David Frydman wrote:Tony,
Am I correct that you are saying that the large scale geometry is flat or almost flat, but on the small scale such as the solar system or indeed a galaxy the geometry is not flat.
Or are you saying that the flatness extends even to local measurements even on the Earth.
Can you reiterate what the term flatness means in this context.
How does flatness react in the presence of dense and heavy objects that distort space?
I think part of what you are saying is that locally on the scale of the solar system, measrements would only be affected by flatness to a very small degree, so that flatness is not a major component of how we see our local neighbourhood.
It is only when we measure very large distances that flatness is seen/
Is this correct?
Most of our everyday experience is consistent with a "flat" geometry in which parallel lines don't converge and the angles of a triangle add up to 180 degrees.
However, on relatively "small" scales such as that of the solar system or our galaxy, the geometry can be distorted by the gravitational effect of objects such as stars, and this will cause parallel lines that pass close to such objects to diverge. Thus we can't easily test the "flatness" of the Universe by making "local" measurements, and tests of "flatness" have to involve much larger scales.
Obviously we can't draw triangles that have sides that are billions of light years in length, measure their angles and check whether these add up to exactly 180 degrees, so astronomers have to devise more indirect tests.
One such test is to measure the size of the tiny fluctuations seen in the Cosmic Microwave Background radiation. The Big Bang theory predicts the size (approx a degree across) that these fluctuations should be in a "flat" universe and measurements made by satellites such as WMAP have shown this to be the case (at least down to the accuracy possible using the available technology and time).
A "flat" Universe is also one which, in the absence of "dark energy", would have the density that would make it critically balanced between expanding forever and eventually contracting. Given that the most favoured versions of the Big Bang models actually predict the Universe to be "flat", cosmologists were very relieved to find this prediction confirmed by WMAP.