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:I also like your point about trusting experts in science. To some extent, this is necessary -- I'm not sure I have any personal reason to believe in the germ theory of disease, much less general relativity: I'm just taking someone's word for it. Obviously how much we should trust the experts on a particular subject depends on a lot of things. I bet some philosopher of science has thought hard about this -- I'd be interested to read the results! --[[User:MarkGall|MarkGall]] 00:33, 7 October 2009 (EDT) (hope I didn't forget to respond to anything!)
:I also like your point about trusting experts in science. To some extent, this is necessary -- I'm not sure I have any personal reason to believe in the germ theory of disease, much less general relativity: I'm just taking someone's word for it. Obviously how much we should trust the experts on a particular subject depends on a lot of things. I bet some philosopher of science has thought hard about this -- I'd be interested to read the results! --[[User:MarkGall|MarkGall]] 00:33, 7 October 2009 (EDT) (hope I didn't forget to respond to anything!)
:Fantastic job on [[complex number]], by the way.
:Fantastic job on [[complex number]], by the way.
I'm sorry for butting in here, but something caught my eye:
*"Do you think it impossible that General Relativity is not correct?"
As physicists, we rarely talk about theories in terms of "correct" or "incorrect," simply because there's more nuance to it than that. Theories are tools, so we tend to judge them not in terms of absolute right and wrong, but rather in terms of degrees of usefulness.
Consider the Newtonian formulation of gravity. Under certain conditions, like the motions of planetary bodies in the solar system farther from the sun than the Earth is, the Newton equations provide very accurate predictions. That is, if you put known values into the equations and get answers out, the answers will very closely match your observations. But under other conditions, like the motion of Mercury, the Newton equations give answers that don't match observations. Does that mean the equations are absolutely incorrect? Well, no. It just means that those equations aren't a ''complete'' formulation of gravitation. They're an approximation. Which is why today physicists typically refer to the "Newtonian approximation," rather than the Newtonian theory.
For hundreds of years, Newton's formulation of gravity was believed to be ''correct.'' Later, we made observations that showed Newton's formulation was an approximation, not a complete description of how bodies behave in gravitational fields. Does that mean that Newton's formulation is now ''incorrect?'' No, it just means we better understand the limits of Newton's approximation.
Which brings me back to my point: As of today, we have ''no'' understanding whatsoever of the limits of general relativity. So far, every observation we've made about the universe, from falling apples to the motions of the most distant galaxies, fit perfectly into general relativity. Does that mean general relativity is ''correct?'' Of course not! It just means that general relativity appears to be a ''very good'' approximation. If we later discover the limits of that approximation — say for example, observations of certain astronomical objects can't be explained within the math of general relativity — does that mean general relativity is ''incorrect?'' No, that would just mean we better understand the limits of the approximation.
If we want to talk about the "correctness" or "incorrectness" of a theory, we need to understand (in my opinion) that we're operating on a spectrum. At one end, we have "this theory makes no predictions at all that agree with observations." At the other, we have "every prediction this theory makes agrees with observations." Most theories in physics lie somewhere to the right of the middle of that spectrum: most predictions made by theory X are supported by observations, but not all of them. Only a few theories are on the far right edge of the spectrum, where ''no'' observations have yet been made that contradict the theory. These theories are, for obvious reasons, generally the youngest of all theories, simply because we're not motivated to come up with new theories until existing theories have been called into question by observation.
Right now, special and general relativity, quantum electrodynamics, quantum chromodynamics and the Standard Model are all on the far right edge of the spectrum. To date, none of those theories has been contradicted by experimental evidence. Of those, my personal opinion is that the Standard Model is the closest to being contradicted. Under that theory, given certain circumstances ''X'' there's a 95% confidence that we'll detect the Higgs. So far, we haven't detected the Higgs at that energy level, or some significantly higher energy levels. Does that mean the Higgs doesn't exist? No, it just means we failed to find it in places where the theory says it ''could'' have been found. So we keep looking. If it doesn't appear after a good, long search, then the Standard Model will need revising. In that case, will the Standard Model be declared "incorrect?" No, we won't just toss it in the bin and start over. We'll say "Okay, the Standard Model is incomplete, let's improve it."
Theories like the various quantum gravity and electrostrong proposals aren't anywhere on that spectrum yet, because we've yet to refine them to the point where they make unique testable predictions. A theory that doesn't predict anything that isn't predicted by another theory isn't really a theory at all; it doesn't go "out on a limb." Once quantum gravity and electrostrong theories are mature enough to go out on that limb, then we'll be able to judge whether their predictions match up with observations.
Part of the challenge, of course, is that theoretical physics has very nearly explained everything that's ever been observed. In order to come up with new, better theories, we need new observations, and for that we're going to need better telescopes and colliders. Right now, the theoreticians are a couple of steps ahead of the engineers, and believe me when I say it's a frustrating time to be a physicist.
Anyway, getting back to the point: Is it possible that general relativity is not ''complete?'' Of course it is. I'll even go one step further and say that it's ''practically guaranteed'' that general relativity is incomplete, just like Newton's theory before it was incomplete, and Galileo's theory before that was incomplete. But in order to call general relativity (or any other theory in physics) ''incorrect,'' it seems to me that we'd have to put it all the way at the end of that spectrum where ''none'' of the predictions made by the theory match up with observations. That's simply not true, so in that interpretation, no, it's not possible that general relativity is "not correct."
So if you want to think of it this way, the question can be answered truthfully with either a yes or no, depending on what "incorrect" means when we apply it to a theory in physics.
Science in general, and physics in particular, concerns itself with objective truth, the observed versus the unobserved, seen versus unseen. But a theory is not a statement of objective truth. It's just a tool for making predictions, and as such it's neither correct nor incorrect, but instead is described as being more useful or less useful.
Anyway, I suppose that's neither here nor there, but I saw this discussion here and felt like chiming in with my perspective.--[[User:KSorenson|KSorenson]] 17:17, 12 November 2009 (EST)
== Pictures, etc. ==
== Pictures, etc. ==