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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Kevin Wampler schrieb:

>>>> Well, AFAIK there's actually no fundamental reason to apply 
>>>> different "measuring tapes" to time and space: 
>>>
> 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.

Well, yes, I guess that's one way to express what I said: We don't need 
different "measuring tapes" for time and space. How distance is measured 
"diagonally" in spacetime is another story.

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Kevin Wampler schrieb:
> 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.

Maybe you'd first need to define "point": Are you talking about a point 
in 3D space which extends along time - i.e. a line in 4D space - or an 
actual 4D point that only exists at a certain time T?

In the former case, this is actually a non-issue: Either you can find 
(true) points on that line that /can/ be reached at /exactly/ light 
speed, or you cannot reach that other line at all.


In the latter case, you can define the spacelike distance between the 
points as the minimum difference between the spacelike component of two 
intersecting lightlike geodesics running through each of the points 
respectively.

Or, to eliminate the problem of "far-away" spacetime being curved, you 
can have a look at all possible sequences of points that can be 
connected with lightlike geodesics, compute the vector sum of the 
spacelike components, and define the spacelike distance as the minimum 
length of any such vector sum.

In the end it will boil down to defining the spacelike distance as the 
length of the spacelike component of the shortest "direct" geodesic 
between the points.

(Note that of course this leaves the definition of distance subject to 
your frame of reference, as it defines the orientation of the spacelike 
components of spacetime, but that's a known effect in relativistic physics.)

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Kevin Wampler schrieb:

> 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.

Yes...

> 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?

Well, your original statememt was that "distances are measured 
differently in time than in space", not "distances are computed 
differently in spacetime than in space", so I took this as talking about 
"measuring tapes", not the math to combine space and time components of 
distance into spacetime distance.

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somebody schrieb:

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

"Can you hear me, bomb?" :-)

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somebody wrote:
> "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?

Oh you really think that 2D only beings discovery might have gone 
unnoticed? I don't think so, I think is perfectly safe to say that if 
that kind of world exist it has not been discovered, or do you know 
otherwise?

I think your question is pointless, anyone would had pointed out that 
the 2D beings actually do exist, such a news would be common knowledge 
by now. Otherwise people wouldn't be wondering:

http://www.unexplained-mysteries.com/forum/index.php?showtopic=163191
http://www.physicsforums.com/archive/index.php/t-185785.html
http://teamikaria.com/4dforum/viewtopic.php?f=5&t=1103

How do I know that? looks like you are the only one that it doesn't.

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"Saul Luizaga" <sau### [at] netscapenet> wrote in message
news:4ae01d8b$1@news.povray.org...
> somebody wrote:
> > "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?
>
> Oh you really think that 2D only beings discovery might have gone
> unnoticed?

No, but that's not what you said. You said "ANd nobody knows if we were or
not 2D beings." Well, if lack of disclosure of discovery is proof (faulty
reasoning), well, everybody knows that we were not 2D beings (probably a
correct statement, at least more sensible than its negative).

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