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mkline55
2012-Oct-02, 02:13 PM
I look around at all the theories and the mathemetics used to describe the universe, and am reminded of the complex mathematics used to describe a geocentric universe. The math was very complex, but it worked. By using spirals, astronomers could predict with fair accuracy the positions of the planets and constellations, seasonal changes, even the occurrences of eclipses. I believe Galileo (and likely others) built on Copernicus' theories and proposed a heliocentric model that made the mathemetics simpler. Unfortunately, Galileo assumed circular orbits, so his predictions were no better than those offered by the geocentric model. Wasn't it Newton who proposed gravitational forces ruled, and eliptical orbits existed?

We've come a long way since that time, and I'm certainly no Galileo or Newton, not even a pretty good mathemetician, but the complex math used today just has that feel of being overtaxed. I'm not suggesting the math is wrong. Instead, is there some other frame of reference that would make the math simpler? And, before someone asks, no, I don't have a suggested reference frame, just a curious mind.

grapes
2012-Oct-02, 02:29 PM
Wasn't it Newton who proposed gravitational forces ruled, and eliptical orbits existed?
It was Kepler that came up with elliptical orbits, but yeah Newton showed that a gravitational force would account for elliptical orbits.


We've come a long way since that time, and I'm certainly no Galileo or Newton, not even a pretty good mathemetician, but the complex math used today just has that feel of being overtaxed. I'm not suggesting the math is wrong. Instead, is there some other frame of reference that would make the math simpler? And, before someone asks, no, I don't have a suggested reference frame, just a curious mind.Weird, it has a overly-simplified feel to me... :)

Shaula
2012-Oct-02, 02:30 PM
The complexity comes in because these days the models do much more than they did before. They cover extreme situations, marry up cosmology and particle physics, work on scales unimaginable to people a few centuries ago. When you get down to it there are two main theories, GR And the Standard Model. GR has complex maths but it is hard to imagine a simple set of premises than those that it has. It might be an idea or read up on where the Relativity theories came from. They have a core set of amazingly basic postulates and everything is derived from there. They are one of those models which start from simplicity and end up complex. The Standard model is pretty complex too, being based on quantum fields. It has a more complex set of underlying rules but they are very precise for many predictions.

As to your question: maybe. Maybe like String theory we will find a simpler overarching theory that explains it all. None is in sight yet. Have a read on M-theory and how the concept of dualities linked up the 5 existing String Theories for one way it might happen. But who knows! I certainly would never predict the 'end of science' or that we have an ultimate theory.

Hornblower
2012-Oct-04, 02:34 PM
I look around at all the theories and the mathemetics used to describe the universe, and am reminded of the complex mathematics used to describe a geocentric universe. The math was very complex, but it worked. By using spirals, astronomers could predict with fair accuracy the positions of the planets and constellations, seasonal changes, even the occurrences of eclipses. I believe Galileo (and likely others) built on Copernicus' theories and proposed a heliocentric model that made the mathemetics simpler. Unfortunately, Galileo assumed circular orbits, so his predictions were no better than those offered by the geocentric model. Wasn't it Newton who proposed gravitational forces ruled, and eliptical orbits existed?
For a purely kinematic exercise, a heliocentric model is simpler in the Occam's Razor sense, with a single annual term for the Earth's orbital motion replacing separate epicycles for each planet's motion in a geocentric model. For any given planet, the two models are equivalent vector resultants and give the same result if the same mathematical assumptions are made for each one.

As I understand it, Ptolemy assumed eccentric circular orbits with variable angular velocities, combined with annual epicycles. For the low eccentricities, these circles were pretty good approximations of the ellipses later found by Kepler. Copernicus proposed the heliocentric model for philosophical Occam's Razor reasons, not because of accuracy issues. He reverted to Aristotle's ideal of constant-velocity circular terms, and as a result he needed some fudge terms to get positional accuracy as good as Ptolemy's. For any given planet his model was sometimes more messy than Ptolemy's model. Kepler cleaned up the Copernican rough draft with his ellipses and the three laws describing them. This model could be transformed into a geocentric model with the orbits and epicycles being Keplerian ellipses rather than circles, with no loss of accuracy.

As far as I can tell, Galileo used his discovery of Jupiter's moons as an additional argument in favor of Copernicus, but did not do any real quantitative work on the problem. Most of his research in physics was involved with Earthbound problems. It was Newton's simple gravitational theory that provided a dynamic argument that clinched the heliocentric model.




We've come a long way since that time, and I'm certainly no Galileo or Newton, not even a pretty good mathemetician, but the complex math used today just has that feel of being overtaxed. I'm not suggesting the math is wrong. Instead, is there some other frame of reference that would make the math simpler? And, before someone asks, no, I don't have a suggested reference frame, just a curious mind.

The complex math of modern physics deals with relativistic and quantum-mechanical issues that Newton and his predecessors could not have anticipated, because of the limitations of their observational capabilities at the time.

Reference: Toulmin and Goodfield, The Fabric of the Heavens, 1960