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→Gravity: new section
:Thanks, I appreciate it! Yet another distraction from those late-night problem sets. Is there a page where I can learn how to block correctly? --[[User:MarkGall|MarkGall]] 19:19, 6 October 2009 (EDT)
:Thanks, I appreciate it! Yet another distraction from those late-night problem sets. Is there a page where I can learn how to block correctly? --[[User:MarkGall|MarkGall]] 19:19, 6 October 2009 (EDT)
== Gravity ==
I finally got around to reading the gravity material in [[Talk:Essay:Quantifying_Openmindedness]],
and there are a lot of correct things, a few things that may miss the point slightly, and a few instances of people talking past each other unnecessarily.
First, you are absolutely right that the divergence theorem establishes an exponent of exactly 2 for divergenceless vector fields in flat Euclidean space. But there's no reason to require that the gravitational "field" be divergenceless. In fact, it could be argued that "dark energy" creates the nonzero divergence, if people used a pure classical gravitational "field", which they don't.
Remember that Newton's formula was a mathematically exact consequence of Kepler's laws (ellipses, focus, equal-area law, etc.), which were an exact geometrical formulation from Brahe's not-completely-exact observations. And that all this was done hundreds of years before the divergence theorem. Newton was exactly matching Kepler's laws, and therefore set the exponent to exactly 2. That was exactly the correct thing to do, in terms of the observations available at the time.
But I think the reasoning in terms of geometry and divergences and "the force spreading out over a greater area" isn't right. The notion of forces being inversely proportional to the square of the distance is something that comes from optics and electromagnetism. We know that light power must diminish exactly as the square of the distance because it contains energy, energy is conserved, and the vacuum is completely transparent. But there is no such requirement for the gravitational "field" of the Sun. It doesn't emit energy. If gravity worked differently, Kepler's geometrical laws might have been different, and Newton very well might have made the force inversely proportional to r<sup>3</sup>. He was fitting data; he knew nothing about divergences or the flatness of space.
Andy also makes the very valid point that a mathematical theory must obey physical observations, and, if it doesn't, that theory needs to be re-examined. So the question might well have been worded as:
*Do you think that is impossible that the correct behavior of gravity is that of Newtonian gravity, but with the gravitational force proportional to 1/r<sup>2.00000001</sup>, rather than 1/r<sup>2</sup>?
We could make other similar questions:
*Do you think that is impossible that the formula F = ma (or E = mc<sup>2</sup>, or E = hν, or any other famous formula) is not correct?
But formulating the gravity question in terms of an exponent of 2.00000001 may not be the right way to formulate the question. It is well known that alternative exponents don't work. This was tried around 1900, to explain the anomalous perihelion shift of Mercury, but it didn't work. There is no one exponent that works for both Mercury and Earth. General Relativity is the accepted better explanation, though it is known that there are problems with that -- quantum gravity, cosmological constant, dark energy, and a peculiar behavior of the Voyager spacecraft.
Now one ''could'' ask whether the person is openminded enough to question the "experts" that have analyzed the Mercury data, and understand General Relativity, and have crunched the numbers. After all, very few people have crunched the numbers; they depend on perceived "experts". So, in view of question 13, this may be a valid question to ask:
*Do you think it impossible that General Relativity is not correct?
But I doubt that many people who doubt General Relativity believe that going back to Newton's theory with a different exponent is the way to go. Unless, of course, they have crunched those numbers.
[[User:PatrickD|PatrickD]] 00:17, 7 October 2009 (EDT)