Curved or Flat? Decoding the Distance Measurements in Space

[asprin]

My first post here, this question may have been asked before and answered already, if so a link would be appreciated.

When we measure interstella distances are we measuring curved space distances or flat space distances?

Putting it another way...

Are we able to determine the curvature sufficiently to measure the distance?

As we use Light years as a measuring tool, velocity over distance. Do we assume flat distances or curved distances, curved distances being considerably longer than flat ones?

Sorry if the question is all confused.

 

[Chronos]

The short answer is, there is no way to directly measure it. We can only derive it by measuring the energy and mass density and approximating it geometrically.

 

[Garth]

First define your ruler. Then define a method of measuring with that ruler by finding some effect that varies with distance and some rule that relates that effect with the distance.

Two standard rulers are the "standard candle" and the "standard ruler". That is the apparent magnitude of an object that can be compared with its Absolute magnitude, such as the recent measurements of the brightness of distant Type IIa supernovae or the more traditional Cepheid variables. Or measure the apparent angular diameter of an object of which you think you know its actual diameter, such as the angular diameter of spiral galaxies. By using the brightness of a Cepheid variable in Andromeda and then the relative diameters of other galaxies Hubble discovered his red shift law; the spectra of distant galaxies suffers a red shift that is proportional to its distance. So we now have a red shift measurement of distance as well.

By developing your rule, or relationship between say red shift and distance, using the mathematics of curved surfaces you are defining the distance being measured as the curved distance along the surface of curved space-time. You are integrating, or adding up, lots of small "flat" distances together such that the number of these infinitesimal distances tends to infinity as the length of each one tends to zero. A lumpy chain thereby becomes a smooth piece of string stretched out across the curvature of space-time.