As I know I’ve said many times around here before, c is just a conversion factor. We multiply lengths in miles by 5280 to get lengths in feet. We multiply lengths in seconds by c to get lengths in meters. That’s why.
Yes, but the difference in your analogy is that c is a fundamental value in nature, whereas measures such as a mile or a foot are dependant on the speed at which you can march your troops or the shoe size of your current king. We convert c in to units that are more ordinary to us, such as miles/hour, meters/second, or furlongs/fortnight (what?), but like pi in trigonometry and natural mathematics, c represents a specific and invariant value regardless of what units you use to state it.
Fundamentally, we don’t know why c ~ 2=3.0x10[sup]8[/sup] m/s, any more than we know “why” Planck’s Constant, the Gravitational Constant, the permeability of vacuum, mass of an electron, et cetera. They just…are. The fact that they are what they are, and that even moderate variations upon them would result in physical laws that are so different from what we experience that normal gravitational, molecular, and even atomic structures would not exist causes some to argue the case for some deliberate selection by a supernatural intelligent. This is rather an upside-down argument–it assumes that we have to exist in order to experience the universe rather than we being a happy but incidental result of a physics that permits stable, self-replicating structures–but it does appeal to one’s desire for a purpose, a reason for existance, and of course, our fear of the Coming of the Great White Hankerchief.
Stranger
Okay, maybe I should be a little clearer. We multiply by about 3e8 to convert from measurements of lengths in seconds to measurements in lengths in meters. We know exactly why that’s the value of c in systems of units using meters and seconds for the same reason we know the conversion factor from miles to feet: it’s an artifact of the units we’ve picked. In fact, usually physicists nowadays will use a system of units in which c takes the value 1.
The whole reason it seems mysterious is that for the longest time we’ve been laboring under the collective delusion that there is any difference between length and time.
Or, as Douglas Adams put it:
What’s cool about relativity (and particle physics, and the hopeful eventuality that someone will come along with a theory that combines both of them) is how it reduces everything to a few fundamental constants. What’s frustrating about physics is how those constants don’t seem to mean anything in particular.
But then, if we knew both The Question and The Answer…Ka-flooie!
Okay, I’ll cut it out with the Hitchhiker’s references now. Off to bed.
Stranger