10-27-2004, 02:36 AM
Hi,
Newton's laws: simple partial differential equations in Euclidean space. Material that could be covered in a senior high school math class. Even the Lagrangian and Hamiltonian formulations can be worked out by college sophomores. All general cases have either been solved (i.e., the constants of the motion have been developed) or the impossibility of a general solution has been shown.
Special relativity: adds rotational invariance in Lorentz space. Primarily a description of electrodynamics, so no real comparison to Newton is possible (in effect, special relativity still occurs in a Newtonian space -- Euclidean and with action at a distance for gravity). Real understanding requires math at about a sophomore to junior college level. Many real situations are neither solved nor shown to be insolvable.
General relativity: takes one completely out of a Euclidean space. Requires a pretty good grasp of advanced geometry. Few schools have an undergraduate course in this field that even begins to really cover it. Few undergraduates have enough math sophistication to even realize their ignorance. A few special cases have been solved, but most cases are still beyond the ability of NOBEL level physicists.
"As simple as Newtons laws"? Possibly, in the sense that if one is ignorant of all of them, they are all the same.
--Pete
Ghostiger,Oct 25 2004, 08:55 PM Wrote:Both theories of relativity are as simple as Newtons laws, but they are harder grasp from the perspective our senses opperate in.
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Newton's laws: simple partial differential equations in Euclidean space. Material that could be covered in a senior high school math class. Even the Lagrangian and Hamiltonian formulations can be worked out by college sophomores. All general cases have either been solved (i.e., the constants of the motion have been developed) or the impossibility of a general solution has been shown.
Special relativity: adds rotational invariance in Lorentz space. Primarily a description of electrodynamics, so no real comparison to Newton is possible (in effect, special relativity still occurs in a Newtonian space -- Euclidean and with action at a distance for gravity). Real understanding requires math at about a sophomore to junior college level. Many real situations are neither solved nor shown to be insolvable.
General relativity: takes one completely out of a Euclidean space. Requires a pretty good grasp of advanced geometry. Few schools have an undergraduate course in this field that even begins to really cover it. Few undergraduates have enough math sophistication to even realize their ignorance. A few special cases have been solved, but most cases are still beyond the ability of NOBEL level physicists.
"As simple as Newtons laws"? Possibly, in the sense that if one is ignorant of all of them, they are all the same.
--Pete
How big was the aquarium in Noah's ark?