ellis@spar.UUCP (Michael Ellis) (05/15/85)
From John Williams: > We just happen to exist in the inertial frame. I believe that inertial reference frames are free from the effects of gravitation/acceleration. In such frames, things float a lot. And they don't fall. Or am I confused? >But I think the main point is that time and space are not >interchangeable. They have a relationship. You can't simply >transform one to the other. Your statements could easily be mistaken. For instance, I believe I can transform time and space between any inertial reference frames that shared the same origin at time t=T=0 as below: ============================================================================= X + vT T + vX --------- x = ------- t = ------ [ B = \/ 1 - v*v ] where: B B x,t and X,T are space and time coordinates in two coordinate systems that are separating at speed v along the x (X) axes, where distance units are c = speed of light. The other two spatial coordinates remain unchanged. ============================================================================= The above transformation DOES interchange time and space, sort of, using a sloppy sort of language. Such language is not really much more accurate when applied to rotations, which these formulae resemble. (Measuring time in imaginary units yields formulae that are formally identical to rotations) These are, of course, the Lorentz transforms. And they are simple transforms. Thus, I can `simply transform from one to the other'. QED. Such moronic argument as the above may occasionally result from the unclear language sometimes used in these strange relativity debates. So we have some who say: Time is remarkably similar to a spatial dimension. The two are formally identical when time is measured in imaginary `units'. Any qualitative difference results from this imaginary multiplier. Those opposed are just saying: Time is essentially different, because it does not transform exactly as a normal spatial dimension. The spatial dimensions are thoroughly confusable and lack unique directions, whereas the direction of time is unmistakable; furthermore, in special relativity, all transforms between inertial reference frames will have some essential agreement about where the future and past belong. You could argue this forever, and all be correct. BTW, I believe that in general relativity, the `ict' notation for time tends to be disfavored because it only messes things up. On the other hand, there are those weird time/space role switches that occur near black holes as mentioned by Kenn Barry. >The inertial frame isolates time as the mobile dimension. >All things tend to seek the same inertial frame. It is this >frame that determines the direction of time. Several comments: First, as mentioned by Kenn Barry, near black holes, space can also take on the `one way, no stopping' MOBILE character of time. Second, pick the frames of any two objects that are floating off in opposite directions in space. In what way are they seeking the same reference frame? Finally, its not clear that one can always isolate a single `direction of time'. For instance, plot the worldlines of two objects near an event horizon of a black hole -- one within that is destined to shortly encounter the singularity, and one without that will go sailing out away from the black hole forever. Such objects cannot even be placed within the same coordinate system; they certainly cannot agree on a direction of time, and they will never seek the same inertial frame. I think these might even be in accordance accepted theory. But maybe I'm wrong... SMASH CAUSALITY!! -michael