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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] netscape net> 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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clipka wrote:
> 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 all cases I'm referring to a point as a 4D point in spacetime since
there's no intrinsically unique way to extend a 3D point along time.
> (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.)
If you fix a reference frame there's certainly plenty you can do to
define spacetime distances in a consistent way. If you want to
consistently measure distances independent of the reference frame, then
you're pretty much stuck with what the Minkowski metric tells you. Of
course this metric gives you a single value for the distance (not
independent time and space distances) and thus can't really be used to
measure pure-spatial distances.
Not that this is necessarily inconsistent with what you said, I just
thought I'd point out (in case you weren't already fully aware) that if
you're going to measure spacetime distances independent of the reference
frame then the way to do it is to use the Minkowski distance and forget
about trying to determine what the "spatial" distance is at all.
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somebody wrote:
> "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),
I deed, because in all fairness we don't know this for sure, I stand
correct.
> well, everybody knows that we were not 2D beings (probably a
> correct statement, at least more sensible than its negative).
sensible? I don't think so since it has the same exact meaning.
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"Saul Luizaga" <sau### [at] netscapenet> wrote in message
news:4ae0df6a$1@news.povray.org...
> somebody wrote:
> > well, everybody knows that we were not 2D beings (probably a
> > correct statement, at least more sensible than its negative).
> sensible? I don't think so since it has the same exact meaning.
If a statement and its negative have the exact same meaning, they are both
nonsense :P. But, I'll compromise: I'm pretty sure many, many more people
know that we were not 2D beings than those who know that we were (whatever
either statement means).
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somebody wrote:
> If a statement and its negative have the exact same meaning, they are both
> nonsense :P. But, I'll compromise: I'm pretty sure many, many more people
> know that we were not 2D beings than those who know that we were (whatever
> either statement means).
Yeah this is more proper, thanks for understanding, but anyway not
necessarily true.
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