>I disagree with Keith and Moorad, and agree with George here. It is true
>that Lorentz signature effects give the time-like direction in spacetime a
>different geometric character than the space-like directions. But this is
>no reason to consider the time-like direction as having a different
>engineering dimension than the space-like directions, and to measure them in
>different units. Just which direction in spacetime constitutes the
>time-like direction depends on the particular Lorentz frame used.
>Different frames have their respective time direction pointing in somewhat
>different directions. But different frames still refer to the *same*
>underlying Minkowski spacetime manifold with only different coordinate
>labels on the spacetime points (events). Since the time-direction in one
>frame is a mixture of time and space directions in another frame it is
>cumbersome to consider the time dimension as having a different
>(engineering) dimension than the spatial ones -- even though it contributes
>to the metric with an opposite sign.
>
>Also it is possible to make an analytic continuation of the time direction
>by the Wick rotation t --> i*t in the complex plane which then gives
>spacetime a purely Euclidean character (but with complex dimensions). If a
>quantity is represented by a complex number we usually do not represent its
>imaginary part with a different engineering dimension than its real part.
>For instance, consider the concept of an electrical impedence. Both the
>real and imaginary parts have the dimension of J/(s*A^2) = 'ohm' even
>though the imaginary reactance part behaves differently mathematically,
>i.e. algebraically, than the real resistance part in calculations.
>
>Also, because time has an arrow whereas space does not is not a valid
>reason to give time-like spacetime intervals a different engineering
>dimension than space-like spacetime intervals. The fact that time has an
>arrow does not come from relativity. It comes from thermodynamics (and
>also from the breakdown of CP invariance in certain elementary particle
>interactions). These arrows have nothing to do with the local geometric
>structure of spacetime. In addition, it is conceivable and some
>observations suggest that it may be possible that space *does* have an arrow
>as well. (See Nodland & Ralston, Phys. Rev. Lett., Apr. 21, 1997, "Is the
>Universe Birefringent?".) The existence or absence of an arrow for
>some directions of spacetime is a issue separate from whether or not
>the value of the speed limit of causation c = 299792458 m/s acts solely in
>the equations of physics as a unit conversion factor. It converts
>spacetime intervals denominated in 'temporal' units to spacetime intervals
>denominated in 'spatial' units, and is analogous to the unit conversion
>factor in thermodynamics of 4.184 J/cal which converts between
>energy changes denominated in 'heat' units and energy changes denominated
>in 'work' units.
>David Bowman
>dbowman@gtc.georgetown.ky.us
>
>P.S. I'd like to here Don Page's thoughts on this matter of whether or not
>'c' is a conversion factor analogous to the relationship between joules and
>calories.
I think I made it very clear in my previous posts that the constancy of the
speed of light is a fundamental feature of nature and has nothing to do with
what units we use in physics. The relation between calorie and joule is
precisely the same as the relation between inch and centimeter. It was a
historically man made problem which came about when people used two
different units to describe the same thing, energy and length, respectively.
No more no less. For the same reason, Planck's E = h f and de Broglie's p =
h/ lambda are fundamental features of nature (or our understanding of nature
if you like) and not mere conversion factors. These findings of Planck and
de Broglie indicate the fundamental particle/wave duality of nature (or our
understanding of nature if you like).
Moorad