Tau of SR

There seems to be a concept that one component of a coordinate has
significance. In particular, that the t in x,y,z,t has the meaning of a
clock reading. The clock reading I call the biological time. That's the
rate of aging, the clock speed, the lifetime of a muon, etc. My
understanding is that that time is the Tau = sqrt(dt^2 - dx^2 - dy^2 -
dz^2). That time value does not change with any change in velocity (or
"reference frame").

In an observers own reference frame his clock follows the Tau. dx = dy =dz
= 0, so Tau == t.

When one changes velocity, the coordinate system is basically rotated. The
individual coordinates have little meaning, including t. Compare a 4-space
rotation with a 3-space rotation. Consider looking at the eastern night
sky. Assign every star an x,y,z coordinate relative to your viewing angle.
Now rotate your head to look at the western sky. Perform the rotation of
the coordinate system that we all feel comfortable about. How did those x
values change so drastically. Boy, there's motion much faster than the
speed of light. NOT.

Isn't it the same with the t component of the 4-vectors? The component has
little to no meaning in itself. But taken as a whole, it does. With the
x,y,z rotation, all the distances between objects remain consistent. With
the x,y,z,t rotations (velocity changes), all the Taus between events remain
consistent.

Ned Phipps


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