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.

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clipka wrote:
> Darren New schrieb:
>> clipka wrote:
>>> Well, AFAIK there's actually no fundamental reason to apply different 
>>> "measuring tapes" to time and space: 
>>
>> It's not measured *quite* the same way... The distance between two 
>> events is sqrt(x*x+y*y+z*z-t*t) Note the - sign.
> 
> It /is/ measured in the same way - it's just that the Pythagorean 
> theorem doesn't hold in our peculiar (3+1)D universe...

I fail to see how stating that the Pythagorean theorem doesn't hold 
isn't just another way of saying that distances are measured differently 
in our spacetime?

Is you point that in space time there *is* a well-defined notion of 
distance which unifies both the spatial and temporal aspects, and thus 
we don't really need to use one set of units for space and another set 
for time?  Your comment about light-seconds would make more sense in 
this context.  If this is the case perhaps I've been misunderstanding 
your point form the beginning, since I'd surely agree with this.

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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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Kevin Wampler wrote:
> Darren New wrote:
>>
>> Yes. I wasn't sure if that counted as a euclidian space or not. :-)
>>
> 
> It doesn't, but it does share the property that the metric tensor is 
> constant over the entire space.



-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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Orchid XP v8 wrote:
> Kevin Wampler wrote:
>> Darren New wrote:
>>>
>>> Yes. I wasn't sure if that counted as a euclidian space or not. :-)
>>>
>>
>> It doesn't, but it does share the property that the metric tensor is 
>> constant over the entire space.
> 
>  my head asplode


It was just a fancy way of saying that there's a sense in which the 
spacetime isn't "curved"; which I probably should have just said in the 
first place since the way I phrased it should really be made more 
precise to be accurate anyway.

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On 20-10-2009 12:41, Invisible wrote:
> Saul Luizaga wrote:
> 
>> I don't know if some day would be possible but would be great to visit 
>> a 4D world and meet 4D people :-D
> 
> I should point out that a rotation in 4D can leave your body in mirror 
> image. If you go to 4D-land, turn around the "wrong" way, and then come 
> back, your body will be inverted.
> 
> Why would you care? Well... certain biological molecules are chiral, 
> so... good luck assimilating your food. :-P
> 

Book reference: 'Doorways in the sand' Roger Zelazny

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On 21-10-2009 19:00, 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?

Yes there is, but you have to keep in mind that the points here are 4 
dimensional points. i.e we are talking about two events that take place 
in two places that happen closer in time than the light needs to go from 
one place to the other.

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"Saul Luizaga" <sau### [at] netscapenet> wrote in message
news:4adf1059$1@news.povray.org...

> ANd nobody knows if we were or not 2D beings.

How do you know that?

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somebody wrote:
> How do you know that?
nobody has ever proved it.

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"Saul Luizaga" <sau### [at] netscapenet> wrote in message
news:4adfcffe@news.povray.org...
> somebody wrote:

> > How do you know that?

> nobody has ever proved it.

How do you know that?

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