# Does “Infinite Universe” Imply Infinite Mass?

In accordance with the FLRW Metric with a curverature of $k=0$ (as observationally supported by several of NASA's experiments including WMAP, Planck satellite, DASI, etc.) the universe is spatially infinite. Of course, our observable universe is finite, but as far as we know, there is simply no edge to the universe. Does this imply that there is a non-finite amount of mass in the isotropic and homogeneous universe, assuming a Euclidean geometry?

• Well we don't know. The universe could be infinite but empty past some distance so still have a finite mass. The seems unlikely. The universe might not be infinite either. – Brandon Enright Nov 9 '14 at 4:08
• "Euclidean geometry" and any kind of special/general relativity do not mesh well. Other than that, I believe the answer is "Yes." – ACuriousMind Nov 9 '14 at 4:40
• Would you mind elaborating just a little bit? Or would you care to link me to somewhere I can read about the Euclidean geometry vs Relativity? – Goodies Nov 9 '14 at 5:19
• Well, It was actually the claim of Einstein that "For infinitely small four-dimensional regions the theory of relativity in the restricted sense is appropriate, if the coordinates are suitably chosen." that allowed him to assume that at this level the field is flat in order to use SR. – bright magus Nov 9 '14 at 10:40
• @Goodies General relativity, in a nutshell, is the description of spacetime as a Riemannian manifold, such that the topology is affected by mass (and the rest of the stress energy tensor). In Euclidean space light would travel in straight lines. In general relativity they follow what we would think of as curved paths. This is why we observe gravitational lensing and event horizons. – zibadawa timmy Nov 9 '14 at 12:35

## 2 Answers

The question is complicated by a lack of vocabulary for many features of the universe. The universe is thought to be "boundless" but finite. But that is not the same thing as "infinite". It simply has no edges or ends. That is a consequence more of the effect of curved space than of anything else. If you try to travel to the "edge" of the universe, you eventually return to where you started. That is because it is impossible for straight lines to exist in curved space and also impossible to even determine if you are travelling a straight line. All measures of your trajectory are also bent. That is why the world is better described by Riemannian or Minkowsky space. In both, the Euclidean idea that parallel lines never meet is no longer true. Neither supports the existence of parallel lines.

Like singularities in relativity, infinities most likely do not exist in any form. Relativity is a classical theory and has the limitations of one. Where "singularities" exist in General Relativity, the theory and math break down. Divisions by 0 do not give infinities except in peoples' wishes. In any case, the use of imaginary time rather than real time (Wick Rotation) reduces a Minkowsky space problem in D dimensions plus time to one in Euclidean space of D+1 dimensions. The singularities then do not exist, nor do the infinities. Calculations to the moment of the Big Bang and before then appear possible. It may even be possible to determine why the universe began if details of the particle physics can be worked out.

The volume of the universe is infinite, therefore there must be an infinite number of worlds. But not all of them are populated; therefore only a finite number are. Any finite number divided by infinity is as close to zero as makes no odds, therefore we can state that the population of the Universe to zero, and anyone you have ever met is merely a figment of your imagination.

We can consider the universe to be infinite from our point of reference . But we also know that the universe is mainly empty space. However, we do not know (and may never know) the true shape and extent of the universe so we cannot claim that it is truly infinite. Therefore, the mass of the universe is finite.

This question borders on theology. Based on what we know about the extent of the universe and how we may travel within it, we cannot ever know many of the answers.

• This answer makes many incorrect assertions and conclusions. As a trivial example, if we assume an infinite number of worlds, and not all of them are populated, there can still be an infinite number which are populated. Similarly, it does not follow that the mass of the universe is finite, from "we do not know... so we cannot claim that [the universe] is truly infinite." – Michael Petito Aug 21 '16 at 5:03

## protected by Qmechanic♦Oct 6 '16 at 17:54

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