High School Estimates — True Size of the Universe?

[PAllen]

As Ibix says, the bread example isn't very good, but PAllen's example is brilliant. There's no contradiction between having an infinite universe and it expanding; it's a property of all spacetime.

Actually, it is only a possible property of very special spacetimes. It is a feature of geometry that is hard to visualize in a 3x1 spacetime. If you imagine the case of a 1x1 spacetime (1 spatial dimension, 1 time dimension) and closed, then you can say an expanding geometry is like the surface of a cone with the apex downward and time running upward (note, the spacetime is just the surface, and 'space' is just a circle at each time). The surface of a cylinder would be a static universe. Note how it is a feature of the geometry.

In technical terms, the question is whether the spacetime manifold admits an everywhere expanding timelike congruence. This is a rare property of manifolds. For example, it is not possible in Minkowski space (Minkowski space admits an exapnding congruence - the Milne congruence - within the future light cone of an event, but it does not admit a global expanding congruence).

 

[javisot]

Actually, it is only a possible property of very special spacetimes. It is a feature of geometry that is hard to visualize in a 3x1 spacetime. If you imagine the case of a 1x1 spacetime (1 spatial dimension, 1 time dimension) and closed, then you can say an expanding geometry is like the surface of a cone with the apex downward and time running upward (note, the spacetime is just the surface, and 'space' is just a circle at each time). The surface of a cylinder would be a static universe. Note how it is a feature of the geometry.

In technical terms, the question is whether the spacetime manifold admits an everywhere expanding timelike congruence. This is a rare property of manifolds. For example, it is not possible in Minkowski space (Minkowski space admits an exapnding congruence - the Milne congruence - within the future light cone of an event, but it does not admit a global expanding congruence).

(When I said it was a property of all spacetime, I didn't say it was a property of all spacetimes. We're talking specifically about an infinite, expanding universe. But it's always good to clarify that)

 

[timmdeeg]

I’ve used the following analogy to picture an infinite expanding universe. Consider the universe as an (countably) infinite collection of cubic boxes of e.g. gas (at any time you can put them together mentally to make a continuous whole). Double the side of each box, you still have the same total volume (infinite) but the density in each box has decreased by a factor of 8, and distances between reference points within each box have doubled. This process can be repeated any number of times in both directions (shrinking into the past, or expanding into thr future). At all times, volume is just infinite, but density increases without bound into the past.

Why can't one simply argue that in an infinite expanding universe the distance between any two comoving objects grows without limit?