The Cosmological Principle and the Universe

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Discussion Overview

The discussion revolves around the cosmological principle and its implications for the structure and amount of matter in the universe. Participants explore theoretical models of the universe's geometry, including flat and finite configurations, and engage in a debate regarding the definitions and measurements involved in these concepts.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants propose that the cosmological principle implies an infinite amount of matter in a flat and unbounded universe.
  • Others argue that the cosmological principle allows for a spatially finite universe with a finite amount of matter, particularly if it has the geometry of a 3-sphere.
  • A participant questions the implications of a 3-torus geometry in relation to the cosmological principle.
  • It is suggested that a 3-torus does not comply with the cosmological principle unless it is a flat 3-torus, which falls under the flat category.
  • There is a discussion about the nature of ratios involving infinities, with some participants indicating that such ratios are not well-defined.

Areas of Agreement / Disagreement

Participants express competing views regarding the implications of the cosmological principle and the geometrical configurations of the universe. The discussion remains unresolved, with differing opinions on the nature of spatial geometries and the implications for matter in the universe.

Contextual Notes

Limitations include undefined terms in the discussion, such as the numerator and denominator in ratios involving infinities, and the specific conditions under which the cosmological principle applies to different geometries.

greswd
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The cosmological principle seems to hold well, and would imply an infinite amount of matter in the universe if the universe is flat and unbounded
 
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Your question has an undefined numerator, an undefined denominator and is unmeasurable.
 
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greswd said:
The cosmological principle seems to hold well, and would imply an infinite amount of matter in the universe

No, it wouldn't, since the cosmological principle by itself allows a spatially finite universe containing a finite amount of matter, provided it has the spatial geometry of a 3-sphere.
 
Vanadium 50 said:
Your question has an undefined numerator, an undefined denominator and is unmeasurable.
wouldn't the ratio be the odds of the guess being correct?

And just asking on what one might think the odds are
 
PeterDonis said:
No, it wouldn't, since the cosmological principle by itself allows a spatially finite universe containing a finite amount of matter, provided it has the spatial geometry of a 3-sphere.
what about a 3-torus?
 
greswd said:
what about a 3-torus?

A 3-torus does not obey the cosmological principle (unless you mean a flat 3-torus, which falls into the "flat" category below). Only three spatial geometries do: 3-sphere (constant positive curvature), flat (zero curvature), 3-hyperboloid (constant negative curvature).
 
greswd said:
wouldn't the ratio be the odds of the guess being correct?

Only if the ratio is a ratio of finite numbers.

greswd said:
just asking on what one might think the odds are

And what @Vanadium 50 was telling you is that this question is unanswerable because the ratio of two infinities is not well-defined.

Thread closed.
 

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