Kevin Wampler wrote:
> clipka wrote:
>> Kevin Wampler schrieb:
>>
>>> I think that this becomes problematic for measuring between points 
>>> which aren't connectible by a lightlike geodesic, but maybe there's 
>>> some clever way around that (although I don't see how).
>>
>> Well, if two points cannot be reached from one another - is there 
>> /any/ way to assign a distance to these points at all?
>>
>> So I think this is a non-issue.
> 
> In this context a lightlike geodesic refers to a path in spacetime which 
>  light would follow, and I meant to imply that defining the distance 
> between points which could only be connected by going *slower* than 
> light would also be hard to define uniformly.

In light of one of your other comments I think I now understand what 
point you're making: we can treat space-time distances in a common set 
of units by treating distances as times via the speed of light.  In 
which case I'd agree, and it fact the necessity for this clearly falls 
out of being able to have a single number represent the distance at all.

I still don't see how it's relevant for my initial comment that the 
space and time coordinates are treated differently though, since they 
are most definitely factor into the distance function in different ways. 
  Stated another way, swapping the time axis with a space axis is *not* 
in the symmetries of Minkowski spacetime, but swapping any of the space 
axes *is*, and this there's something "different" about the time axis. 
Otherwise why bother saying (3+1)D instead of just 4D?

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