Speed of Light Barrier

I've followed this thread up to the current post... I'm studying special relativity with a physics buddy of mine, who's putting together some ConcepTests for Special Relativity (as well as the basics of quantum). It's cool stuff he's doing, I'm excited about it.Anyway, I still have this nagging question that I can't resolve, given this picture. JustinC reiterated the same question I think, after reading your explanation here. I'll post two versions of the question; the longer version is more correct, but it's good to try and summarize what you want to say in just a few words. For evidence of that, please review the mess I've made of these last two paragraphs

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Short version:
Why is the length of the vector equal to (or related) to 3X10^8m/s?Long version:
In your explanation, light travels such that the vector has no time component. If that's true, then I don't understand why light has the actual velocity that we measure it to be. Why couldn't that velocity be 3m/s? Why not 3X10^88m/s? How does the actual measured velocity of the speed of light relate to the fact that light has no time component? In this view, does it fall out directly from the hyperbolic relationship between spatial coordinates and time coordinates? I don't think that would answer it either... I just can't understand why this vector would have one length, as opposed to any other.

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OK, thanks again for all your willingness to entertain questions. I'm really enjoying your posts. So you have my heartiest "Welcome to EVCForum!" BenThis message has been edited by Ben, Saturday, 2005/07/16 09:57 AM

Son Goku,Thanks for your reply. I find your answer to be insightful and I see how you're thinking about my question. But my intended question requires a bit of a different answer; I think cavediver sees that, and has addressed my question as I intended it to be read. Let me try and restate it. Your argument is that we could have defined different units, in order to get "the speed of light" to be any number we want, and of course that's right.But if measure in meters and seconds, we always get the speed of light to be 3x10^8m/s. This has to do with the relationship between space and time. My question is, why do we find THIS relationship between space and time? What is it that makes us measure the speed of light to be 3x10^8m/s, and not 1m/s. Because, although it's possible to measure the speed of light as 1(length unit "A")/(time unit "B"), it's impossible (theoretically) or never-been-done (experimentally) to measure the speed of light, in m/s, as anything but 3x10^8m/s.Something has fixed the relationship between space and time to be very specific, and I want to know what is fixing it that way.Bah, that didn't help at all I think. Well, if not, then I'll drop it; I'm satisfied with cavediver's previous answer (thanks for that).Ben

Thanks Percy. Try Message 8 or Message 5; they both mention Greene.I think I get the idea of a space/time vector of static length which rotates (knowing, and possibly understanding the fudging cavediver mentioned about hyperbolic sin/cos).What I don't get is why the length of that vector is the length that it is. Or another way to restate the same question (I think) is, why does OUR space-time necessitate a "c" of 3x10^8m/s in order for
the space-time interval to be invariant? Why doesn't "c" just have some other arbitrary value? All that means is that space and time need to be mixed in different proportions in order to get an invariant. Why did we get THESE proportions of space and time which mix together to give us an invariant?I doubt I'm saying this correctly. I studied space/time invariance 8 years ago, and refreshed it in 3 minutes on the web.BenEdited to fix message link formattingThis message has been edited by Ben, Tuesday, 2005/07/19 07:53 AM