obvious so much that their democracy lost three wars to plutocracy in 250 years. Thereafter democracy, or even a republic was not to be seen in Greece again for nearly 2150 years. I claim that’s related. The lack of necessary criticism. It may show up in politics, but it trains best in physics.

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 SIMPLEST DERIVATION BLACK HOLE:

 Let’s assume light had a mass, m. (OK, modern physics assumes that light has no mass… otherwise modern physics would not be coherent. But that does not prove that light has, indeed, no mass!)

 If the mass of light were small enough, it would not be experimental detectable.

 Now let’s equate the energy of said mass to 1/2 mvv, the traditional kinetic energy. (Purists who know the Special Theory of Relativity will scream, as this is only the leading term in E = mcc.)

If the star is massive enough, it will bring light to a standstill, by pulling on it hard enough (forget about the geodesics of General relativity!)

 Now the potential gravitational energy of a mass m located at radius R in the gravitational field of a star of mass M is: GmM/R .

 Equating the kinetic energy with the gravitational potential energy:

 1/2 mvv = GmM/R. Putting v=c, the speed of light, eliminating the m’s, we get:

 R = 2 GM/cc

 This is the so-called Schwarschild Radius. When a star of mass is smaller than R, light can’t get out. That reasoning was made by the super mathematician and physicist Pierre Simon de Laplace in the Eighteenth Century. That is, during the Enlightenment. Laplace concluded that “les objets les plus massifs de l’univers ne peuvent etre vus (the most massive objects in the universe may not be seen). [To be entirely fair, an obscure Brit seems to have had the same idea too, at the time.]

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 GRAVITON BLACK HOLE, IN ANALOGY TO PHOTON BLACK HOLE:

 Laplace above made the hypothesis of what some physicists in 1929 came to call the “photon”, the particle of light. Meanwhile De Broglie rolled out his hypothesis that to each body a wave is associated. Although that does not prove the converse, namely that, to each wave a particle is associated, physicists take this for granted. 

 That there are gravitational waves, there is no doubt. Why? Because if one wiggles around a source of gravitation (say, a star), the direction of the incoming pull will vary, so a distant observer will be tugged back and forth. As the distance from the source augments, this will organize itself in nice waves.

 Backtracking conceptually, one gets particles of gravitation similar to particles of light, the gravitons. 

 Why not to play the game above?

 I made this smart remark one day to a Field Medalist specialist of General Relativity. He literally got enraged, fuming, repeating the offending sentence to himself, but unable to find a smart repartee. Indeed. There is none.

 If one plays the game above, the game Laplace first played, no graviton will be able to exit a sufficiently massive star, so the star, not only will not be seen, but not be felt. No wonder my friend got enraged.

 Could that really happen? Why not? Where would the energy go? if one insisted to keep the conservation of energy law? Well, what about coming out somewhere else as Dark Energy? 

 (Remember, we do not know, at all, about the dimensional structure of the universe; so energy could leak, through another dimension; a similar argument is central to some ultra modern theories of gravitation.)

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 PLANCK LENGTH MEANING; NO HIGH ENERGY GRAVITON:

 Another avenue of meditation is to observe that the Schwarschild Radius also exist for a graviton of mass m. It’s 2Gm/cc.

 The graviton’s own mass pulls the graviton itself towards itself. At high enough energy, the graviton becomes a contradiction onto itself.

 2G (hv/cc)/cc = 2G hv/cccc.  … Lv =c, v = c/L

Thus: L = square root (2G h/ccc)

 This “L” is the Planck Length. If the graviton’s matter wave  is confined within “L”, nothing will come out…

 It goes without saying that all of this ought to be taken with a grain of salt. First of all, the real structure of elementary particles is completely unknown. 

 String theory and M theory are attempts to guess said structure. However they assumed topological properties (such as compacity, locality, separability) that basic Quantum Theory violates enthusiastically. So they miss the essence conceptually, right from the start.

 Nevertheless, the reasonings above form the core of Quantum Gravity, the first order approximation. If that has no bearing on reality, neither will the rest.

 One of the main interests of the advancement of science is that it forces us to advance and refine what we mean by reason. In a world where the survival of the many will be increasingly in question, and depends essentially upon ever mightier reason, this is of the essence.

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Patrice Ayme