Divine Intervention and Dark Matters

© Fernando Caracena 2012

Using God as a hypotheses to Save the Equations


In quoting scientists regarding God, the meaning of what they say is sometimes mistaken. Scientists are people like everybody else, so that they are likely to have varying opinions about God. But sometimes their comments are taken to imply an atheistic or agnostic attitude, when something else may have been intended. There is for example, the famous response of Pierre Simon Laplace to Napoleon, who having received a set of Laplace's great work, “Le Mécanique Céleste, told him, “I see no mention of God in this work”, to which Laplace answered, "Sir, I have no need of that hypothesis." 1



The answer given to Napoleon by Laplace is in the same spirit as an answer given by P A M Dirac (who is famous for his great contributions to quantum theory, especially for his relativistic electron theory) to a friend visiting friend who had always know Dirac as a bachelor. When he received his friend in his house, a woman kept coming in and serving them. Finally the guest no longer being able to contain his curiosity asked, “Who is that woman who keeps coming in here?” Dirac replied, “That is Wigner's sister.” The story is that Dirac had recently married Wigner's sister, and he used that handle, “Wigner's sister” rather than “My wife” to describe her. There are several such stories about Dirac in Graham Farmelo's biography of him (published June 28, 2011), “The Strangest Man.”



The use of the term, “God,” by scientists in modern times is discussed in a British article in the Telegraph, “Has Stephen Hawking ended the God debate?” Newton, who came up with a mathematical, self consistent theory of gravity, mentioned God freely, and invoked Divine intervention as a way that discrepancies came up between his calculations of planetary orbits and observation. God was used to save the equations. When Newton came up with his famous law of gravity, he said, “I make no hypotheses.” His law of gravity was an observation of how gravity worked, couched in mathematical terms. Laplace, using only Newton's equation for gravity and equations of motion, was able to describe almost every detail of the motion of the planets in our solar system. There was one small glitch in the system that needed to be eliminated for it to be perfect: the precession of the perihelion of Mercury's orbit was off by 43 seconds of arc per century. For a couple of centuries, physicists struggled, trying to eliminate this glitch. In the 20th Century, this imperfection in the Newtonian scheme was finally eliminated by Albert Einstein's General Theory of Relativity.


What Laplace was really saying to Napoleon was, "Unlike Newton, I am able to use his mechanics and his law of gravity to be able to account for all planetary motions, without having to resort to Divine corrections of minor details."



Dark clouds over contemporary physics


Dark matter


The theory of gravity produced by relativity was still not perfect because of an effect discovered in the early 20th Century that conflicted not only with relativity, but with the Newtonian scheme. Since the gravity theory already accounted almost perfectly for the motion of the Solar System, astrophysicists pushed the scheme harder by applying it to the rotation of galaxies. Research on the statistical distribution of star types in our local galaxies, as well as the relationships between their absolute brightness and mass, gave scientists a basis for estimating the mass distributions in galaxies. Since the luminous matter is a collection of stars, and they represent most of the mass of planetary systems (the Sun represents 99.86% of the Solar System's total mass), it became possible to estimate the mass distributions of galaxies based on the distribution of their absolute brightness. Because of the Doppler effect, it also becomes possible to estimate the rotational velocity of stars in galaxies. From knowledge of the distribution of mass in a galaxy and how fast the stars are rotating, is was a small step to see if the force of gravity was sufficient to keep all the stars in orbit about the center of the galaxy. It turned out that there was not enough luminous matter in galaxies to hold them together by gravitational force by a wide margin outside the limits of error of all estimates. To make the dynamics of galaxies consistent with gravitational forcing, scientists suggested that galaxies formed around vast, lumpy clouds of dark matter, which interacts with ordinary matter predominantly through gravity, and either very weakly or not at all through any other mechanism.


Dark energy


Another paradox encountered in astronomy concerns the expansion of the universe. During the decade, 1920-30, the astronomer Edwin Hubble discovered that the whole universe is expanding at a rate that is proportional to the distance each portion of it is from the observer: v = H * r. Here v represents the recessional velocity of a part of the universe that is a distance r from us. The constant of proportionality is called Hubble's Constant (H= 70 km/sec/megaparsec, where 1 megaparsec= 3 million light years, one light year being the distance that light travels in one year). A question that would naturally follow from this observation and noting the action of the gravitational attraction of all the parts of the universe is “How long can the expansion of the universe last?” There should be a slowing down of the expansion of the universe with time. Will it collapse back on itself, or will it keep expanding forever? Compared with the time scale of the universe, about 10 billion years, our lifetime is but a flash. The entire history of our race, about 100, 000 years, would be insufficient to see a deceleration of Hubble expansion. However, we do have a cosmic time scale to which we can refer such questions


Because of the finiteness of the speed of light in a vacuum (3 x 108 meters/sec.), everything we see in the night sky is history. Light takes about 8 min 19 sec to reach us from the Sun, and about 1.3 sec to reach us from the moon. Light from Alpha Centuri, a virtual twin of our Sun, takes about 4 years to reach us. The Milky Way (our own galaxy) is between 100,000 and 120,000 light years across, depending on how you decide where the edge of it is. The farthest we look out with our telescopes, the farther back in time we see. Through gravitational lensing, space telescopes, and advances in optical and electronic imaging, we have arrived at the point to where we can look back almost to the time of the Big Bang, when our universe came in to existence. We are therefore able to answer the question of the acceleration of the expansion of the universe with time based on modern observations.


The answer is that the universe is accelerating its expansion. Faced with this fact, physicist have scrambled to find a reason for this acceleration. The physical explanation for this is a postulated, large-scale distribution of dark energy which causes this acceleration.


Faced with the necessity of some other explanation, it is revealing of modern attitudes that astrophysicists did not invoke Divine intervention, but rather postulated the existence of a dark matter that does not interact with ordinary matter by any force other that that of gravity.


95.4% of the Universe is Weird Stuff


As it stands today, astrophysicist propose that only 4.6 % of the universe is visible, and that there is a necessary 95.4% invisible stuff to be able to account for how all that visible stuff moves. Newton invoked small Divine interventions to account for minor discrepancies between his calculations of planetary motion and observations; but in modern times, scientists invoke huge effects from weird stuff to make their equations work, being very reluctant to use God as an explanation.


1Mathematicians and Other Oddities of Nature

Laplace, Pierre Simon: French mathematician who usually receives credit for proving the stability of the solar system. In my thesis I suggest that it was Lagrange who actually did so. Though I have not been able to demonstrate this yet, I think it was Laplace's writing of Celestial Mechanics, an enormous, five volume tome of celestial mechanics, that established him as the Prince of Celestial Mechanicians. When presented with a copy of some of the initial volumes, Napoleon is said to have remarked, "I see no mention of God in this work". Laplace is said to have replied, "Sir, I have no need of that hypothesis." (In an addition to the story, the tale was related to Lagrange, who added "Ah, but it is such a beautiful hypothesis; it explains a great many things!"

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