Geometry of Spacetime

[geordief]

I have posted here before  in the Homework section  when I feel my question is  very elementary and  hope I can "do it again.......

 

So... if we preclude relative  motion between objects  from the scenario  could   the geometry of spacetime  be described as  Euclidean **?

 

So ,if  objects are  (can they be? Is there any point ?) treated as static vis a vis one another can they be modeled consistently  in a Euclidean way or  does one still have to take into account the different  distances between objects?

**by "Euclidean" I mean the geometry I learned at school;we never called it "Euclidean" ,it was just "geometry"

[Markus Hanke]

45 minutes ago, geordief said:

So... if we preclude relative  motion between objects  from the scenario  could   the geometry of spacetime  be described as  Euclidean **?

No, it’s Minkowskian. That means that - within the metric - the time and space parts have opposite sign. This gives spacetime a type of hyperbolic geometry. In Euclidean geometry, all parts of the metric have the same sign.

47 minutes ago, geordief said:

So ,if  objects are  (can they be? Is there any point ?) treated as static vis a vis one another can they be modeled consistently  in a Euclidean way or  does one still have to take into account the different  distances between objects?

No, this cannot be done in a consistent manner. In Euclidean geometry, for example, speeds add linearly - if you ride on a very fast rocket, and shine a torch light into the direction of motion, this would give you a superluminal ray of light. Obviously that is not what happens in the real world.

 

[swansont]

8 hours ago, geordief said:

 **by "Euclidean" I mean the geometry I learned at school;we never called it "Euclidean" ,it was just "geometry"

Euclidean geometry corresponds to Newtonian physics. As Markus has noted, what we have is Minkowskian, because relativity is the best description of spacetime.