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Talk:Theory of relativity (view source)
Revision as of 22:18, November 11, 2009
, 22:18, November 11, 2009no edit summary
:::It's sometimes tricky to say what exactly are the "assumptions" in a theory, but I thnik I agree with NgSmith on this point. One can derive the Lorentz transformations by assuming that the speed of light is the same in all reference frames. Einstein himself wrote a neat short piece "Simple Derivation of the Lorentz Transformation" that does this, even if it's not entirely rigorous. It's available online and quite lives up to its name. Others have done a more careful job of deriving the transformations. You're right that the Lorentz transformations do show we can't go above c, but I think it's more accurate to view this as a consequence of the assumption (c constant in all frames) underlying Lorentz, rather than viewing the Lorentz transformations themselves as the assumption. But I understand this is all up to debate and really comes down to how we want to formalize the theory. --[[User:MarkGall|MarkGall]] 15:40, 11 November 2009 (EST)
:::It's sometimes tricky to say what exactly are the "assumptions" in a theory, but I thnik I agree with NgSmith on this point. One can derive the Lorentz transformations by assuming that the speed of light is the same in all reference frames. Einstein himself wrote a neat short piece "Simple Derivation of the Lorentz Transformation" that does this, even if it's not entirely rigorous. It's available online and quite lives up to its name. Others have done a more careful job of deriving the transformations. You're right that the Lorentz transformations do show we can't go above c, but I think it's more accurate to view this as a consequence of the assumption (c constant in all frames) underlying Lorentz, rather than viewing the Lorentz transformations themselves as the assumption. But I understand this is all up to debate and really comes down to how we want to formalize the theory. --[[User:MarkGall|MarkGall]] 15:40, 11 November 2009 (EST)
:::Regarding the complexity of relativity, yes. Relativity is mathematically complex. While it's true that a lot of special relativity can be handled with basic algebra, the geometric interpretation depends on a good understanding of hyperbolic trigonometry, which is reasonably advanced math. General relativity, of course, is based on differential geometry and tensor calculus, which are highly advanced subjects in math. They are mathematically challenging theories, no question.
:::I'm not sure that's a good criticism, though. I'm open to the possibility that I'm wrong, of course, but the mere fact that there's a lot of math doesn't seem to be a strong leg to stand on. Math, after all, can be learned by anyone with patience.
:::(Just like posts with "much verbosity" can be read and understood by anyone with patience, but that's getting off the subject.)
:::On the topic of assumptions, I'm not sure what else to say that I didn't say above. Special relativity does not ''assume'' that ''v'' cannot equal or exceed ''c.'' It ''assumes'' that the measured speed of light in a vacuum is the same in all reference frames. It then goes on to ''predict'' that under acceleration ''v'' cannot reach ''c.'' I agree, that alone would be a very difficult prediction to test. Fortunately, special relativity also ''predicts'' that proper time in a moving reference frame runs slower than proper time at rest, in proportion to ''v,'' and that prediction is ''not'' difficult to test. We accelerate particles with known half-lives to high fractions of ''c'' and then observe how long it takes them to decay. After enough such tests, the relationship between proper time in the moving frame and proper time at rest can be measured with a high degree of statistical precision. (This is known as the Rossi-Hall experiment, and was first done in 1940.)
:::As for the other point about "absurd physical discontinuities" and the example given in the article — and believe me when I tell you I'm trying to say this as respectfully as I can — I'm afraid your math is simply flawed. The example given in the article is that if you take a massive particle, accelerate it to the limit c, ''and then also'' reduce its rest mass to the limit zero, you get a different momentum from that of a photon. At the risk of sounding pedantic, of course you do. Rest mass is not a variable in the equations of special relativity; it's not mathematically meaningful to take its value at a limit, because it's a constant. You could just as easily take the value of the gravitational constant ''G'' at the limit zero, but you wouldn't get physically meaningful results, because ''G'' does not vary. Saying that the equations break when you break the equations is, it seems to me, pretty tautological.--[[User:KSorenson|KSorenson]] 17:18, 11 November 2009 (EST)