Posted on 01/06/2005 5:29:32 PM PST by PatrickHenry
I just figured it out. Here is a sketch. In Minkowski version of relativity, there are three (real) space dimensions and one imaginary time dimension, so one gets a point as (x,y,z,it) where i*i=-1.
Any-time like dimension must have an imaginary property like this else it would be space-like. If there's another time like dimension, it cannot have "i" as a tag (else it would have been the one above) but it could have a "j" with j*j=-1 and we get (x,y,z,it,js). The time coordinates are t and s.
The metric (or square fo the distance between points) is just ((x1,y1,z1,it1,js1)-(x2,y2,z3,it2,jt2))**2 which has terms ijt1t2. Well, ij cannot be real, cannot be "i" and cannot be "j" so it must be something else: "k." This leads to the relations ij=k, i**2=j**2=k**2=-1 and a point must be (x,y,z,it,js,kr) which does work out algebraically. But there are now 3 time-like dimensions and the whole system doesn't look like relativity theory. That's ok.
The journey is its own reward.But it'd feel good to get out of the rain.Unless you're crossing a desert on a horse with no name.
Unless you're crossing a desert on a horse with no name.
But it'd feel good to get out of the rain.
And touch the green, green grass of home.
"If you don't have a clear idea of clocks ticking away, the idea of a direction of time - a "before" and "after" - doesn't have any clear meaning." -Martin Rees
My pet theory is that time does not exist. The concept of time was "invented" by humans in an attempt to understand the universe, including physical travel, birth, life, and death. Maybe the past, the present and the future are in different dimensions of space all at once, at the same "time".
Mmmm... Quaternions!
Interesting. I understand the math, although I have no idea how to envision extra time dimensions. (I'm fine with extra space dimensions, e.g. the oversphere in Flatland). Oh well, guess I need a few dozen more courses on theoretical physics.
Actually, my post is partially in error. The extra (third) time dimension doesn not arise from the metric in flat space. It arised from dynamics where one must take velocities. A term like dx/dt is ok as is dx/d(it) which is idx/dt but idt1/jdt2 causes problems.
This does lead to quaternions (1840s, Hamilton) and later to Clifford algebras.
I'm not sure what the physical implications of extra time would be. I guess, one still has time-like and space-like distances (things can only be linked causally if they have time-like separations.)
You are one "Democrap" with a wealth of useful BS! Thanks!
You better hope the "Latin Scholar" Centurion from "The Life of Brian" doesn't catch up with you. You'll have to write the corrected version on the side of the Roman garrison's HQ building a hundred times, or lose a sensitive portion of your anatomy.
;-)
Well, you are right, we certainly are good for a laugh.
I have heard it suggested that Time is just duration of conciousness in the mind of man. Not one of the stars cares or knows about this mythical creature, TIME.
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