meter in time
quick idea. totally unrelated to the other half-finished post i have for this, but i'm in the middle of the common app essay when i came up w/ this idea (yes the essay is related). will jot it down before i forget.
i've mentioned the idea of a meter in time to a few ppl, as a semi-joke, but i think i can elaborate now:
current definition of a meter: k m/s, where k=299 792 458, i.e. the distance traveled by a laser in 1/k seconds
time, according to relativity, is just another dimension, and since there can be space-time diagrams where time replaces one of the space dimensions, a meter in time may be defined to coincide w/ a meter in the other dimensions
if time is to be in meters, speed is unitless, so let's make name a time/space ratio for stuff w/ the new concept
a stationary does not travel in space, only in time, so its time/space ratio is undefined
define light at a time/space ratio of 0
so if light travels k meters in space for every 1 second that a stationary object travels in time, a meter in time is equal to 1/k second,
so if an object travels w/ a time/space ratio of 2, it is traveling 2 meters in time (2/k sec) for every meter it travels in space, so its conventional speed is...
wait shit i'm stuck on reference frame changes... for light i had speed relative to stationary observer and not itself...
shit shit shit...
back to college essay, more on this later.
i've mentioned the idea of a meter in time to a few ppl, as a semi-joke, but i think i can elaborate now:
current definition of a meter: k m/s, where k=299 792 458, i.e. the distance traveled by a laser in 1/k seconds
time, according to relativity, is just another dimension, and since there can be space-time diagrams where time replaces one of the space dimensions, a meter in time may be defined to coincide w/ a meter in the other dimensions
if time is to be in meters, speed is unitless, so let's make name a time/space ratio for stuff w/ the new concept
a stationary does not travel in space, only in time, so its time/space ratio is undefined
define light at a time/space ratio of 0
so if light travels k meters in space for every 1 second that a stationary object travels in time, a meter in time is equal to 1/k second,
so if an object travels w/ a time/space ratio of 2, it is traveling 2 meters in time (2/k sec) for every meter it travels in space, so its conventional speed is...
wait shit i'm stuck on reference frame changes... for light i had speed relative to stationary observer and not itself...
shit shit shit...
back to college essay, more on this later.