High School Is the Universe infinite or not?

[Peter Martin]

Multiplication and division by zero yields nonsensical results. I fail to see to any reason to take such derivations seriously. It more accurately reflects, imo, the failure of our mathematical conceptions to properly model the universe.

Division by zero is indeed undetermined but multiplication by zero is not. Zero times any number equals zero. But, for example, 12 divided by zero would have to be a number which when multiplied by zero equalled 12. But we've already agreed that that's impossible.

 

[Bandersnatch]

since the "universe" is expanding and we have an "horizon" where the relevant speed reaches the speed of the light

The cosmic event horizon is not coincident with the Hubble sphere. These two are the same only in universes devoid of matter and radiation, with dark energy component only (so called de Sitter universes).
In a universe like ours, the expansion rate falls down with time, allowing signals from beyond the Hubble sphere to reach us in finite time.

Notice how the Hs and EH tend to converge to a common value reflecting the universe becoming incereasingly dark energy-dominated.
(Graph source)

 

[Pjpic]

But on a personal level I am very interested in keeping a discussion of "is the universe infinite or not," which is the topic of this thread, on a scientific basis.Maybe there are different definitions for "universe" and for "infinity"; that might be causing some confusion. Even "is", might have different definitions (maybe it is limited to "only as far as we know" )

 

[PeterDonis]

I am very interested in keeping a discussion of "is the universe infinite or not," which is the topic of this thread, on a scientific basis.

See my post #26. I don't see what more we can say scientifically on the question than that.

 

[phinds]

But on a personal level I am very interested in keeping a discussion of "is the universe infinite or not," which is the topic of this thread, on a scientific basis.

addressed in post #26

Maybe there are different definitions for "universe" and for "infinity"; that might be causing some confusion. Even "is", might have different definitions (maybe it is limited to "only as far as we know" )

Only if you are making up your own definitions.

EDIT: I see Peter beat me to it.

 

[marce]

- As some of you aleady pointed out; there is a big pitfall of assigning infinity to the universe(possibly);
infinity is a mathematical concept and does not exist in nature. This may seem childish but it isnt't;
if the universe corresponds to a physical version of inifinity I would call it phy-inifinite.
This reduces the effect of posting an absoluteness (concept) to the physical word.
What may help is that those of you who know mathematics know that there are different classes
of infinity. The infinity-class for the range of whole numbers is a different kind then the infinity-class for
the range of real numbers. If the universe would be phy-infinite, then for instance a set of phy-laws
must be developed leading to that result such as QM or GR.

The same pitfall arises,according to me, in string-therory where the most elementary building-block
is a one dimensional string. Same arguments apply; dimensions do not exist in nature, perhaps
phy-dimensions,subttle or isn't it ...?

M.

 

[Gerhard Mueller]

Hi,
may be another view could help: Is the size of the universe measurable?
If a method could be identified, which allows to determine the size of the universe, then the universe has a finite size.
(Any thinkable means for this kind of measurement would be allowed)

 

[PeterDonis]

Is the size of the universe measurable?

It depends. The problem is light travel time; any measurement of the size of the universe has to involve light signals (or something equivalent) traveling across the universe. If the universe is spatially infinite, such a measurement could never complete; but it's also possible for it not to complete if the universe is spatially finite.

 

[PeterDonis]

This topic has been discussed sufficiently. Thread closed.