0
votes
4answers
108 views

How to determine “timelike”-ness without using a coordinate system?

It has been stated here that: we can say, without introducing a coordinate system, that the interval associated with two events is timelike, lightlike, or spacelike. This assertion appears at ...
2
votes
0answers
35 views

Can a value of “length, in meters” be attributed to a pair of ends which are rigid (but not at rest) to each other? [duplicate]

The definition of the SI base unit "metre" [1] doesn't seem to rule out explicitly that a certain value of "length, in meters" could be attributed to a pair of ends which are rigid to each other, but ...
2
votes
0answers
61 views

If two ends were a certain “length” apart were they therefore at rest (or at least rigid) to each other? [closed]

Considering the definition of the SI unit of "length" [1] and [2 (" method a.")] I'm missing any requirements about the two "ends" of the required "path travelled by light" being "at rest to each ...
2
votes
0answers
70 views

Can we derive the relation between proper time and the spacetime interval?

In GR, it's usually taken for granted - or as a definition - that the time measured by an observer's clock is related to the geometry in a very simple way, $d\tau^2 = |ds^2|$. This is easy enough to ...
0
votes
0answers
20 views

How to express “curvature scalars” in terms of "discrete curvature values $\kappa_n$?

We know from MTW [1] and Synge [2] how, for participants who were (pairwise) rigid to each other, it may be determined whether or not they were straight to each other, plane to each other, or ...
9
votes
1answer
378 views

Can masses move in 2+1 gravity?

I would like to understand basic concepts of the general relativity in 2+1 spacetime. As far as I know, GR predicts that such a spacetime is flat everywhere except for the point masses which create ...
1
vote
2answers
80 views

What is a geometrical object?

From the Wikipedia link for Geometry: Geometry (Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position ...
5
votes
2answers
96 views

Which causal structures are absent from any “nice” patch of Minkowski space?

Which "causal separation structures" (or "interval structures") can not be found among the events in "any nice patch ($P$) of Minkowski space"?, where "causal separation structure" ($s$) should be ...
0
votes
2answers
126 views

Limit on velocity in Minkowski Spacetime geometry

Let A be a rocket moving with velocity v. Then the slope of its worldline in a spacetime diagram is given by c/v. Since it is a slope, c/v = tan(theta) for some theta > 45 and theta < 90. Does ...
5
votes
2answers
294 views

Space-time geometry and metric

I am confused in one question in general relativity, why we can always express a space-time geometry only by metric. It means a metric, which is just about distance in tangent space, can tell us all ...
10
votes
6answers
2k views

Experimental evidence of a fourth spatial dimension?

As human beings, we observe the world in which we live in three dimensions. However, it is certainly theoretically possible that more dimensions exist. Is there any direct or indirect evidence ...