Infinite vs Expanding Universe: A Physics Conundrum Explained

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Discussion Overview

The discussion revolves around the concepts of an infinite universe versus an expanding universe, exploring the implications of each idea within the realms of physics and cosmology. Participants examine the definitions of expansion, the nature of space, and the relationship between matter and the universe's geometry, with a focus on theoretical and conceptual aspects.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants argue that defining expansion requires a measurable boundary, suggesting that if the universe is infinite, it cannot be expanding in the traditional sense.
  • Others propose that the universe can be infinite and still experience expansion, emphasizing that expansion does not necessitate a boundary, similar to the surface of the Earth.
  • A participant suggests that while the universe may be infinite, the matter within it is spreading out, leading to an increase in distance between objects without implying a boundary change.
  • Some participants discuss the balloon analogy, noting that while it illustrates expansion, it may not fully capture the complexities of three-dimensional spacetime expansion.
  • There is mention of metric expansion, where the distance between comoving points increases, which some argue is observable through phenomena like Hubble's law.
  • One participant highlights the distinction between the movement of objects within space and the expansion of space itself, questioning whether space is expanding to accommodate matter or if matter is simply dispersing within existing space.
  • Another participant references the concept of parallel transport in relativity to illustrate how distances can change in an expanding universe without local motion.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between an infinite universe and expansion, with no consensus reached. Some agree on the concept of metric expansion, while others challenge the applicability of the balloon analogy and the implications of boundaries.

Contextual Notes

Participants acknowledge limitations in their analogies and definitions, particularly regarding the complexities of spacetime and the nature of expansion versus movement. The discussion reflects ongoing uncertainties and assumptions about the universe's structure.

  • #61
m k said:
Would you say that infinity of natural numbers is quite small among infinities?
You would have to define "small" in this context. And give a threshold for "quite". It is not clear how one would compare the infinite cardinality of the natural numbers with the positive infinity in the two-point compactification of the real numbers.

In any case, this is irrelevant to the discussion at hand.
 
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  • #62
m k said:
Would you say that infinity of natural numbers is quite small among infinities?
Google "hierarchy of infinities"
 
  • #63
m k said:
Would you say that infinity of natural numbers is quite small among infinities?
It is quite similar to infinity of whole numbers
 
  • #64
Comeback City said:
It is quite similar to infinity of whole numbers
I don't get "similar". Since both are cardinalities of sets then either they have the same Aleph number, in which case they are identical not similar, or they have diffrerent Aleph numbers, in which case they are different (and not similar).
 
  • #65
phinds said:
I don't get "similar". Since both are cardinalities of sets then either they have the same Aleph number, in which case they are identical not similar, or they have diffrerent Aleph numbers, in which case they are different (and not similar).
Well, infinity + 1 = infinity, so I'm going to read some more about infinity!
 
  • #66
Comeback City said:
Well, infinity + 1 = infinity
Yes, Aleph1 + 1 = Aleph1 and Aleph2 +1 = Aleph2. That does NOT make Aleph1 identical to, or similar to, Aleph2

, so I'm going to read some more about infinity!
Good idea. That will likely dispel your misunderstanding.
 
  • #67
phinds said:
that has nothing at all to do with your statement

Good idea. That will likely dispel your misunderstanding.
You should read more about "comic relief" :wink:
 
  • #68
Comeback City said:
You should read more about "comic relief" :wink:
Doesn't that have something to do with Billy Crystal and Whoopie Goldberg? They are not infinite.
 
  • #69
phinds said:
Doesn't that have something to do with Billy Crystal and Whoopie Goldberg? They are not infinite.
Yeah you got me again :woot::thumbup:
 
  • #70
nikkkom said:
This is not true. Not every physics theory has to have problems.
I never said a physics theory has to have problems, I said they are all known to be incomplete. Which is true.
 
  • #71
Drakkith said:
Hi Ken. What are your thoughts on when we can reasonably say that the predictions of GR probably aren't correct?
I don't think we can say when a prediction probably isn't correct, we simply have to test it. What is the track record of theories that we thought were probably not correct, versus ones we probably thought were? It's cherry picking, but still I'd say that track record is not good at all. For example:
We thought for thousands of years that geocentric models were probably correct and would not significantly change in the future.
We thought for hundreds of years that Galilean relativity was probably correct, so when Maxwell's equations treated the speed of light as a constant of the theory, most physicists thought that had to be incorrect.
Eddington thought that Chandrasekhar's theory of white dwarfs was probably incorrect because it predicted a maximum mass, above which no static solution was possible without drastic changes to the star. He reasoned that something missing from Chandrasekhar's approach would guarantee stability.
Einstein thought that quantum mechanics had to be wrong because it violated local realism.
And so on.
 
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  • #72
phinds said:
Yes, Aleph1 + 1 = Aleph1 and Aleph2 +1 = Aleph2. That does NOT make Aleph1 identical to, or similar to, Aleph2
So do the infinite sets of natural numbers and whole numbers have the same or different Aleph numbers? Wikipedia is saying that natural numbers have an Aleph number of 0 (Aleph-naught). It doesn't mention whole numbers, but whole numbers are just natural numbers with 0. Is it safe to assume infinite series of whole numbers also has Aleph number of 0?
 
  • #73
Comeback City said:
So do the infinite sets of natural numbers and whole numbers have the same or different Aleph numbers? Wikipedia is saying that natural numbers have an Aleph number of 0 (Aleph-naught). It doesn't mention whole numbers, but whole numbers are just natural numbers with 0. Is it safe to assume infinite series of whole numbers also has Aleph number of 0?
Yes, they are the same. It's the reals, as I recall, that is the first instance of Aleph1
 
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  • #74
phinds said:
Yes, they are the same. It's the reals, as I recall, that is the first instance of Aleph1
The continuum hypothesis is the statement that the cardinality of the reals is Aleph 1. Its truth or falsity is not decidable (under the usual axioms of set theory).
 

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