X-Message-Number: 19231 From: "Technotranscendence" <> References: <> Subject: Re: spacetime Date: Sat, 8 Jun 2002 08:14:49 -0400 On Fri, 7 Jun 2002 10:19:15 EDT Robert Ettinger wrote: > One can use (any) spatial coordinates to designate two locations, and from > these derive an invariant distance. One can also incorporate time > coordinates, and using these and the space coordinates together one can > derive an invariant "interval" between two events. A simple formula gives the > relationship, using the same "units" of "length" for space and for time. The invariant distance assumes the same reference frame. The point between Einstein's "interval" was that spatial distance (and temporal duration) is (are) _not_ invariant across inertial references frames, but that interval was. > This is enlightening in some ways and certainly useful, but it is also > confusing--and I suspect the experts are confused sometimes in some ways. The > problem is partly analogous to the use of the same "dimensions" for work and > for torque, or for torque and the work done when a torque acts through an > angular displacement. We need a better system. I don't know if, for that reson, this means "[w]e need a better system." IIRC, one could play the relativity equations the other -- putting interval in units of time -- which I've actually seen done in some places. (I don't recall where.) The spatial distance would just drop out. E.g., IIRC, with STR: dS^2 = dx^2 - c^2*dt^2 (or was it dt^2 - c^2*dx^2; anyway, it's the c*t that yields units in distance) we could just divide through by c^2 and get: dR^2 = dx^2/c^2 - dt^2 (it's the x/c that yields units in time) where the units for R would be time. (And R = S/c, of course.) Of course, this doesn't solve your confusion problem. We've just flip-flopped the dimensions from spatial to temporal. Cheers! Dan http://uweb.superlink.net/neptune/ For a list of my works see: http://uweb.superlink.net/neptune/MyWorksBySubject.html Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=19231