Space doesnt need bounds to have shape (Riemann 1854)

[Martin]

http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Riemann.html

 

to be accorded the right to lecture at the university Riemann had to present a talk on something

he prepared 3 lectures, two on electricity and one on geometry, and he let Gauss choose which he should give

Gauss chose the one on geometry

 

this talk was on the foundations of geometry and it showed how a space can have shape and curvature and all that good stuff without living in any larger surrounding space and without having any boundaries

 

this talk was given in 1854

 

Georg Friedrich Bernhard Riemann lived 1826-1866. He was extraordinary creative, like Mozart, except it was in math instead of music.

Einstein 1915 general relativity is based on Riemann 1854 talk.

 

a new poster just came here and said that space must be bounded in order to have shape. this is not true. go back 150 years to Göttingen and learn it from Riemann.

[zazzzoom]

the universe is not all the stars and planets and galaxies in space

 

the universe is all matter energy time and space

a true concept of what matter and energy are is necessary to have a true concept of the universe you got as far as e=mc2 that tells you matter and energy are the same thing but you don't know what matter and energy is.

a true concept of all space is necessary to have a true concept of the universe you don't even know what space is or what makes it different from matter and energy.

a true concept of all the past present and future is necessary to have a true concept of the universe and you don't ever know what time is

[BlackHole]

True, space can be unbound and still have a size (like a sphere or a balloon) but if space is infinite (has no size and no age), i think it contradicts the big bang theory.

[Severian]

True, space can be unbound and still have a size (like a sphere or a balloon) but if space is infinite (has no size and no age), i think it contradicts the big bang theory.

 

An infinite universe can still have size and age, because there are charateristic sizes inherent with the metric.

[BlackHole]

An infinite universe can still have size and age, because there are charateristic sizes inherent with the metric.

 

But if space is a 2-dimensional plane, it is flat and infinite.

 

AFAIK, there are really only two possibilites: a flat, infinite universe or a flat and finite universe with nontrivial topology in which the universe 'wraps around' spatially.

 

http://arxiv.org/abs/astro-ph/9802012

http://arxiv.org/abs/gr-qc/0005128

http://arxiv.org/abs/gr-qc/9911049