Quote:
|
Originally Posted by KenWittlief
so what does that do to Einsteins equation? does it become invalid as light slows down, but the bonds become stronger?
one of the things that has always blown my mind is that Einsteins equation has no K factor - no constant to balance it.
Think about that for a while. The units of energy, mass, and distance and time (defining the speed of light) had all been defined before Einstein came up with his famous equation
BUT the units came out perfect - there is no correction (fudge) factor
E = MC^2
so what happens to it now?!
|
There
is a constant of proportionality; in this case, with these units, it's 1. But that's a deliberate consequence of the use of SI base units. Any combination of SI base units, by definition, when equated with a different (but dimensonally equivalent) combination of base units, automatically generates this result. But if we defined
E in British thermal units (BTU),
m in electron volts (eV; mass as energy is a consequence of the
E =
mc2 equation), and
c in astronomical units per fortnight (AU/fortnight), there is a distinctly non-unity constant of proportionality. So it's not as if scientists and mathematicians dreamed up these units, and one day, Einstein crunched the numbers and, magically, it worked. It was defined this way, because it's convenient.
And incidentally, if we're just talking about fundamental dimensions*, then of course it works—you wouldn't have much of a physical law, if the sides of the equation were dimensionally different.
So, basically, the equation doesn't change dimensions. Energy is defined fundamentally as [M][L]
2[T]
-2, and mass is [M]. And if the speed of light (in a vacuum, to be precise) changed, then any quantities derived from it would also change proportionally—but the fundamental unit [L][T]
-1 would remain the same. So the equation would still hold, with a different
c, which changes with time (and more than likely spawns a horde of differential equations describing some other previously-static quantities changing proportionally with time).
*Fundamental dimensions are units such as [L], [M] and [T] (length, mass and time, respectively), which form the basis for dimensional analysis.