stbenge wrote:
> It's good to know that some people are taking the idea of a fourth 
> spatial dimension seriously. A lot of people argue that time is the 
> "true" 4th dimension, but that idea just doesn't sit well with me, even 
> though I don't have a lot of knowledge in this area.

I agree that it seems sort of like cheating to call time the fourth 
dimension, but there are some extremely good reasons for doing so. 
Foremost among these is that, due to special relativity, time and space 
can't be cleanly pulled apart like they can under a more classical model 
of physics.

In the "common sense" viewpoint we have a three-dimensional universe 
which is changing over time, so that at each time the entire 3d universe 
has some "state".  If you wanted to look at this is a four-dimensional 
space, you'd just stack these 3d universe-states together along a single 
other dimension representing time.  This gives you a 4d space, but under 
this view it's perfectly possible to the time dimension as somehow 
"fake".  The key point here, however, is that the common sense view is 
possible because these 3d "slices" of things happening at the same time 
are always parallel (and thus never intersect).

Under special relativity, unfortunately, this model is no longer the 
most natural.  The reason is that there is no longer a well-defined 
meaning to "things happening at the same time" as there was before. 
Instead, this meaning is dependent on your velocity (or rather the 
relative velocities of objects to you).

If we go back to the 4d model of the universe we'd built up for the 
common sense viewpoint, the interpretation now is that the *angle* of 
the 3d slice corresponding to everything "happening at the same time" 
changes with your velocity.  Thus it's not possible to pull the space 
apart into a bunch of well-defined 3d universe-states anymore, but 
instead you need to keep time in there are a proper fourth dimension.

It is worth nothing, however, that the time dimension is *not* identical 
to the space dimensions (one would hope not!) and distances are measured 
differently in time than in space.  Nevertheless this doesn't prevent it 
from being a proper dimension, it just means that the space has a 
different geometry than you'd get from treating time just like another 
spatial dimension.

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