It seems the concept of Time as a dimension, analogous to space, is a

limiting, even misleading, factor in physics today. Time is a conceptual

frame of reference convenient for comparing the rate of change of two

objects, trivially:

Rate of delta_A delta_A/delta_t

--------------- = ---------------

Rate of delta_B delta_B/delta_t

That's all Time is, really -- a frame of reference, another way of

stating change or cycles. Look at your wrist watch. It's much easier to

talk in terms of "seconds" than in terms of number of quartz vibrations.

"Hey, Fred, meet me for supper after 2,098,234,555 vibrations."

Prior to 1956, one second was defined as the fraction 1/86,400 of the

mean solar day. From 1956 to 1967, it was the ephemeris second, defined

as the fraction 1/31556925.9747 of the tropical year at 00h 00m 00s 31

December 1899. The second is currently defined as the duration of

9,192,631,770 periods of the radiation corresponding to the transition

between the two hyperfine levels of the ground state of the cesium-133

atom.

The above relation can be very *inconveniently* written as:

Rate of delta_A delta_A/(9,192,631,770 periods of ... cesium-133)

--------------- = -------------------------------------------------

Rate of delta_B delta_B/(9,192,631,770 periods of ... cesium-133)

It should be obvious that *any* constant frame of reference will do:

Rate of delta_A delta_A/delta_C

--------------- = ---------------

Rate of delta_B delta_B/delta_C

By now you're probably screaming at me to make the obvious

simplification:

Rate of delta_A delta_A

--------------- = -------

Rate of delta_B delta_B

And this works great, locally, but it's darned inconvenient to work

with mathematically on a larger scale.

So what's the problem with treating Time as a dimension? No problem, so

long as it's recognized for the invention of convenience that it is. But

this paradigm carries with it some heavy baggage:

- Time travel, which must be possible, given the dimensionality of Time.

The Past is "out there," with all the paradoxes this poses.

- Creation of many an ill-conceived Star Trek episode.

Well, I'll get off my soapbox now, before the tomatoes start flying...

-=Lord Sludge=-